GATE Exam 2021 Life Sciences (XL) Question Paper With Answer Key

GATE-2021

XL: Life Sciences

GA-General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Gauri said that she can play the keyboard __________ her sister.

(A)  as well as

(B)  as better as

(C)  as nicest as

(D)  as worse as

Answer: (A)

2. A transparent square sheet shown above is folded along the dotted line. The folded sheet will look like ________.

Answer: (B)

3. If θ is the angle, in degrees, between the longest diagonal of the cube and any one of the edges of the cube, then, cos θ =

(A)  1/2

(B)  1/√3

(C)  1/√2

(D)  √3/2

Answer: (B)

4. If  then the value of x is:

(A)  2

(B)  4

(C)  6

(D)  8

Answer: (B)

5. Pen : Write :: Knife : _________

Which one of the following options maintains a similar logical relation in the above?

(A)  Vegetables

(B)  Sharp

(C)  Cut

(D)  Blunt

Answer: (C)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

6. Listening to music during exercise improves exercise performance and reduces discomfort. Scientists researched whether listening to music while studying can help students learn better and the results were inconclusive. Students who needed external stimulation for studying fared worse while students who did not need any external stimulation benefited from music.

Which one of the following statements is the CORRECT inference of the above passage?

(A)  Listening to music has no effect on learning and a positive effect on physical exercise.

(B)  Listening to music has a clear positive effect both on physical exercise and on learning.

(C)  Listening to music has a clear positive effect on physical exercise. Music has a positive effect on learning only in some students.

(D)  Listening to music has a clear positive effect on learning in all students. Music has a positive effect only in some students who exercise.

Answer: (C)

7. A jigsaw puzzle has 2 pieces. One of the pieces is shown above. Which one of the given options for the missing piece when assembled will form a rectangle? The piece can be moved, rotated or flipped to assemble with the above piece.

Answer: (A)

8. The number of students in three classes is in the ratio 3:13:6. If 18 students are added to each class, the ratio changes to 15:35:21.

The total number of students in all the three classes in the beginning was:

(A)  22

(B)  66

(C)  88

(D)  110

Answer: (C)

9. The number of units of a product sold in three different years and the respective net profits are presented in the figure above. The cost/unit in Year 3 was ` 1, which was half the cost/unit in Year 2. The cost/unit in Year 3 was one-third of the cost/unit in Year 1. Taxes were paid on the selling price at 10%, 13% and 15% respectively for the three years. Net profit is calculated as the difference between the selling price and the sum of cost and taxes paid in that year.

The ratio of the selling price in Year 2 to the selling price in Year 3 is ________.

(A)  4:3

(B)  1:1

(C)  3:4

(D)  1:2

Answer: (A)

10. Six students P, Q, R, S, T and U, with distinct heights, compare their heights and make the following observations.

Observation I: S is taller than R.

Observation II: Q is the shortest of all.

Observation III: U is taller than only one student.

Observation IV: T is taller than S but is not the tallest.

The number of students that are taller than R is the same as the number of students shorter than ______.

(A)  T

(B)  R

(C)  S

(D)  P

Answer: (C)

Chemistry (XL-P)

1. The geometry of Fe(CO)5 is

(Given: Atomic number of Fe = 26)

(A)  pentagonal planar

(B)  square pyramidal

(C)  trigonalbipyramidal

(D)  trigonal pyramidal

Answer: (C)

2. The structure of the major product Q of the following reaction is

Answer: (A)

Q.3 – Q.5 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

3. The time taken by a first order reaction to reach 90% completion is 20 s. The time taken for the reaction to reach 50% completion is ___________ s (rounded off to the closest integer).

Answer: (6 to 6)

4. The ground state energy of an electron in a hydrogen atom is –13.60 eV. The energy of the electron in the third excited state is _________eV (rounded off to two decimal places).

Answer: (-0.86 to -0.84)

5. A solution of a compound shows an absorbance of 0.42 at 275 nm in a cuvette with 0.1 dm light path. The molar absorptivity of the compound is ε275 = 8.4 × 103 M–1 cm–1. The concentration of the compound is ______× 10–5 M (rounded off to the closest integer).

Answer: (5 to 5)

Q.6 – Q.9 Multiple Choice Question (MCQ), carry TWO mark each (for each wronganswer: – 2/3).

6. The CORRECT order of acidity of the following compounds is

(A)  II > I > III

(B)  II > III > I

(C)  III > II > I

(D)  III > I > II

Answer: (B)

7. The O–O bond order in O22– species is

(A)  0.5

(B)  1.0

(C)  1.5

(D)  2.0

Answer: (B)

8. For a reaction, X → Products

Group I contains three plots of reactant concentrations as functions of time, where x = concentration of reactant X at time t; x0 = concentration of reactant X at initial time, t = 0. Group II gives a list of different orders of reaction. Match the plots with the order of the reaction.

(A)  (P) – (1), (Q) – (2), (R) – (3)

(B)  (P) – (3), (Q) – (2), (R) – (1)

(C)  (P) – (2), (Q) – (3), (R) – (1)

(D)  (P) – (2), (Q) – (1), (R) – (3)

Answer: (C)

9. The structure of the major product S of the following reaction is

Answer: (B)

Q.10 – Q.11 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).

10. The CORRECT combination(s) of Y and T for the following elimination reaction is(are)

Answer: (B; D)

11. Among the following, the diamagnetic species is(are)

(Given: Atomic numbers of Fe = 26, Co = 27, and Ni = 28)

(A)  [CoF6]3−

(B)  [Ni(H2O)6]2+

(C)  [Fe(CN)6]4

(D)  [Co(NH3)6]3+

Answer: (C; D)

Q.12 – Q.15 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

12. Given the following standard heats of formation, ∆fH(P, g) = 314. 6 kJ mol−1, ∆fH(PH3, g) = 5. 4 kJ mol−1, and ∆fH (H, g) = 218. 0 kJ mol−1, the average bond enthalpy of a P–H bond in PH3(g) is __________ kJ mol−1(rounded off to one decimal place).

Answer: (321.0 to 321.2)

13. The total number of possible geometrical isomer(s) for [PtBrCl(NH3)(py)]0 is _______.

(Given: py = Pyridine and atomic number of Pt = 78)

Answer: (3 to 3)

14. Given the standard reduction potentials and  the potential of the following cell

Ag+(aq. , 1 mM) + Mg(s) ⇌ Ag(s) + Mg2+(aq. , 0. 2 M)

at 25 °C is___________ V (rounded off to two decimal places).

(Given: Faraday constant = 96500 C mol−1, Gas constant R = 8.314 J K−1mol−1)

Answer: (3.00 to 3.02)

15. The freezing point of 80 g of acetic acid (freezing point constant 3.9 K kg mol−1) was lowered by 7.8 K due to the addition of 20 g of a compound. The molar mass of the compound is _____________ g mol−1 (rounded off to closest integer).

Answer: (125 to 125)

Biochemistry (XL-Q)

Q.1 – Q.10 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Which one of the following molecules (~ 1mg/mL) do NOT absorb at 280 nm in an aqueous solution of pH 7.00 at room temperature?

(A)  Poly deoxy-Guanylate (poly dG)

(B)  Adenosine triphosphate

(C)  Phenylalanine

(D)  Tyrosine

Answer: (C)

2. A molecule that forms a donor-acceptor energy transfer pair with the dansyl group is ______

(A)  Aspartate

(B)  Histidine

(C)  Lysine

(D)  Tryptophan

Answer: (D)

3. The stationary phase used in gel filtration chromatography is composed of ___

(A)  Blue dextran

(B)  Carboxymethyl (CM) cellulose

(C)  Diethylaminoethyl (DEAE) cellulose

(D)  Sepharose

Answer: (D)

4. According to the “wobble hypothesis” inosine at the third position of the anticodon cannot form hydrogen bonds with ________

(A)  Adenine

(B)  Cytidine

(C)  Guanine

(D)  Uracil

Answer: (C)

5. pKa value of the guanidinium group of Arginine is _____

(A)  4.30

(B)  7.40

(C)  9.20

(D)  12.50

Answer: (D)

6. The non-coenzyme vitamin is ________

(A)  Ascorbic acid

(B)  Folic acid

(C)  Nicotinic acid

(D)  Thiamine

Answer: (MTA)

7. Telomerase has a function similar to __________

(A)  DNA dependent DNA polymerase

(B)  RNA polymerase

(C)  DNA gyrase

(D)  Reverse transcriptase

Answer: (D)

8. Which one of the following enzymes is used in Polymerase Chain Reaction ?

(A)  Klenow fragment

(B)  Taq polymerase

(C)  T7 polymerase

(D)  Primase

Answer: (B)

9. In hepatocytes, the detoxification of drugs occurs in ______

(A)  Golgi apparatus

(B)  Nucleolus

(C)  Rough endoplasmic reticulum

(D)  Smooth endoplasmic reticulum

Answer: (D)

10. Which one of the following antibiotics can form an ion channel in the bacterial membrane?

(A)  Ampicillin

(B)  Gramicidin A

(C)  Gentamicin

(D)  Rifampicin

Answer: (B)

Q.11 – Q.12 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

11. Which one of the following cells lack hypoxanthine-guanine phosphoribosyltransferase (HGPRT)?

(A)  B Cell

(B)  T Cell

(C)  Macrophage

(D)  Myeloma Cell

Answer: (D)

12. Which of the following lipids is non-ionic?

(A)  Sphingomyelin

(B)  Galactocerebroside

(C)  Lecithin

(D)  Phosphatidyl inositol

Answer: (B)

Q.13 – Q.20 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).

13. Anti-B antibodies are present in the serum of ________

(A)  Blood group A

(B)  Blood group B

(C)  Blood group AB

(D)  Blood group O

Answer: (A; D)

14. Which of the following are energy requiring processes?

(A)  Facilitated diffusion

(B)  Active transport

(C)  Nonmediated transport

(D)  Na+/K+transport

Answer: (B; D)

15. Which of the following are correctly paired?

(A)  Replication: DnaA

(B)  Recombination: RecA

(C)  DNA repair: Rho factor

(D)  Transcription: Sigma factor

Answer: (A; B; D)

16. The high energy compound(s) is/are:

(A)  Phosphoenol pyruvate

(B)  Adenosine monophosphate

(C)  1,3-Bisphosphoglycerate

(D)  Vitamin K

Answer: (A; C)

17. Given below are four plots obtained from separate experiments on enzyme inhibition kinetics. The velocity (v) of the reaction is plotted at varying concentrations of substrate (s) and inhibitor (I). The plot(s) corresponding to competitive inhibition is/are

(A)  (i)

(B)  (ii)

(C)  (iii)

(D)  (iv)

Answer: (A; C)

18. With respect to sodium dodecyl sulphate – polyacrylamide gel electrophoresis (SDS-PAGE), which of these statement(s) is/are true?

(A)  Ethidium bromide is used to track the progress of electrophoretic mobility

(B)  β-mercaptoethanol is used to reduce disulphide bonds

(C)  The protein migrates towards the anode

(D)  The lower molecular weight protein migrates slower than the larger molecularweight protein

Answer: (B; C)

19. In the plot given below, the solid line represents oxygen binding to hemoglobin under physiological conditions. The broken line represents the condition(s) of

(A)  High CO2 concentration

(B)  Increase in 2,3- Bisphosphoglycerate concentration

(C)  High pH

(D)  Loss of cooperativity

Answer: (C)

20. Considering the open chain forms, which of the following pair(s) represent/s an epimer?

(A)  D-mannose and D-fructose

(B)  D-glucose and D-mannose

(C)  D-glucose and D-fructose

(D)  D-galactose and D-glucose

Answer: (B; D)

Botany (XL-R)

Q.1 – Q.7 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Wheat plants treated with prolonged cold temperature at the seedling stage flower earlier than the untreated control. Seeds collected from these treated individuals, however, give rise to plants that do not flower early. This phenomenon is called

(A)  vernalization.

(B)  temperature acclimation.

(C)  photoperiodism.

(D)  adaptation.

Answer: (A)

2. Which ONE of the following plant taxa contains vascular tissue (xylem and phloem) but not woody tissue?

(A)  Oak

(B)  Moss

(C)  Pine

(D)  Fern

Answer: (D)

3. Which ONE of the following statements regarding spores and gametes is CORRECT?

(A)  Spores can directly undergo mitosis whereas gametes cannot.

(B)  Gametes can directly undergo mitosis whereas spores cannot.

(C)  Neither spores nor gametes can directly undergo mitosis.

(D)  Both spores and gametes can directly undergo mitosis.

Answer: (A)

4. Which ONE of the following organelles controls gravitropism in the roots of higher plants?

(A)  Chromoplast

(B)  Amyloplast

(C)  Chloroplast

(D)  Etioplast

Answer: (B)

5. Phytoalexins play important role in plant defense against pathogens. Choose the INCORRECT option related to phytoalexins.

(A)  Phytoalexins belong to secondary metabolites.

(B)  Phytoalexins have antifungal activity.

(C)  Phytoalexins are abundant in plants under normal condition.

(D)  Different hosts produce phyallexins of varying chemical nature.

Answer: (C)

6. The figure shows the germination percentage of imbibed seeds treated with the given sequence of red (R) and far-red (F) light (each exposure lasting 5 min). The percentage of germination was scored after 72 hours in darkness at 25 °C. Based on this, which ONE of the following options is CORRECT?

(A)  Red light induces seed germination whereas far-red light inhibits it.

(B)  Red light inhibits seed germination whereas far-red light induces it.

(C)  Both red and far-red light inhibit seed germination.

(D)  Both red and far-red light induce seed germination.

Answer: (A)

7. The structures of four plant hormones are shown. Identify the CORRECT hormone that is responsible for bending of coleoptile of canary grass in response to unidirectional white light.

Answer: (A)

Q.8 – Q.9 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).

8. Which of the following cellular component(s) is/are NOT part(s) of cytoskeleton in Angiosperms?

(A)  Microtubules

(B)  Microfilaments

(C)  Intermediate filaments

(D)  Centrioles

Answer: (C; D)

9. Which of the following enzyme(s), when overexpressed, would result in rice grains with increased β-carotene content?

(A)  Phytoene synthase

(B)  Carotene desaturase

(C)  β-glucoronidase

(D)  Enolpyruvalshikimate-3-phosphate synthase (EPSPS)

Answer: (A; B)

Q.10 Numerical Answer Type (NAT), carry ONE mark (no negative marks).

10. In spiral phyllotaxis, leaves are initiated sequentially on the meristem with two successive primordia being separated by golden angle. If a plant follows right-handed spiral phyllotaxis when looked down the meristem, then the angle between two successive leaves would be _________degrees (with correct sign, round off to one decimal place).

Answer: (137.4 to 137.6 OR -137.6 to -137.4)

Q.11 – Q. 15 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

11. Match the cell/tissue types in GROUP I with their corresponding total DNA content in GROUP II of a typical diploid Angiosperm species and choose the CORRECT option (C denotes DNA content in haploid genome).

(A)  P-1, Q-2, R-3, S-5

(B)  P-2, Q-2, R-1, S-5

(C)  P-1, Q-2, R-1, S-5

(D)  P-2, Q-1, R-2, S-4

Answer: (B)

12. Match the modified organs in GROUP I with their corresponding prototypic forms in GROUP II and choose the CORRECT option.

(A)  P-1, Q-2, R-2, S-1

(B)  P-2, Q-1, R-1, S-2

(C)  P-1, Q-2, R-1, S-2

(D)  P-1, Q-1, R-2, S-1

Answer: (A)

13. The diagram describes the ABC model of flower patterning in Arabidopsis where the A, B and C functions are operational in the whorls (1+2), (2+3) and (3+4), respectively, in the wild-type flower. Removal of A or C function results in the floral organ arrangements as (carpel; stamen; stamen; carpel) or (sepal; petal; petal; sepal), respectively. Based on these observations, which ONE of the following molecular pathways is CORRECT for floral organ pattern generation? Arrow indicates activation and bar indicates inhibition.

Answer: (C)

14. Find the CORRECT match among the plant species in GROUP I, the predominant phytochemical in GROUP II and the economic/medical use in GROUP III.

(A)  P-i-1, Q-ii-3, R-iii-4, S-v-5, T-iv-2

(B)  P-ii-1, Q-iii-2, R-i-3, S-v-5, T-iv-4

(C)  P-ii-1, Q-iii-2, R-v-4, S-i-3, T-iv-5

(D)  P-i-2, Q-ii-3, R-iv-1, S-iii-5, T-v-4

Answer: (B)

15. Match the genetically modified crop in GROUP I with the corresponding genetic element in GROUP II.

(A)  P-3, Q-1, R-4, S-2

(B)  P-1, Q-3, R-2, S-4

(C)  P-2, Q-1, R-4, S-3

(D)  P-3, Q-2, R-4, S-1

Answer: (A)

Q.16 – Q.18 Multiple Select Question (MSQ), carry TWO mark each (no negative marks)

16. To understand the mechanism of systemic acquired resistance (SAR), a team of researchers isolated a mutant with reduced SAR response. Sequencing of this mutant revealed homozygous mutations in two genes, X and Y. Which of the following experiment(s) would test whether the mutant phenotype is caused by mutation in either or both the genes?

(A)  Complement the mutant with X or Y and analyze the phenotype in each case.

(B)  Complement the mutant with both X and Y and analyze the phenotype.

(C)  Cross the mutant with wild-type and analyze the segregation pattern of thephenotype.

(D)  Compare the expression of X and Y in mutant and wild-type plants.

Answer: (A; B; C)

17. The observations of an experiment on seed germination in various genotypes under different light conditions are given, where √ and X indicate germination and the lack of it, respectively.

(A)  All the three light qualities– blue, red and far-red – are required for seedgermination.

(B)  Any one of the three light qualities – blue, red and far-red – is sufficient toinduce seed germination.

(C)  The CRY1, phyA and phyB proteins are required for blue, red and far-red lightperception, respectively.

(D)  The VP1 protein is unlikely to be involved in light perception.

Answer: (B; D)

18. Which of the following option(s) is/are CORRECT in the context of hybrid plant generation using Barnase/Barstar-based male sterile lines?

(A)  Barnase inhibits Barstar.

(B)  Barstar inhibits Barnase.

(C)  Barnase and Barstar are used to generate the male sterile line and the restorerline, respectively.

(D)  Barnase and Barstar are used to generate the restorer line and the male sterileline, respectively.

Answer: (B; C)

Q.19 – Q.20 Numerical Answer Type (NAT), carry TWO mark each (no negative marks)

19. In a diploid plant species, the T allele produces tall individuals and is completely dominant over the t allele that produces short individuals. Similarly, the W allele produces round seeds and is completely dominant over the w allele that produces wrinkled seeds (assume T and W loci not linked). If a parent with TTWW genotype is crossed to another parent with ttww genotype, the fraction of the F2 population produced by the fusion of both recombinant gametes would be ___________. (Round-off to two decimal places.)

Answer: (0.25 to 0.25)

20. In a population of a diploid plant species obeying Hardy-Weinberg equilibrium, a locus regulating flower color has two alleles R and r. Individuals with RR, Rrand rr genotypes produce red, pink and white flowers, respectively. If the ratio of red, pink and white flower-producing individuals in the population is 6:3:1, then the frequency of r allele in the population would be __________%.

(Round-off to two decimal places.)

Answer: (25 to 25)

Microbiology (XL-S)

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Antonie van Leeuwenhoek observed several microscopic organisms under his hand-made microscope. He described them as

(A)  Bacteria.

(B)  Fungi.

(C)  Animalcules.

(D)  Bacteriophages.

Answer: (C)

2. Which ONE of the following pathways oxidizes 1 mole of glucose to 2 moles of pyruvic acid along with one mole each of ATP, NADH and NADPH, in Pseudomonas, but not in Bacillus spp.?

(A)  Gluconeogenesis

(B)  Embden-Meyerhoff Pathway (EMP)

(C)  Entner-Doudoroff (ED) Pathway

(D)  Pentose Phosphate Pathway (PPP)

Answer: (C)

3. Water balance in extreme halophiles such as Halobacterium is maintained by cell surface glycoproteins consisting of

(A)  glycine and lysine.

(B)  lysine and histidine.

(C)  glycine.

(D)  aspartate and glutamate.

Answer: (D)

4. Nocardia spp. are not amenable to the classical method of Gram staining due to the presence of

(A)  N-acetyltalosaminuronic acid in the cell wall.

(B)  thick peptidoglycan.

(C)  mycolic acid.

(D)  keto-deoxy-octulosonic acid.

Answer: (C)

5. Protists belonging to the genus Trichonympha thrive in the gut of termites. They help the termites use wood as a food source. This relationship is an example of

(A)  parasitism.

(B)  competition.

(C)  commensalism.

(D)  mutualism.

Answer: (D)

Q.6 – Q.9 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).

6. Which of the following is/are used as electron donor/s for CO2 reduction during photosynthesis in purple sulfur bacteria?

(A)  Hydrogen sulfide

(B)  Thiosulfates

(C)  Methane

(D)  Sulfates

Answer: (A; B)

7. Which of the following catalyze(s) substrate-level phosphorylation?

(A)  ATP synthase

(B)  Succinate thiokinase

(C)  Phosphofructokinase

(D)  Pyruvate kinase

Answer: (B; D)

8. Which of the following method(s) can be applied to identify a bacterial species?

(A)  Fluorescent in situ hybridization (FISH)

(B)  Polymerase chain reaction (PCR) followed by sequencing of the amplicon

(C)  Gram staining

(D)  Acid-fast staining

Answer: (A; B)

9. Which of the following event(s) would contribute to the induction of lac operon in a wild-type strain of E. coli?

(A)  Accumulation of allolactose in the cell

(B)  Direct binding of cAMP to the promoter DNA

(C)  Binding of cAMP to a specific protein leading to its interaction with thepromoter

(D)  Elimination of cAMP from the cell

Answer: (A; C)

Q.10 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

10. One mole of a circular bacterial plasmid was digested with a high-fidelity restriction enzyme. The plasmid has five restriction sites for the enzyme used. The number of moles of fragments released upon cleavage at all sites is________.

Answer: (5 to 5)

Q.11 – Q.16 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

11. Under anaerobic fermentative growth conditions, one mole of glucose yields 22 grams of Streptococcus faecalis or 8.6 grams of Zymomonasmobilis. The molar growth yield (YATP) for (i) S. faecalis and (ii) Z. mobilis will be

(A)  (i) 11 and (ii) 4.3

(B)  (i) 22 and (ii) 4.3

(C)  (i) 22 and (ii) 8.6

(D)  (i) 11 and (ii) 8.6

Answer: (D)

12. The order of abundance of quinones (ubiquinone [UQ], menaquinone [MQ] and demethylmenaquinone [DMQ]) in E. coli growing anaerobically on fumarate is

(A)  UQ > DMQ > MQ

(B)  MQ > DMQ >UQ

(C)  MQ = DMQ > UQ

(D)  MQ > UQ > DMQ

Answer: (B)

13. What is the number of ATPs generated per molecule of NADH during oxidative phosphorylation in E. coli via (i) NDH-1 and cytochrome bo complex or (ii) the NDH-2 and cytochrome bd complex? (Assume H+/ATP =3)

(A)  (i) 2.00 and (ii) 3.67

(B)  (i) 3.00 and (ii) 2.67

(C)  (i) 2.70 and (ii) 0.67

(D)  (i) 2.50 and (ii) 0.50

Answer: (C)

14. Match the Immunoglobulin classes with their function

(A)  (i)- (s), (ii)-(p), (iii)-(q), (iv)-(r)

(B)  (i)- (p), (ii)-(t), (iii)-(q), (iv)-(r)

(C)  (i)- (q), (ii)-(p), (iii)-(t), (iv)-(r)

(D)  (i)- (r), (ii)-(p), (iii)-(t), (iv)-(s)

Answer: (A)

15. The figure shows the profiles of quantitative real-time PCR (qRT-PCR) tests for SARS-CoV-2 conducted on the throat swab samples of three individuals (X, Y and Z). Tests were carried out under identical conditions. Dotted line represents the threshold fluorescent value. Identify the correct statement on the status of the COVID-19 tests of the individuals based on their qRT-PCR profiles.

(A)  X and Y are negative; Z is positive

(B)  X and Y are positive; There is no apparent difference in their viral load

(C)  X and Y are positive; X has the highest viral load

(D)  X and Y are positive; Y has the highest viral load

Answer: (C)

16. The rate of appearance of recombinant E. coli strains containing different genes after a mating between Hfr and F− strains is shown in the graph (left). The approximate location of different genes (p, q, r, s, t, x, and y) along the Hfr chromosome is also shown (right). Based on this information, identify the recombinants X, Y and Z.

(A)  X is x+, Y is r+and Z is p

(B)  X is p+, Y is r+and Z is x

(C)  X is x+, Y is p+and Z is r

(D)  X is p+, Y is x+and Z is r

Answer: (B)

Q.17 – Q.20 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

17. The genome of a bacterium encodes for 10 different surface antigens, whose expression can be turned ‘ON’ or ‘OFF’ randomly and independently. The number of possible antigenic combinations is__________.

Answer: (1024 to 1024)

18. Suppose the mRNAs in a newly discovered bacteria are composed of only two distinct nucleotides (as opposed to four found in all known organisms). Considering that the organism has no nucleotide modification systems, the number of nucleotides required per codon to encode at least 20 distinct amino acids will be________.

Answer: (5 to 5)

19. The decimal reduction time (D) for reducing 1012 spores of Clostridium botulinum to 1 spore at 111°C will be_______ min (in integer). The D value is 0.2 min at 121°C. The increase in temperature required to change D to 1/10th of its initial value (Z value) is 10°C.

Answer: (24 to 24)

20. The generation time of E. coli is 30 minutes. For an exponentially growing culture, the initial number of bacteria required to reach a number of 109 in 2 hours is_________×107 (round off to two decimal places).

Answer: (6.20 to 6.30)

Zoology (XL-T)

Q.1 – Q.7 Multiple Choice Question (MCQ), carry ONE mark each (for each wronganswer: – 1/3).

1. Ichthyophis belongs to which of the following Class?

(A)  Mammalia

(B)  Reptilia

(C)  Amphibia

(D)  Aves

Answer: (C)

2. The two homologous genes occurring in different species are called

(A)  paralogous

(B)  orthologous

(C)  pseudologous

(D)  prologous

Answer: (B)

3. The expression of holandric genes causes which of the following genetic trait in humans?

(A)  Haemophilia

(B)  Sickle cell anaemia

(C)  Down’s Syndrome

(D)  Hypertrichosis

Answer: (D)

4. Assume that the anticodon for an unknown amino acid is 3ʹ AUG 5ʹ. The corresponding code on DNA sequence would be

(A)  3ʹ TAC 5ʹ

(B)  5ʹ TAG 3ʹ

(C)  3ʹ ATG 5ʹ

(D)  5ʹ ATG 3ʹ

Answer: (C)

5. The Organ of Corti is found in which of the following parts of human body?

(A)  Heart

(B)  Inner ear

(C)  Kidney

(D)  Nasal cavity

Answer: (B)

6. In adult athletes, muscles grow larger when exercised and are capable of regeneration after injury. This is due to proliferation and differentiation of

(A)  satellite cells

(B)  myelin sheath

(C)  oxyntic cells

(D)  choanocytes

Answer: (A)

7. The term innate behavior is a sort of animal behavior that is

(A)  triggered by an environmental change

(B)  learnt by hit-and-trial approach

(C)  trained and taught by the parent

(D)  fixed developmentally at the genetic level

Answer: (D)

Q.8 – Q.10 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

8. A man, whose mother and father had blood groups A and O respectively, marries a woman with blood group AB. If the man has blood group A, then the number of different blood groups possible among their children will be _________ (in integer).

Answer: (3 to 3)

9. A population of snakes in an isolated island is in Hardy–Weinberg equilibrium for a gene with only two alleles (A and a). If the allelic frequency of A is 0.6, then the genetic frequency of Aa is _________ round off to 2 decimal places).

Answer: (0.48 to 0.48)

10. In the structure of a polypeptide, one α-helix (3.613 helix) contains 32 intra-chain hydrogen bonds. The number of turns in the helix will be _________(in integer).

Answer: (10 to 10)

Q.11 – Q. 16 Multiple Choice Question (MCQ), carry TWO marks each (for each wronganswer: – 2/3).

11. Match the terms in Column I with the specific descriptions in Column II.

(A)  P-(iii), Q-(vi), R-(i), S-(v), T-(ii), U-(iv)

(B)  P-(v), Q-(ii), R-(iii), S-(vi), T-(i), U-(iv)

(C)  P-(ii), Q-(iv), R-(vi), S-(v), T-(i), U-(iii)

(D)  P-(iii), Q-(vi), R-(ii), S-(v), T-(iv), U-(i)

Answer: (A)

12. Match the autoimmune diseases in Column I for the self-antigens in Column II.

(A)  P-(i), Q-(ii), R-(iii), S-(iv)

(B)  P-(ii), Q-(iii), R-(iv), S-(i)

(C)  P-(iii), Q-(i), R-(iv), S-(ii)

(D)  P-(iv), Q-(i), R-(ii), S-(iii)

Answer: (B)

13. Match the types of cell movements during gastrulation in Column I with the descriptions in Column II.

(A)  P-(ii), Q-(iii), R-(iv), S-(i)

(B)  P-(iv), Q-(i), R-(iii), S-(ii)

(C)  P-(ii), Q-(iv), R-(i), S-(iii)

(D)  P-(iii), Q-(ii), R-(iv), S-(i)

Answer: (C)

14. Match the therapeutic factors in Column I with the applications in Column II.

(A)  P-(ii), Q-(iv), R-(v), S-(iii), T-(vi)

(B)  P-(ii), Q-(v), R-(i), S-(iv), T-(iii)

(C)  P-(v), Q-(vi), R-(iv), S-(iii), T-(i)

(D)  P-(iii), Q-(iv), R-(ii), S-(v), T-(vi)

Answer: (A)

15. Match the cell organelles in Column I with the appropriate functions in Column II.

(A)  P-(ii), Q-(iii), R-(v), S-(i), T-(iv)

(B)  P-(iv), Q-(v), R-(i), S-(ii), T-(iii)

(C)  P-(iv), Q-(v), R-(iii), S-(i), T-(ii)

(D)  P-(ii), Q-(iii), R-(i), S-(v), T-(iv)

Answer: (D)

16. Cohesin and Condensin proteins of eukaryotes belong to which one of the following groups?

(A)  Structural maintenance of chromosomes (SMC) proteins

(B)  Histones

(C)  DNA polymerases

(D)  Topoisomerases

Answer: (A)

Q.17 – Q.18 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).

17. Which of the following options represent the animals as Endemic to India?

(A)  Pygmy Hog

(B)  Mountain Bongo

(C)  Hirola

(D)  Purple Frog

Answer: (A; D)

18. Which of the following amino acids contain more than one chiral center?

(A)  Leucine

(B)  Isoleucine

(C)  Serine

(D)  Threonine

Answer: (B; D)

Q.19 – Q.20 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

19. An enzyme catalyzes the conversion of 30 μM of a substrate to product at reaction velocity of 9.0 μM s1. When [Et] = 30 nM and Km = 10 μM, Kcat / Kmof enzyme will be n × 107 M1s1. The value of n is _________ (in integer).

Answer: (4 to 4)

20. A cross is made between two animals of genotypes AaBb x AaBb, where loci A and loci B assort independently. The progeny of this dihybrid cross was then allowed to self-cross. The proportion of the progeny that showed segregation for loci A (i.e., produce A- and aa progeny) in % will be_________ (in integer).

Answer: (50 to 50)

Food Technology XL (U)

Q.1 – Q.10 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. In a typical bacterial growth curve, the first order kinetics for growth rate is observed in

(A)  Lag phase

(B)  Log phase

(C)  Stationary phase

(D)  Decline phase

Answer: (B)

2. Which of the following microorganisms is NOT a causative agent for foodborne diseases?

(A)  Campylobacter jejuni

(B)  Clostridium perfingens

(C)  Norovirus

(D)  Borreliaburgdorferi

Answer: (D)

3. Which one of the followings is NOT a fermented food product?

(A)  Tofu

(B)  Vinegar

(C)  Sauerkraut

(D)  Tempeh

Answer: (A)

4. The Protein Efficiency Ratio (PER) is defined as

(A)  Percentage of absorbed nitrogen retained in the body

(B)  Weight gain in body mass (in gram) per gram protein intake

(C)  Ratio of essential and non-essential amino acids in a protein

(D)  Percent in vitro digestibility of a protein

Answer: (B)

5. Which one of the following enzymes sequentially releases maltose from starch?

(A)  α−Amylase

(B)  β− Amylase

(C)  Glucoamylase

(D)  Pullulanase

Answer: (B)

6. Highest mole % of amino acid mixture present in glutenin of wheat gluten are

(A)  Glutamine and glutamic acid

(B)  Serine and lysine

(C)  Alanine and tryptophan

(D)  Proline and glycine

Answer: (A)

7. Which one of the following compounds is present in soybean and acts asphytoesterogen?

(A)  Tangeretin

(B)  Lutin

(C)  Quercetin

(D)  Genistein

Answer: (D)

8. Which one of the followings is an oligosaccharide?

(A)  Xanthan

(B)  Alginate

(C)  Raffinose

(D)  Gellan

Answer: (C)

9. Bittering agent in grape fruit formed after juice extraction under acidic conditions is

(A)  Quinine

(B)  Theobromine

(C)  Isohumulone

(D)  Limonin

Answer: (D)

10. Difference between adsorption and desorption isotherms is known as

(A)  Hysteresis

(B)  Dryness

(C)  Evaporation

(D)  Dehydration

Answer: (A)

Q.11 – Q.13 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

11. The conversion of pyruvate to lactic acid in homolactic fermentation iscatalyzed by

(A)  Lactate dehydrogenase

(B)  Pyruvate dehydrogenase

(C)  Lactase

(D)  Pyruvate decarboxylase

Answer: (A)

12. Which one of the following statements is INCORRECT with respect to Controlled Atmosphere Package (CAP) and Modified Atmosphere Package(MAP) of agro- produce?

(A)  CAP and MAP limit microbial as well as biochemical activities.

(B)  Gas composition inside a MAP during the storage is continuously monitored andregulated.

(C)  CAP implies a greater degree of precision than MAP in maintaining specific levelsof the gas composition.

(D)  Modification of the atmosphere inside a MAP is achieved by natural interplaybetween respiration of products and permeation of gases through the packagingfilm.

Answer: (B)

13. Match unit operation in Column I with its application in food processing in Column II.

(A)  P-2, Q-4, R-2, S-I

(B)  P-2, Q-3, R-4, S-1

(C)  P-4, Q-1, R-2, S-3

(D)  P-4, Q-2, R-1, S-3

Answer: (B)

Q.14 – Q.19 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).

14. Which of the followings are correct pair of GRAS chemical food preservative, affected organism and given food matrix?

(A)  Sodium lactate-Bacteria-Pre-cooked meat

(B)  Caprylic acid-Insects-Cheese wraps

(C)  Dehydroacetic acid-Molds-Squash

(D)  Sodium nitrite-Clostridia-Meat curing preparations

Answer: (A; D)

15. Choose the correct pair of pigment and their corresponding color in plantproducts

(A)  Carotene-Yellow-orange-Peppers

(B)  Betanin-Purple/red-Cactus pear

(C)  Lycopene-Red-Red beets

(D)  Flavanols-Orange-red-Cauliflowers

Answer: (A; B)

16. Which of the following compounds act as anti-nutritional factors?

(A)  Phytate

(B)  Isoflavones

(C)  Trypsin Inhibitor

(D)  Resveratrol

Answer: (A; C)

17. Which of the followings is/are commonly used medium/media in thesupercritical fluid extraction of spices and tea?

(A)  Water

(B)  Carbon dioxide

(C)  Dichloromethane

(D)  Carbon dioxide with Ethanol

Answer: (A; B; D)

18. Which of the following expressions represent the Reynolds number of a fluid flowing through a uniform circular cross section pipe?

Answer: (A; B)

19. Which of the following combinations of analytical equipment, property measured and food property are correct?

(A)  Particle size analyzer – particle size distribution – span value

(B)  Texture profile analyzer – morphology – chewiness

(C)  Differential scanning calorimeter – glass transition temperature – degree of caking

(D)  Capillary viscometer – viscosity – sensory

Answer: (A; C)

Q.20 Numerical Answer Type (NAT), carry TWO mark (no negative marks).

20. Dry air is fed into a tray dryer. The percentage relative humidity of the air leaving the dryer is 60% at 70°C and 101.35 kPa. If, saturated vapour pressure of water at 70°C is 31.2 kPa, the humidity of the air leaving the dryer in kg water per kg dry air (round off to 3 decimal places) will be ________.

(Given : Molecular weight of water and air are 18.02 g mol-1 and 28.97 g mol-1respectively)

Answer: (0.135 to 0.150)

GATE Exam 2021 Humanities & Social Sciences (XH) Question Paper With Answer Key

GATE-2021

XE: Humanities & Social Sciences

GA-General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Consider the following sentences:

(i) After his surgery, Raja hardly could walk.

(ii) After his surgery, Raja could barely walk.

(iii) After his surgery, Raja barely could walk.

(iv) After his surgery, Raja could hardly walk.

Which of the above sentences are grammatically CORRECT?

(A)  (i) and (ii)

(B)  (i) and (iii)

(C)  (iii) and (iv)

(D)  (ii) and (iv)

Answer: (D)

2. X came out of a building through its front door to find her shadow due to the morning sun falling to her right side with the building to her back. From this, it can be inferred that building is facing _________

(A)  North

(B)  East

(C)  West

(D)  South

Answer: (D)

3. 

In the above figure, O is the center of the circle and, M and N lie on the circle.

The area of the right triangle MON is 50 cm2.

What is the area of the circle in cm ?

(A)  2π

(B)  50π

(C)  75π

(D)  100π

Answer: (D)

4. If 

then, the value of the expression ∆ 2 ⊕ 3 ∆ ((4 ⨂ 2) ∇ 4) =

(A)  −1

(B)  −0.5

(C)  6

(D)  7

Answer: (D)

5. “The increased consumption of leafy vegetables in the recent months is a clear indication that the people in the state have begun to lead a healthy lifestyle”

Which of the following can be logically inferred from the information presented in the above statement?

(A)  The people in the state did not consume leafy vegetables earlier.

(B)  Consumption of leafy vegetables may not be the only indicator of healthy lifestyle.

(C)  Leading a healthy lifestyle is related to a diet with leafy vegetables.

(D)  The people in the state have increased awareness of health hazards causing by consumption of junk foods.

Answer: (C)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

6. Oxpeckers and rhinos manifest a symbiotic relationship in the wild. The oxpeckers warn the rhinos about approaching poachers, thus possibly saving the lives of the rhinos. Oxpeckers also feed on the parasitic ticks found on rhinos.

In the symbiotic relationship described above, the primary benefits for oxpeckers and rhinos respectively are,

(A)  Oxpeckers get a food source, rhinos have no benefit.

(B)  Oxpeckers save their habitat from poachers while the rhinos have no benefit.

(C)  Oxpeckers get a food source, rhinos may be saved from the poachers.

(D)  Oxpeckers save the lives of poachers, rhinos save their own lives.

Answer: (C)

7. 

A jigsaw puzzle has 2 pieces. One of the pieces is shown above. Which one of the given options for the missing piece when assembled will form a rectangle? The piece can be moved, rotated or flipped to assemble with the above piece.

Answer: (A)

8. The number of hens, ducks and goats in farm P are 65, 91 and 169, respectively. The total number of hens, ducks and goats in a nearby farm Q is 416. The ratio of hens:ducks:goats in farm Q is 5:14:13. All the hens, ducks and goats are sent from farm Q to farm P.

The new ratio of hens:ducks:goats in farm P is_____

(A)  5:7:13

(B)  5:14:13

(C)  10:21:26

(D)  21:10:26

Answer: (C)

9. 

The distribution of employees at the rank of executives, across different companies C1, C2, …, C6 is presented in the chart given above. The ratio of executives with a management degree to those without a management degree in each of these companies is provided in the table above. The total number of executives across all companies is 10,000.

The total number of management degree holders among the executives in companies C2 and C5 together is_____.

(A)  225

(B)  600

(C)  1900

(D)  2500

Answer: (C)

10. Five persons P, Q, R, S and T are sitting in a row not necessarily in the same order. Q and R are separated by one person, and S should not be seated adjacent to Q.

The number of distinct seating arrangements possible is:

(A)  4

(B)  8

(C)  10

(D)  16

Answer: (D)

Reasoning and Comprehension (XH-B1)

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. According to a recent article in a medical journal, consuming curcumin (from turmeric) significantly lowers the risk of COVID-19. The researchers draw this conclusion from a study that found that people who consumed one or more teaspoons of curcumin extract everyday were half as likely to be diagnosed with the disease as people who did not consume curcumin.

Which of the following, if true, most weakens the argument in the article?

(A)  In another study, people who were given a zinc supplement everyday were more than four times less likely to be diagnosed with COVID-19 as those who did not.

(B)  All the participants in this study were from the same state where no other spices or herbs are consumed.

(C)  The participants who consumed curcumin were also more likely to exercise than those who did not.

(D)  In another study, COVID-19 patients who were given curcumin were no more likely to recover than others.

Answer: (C)

2. Froot Inc. carried out an internet advertisement campaign for its new beverage CocoLoco. After the campaign, the director of the advertising company conducted a survey and found that the CocoLoco sales were higher than that of TenderJoos a competing product from Joos Inc. The agency concluded that the internet advertising campaign is more effective than advertising through other media.

Which of the following statements could strengthen the conclusion above by the agency?

(A)  A Rs. 2 discount was offered on CocoLoco during the campaign period.

(B)  CocoLoco sales were higher than those of TenderJoos before the internet campaign.

(C)  A newspaper advertisement campaign the previous year did not increase CocoLoco sales.

(D)  During the campaign for CocoLoco, Joos Inc. did not advertise TenderJoos at all.

Answer: (C)

3. An e-commerce site offered a deal last month conditional on the customer spending a minimum of Rs. 500. Any customer who buys 2 kg of fresh fruit will receive a hand mixer and any customer who buys 2 kg of fresh vegetables will receive a vegetable chopper.

Which of the following is NOT a possible outcome of the above?

(A)  A customer purchased 3 kg of fresh fruit and did not receive a vegetable chopper.

(B)  A customer purchased items for ₹500 which included 1 kg of vegetables and received a hand mixer.

(C)  A customer purchased items for Rs. 500 which included 2 kg of vegetables and 1 kg of fruit and received a hand mixer.

(D)  A customer purchased items for Rs. 300 which included 2 kg of fruit and received neither a hand mixer nor a vegetable chopper.

Answer: (C)

4. Writers of detective fiction often include an incompetent detective as a foil for the brilliant investigator-protagonist as they follow different paths in trying to solve the crime. In the individual accounts, the incompetent detective is frequently distracted by the culprit’s careful plans, while the competent investigator solves the case after a final confrontation. Analysts of such fiction believe that the authors select this story-telling technique to provide readers with more complexities in the form of misleading clues, while figuring out the crime.

Which of the following statements most logically follows from the passage above?

(A)  A detective story is considered well-written if the brilliant investigator is accompanied by an incompetent detective.

(B)  Writers of detective fiction use the contrast of an incompetent detective to mainly show how complex the investigation is.

(C)  Writers of detective fiction never write stories where the incompetent detective solves the case.

(D)  Writers of detective fiction use two investigative accounts to make it difficult for the reader to figure out the outcome.

Answer: (D)

5. The first (P1) and the last (P6) parts of a single sentence are given to you. The rest of the sentence is divided into four parts and labelled (L,M,N,O). Reorder these parts so that the sentence can be read through correctly and select one of the options given.

P1: Studies of several Sahitya Akademi award winners show that…

L: or encounter professional

M: and invariably develop a strained relationship with other literary figures

N: they often publish very little

O: after winning the prize

P6: …envy and rivalry.

The correct order is:

(A)  NOLM

(B)  MLON

(C)  ONML

(D)  MOLN

Answer: (C)

Q.6 – Q.10 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

6. Gerrymandering refers to the targeted redrawing of election constituencies so as to benefit a particular party. This is especially important where the electoral system is “first past the post” in each constituency (i.e. one winner is selected in each constituency based on a majority of votes won) and where there is no other provision for proportional representation (as for example in the German system). For a simple illustration of gerrymandering, if a region consists of districts 1, 2, 3, …, 9 with districts 1, 2, 3, 4, 5, 6 favouring party P and 7, 8, 9 favouring party Q, then grouping of districts to constituencies as {1,2,3}, {4,5,6}, {7,8,9} will give two seats to party P and one seat to party Q, whereas the grouping {1,2,7}, {3,4,8}, {5,6,9} will give all three seats to party P, as they will secure a majority in each constituency.

Which of these statements can be deduced from the above?

(A)  Gerrymandering implies that constituency boundaries can sometimes be drawn to favour one party over the other.

(B)  Gerrymandering implies that proportional representation is impossible when districts are grouped to form constituencies.

(C)  To counteract gerrymandering political parties should concentrate on districts where they are favoured.

(D)  The grouping of districts to constituencies has very little impact on proportional representation.

Answer: (A)

7. X-ray examination of a recently discovered painting that some authorities judge to be a self-portrait by Michelangelo revealed an under-image of a woman’s face. Either Michelangelo or some other artist must have repainted over the first painting that had now been seen on the canvas. Because the woman’s face also appears on other paintings by Michelangelo, this painting is determined to indeed be an authentic painting by Michelangelo.

Which of the following assumptions must be made in reaching the conclusion above?

(A)  When an already painted canvas of an artist is used, the second artist using that canvas for a new painting is usually influenced by the artistic style of the first.

(B)  Several painted canvases that art historians attribute to Michelangelo contain under-images that appear on at least one other of Michelangelo’s paintings.

(C)  Subject or subjects that appear in authenticated paintings of Michelangelo are rather unlikely to show up as under-images on painted canvases not attributed to Michelangelo.

(D)  No painted canvas can be attributed to a particular artist with certainty without an X-ray analysis.

Answer: (C)

8. This season _______ tourists visited Ladakh than last season; however, ______ to be the biggest tourist destination in India. The tourism department explains that the number of tourists to India has ______ relative to previous years, ________ have chosen to visit Ladakh.

Select the correct sequence of phrases to fill in the blanks to complete the passage above.

(A)  more / for the first time in many seasons it does not appear / increased / and it seems that most

(B)  fewer / as in the past, it appears / in fact decreased / but it seems that only a small proportion

(C)  fewer / for the first time in many seasons it appears / in fact decreased / but it seems that most

(D)  more / this season as well, it appears / in fact decreased / but it seems that a large proportion

Answer: (C)

9. Reorder the sentences in (1) – (5) such that they form a coherent paragraph.

(1) In fact, dozens of languages today have only one native speaker still living, and that person’s death will mean the extinction of the language: It will no longer be spoken, or known, by anyone on earth.

(2) Many languages are falling out of use and are being replaced by others that are more widely used in the region or nation, such as English in Australia or Portuguese in Brazil.

(3) Many other languages are no longer being learned by new generations of children or by new adult speakers.

(4) An endangered language is one that is likely to become extinct in the near future.

(5) Unless the trends are reversed, these endangered languages will

become extinct by the end of the century.

(Adapted from What is an Endangered Language by A. Woodbury.)

(A)  2 3 1 4 5

(B)  2 3 5 4 1

(C)  4 1 5 2 3

(D)  4 2 3 1 5

Answer: (D)

10. The first (P1) and the last (P6) parts of a single sentence are given to you. The rest of the sentence is divided into four parts and labelled L,M,N,O. Reorder these parts so that the sentence can be read correctly and select one of the sequences below.

P1: For a little while…

L: it was a common belief

M: right after the treaty of Versailles

N: that Germany had caused World War I not just by her actions

O: held by analysts and politicians alike

P6: … but by also encouraging Italy in her own aggressions.

(A)  LMNO

(B)  MLON

(C)  LNMO

(D)  MOLN

Answer: (B)

Q.11 – Q.15 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).

11. After Florentino Ariza saw her for the first time, his mother knew before he told her because he lost his voice and his appetite and spent the entire night tossing and turning in his bed. But when he began to wait for the answer to his first letter, his anguish was complicated by diaorrhea and green vomit, he became disoriented and suffered from sudden fainting spells, and his mother was terrified because his condition did not resemble the turmoil of love so much as the devastation of cholera. Florentino Ariza’s godfather, an old homeopathic practitioner who had been Tránsito Ariza’s confidant ever since her days as a secret mistress, was also alarmed at first by the patient’s condition, because he had the weak pulse, the hoarse breathing, and the pale perspiration of a dying man. But his examination revealed that he had no fever, no pain anywhere, and that his only concrete feeling was an urgent desire to die. All that was needed was shrewd questioning, first of the patient and then of his mother, to conclude once again that the symptoms of love were the same as those of cholera. He prescribed infusions of linden blossoms to calm the nerves and suggested a change of air so he could find consolation in distance, but Florentino Ariza longed for just the opposite: to enjoy his martyrdom.

(Adapted from Love in a Time of Cholera by Gabriel García Márquez.)

The author of the passage is implying that:

(A)  Homeopathy cures love.

(B)  The doctor could not distinguish between love and cholera.

(C)  The doctor could distinguish between love and cholera.

(D)  The symptoms of love and cholera are similar.

Answer: (C; D)

12. Now, it is clear that the decline of a language must ultimately have political and economic causes: it is not due simply to the bad influence of this or that individual writer. But an effect can become a cause, reinforcing the original cause and producing the same effect in an intensified form, and so on indefinitely. A man may take to drink because he feels himself to be a failure, and then fail all the more completely because he drinks. It is rather the same thing that is happening to the English language. It becomes ugly and inaccurate because our thoughts are foolish, but the slovenliness of our language makes it easier for us to have foolish thoughts.

(Adapted from Politics and the English Language by George Orwell.)

The illustration of the man who takes to drink is used to underscore which of the following ideas in the passage above?

(A)  Political and economic causes control deterioration of language.

(B)  Foolish thoughts are enabled by inaccurate language.

(C)  Effect of an action becomes the cause in a cyclic pattern.

(D)  Drinking enables people to have foolish thoughts and slovenly language.

Answer: (B; C)

13. It is a pity that Caste even today has its defenders. The defences are many. It is defended on the grounds that the Caste System is but another name for division of labour, and if division of labour is a necessary feature of every civilised society, then it is argued that there is nothing wrong in the Caste System. Now the first thing to be urged against this view is that Caste System is not merely division of labour. It is also a division of labourers. Civilised society undoubtedly needs division of labour but nowhere is division of labour accompanied by this unnatural division of labourers into watertight compartments, grading them one above the other. This division of labour is not spontaneous or based on natural aptitudes. Social and individual efficiency requires us to develop the individual capacity and competency to choose and to make his own career. This principle is violated in so far as it involves an attempt to appoint tasks to individuals in advance, not on the basis of trained original capacities, but on that of birth. Industry undergoes rapid and abrupt changes and an individual must be free to change his occupation and adjust himself to changing circumstances, to gain his livelihood. (Adapted from Annihilation of Caste by Dr. B.R. Ambedkar.)

Which of the following observations substantiate the arguments found in the passage above?

(A)  Newer generations are unable to change and move away from low-paying family professions, even with changed economic circumstances.

(B)  Sedentary desk jobs are considered to have more value and are in greater demand than those involving manual labour.

(C)  The government’s jobs guarantee programme makes low-level management jobs available across all industries to all graduates in the nation.

(D)  A bus driver becomes an app creator and, in the course of one month, reaches one million downloads on Playstore with a four-star rating.

Answer: (A; B)

14. Imagine that you’re in a game show and your host shows you three doors. Behind one of them is a shiny car and behind the others are goats. You pick one of the doors and get what lies within. After making your choice, your host chooses to open one of the other two doors, which inevitably reveals a goat. He then asks you if you want to stick with your original pick, or switch to the other remaining door. What do you do? Most people think that it doesn’t make a difference and they tend to stick with their first pick. With two doors left, you should have a 50% chance of selecting the one with the car. If you agree, then you have just fallen afoul of one of the most infamous mathematical problems – the Monty Hall Problem. In reality, you should switch every time which doubles your odds of getting the car. Over the years, the problem has ensnared countless people, but not, it seems, pigeons. The humble pigeon can learn with practice the best tactic for the Monty Hall Problem, switching from their initial choice almost every time. Amazingly, humans do not!

(Adapted from an article by Ed Yong in Discover Magazine.)

Which of the following conclusions follow from the passage above?

(A)  Humans calculate the probability of independent, random events such as the opening of a door by dividing the specific outcomes by the total number of possible outcomes.

(B)  Humans find it very difficult to learn to account for the host’s hand in making the event non-random and, thereby, changing the outcome of the event.

(C)  Calculating probabilities is difficult for humans but easy for pigeons; which is why the pigeons succeed where the humans fail.

(D)  Humans are governed by reason, but pigeons are irrational and only interested in the outcome and will do whatever it takes to get food.

Answer: (A; B)

15. The truth is that, despite the recent success of car-makers P and Q, India’s automobile industry is in a state not that different from the bad old days of the license-permit quota raj when two carmakers dominated a captive domestic market with substandard vehicles and with very little, if any, research and development, and low to negligible productivity growth.High tariff barriers have certainly induced foreign automobile makers to enter the Indian market by setting up local operations, but this so-called “tariff jumping” foreign investment has produced an industry that is inefficient, operating generally at a low scale, and whose products are not globally competitive either in terms of cost or of innovation. It is noteworthy that the automobile parts industry, which has faced low tariffs (as low as 12.5%) and has been largely deregulated, has been characterised by higher productivity and much better export performance than the completely-built units’ sector in the years since liberalisation.

(Adapted from an Op-Ed in The Mint.)

Which of the following statements can be inferred from the above?

(A)  Low tariff barriers increase productivity.

(B)  Tariff jumping leads to increases in productivity.

(C)  Deregulation has worked for the automotive parts industry and therefore should be applied to completely-built units.

(D)  P and Q do not invest enough in research and development.

Answer: (A; C; D)

Economics (XH-C1)

Q.1 – Q.20 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. A firm finds that for the product that it produces, its (own) price elasticity of demand is 4. Currently, the firm is selling 2000 units per month at Rs. 5 per unit. If it wishes to increase its sales by 10%, it must

(A)  lower its price by 4%

(B)  lower its price by 2%

(C)  lower its price by 2.5%

(D)  increase its price by 2%

Answer: (C)

2. “Inflation increases the average level of prices”. Which of the following is(are) necessarily implied by this statement:

(i) The prices of commodities exceed income

(ii) Money supply grows at a higher rate than the real GDP

(A)  Only (i)

(B)  Only (ii)

(C)  Both (i) and (ii)

(D)  Neither (i) nor (ii)

Answer: (B)

3. For the production function Q = F(K, L) = √KL with PK = 4 and PL = 2, find the values of K and L that will minimize the cost of producing 2 units of output.

(A)  K = 2√3 ; L = 3√2

(B)  K = 2√2 ; L = √2

(C)  K = √2 ; L = 2√2

(D)  K = 2 ; L = 2

Answer: (C)

4. If the sum of price elasticities of imports and exports of a country exceeds unity, then a depreciation of domestic currency will ultimately result in

(A)  contraction in trade deficit of the country

(B)  widening of trade deficit of the country

(C)  an uncertain net effect on the trade balance

(D)  a huge outflow of foreign portfolio capital from that country

Answer: (A)

5. To determine the relationship between y and x1, Rohit estimated two different OLS models. In the first model, Rohit regressed y on x1 and x2 as given below

y = β0 + β1x1 + β2x2 + u (1)

In the second model, Rohit regressed y only on x1 as given below

y = δ0 + δ1x1 + v             (2)

The estimated coefficients of x1 in the above two models are exactly same.

From this observation we can state conclusively that

(A)  Only (i) is true

(B)  Only (ii) is true

(C)  Either (ii) or (iii) or both are true

(D)  Neither (ii) nor (iii) is true

Answer: (C)

6. XYZ Co. Ltd. is a costless monopoly from suburban Mumbai producing and selling exotic mushrooms. The demand for mushrooms is given by

Q = 700 − 100P. Do you agree that XYZ will have a maximum possible

total revenue of Rs. 1500?

(A)  Yes, the maximum possible total revenue is Rs.1500

(B)  No, the maximum possible total revenue is less than Rs.1500

(C)  No, the maximum possible total revenue is more than Rs.1500

(D)  No, the maximum possible total revenue cannot be estimated

Answer: (B)

7. In a demand function estimation of a good X, a researcher collected data on various households’ consumption of good X (Qx) for various price levels. The researcher also collected data on household income (M) and household size (S). The estimated regression result is

log Qx = −0. 345(0. 111) − 1. 543(2. 345) log Px + 1. 123(0. 012) log M + 0. 234(0. 123) log S

where Px is price per unit of X. The values in the parentheses are the standard errors of the estimated coefficients. From the estimation one can conclude that

(A)  the demand for good X is highly elastic

(B)  X is an inferior good

(C)  the estimated price elasticity of demand is not statistically significant

(D)  the estimated price elasticity of good X is 2.345

Answer: (C)

8. Consider a duopoly market in which the market demand function is as follows: P = 40 − Q. For the two firms producing with identical marginal costs of 10, the Bertrand-Nash equilibrium price will be:

(A)  40

(B)  10

(C)  20

(D)  30

Answer: (B)

9. What would be the consequences for the OLS estimator if heteroscedasticity is present in a regression model but ignored? Assume that all the other classical assumptions are valid.

(A)  It will be biased

(B)  It will be inconsistent

(C)  It will be unbiased but inefficient

(D)  It will be unbiased but inconsistent

Answer: (C)

10. Walras’ Law implies that if there are N markets in the economy, then one only needs to find equilibrium prices in

(A)  N − 2 markets

(B)  N − 1 markets

(C)  N + 1 markets

(D)  all the N markets

Answer: (B)

11. There are many reasons why a poor country may fail to catch up with a rich neighbour. Which of the following is NOT one of these reasons?

(A)  The poor country may have more rapid population growth

(B)  The rich country may have more human capital

(C)  The poor country may have a higher saving ratio

(D)  The rich country through trade may be more integrated with the world economy

Answer: (C)

12. In a two country model, an increase in foreign country’s national income generally leads to:

(A)  increased exports and increased domestic output

(B)  decreased exports but increased domestic output

(C)  decreased exports and decreased domestic output

(D)  increased exports but decreased domestic output

Answer: (A)

13. Piku faces a lottery with outcomes of Rs. 24, Rs. 12, Rs. 48 and ₹6 given by the following probability distribution

She is indifferent between the lottery and receiving Rs. 28 with certainty. Given the information we can conclude that Piku is a

(A)  risk lover

(B)  risk averse

(C)  risk neutral

(D)  hedger

Answer: (A)

14. Consider a regression model y = β0 + βx + u where the continuous variable y is regressed on a dummy variable x, which takes the value either 1 or 0.

However, the model was estimated using the instrumental variable (IV) estimation method, wherein the indicator variable z is used as an instrument of x.

Let

 be the sample averages of y when z takes the value 1 and 0, respectively

 be the sample averages of x when z takes the value 1 and 0, respectively

  be the sample averages of y when x takes the value 1 and 0, respectively

  be the sample averages of z when x takes the value 1 and 0, respectively

Answer: (C)

15. Assuming that external economies exist, when demand increases in a perfectly competitive market, in the long-run, the price of the product

(A)  rises above the initial price (before the demand increase) and quantity increases

(B)  remains the same as the initial price (before the demand increase) and quantity increases

(C)  falls below the initial price (before the demand increase) and quantity increases

(D)  equals the initial price (before the demand increase) and quantity decreases

Answer: (C)

16. Consider an individual who maximizes her expected utility having Bernoulli utility function u(w) = α − βerw; w > 0 is wealth. The individual displays _________ relative risk aversion.

(A)  constant

(B)  increasing

(C)  decreasing

(D)  uncertain

Answer: (B)

17. For an open economy, the ‘twin deficits’ can be expressed by:

[where S = Savings; I = Gross Private Investment; G = Government Expenditures; TR = Transfer Payments; TX = Taxes; X = Exports; M = Imports and NFIA = Net Factor Income from Abroad]

(A)  S − I = [G − TR − TX] + [X − M]

(B)  I − S = [G + TX − TR] + [M − X]

(C)  S − I = [G + TR − TX] + [X − M]

(D)  I − S = [TX − G + TR] + [NFIA]

Answer: (C)

18. If expectations about inflation are formed as per the rational expectations hypothesis, then the short-run Philips curve will be

(A)  negatively sloped

(B)  parallel to the vertical axis

(C)  parallel to the horizontal axis

(D)  coinciding with the NAIRU

Answer: (B)

19. As economic development proceeds, income inequality tends to follow a(n) ________ curve.

(A)  asymptotically convex

(B)  inverted U-shaped

(C)  V-shaped

(D)  S-shaped

Answer: (B)

20. India has the highest amount of foreign debt in the form of

(A)  Non Resident Indian (NRI) Deposits

(B)  Commercial Borrowings

(C)  Loans taken from the International Monetary Fund

(D)  Loans taken from the Bank of England

Answer: (B)

Q.21 – Q.25 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

21. Let A and B be two events with probabilities P(A) = 3/4 and P (B) = 1/3; then which of the following options is true?

Answer: (B)

22. If  is an unbiased and consistent estimator of the population variance, then one can conclude that  a(an) __________ estimator of the population standard deviation.

(A)  unbiased and consistent

(B)  biased and consistent

(C)  unbiased and inconsistent

(D)  biased and inconsistent

Answer: (B)

23. Consider the following demand−supply model, where

Demand function: P = Q2 − 12Q + 35

Supply function: 4P − 3Q = 0

The stable market equilibrium price-quantity combination will be

Answer: (A)

24. Trisha’s consumption preference on biryani (x) and pudding (y) is given by the utility function U(x, y) = x + 4y. The price per unit of biryani is Rs. 2 and the price per unit of pudding is Rs. 3. Trisha’s total income is ₹120. However, she faces an extra quantity constraint as she is not allowed to consume biryani more than 60 units and pudding more than 30 units. The optimum quantity of biryani and pudding consumed by Trisha is

(A)  (x∗ y∗) = (30, 20)

(B)  (x∗, y∗) = (15, 30)

(C)  (x∗, y∗) = (30,15)

(D)  (x∗, y∗) = (60, 0)

Answer: (B)

25. Consider a Cournot type n-firm natural spring oligopoly where the market demand for natural spring water is given by P(Q) = a − Q, a > 0. The n firms are symmetric. Each firm incurs a bottling cost of Ci = cqi, c > 0 and a > c. The equilibrium market price will be

Answer: (B)

Q.26 – Q.30 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).

26. Goods and Services Tax (GST) is

(A)  a ‘destination based’ consumption tax

(B)  an origin based tax assigned to the State of origin where the sale takes place

(C)  an indirect tax

(D)  a modified form of value added tax

Answer: (A; C; D)

27. Consider an intersection of roads without any traffic light. Two cars A and B approach an intersection and they want to proceed as indicated by respective arrows in the following diagram. If both proceed without stopping and there is an accident, then A would have a payoff of −100 and B would have a payoff of −500 (since B is responsible for the accident). If one stops, and the other proceeds then the payoff is: −5 and 10, respectively. If both of them stop, then it takes a little longer to reach their respective destinations, they have a payoff of −5 each. Find the Pure Strategy Nash Equilibrium (PSNE) of the players (Car drivers).

(A)  (Car A, Car B) = (Stop, Stop)

(B)  (Car A, Car B) = (Stop, Proceed)

(C)  (Car A, Car B) = (Proceed, Stop)

(D)  (Car A, Car B) = (Proceed, Proceed)

Answer: (B; C)

28. A Government Security (G-Sec)

(A)  is a tradeable instrument issued by the Central Government

(B)  is a tradeable instrument issued by State Governments

(C)  can have maturity of only more than one year      

(D)  cannot be considered as ‘gilt-edged’ instrument

Answer: (A; B)

29. If a country has flexible exchange rate regime with perfect capital mobility, then according to the Mundell-Fleming Model, an expansionary fiscal policy will lead to

(A)  no change in output

(B)  reduced net exports

(C)  appreciation of nominal exchange rate

(D)  expansion of output

Answer: (A; B; C)

30. The basic tenets of ‘Monetarism’ are

(A)  acceptance of the ‘quantity theory’ approach to macroeconomic analysis

(B)  a strict rule based monetary policy

(C)  a monetary approach to the balance-of-payments and exchange-rate theory

(D)  an active stabilization policy through expansionary monetary/fiscal policies

Answer: (A; B; C)

Q.31 – Q.40 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

31. Two farmers, Rohit and Harish, graze their animals on a common land. They can choose to use this common resource ‘lightly’ or ‘heavily’ and the resulting strategic interaction may be described as a simultaneous-move game. The payoff matrix is given below:

The minimum value of the discount rate (where the discount rate is less than one) under infinite repetition of the game where the threat strategy (“Graze lightly if the opponent also grazes lightly, whereas, if the opponent renege then always graze heavily in all the future periods”), is a Sub-game Perfect Nash Equilibrium (SPNE) and, both the farmers graze their animals lightly is _______ (round off to one decimal place).

Answer: (0.6 to 0.6)

32. Suppose Vijay has purchased a high-speed car worth Rs.1000000. During the purchase, an Insurance company has shared the latest available road safety survey, wherein it is mentioned that, due to heavy congestion on roads, there is 40% chance of an accident within the first year of car purchase resulting in loss of the car value by 60%. Vijay’s utility function for wealth (W) is given by U(W) = ln(W). If Vijay plans to buy an accident insurance having a premium of 30%, then he will purchase an insurance of Rs. ____________ (round off to the nearest integer).

Answer: (950000 to 999999)

33. Consider the following Table.

(All values are in Rupees Thousand Crore)

Based on the given data, the average Broad Money Multiplier for the period April – June is ________ (round off to three decimal places).

Answer: (5.300 to 5.600)

34. Consider two regression models estimated on a sample of 350 observations.

y = β0 + β1x1 + β2x2 + β3x3 + β4x4 + β5x5 + u ———(1)

y = α0 + α1x1 + α2x2 + v ———(2)

The R2 in model (1) is R12 = 0. 3521 and in model (2) is R22 = 0.2314. The value of the test statistic to test the H0: β3 = β4 = β5 = 0 is ________________(round off to three decimal places).

Answer: (21.100 to 21.800)

35. Consider a competitive market where the demand and supply functions are given by qD = 12 − 2P and qS = 4P, respectively. The tax rate per unit of output that maximizes the tax yield (revenue) is __________ (in integer).

Answer: (3 to 3)

36. Suppose the demand for a new pharmaceutical drug, on which the manufacturer has a patent monopoly, is given by: Q = (100 − P)A5 ; where Q is output, P is the price and A is advertising expenditure. Production cost of the patented drug is given by: C(Q) = 60Q. At the firm’s optimal choices, the ratio of advertising expenditure to sales revenue for the pharmaceutical product will be 1: ____ (in integer).

Answer: (8 to 8)

37. Let the rate of inflation in an economy be 4.2%, the growth rate of velocity of money be 2% and, the growth rate of real GDP be 6%. According to Milton Friedman’s ‘k’ percent rule, the rate of growth of money supply for maintaining stable prices will be __________ (round off to one decimal place).

Answer: (4.0 to 4.0)

38. The long-run cost function of all identical firms in a perfectly competitive industry is given by: C = 25q − 3q2 + 1. 5q3

The market demand function is: P = 2500 − 0. 25Q

The number of firms in the industry at equilibrium is __________(in integer).

Answer: (9904 to 9908)

39. Given below is an inter-industry transactions matrix. If final demand for the agriculture sector changes from 150 units to 300 units and for the manufacturing sector changes from 120 units to 200 units, then the output of the agriculture sector should be __________ units (in integer).

Answer: (1860 to 1880)

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40. Consider that a sample of size 3 is randomly drawn from a population that takes only two values, equally likely: − 1 and 1. Let z = max .(x1, x2, x3) where x1, x2, x3 are the sample observations. The expected value of z, E(z) is __________ (round off to two decimal places).

Answer: (0.70 to 0.80)

English (XH-C2)

Q.1 – Q.12 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Which of the following texts is a collection of stories that a group of pilgrims tell each other?

(A)  The Shepheardes Calender

(B)  The Pilgrim’s Progress

(C)  The Canterbury Tales

(D)  Parliament of Fowls

Answer: (C)

2. Which of these is NOT an autobiography?

(A)  Baby Kamble, The Prisons We Broke

(B)  Bama, Karukku

(C)  Mulk Raj Anand, Untouchable

(D)  Om Prakash Valmiki, Joothan

Answer: (C)

3. Writers Workshop and Blaft are ___________.

(A)  niche publishing houses in India that focus on particular genres

(B)  little magazines that were set up by small collectives of writers

(C)  digital archives of performance poetry

(D)  well-known reading circles in 1950s’ Lucknow

Answer: (A)

4. The following lines capture the central trope of a well-known 18th century satirical tract.

“I have been assured by a very knowing American of my acquaintance inLondon, that a young healthy child, well nursed, is, at a year old, a mostdelicious, nourishing, and wholesome food…”

Identify the tract from the options below.

(A)  John Stuart Mill, “On Liberty”

(B)  Francis Bacon, “On Death”

(C)  Jonathan Swift, “A Modest Proposal”

(D)  Robert Graves, “Warning to Children”

Answer: (C)

5. Whose poem does Cleanth Brooks close-read to arrive at his concept of “the well-wrought urn”?

(A)  William Wordsworth

(B)  John Keats

(C)  William Blake

(D)  Alfred Tennyson

Answer: (B)

6. What is common among Charles Dickens’ A Tale of Two Cities, Mahasweta Devi’s Mother of 1084, Shobha Shakti’s Gorilla, and Chimamanda Ngozi Adichie’s Half of A Yellow Sun?

(A)  These novels are set during times of political uprisings.

(B)  These novels are feminist narratives.

(C)  These novels have animals as central characters.

(D)  These novels are picaresque novels.

Answer: (A)

7. Henry James’ essay “The Art of Fiction”, one of the earliest literary critical engagements with the form of the novel, was preceded by his book-length study of __________.

(A)  William Faulkner

(B)  Nathaniel Hawthorne

(C)  Aphra Behn

(D)  Oscar Wilde

Answer: (B)

8. Which of the following is NOT true of Bram Stoker’s Dracula?

(A)  It is considered to be a gothic novel.

(B)  It is narrated mostly through letters.

(C)  Transylvania is an important setting in the novel.

(D)  It is a bildungsroman.

Answer: (D)

9. “The name is H. Hatterr, and I am continuing . . .

Biologically, I am fifty-five of the species.”

The lines above are from an early Indian English novel. Who is the authorof this novel?

(A)  G. V. Desani

(B)  Allan Sealy

(C)  Toru Dutt

(D)  Ruth Prawer Jhabvala

Answer: (A)

10. In Areopagitica, John Milton made an impassioned appeal __________.

(A)  against censorship and for freedom of expression

(B)  for legal reform allowing divorce based on spousal incompatibility

(C)  for freedom of the church from royal control

(D)  against slavery in the New World

Answer: (A)

11. The first institution to teach English Literature in the world is – ___________.

(A)  The University of Oxford, Oxford

(B)  Royal Polytechnic Institution, London

(C)  The College of William and Mary, Williamsburg, Virginia

(D)  Fort William College, Calcutta

Answer: (MTA)

12. Which one of the following texts propounds the aesthetic theory of ‘rasa’?

(A)  Natya Shastra

(B)  Abhigyana Shakuntalam

(C)  Manu Smriti

(D)  Charaka Samhita

Answer: (A)

Q.13 – Q.20 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).

13. Which of the following novels is/are predominantly set in Bombay?

(A)  Kiran Nagarkar, Ravan and Eddie

(B)  Rohinton Mistry, A Fine Balance

(C)  Salman Rushdie, Midnight’s Children

(D)  Aravind Adiga, The White Tiger

Answer: (A; B; C)

14. Which of the following critically rewrite/s canonical English novels?

(A)  J. M. Coetzee, Foe

(B)  Jean Rhys, Wide Sargasso Sea

(C)  Bapsi Sidhwa, Ice-Candy-Man

(D)  Ben Okri, The Famished Road

Answer: (A; B)

15. Of the following, which novelist/s combine/s feminist concerns with magic realism?

(A)  Virginia Woolf

(B)  Toni Morrison

(C)  Kamala Markandaya

(D)  Svetlana Alexievich

Answer: (B)

16. In which of these Shakespearean plays do important female characters disguise themselves as men?

(A)  A Midsummer Night’s Dream

(B)  The Merchant of Venice

(C)  As You Like It

(D)  Twelfth Night

Answer: (B; C; D)

17. The following words in English are clustered according to their origin. Choose the cluster/s that contain/s words drawn from languages of the Indian subcontinent.

(A)  Kedgeree, Punch, Mulligatawny, Candy

(B)  Shampoo, Chintz, Calico, Juggernaut

(C)  Philistine, Echo, Panic, Galaxy

(D)  Anaconda, Cheroot, Bungalow, Dungaree

Answer: (A; B; D)

18. Which of the following is/are true of Charlotte Brontë’s Jane Eyre?

(A)  It was published under the pen-name Currer Bell.

(B)  It was published originally in three volumes.

(C)  It has been read as a critique of heterosexual romance, marriage, anddomesticity.

(D)  The story is told from the point of view of a “madwoman in the attic”.

Answer: (A; B; C)

19. Which of the following is an example/are examples of noir, popular both as fiction and film?

(A)  The Big Sleep

(B)  Murder on the Orient Express

(C)  The Maltese Falcon

(D)  Fargo

Answer: (A; C)

20. Which of the following use/s the device of a ‘story within a story’ withmultiple narrators?

(A)  A Portrait of an Artist as a Young Man

(B)  Wuthering Heights

(C)  Emma

(D)  Heart of Darkness

Answer: (B; D)

Q.21 – Q.30 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

21. Match the following plays with genre or style:

(A)  i-b, ii-d, iii-a, iv-c

(B)  i-a, ii-c, iii-b, iv-d

(C)  i-d, ii-b, iii-c, iv-a

(D)  i-c, ii-d, iii-a, iv-b

Answer: (A)

22. Study the three examples below:

(i) In George Orwell’s novel 1984, the interior ministry of the totalitarian state is called the ‘Ministry of Love’.

(ii) In the genre of horror fiction, the reader knows that the killer is hiding in the closet, but the protagonist does not.

iii) “But Brutus says he was ambitious; And Brutus is an honourable man.”

(William Shakespeare, Julius Caesar)

These are instances of ____________.

(A)  metaphor

(B)  irony

(C)  parody

(D)  synecdoche

Answer: (B)

23. An “implied reader” is a ________.

(A)  reader who participates in creating the meaning of a text

(B)  reader who anticipates authorial intention

(C)  hypothetical reader, not the actual reader, that the text addresses

(D)  reader who reads critically against the grain of the text

Answer: (C)

24. Read the following:

“[…] a text is made of multiple writings, drawn from many cultures and entering into mutual relations of dialogue, parody, contestation, but there is one place where this multiplicity is focused and that place is the reader, not, as was hitherto said, the author. […] the birth of the reader must be at the cost of the death of the Author.”

Which theoretical school does the excerpt best represent?

(A)  Reader-response criticism

(B)  Formalism

(C)  Post-structuralism

(D)  New Criticism

Answer: (C)

25. Literary criticism considers which one of the following texts as offering the strongest support for mimetic theories of art?

(A)  Plato, Republic

(B)  Longinus, On Sublimity

(C)  Horace, The Art of Poetry

(D)  Aristotle, Poetics

Answer: (D)

26. The following is a passage about O. V. Vijayan’s The Legends of Khasak:

The novel is set in a remote village, in the middle of the 20th century. Thenarrative is replete with images of the vast ecosystem of the living and thenon-living, a land potent with dreams and legends.

The analysis presented in this description is congruent with which one ofthe following concepts proposed by Mikhail Bakhtin?

(A)  Chronotope

(B)  Dialogism

(C)  Carnivalesque

(D)  Polyphony

Answer: (A)

27. Which one of the following did NOT happen in 1919, the year the First World War ended?

(A)  The Progressive Writers’ Association was formed in India.

(B)  The radical political activist and philosopher Rosa Luxemborg was murdered.

(C)  Rabindranath Tagore renounced his knighthood.

(D)  James Joyce’s Ulysses was being serialised.

Answer: (A)

28. Assertion P: Dalit narratives tend to be read single-dimensionally

as evoking the reader’s pity at the protagonist’s caste humiliation,

or

as telling the story of heroic protest against discrimination, oras a description of the protagonist’s rise from misery to triumph.

Assertion Q: There is a tendency to keep the Other in the space of difference, as perpetually exotic.

In the context of the assertions above, which one of the following statements is true?

(A)  P and Q are contradictory assertions.

(B)  P and Q are compatible assertions.

(C)  P and Q cannot be read in relation to each other.

(D)  Q is the only explanation for P.

Answer: (B)

29. Some of the recent novels of the Brazilian writer Paulo Coelho were published in multiple languages simultaneously, or immediately after the Portuguese edition.

Which of the following is this phenomenon NOT an evidence of?

(A)  Rebecca Walkowitz’s argument that novels are often ‘born translated’

(B)  The globality of marketplace for books

(C)  Paulo Coelho’s expanding popularity

(D)  The ‘nation’ as the sole frame for understanding literature

Answer: (D)

30. Match the authors in the first column with their respective translators in the second column.

(A)  i-d, ii-c, iii-b, iv-a

(B)  i-c, ii-b, iii-d, iv-a

(C)  i-c, ii-a, iii-d, iv-b

(D)  i-b, ii-a, iii-d, iv-c

Answer: (C)

Q.31 – Q.40 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).

31. Which of the following is/are true about Gilles Deleuze and Felix Guattari’s conception of ‘minor literature’?

(A)  The discussion focuses on the writing of Franz Kafka.

(B)  Minor literature is literature that a minority produces in a major language.

(C)  Minor literature is a form of popular literature.

(D)  Minor literature is literature in a minor language.

Answer: (A; B)

32. Quote P:

“O wild West Wind, thou breath of Autumn’s being,

Thou, from whose unseen presence the leaves dead

Are driven, like ghosts from an enchanter fleeing,

Yellow, and black, and pale, and hectic red,

Pestilence-stricken multitudes: O thou,

Who chariotest to their dark wintry bed

[…]”

Quote Q:

“O golden-tongued Romance with serene lute!

Fair plumed Siren! Queen of far away!”

Which of the following is/are correct?

(A)  Both quotes are examples of apostrophe.

(B)  Both quotes use alliteration.

(C)  Both quotes are examples of aporia.

(D)  Both quotes are examples of personification.

Answer: (A; D)

33. Prolepsis is the representation or assumption in the present, of a future act or development.

(A)  “Six decades later she would describe how at the age of thirteen she had writtenher way through a whole history of literature.” Ian McEwan, Atonement.

(B)  “Horatio, I am dead.” William Shakespeare, Hamlet.

(C)  “In my younger and more vulnerable years my father gave me some advice thatI’ve been turning over in my head ever since.” F. Scott Fitzgerald, The GreatGatsby.

(D)  “Many years later, as he faced the firing squad, Colonel Aureliano Buendía was to remember that distant afternoon when his father took him to discover ice.”Gabriel García Márquez, One Hundred Years of Solitude.

Answer: (A; B; D)

34. Gayatri Chakravorty Spivak’s essay “Can the Subaltern Speak?” proposes which of the following?

(A)  The voice of the subaltern is appropriated by ‘intellectuals’ desiring to speak for the subaltern.

(B)  It is easy to confuse writing about the subaltern with the subaltern speaking for herself.

(C)  All women are subaltern and therefore cannot truly speak.

(D)  The ‘intellectuals’ speaking for the subaltern and the subaltern speaking for herself can be equivalent.

Answer: (A; B)

35. Which of the following is/are example/s of ‘metafiction’?

(A)  Each chapter in a novel is narrated by a different character.

(B)  The reader is a character in the novel who interrupts the story because herealises that he is reading an incomplete text.

(C)  The narrator of the novel travels into the wild and encounters a man whoembodies the horrors of colonial power. The latter then proceeds to tell hisstory.

(D)  A character in a novel encounters a shabbily dressed man. Soon, this man letsus, the readers, know that he is the author of the novel and is contemplating thefuture of this character.

Answer: (B; D)

36. Choose one or more options from below.

In contrast to traditional Historicism, New Historicism _____________.

(A)  rejects the idea that history is an objective narrative of events unfolding in lineartime

(B)  does not make strict distinctions between literary and non-literary texts

(C)  takes a particular interest in the textualisation of the material world

(D)  takes history only to be a background and context for understanding literarytexts

Answer: (A; B; C)

37. “The feminist insistence that ‘the personal is political’ has had profound effects on other genres. Feminist academics in several disciplines now insist that the subjective element must not be left out of the practice of research methods, such as the interview, or of theories of knowledge production (Skeggs 1995; Maynard and Purvis 1994; Reinharz 1992).”

From the passage above, which of the following can be correctlyconcluded?

(A)  The passage argues that interviews and theories of knowledge production arenot examples of research methods.

(B)  ‘The personal is political’ is a feminist argument.

(C)  Skeggs, Maynard, Purvis, and Reinharz are names of feminist scholars.

(D)  The passage argues that the subjective can legitimately be part of researchmethods.

Answer: (B; C; D)

38. “ARE YOU DARK? OR VERY LIGHT?” Revelation came.

“You mean—like plain or milk chocolate?”

Her assent was clinical, crushing in its light

Impersonality. Rapidly, wave-length adjusted,

I chose. “West African sepia”—and as afterthought,

“Down in my passport.” Silence for spectroscopic

Flight of fancy, till truthfulness clanged her accent

Hard on the mouthpiece. “WHAT’S THAT?” conceding

“DON’T KNOW WHAT THAT IS.” “Like brunette.”

“THAT’S DARK, ISN’T IT?” “Not altogether.

Facially, I am brunette, but, madam, you should see

The rest of me. Palm of my hand, soles of my feet

Are a peroxide blond. Friction, caused—

Foolishly, madam—by sitting down, has turned

My bottom raven black—One moment, madam!”—sensing

Her receiver rearing on the thunderclap

About my ears—“Madam,” I pleaded, “wouldn’t you rather

See for yourself?”

In Wole Soyinka’s “Telephone Conversation”, the man seeking to rent aroom responds to the white landlady’s racism by ____________.

(A)  describing black as a spectrum as opposed to a single colour

(B)  being the subservient Black man, who concedes to her definition of race

(C)  locating race squarely in her ways of seeing

(D)  fragmenting the racialised body

Answer: (A; C; D)

39. In Arthur Conan Doyle’s writings featuring Sherlock Holmes, as is the case with much of 19th century British fiction, colonialism appears as objects, events, animals, places, fears and desires. Which of the following support/s this claim?

(A)  Opium dens in London, frequented by Holmes

(B)  The war in which Watson served as a doctor

(C)  The hound in The Hound of the Baskervilles

(D)  The pet animals in “The Adventure of the Speckled Band”

Answer: (A; B; D)

40. “My Papa’s Waltz” by Theodore Roethke

The whiskey on your breath

Could make a small boy dizzy;

But I hung on like death:

Such waltzing was not easy.

We romped until the pans

Slid from the kitchen shelf;

My mother’s countenance

Could not unfrown itself.

The hand that held my wrist

Was battered on one knuckle;

At every step you missed

My right ear scraped a buckle.

You beat time on my head

With a palm caked hard by dirt,

Then waltzed me off to bed

Still clinging to your shirt.

Which of the following can be observed about this poem?

(A)  The form of the poem is that of the Petrarchan sonnet.

(B)  There is a simile in the first stanza.

(C)  Images in the last two stanzas suggest that the father is a working-class man.

(D)  The poem is in rhyming couplets.

Answer: (B; C)

Linguistics (XH-C3)

Q.1 – Q.14 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Which of the following is NOT demonstrated by studies with Great Apes like Koko and Washoe and Sarah?

(A)  The capacity to produce rule-governed, novel messages.

(B)  The capacity for symbolic communication.

(C)  The manual dexterity for signing.

(D)  The ability to teach other members of the species.

Answer: (A)

2. The meaning relax or calm down for the word ‘chill’ is an example of what kind of semantic change?

(A)  Metaphor

(B)  Metonymy

(C)  Synecdoche

(D)  Pejoration

Answer: (A)

3. Match the following communication systems (P-T) to their type (i-vi) and select the correct sequence:

(A)  P-(iii), Q-(v), R-(i), S-(ii), T-(iv)

(B)  P-(v), Q-(vi), R-(ii), S-(iv), T-(iii)

(C)  P-(iv), Q-(v), R-(iii), S-(ii), T-(vi)

(D)  P-(ii), Q-(vi), R-(v), S-(iii), T-(i)

Answer: (A)

4. Statistical learning in language development in infants refers to __________.

(A)  calculating regularities in speech to isolate words

(B)  early mathematical knowledge that infants can demonstrate

(C)  infant data that researchers use to understand language growth

(D)  learning to differentiate phonemes as they are used in spoken words

Answer: (A)

5. If ‘Aam Aadmi’ is translated as ‘Mango Man’, which type of ambiguity does the translation demonstrate?

(A)  Lexical

(B)  Syntactic

(C)  Morphological

(D)  Morphosyntactic

Answer: (A)

6. While most of the historically known writing systems in India tend to write from left to right, identify the one which writes from right to left.

(A)  Kharoṣṭhī

(B)  Brāhmī

(C)  Śāradā

(D)  Grantha

Answer: (A)

7. Identify the pair of words with a circumfix from the list below.

(A)  enlighten, embolden

(B)  enquiring, inquiring

(C)  transformation, transportation

(D)  reduced, repeated

Answer: (A)

8. Which of the following sets illustrates sound symbolism in English?

(A)  mash, splash, bash, crash

(B)  flash, shine, sear, glimmer

(C)  duck, suck, luck, tuck

(D)  forte, piano, allegro, crescendo

Answer: (A)

9. Voice Onset Time (VOT) is an acoustic cue used by our auditory-perceptual systems. Which of the following sounds can be identified using VOT?

(i) Voiced Stops

(ii) Unvoiced Stops

(iii) Prenasalised Stops

(iv) Aspirated Stops

(v) Ejective Stops

(A)  (i), (ii), (iv) but NOT (iii) and (v)

(B)  (i), (ii), (iii), (iv) but NOT (v)

(C)  (iv), (v) but NOT (i), (ii) and (iii)

(D)  (i), (iii), (v) but NOT (ii) and (iv)

Answer: (A)

10. In syntactic terms, which of the following is the odd one out?

(A)  Belle struck the Beast as incompetent.

(B)  Belle regarded the Beast as incompetent.

(C)  Belle identified the Beast as incompetent.

(D)  Belle viewed the Beast as incompetent.

Answer: (A)

11. Which of the following speech errors is NOT expected in natural languages? The items that are swapped are indicated in capitals. The intended phrase is tight-ly pack-ed.

(A)  tighKly paTed

(B)  Pightly Tacked

(C)  PACKly TIGHTed

(D)  tightED packLY

Answer: (A)

12. Language isolates are languages that ____________.

(A)  are not known to be related to any other languages

(B)  are spoken in isolated parts of the world

(C)  have no dialectal or sociolectal varieties

(D)  are separated geographically from other members of their family

Answer: (A)

13. On the new Rs. 2000 note, how many languages can be found in the language panel displaying the denomination of the note?

(A)  Fifteen

(B)  Sixteen

(C)  Seventeen

(D)  Eighteen

Answer: (A)

14. How many unique morphemes can be isolated in this sentence?

(A)  Twelve

(B)  Ten

(C)  Sixteen

(D)  Eleven

Answer: (A)

Q.15 – Q.20 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).

15. “I look forward to visiting teachers”. What does this sentence demonstrate?

(A)  Syntactic ambiguity

(B)  Semantic role ambiguity

(C)  Lexical ambiguity

(D)  No ambiguity

Answer: (A; B)

16. Which of the following pairs of words do NOT stand in troponymous relationship?

(A)  lisp-talk

(B)  limp-walk

(C)  dream-sleep

(D)  wait-fidget

Answer: (A; B)

17. Which of the following areal/typological feature(s) may be seen in a vast majority of the languages of South Asia?

(A)  Compound Verbs

(B)  Retroflexed Sounds

(C)  Non-nominative Subject Case

(D)  Agglutinative Morphology

Answer: (A; B; C)

18. Three different ways of writing a single word in the Mayan script are given below. The glyphs (i-iii) are of a single word [ba’lam] meaning ‘jaguar’. What can we conclude about the Mayan writing system from the examples provided?

(A)  The glyphs can be logograms, mean whole words.

(B)  The glyphs can be syllabic.

(C)  The glyphs use the rebus principle, part sound part meaning.

(D)  The glyphs can be alphabetic, spelling out sounds.

Answer: (A; B; C)

19. Identify symptom(s) of phonological dyslexia.

(A)  The inability to map letters to sounds.

(B)  The inability to pronounce made-up or nonsense words.

(C)  The inability to tell homographs apart.

(D)  The inability to recognise semantic mismatches.

Answer: (A; B)

20. Creolisation and creoles are characterised by which of the following?

(A)  Creolisation is the process of elaborating Pidgin languages.

(B)  Creolisation happens when a Pidgin is learned by young children as a firstlanguage.

(C)  Creoles have elaborated grammars but somewhat limited vocabulary.

(D)  Creole vocabulary is expansive but the grammar is limited and variable.

Answer: (A; B; C)

Q.21 – Q.25 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

21. In the following sentence, you are required to identify the type of aphasia and select the correct sequence from the options given below.

Use of jargon and words that have no meaning are typical of ___________aphasia, while the inability to differentiate between actives and passives is seen in _________ aphasia; some patients use circumlocutions for simple words and this is known as ________ aphasia; in patients with __________aphasia, production and comprehension may be reasonably preserved, butthe ability to repeat an utterance is disrupted.

(A)  Wernicke’s, Broca’s, Anomic, Conduction

(B)  Broca’s, Wernicke’s, Conduction, Dysphonia

(C)  Anomic, Conduction, Broca’s, Wernicke’s

(D)  Dysphonia, Anomic, Wernicke’s, Broca’s

Answer: (A)

22. Match the dialogues in (P-S) to the Gricean Maxim (i-v) that has been flouted to create humour.

(A)  P-(iii), Q-(i), R-(ii), S-(iv)

(B)  P-(i), Q-(v), R-(ii), S-(iii)

(C)  P-(i), Q-(iii), R-(iv), S-(v)

(D)  P-(iv), Q-(ii), R-(iii), S-(i)

Answer: (A)

23. Sign languages have long been used by the deaf communities to communicate amongst themselves. Which of the following is correct?

(A)  Sign language shows duality of patterning with meaningless gestures combining to create single signs.

(B)  Signs in sign languages are dominantly iconic and transparent with respect to the meaning they encode.

(C)  Children who are hearing-impaired do not converge on a language without instruction in signing and/or speaking.

(D)  Sign languages are pidgin like, rudimentary communication systems.

Answer: (A)

24. In the sentence “The gunman sprayed the building with bullets”, the preposition phrase (PP) ‘with bullets’ is attached to ______.

(A)  ‘sprayed’, because it meets the selectional restriction of ‘sprayed’

(B)  ‘sprayed’, because it serves as the adjunct of the verb ‘sprayed’

(C)  ‘the gunman’, because the gunman has the gun

(D)  ‘the building’, because of proximity

Answer: (A)

25. Consider the sentence “Little children marched past the church sang”. Assume the starting rule of the context free grammar describing the language to be S→NP VP, where S is the start symbol, NP is the noun phrase and VP is the verb phrase. For the given sentence, how many words does VP contain?

(A)  One

(B)  Two

(C)  Three

(D)  Four

Answer: (A)

Q.26 – Q.40 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).

26. 

The above figure shows what is called a finite state machine. The machine reads one word at a time and transitions to a new state. The states are indicated by boxes and the transitions by arrows. There are three states S0,S1 and S2 and the last is the final state (indicated by two coincident boxes).The text beside each arrow means the following: DT = determiner (a, an, the), AJ = adjective, NN = noun. The machine starts at S0 and on seeing a

determiner (DT) enters the state S1. Then if it sees an adjective (AJ), i tremains in the same state. But at state S1 if it sees a noun (NN), it enters the final state. The final state is also called the “accept” state. No other states or

state transitions are defined or permitted.

Which of the following will cause the machine to enter S2, the accept state?

(A)  The blue sky

(B)  A vast blue sky

(C)  The sky

(D)  A very blue sky

Answer: (A; B; C)

27. Which of the following has/have been observed in speech perception experiments?

(A)  Speech perception experiments with infants show that they are sensitive at birth to the rhythmic properties of their language, as well as the difference between stress-timed and syllable-timed languages.

(B)  Infants and adults show categorical perception of consonant sounds, that is, the ability to treat what is a continuous acoustic feature as discrete.

(C)  Infants are sensitive to sounds that are not part of the phonemic inventory of the language(s) to which they are exposed, but older children and adults are not.

(D)  The Phoneme Restoration effect seen in speech perception experiments (where people hear phonemes that have been replaced by noise or a cough) shows that  speech is perceived as linear.

Answer: (A; B; C)

28. Language games are a way to manipulate spoken words as the following examples from three languages show. Identify the correct statement(s) below about language games.

(A)  The intent is to disguise or conceal conversation.

(B)  Words are manipulated systematically using defined rules.

(C)  The game manipulation targets varying units of the phonological form.

(D)  Only children use language games.

Answer: (A; B; C)

29. What can be said about the intent and nature of prescriptive rules for languages?

(A)  Provide criteria for written language.

(B)  Characterise the universal grammar of languages.

(C)  Characterise inter-dialectal differences.

(D)  Encode changes to spoken language.

Answer: (A)

30. The use of singular they was voted ‘the word of the decade’ by linguists. Which of the following motivates the singular use?

(A)  The use of they in the singular replaces the sex specific he and she pronouns.

(B)  Using gendered pronouns can lead to gendered interpretations of the messages.

(C)  Sometimes the gender information is not known and it is easier to use they thanhe/she.

(D)  English is a sexist language.

Answer: (A; B)

31. Tok Pisin (Papua New Guinea) is an extended Pidgin/Creole language. Words borrowed from English are modified in various ways. Given the word list below, study the phonological modifications and choose the correct generalisation(s).

(A)  Only single onsets permitted.

(B)  Vowel epenthesis to create syllable nuclei.

(C)  Fortition of fricatives to stops.

(D)  Obligatory null codas.

Answer: (A; B; C)

32. Consider the following set of Phrase Structure Rules in a toy grammar:

[Note: T is tense, P is preposition, V is verb and N is noun; they project their respective phrasal units TP, PP, VP and NP]

TP → NP T VP

VP → (Adverb) V (TP) (PP)

PP → P NP

NP → (Determiner) (Adjective) N

Which of the following sentences can be generated by these rules?

(A)  The golden bells are probably ringing in the church.

(B)  Bells ring to let believers know that mass will begin.

(C)  The golden bells in the church always ring for prayers.

(D)  The silent bells say that the pastor has not visited the bell tower.

Answer: (A; B)

33. Evaluate the following according to the three principles of the Binding Theory and choose the correct statement(s).

(Note: the subscripted <i> indicates co-reference between the arguments

that bear them.)

(A)  The sentence Everyone who meets Tagorei admires himi is permitted by the principles of the Binding Theory.

(B)  The sentence Every one of his followers says that hei likes Tagorei is ruled out by the Binding Theory.

(C)  The sentence Tagorei seems to ask himselfi about effects of education is permitted by the Binding Theory.

(D)  The sentence Everyone who meets himi admires Tagorei is ruled out by the Binding Theory.

Answer: (A; B; C)

34. Given the facts (i-iv) about the World Cup, evaluate the statements using truth conditions and the truth tables of connectors to find the ‘false’ statement(s).

(i) Argentina has won the World Cup twice: 1978, 1986

(ii) Germany has won it four times: 1954, 1974, 1990, 2014

(iii) France has won it twice: 1998, 2018

(iv) Japan has never won it

(A)  If [Argentina won the World Cup in 1986] then [Germany won it in 1998].

(B)  [Germany didn’t win the World Cup in 1986] and [France won it in 1990].

(C)  [Argentina didn’t win the World Cup in 1986] or [Japan has never won theWorld Cup].

(D)  If [Argentina didn’t win the World Cup in 1978] then [France won it in 1990].

Answer: (A; B)

35. For which of the following sentence(s) can the assigned presupposition (P) hold?

(A)  Who discovered the Silverback Slug in 1960?

P: Someone discovered the Silverback Slug in 1960.

(B)  If she had drunk coffee this morning, she would have been more alert.

P: She had not drunk coffee.

(C)  Ruchi’s parents returned to Alaska over the summer.

P: Ruchi’s parents had been to Alaska sometime before the summer.

(D)  The police ordered the students to stop drinking.

P: The students were drunk.

Answer: (A; B; C)

36. Consider carefully the following data from four languages. Which deduction(s) can plausibly be made using the methods of comparative reconstruction?

(A)  Languages A and D are closely related.

(B)  Language A is distantly related to Language C.

(C)  Language D is distantly related to Language B.

(D)  Languages A,B,C and D are all unrelated languages.

Answer: (A; B)

37. Analyse the following Shakespearean sentences, and observe the differences between Early Modern English and Modern English – that is, how you would say these sentences today. What can we say in precise, grammatical terms about the syntactic changes that have occurred?

(A)  The agreement forms of Early Modern English included a different form for 2ndperson, singular subjects.

(B)  In wh-and yes-no questions the main verb can raise to Head, CP [Complementizer Phrase].

(C)  Pronominal forms are unchanged from Early Modern into Modern English.

(D)  Auxiliary verbs could raise to T [Tense] in Early Modern English but not mainverbs.

Answer: (A; B)

38. The following utterances were produced by a child aged 3 years.

(i) Put him in the bathtub.

(ii) We eated gummy bears.

(iii) Thank you for giving us these books.

(iv) I don’t know … I knowed her!

(v) He bited my finger. (After correction: He bitted my finger.)

(vi) I runned in the water.

(vii) I rided on an elephant.

Which of the following statement(s) can be deduced from the data?

(A)  The child differentiates between lexical and non-lexical categories of English.

(B)  The child has acquired the Spec-Head and Complement-Head orders of English.

(C)  The child has acquired case marking in English.

(D)  The child has not yet acquired the rule of past tense formation in English.

Answer: (A; B; C)

39. The human speech production system is characterised by which of the following?

(A)  A laryngeal source

(B)  A vocal tract that acts as a filter

(C)  A vocal tract that acts as a resonator

(D)  A laryngeal resonator

Answer: (A; B; C)

40. Which of the following kinds of evidence are offered in support of an innateness view of the human language ability?

(A)  All humans, no matter how primitive their societies, have the capacity forlanguage.

(B)  Children learn the language(s) in their environment without explicit instruction.

(C)  Speakers of all languages are capable of producing and understanding an infinitenumber of sentences.

(D)  All languages and their grammars change through time.

Answer: (A; B; C)

Philosophy (XH-C4)

Q.1 – Q.20 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. What is the mood of the following syllogistic argument?

All Professors are Academicians.

Some Academicians are Activists.

Therefore, Some Activists are Professors.

(A)  A I I

(B)  I I I

(C)  I A I

(D)  A I A

Answer: (A)

2. What is the formal fallacy committed in the following syllogistic argument?

No Students are tested Covid-positive.

Some Covid-positive cases are not Professors.

Therefore, Some Professors are not Students.

(A)  Fallacy of Exclusive Premises

(B)  Fallacy of Illicit Major

(C)  Fallacy of Illicit Minor

(D)  Fallacy of Excluded Middle

Answer: (A)

3. The Philosophy of Aurobindo may aptly be identified as

(A)  Integral Non-dualism.

(B)  Non-dualism.

(C)  Integral Dualism.

(D)  Dualism.

Answer: (A)

4. Scientists in the Institute of Virology tested Influenza-affected patients in Wuhan for all known acute respiratory diseases but could not establish the cause for their influenza from the set of known causes. Hence, they inferred for the first time that a Novel Corona Virus is the

cause of their disease.

(A)  Method of Residues

(B)  Method of Difference

(C)  Method of Agreement

(D)  Joint method of Agreement and Difference

Answer: (A)

5. In his Republic, Plato makes four-fold classification of the possible objects of knowledge. Where does he place Mathematical Objects?

(A)  Dianoia [Thought]

(B)  Noesis [Understanding]

(C)  Pistis [Belief]

(D)  Eikasia [Imagination]

Answer: (A)

6. According to Plato, which among the following is NOT a cardinal virtue?

(A)  Autonomy

(B)  Courage

(C)  Justice

(D)  Wisdom

Answer: (A)

7. In Plato’s Republic, the guardians of the ideal state reserve the right to govern because

(A)  it is their duty.

(B)  it is their birth-right.

(C)  they are democratically elected.

(D)  they have exclusive command over military power.

Answer: (A)

8. What is true of Rāmānuja’s Viśiṣṭādvaita?

(A)  It accepts the conception of qualified Brahman.

(B)  It accepts the conception of formless and non-qualified Brahman.

(C)  It considers the individual soul/self (cit) as unreal.

(D)  It considers the world (acit) as unreal.

Answer: (A)

9. In the Mīmāmsā system, apūrva stands for a link/relation between

(A)  an act (action) and its fruit.

(B)  the past and the present.

(C)  Perception and Inference.

(D)  Creator and Creation.

Answer: (A)

10. The conception of jīva in Advaita stands for:

(A)  Individual self

(B)  Universal Self

(C)  Liberated self

(D)  Living beings

Answer: (A)

11. What among the following is in conformity with Leibniz’s metaphysical assertion of Pre-established Harmony?

(A)  There is a mutual coordination of mind and body.

(B)  Mind and body are different kinds of substances.

(C)  The mind can causally influence the body.

(D)  Cause of a mental state cannot be any previous state of that mind.

Answer: (A)

12. In Edmund Husserl’s phenomenology, eidetic reduction is meant to provide access to the sphere of

(A)  essential structures of pure psychic processes.

(B)  accidental structures of psychic processes.

(C)  inner experience as such.

(D)  transcendental phenomena.

Answer: (A)

13. In Jaina classification of knowledge, Mati includes

(A)  both Perception and Inference.

(B)  only Perception.

(C)  only Inference.

(D)  Inference and Authority (śruta).

Answer: (A)

14. Among the four Brahmavihāras of Buddhism, ___________ evokes happiness at the joy and success of others.

(A)  Muditā

(B)  Maitrī

(C)  Karuṇā

(D)  Upekṣā

Answer: (A)

15. Read the following verse from Bhagavadgītā carefully.

Karmaṇyevādhikāraste mā phaleṣu kadācana;

Mā karmaphalaheturbhūrmā te sango’stvakarmaṇi.

[Your right is for action alone, never for the results. Do not become theagent of the results of action. May you not have any inclination forinaction.] (Bhagavadgītā 2: 47)

This above quoted verse is a standard reference to:

(A)  Karma-yoga

(B)  Bhakti-yoga

(C)  Jñāna-yoga

(D)  Rāja-yoga

Answer: (A)

16. Which among the following is predominantly a non-dualistic philosophical system?

(A)  Kāṣmir Śaivism

(B)  Śaiva-siddhānta

(C)  Vīra-śaivism

(D)  Vaiṣṇavism

Answer: (A)

17. Gandhi’s doctrine of Trusteeship establishes a normative relationship between labour and capital. Indicate which of the following is NOT in agreement with this doctrine?

(A)  Class struggle is the key to social development and economic equality.

(B)  The capitalists would function only as trustees for the poor and working class.

(C)  The capitalist would keep the surplus wealth in trust in order to have economicequality and solidarity.

(D)  The capitalists would be made to realise the wealth in their hands is the fruit ofthe labour of the workers.

Answer: (A)

18. Which of the following is NOT a pramāṇa in the Nyāya system?

(A)  Anupalabdhi (Non-apprehension)

(B)  Upamāna (Comparison)

(C)  Anumāna (Inference)

(D)  Pratyakṣa (Perception)

Answer: (A)

19. In the Vaiśeṣika system, which of the following is a padārtha (category)?

(A)  Guṇa (Quality)

(B)  Ᾱtman (Spirit/Soul)

(C)  Tejas (Fire)

(D)  Vāyu (Air)

Answer: (A)

20. Identify which among the following is NOT a characteristic of a simple idea according to John Locke.

(A)  Varying in its appearance or conception

(B)  Cannot be further divided into other simple ideas

(C)  Distinctly clear

(D)  Unambiguous

Answer: (A)

Q.21 – Q.40 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).

21. Which of the following are in accordance to Democritus’ cosmology?

(A)  The cosmos has an underlying order.

(B)  Fundamental units of the reality are atoms.

(C)  Atoms are extended but indivisible and indestructible.

(D)  Atoms are weightless, shapeless and always in a state of rest.

Answer: (A; B; C)

22. For Immanuel Kant, which of the following statements are appropriate examples of synthetic a priori judgment?

(A)  2 + 2 = 4

(B)  The shortest distance between two points is a straight line.

(C)  For every action there is an equal and opposite reaction.

(D)  God is a perfect being.

Answer: (A; B; C)

23. In the Sānkhya system, which among the following are antaḥkaraṇas?

(A)  Buddhi (Intellect)

(B)  Ahamkāra (Ego)

(C)  Jñānedriyas (Sensory Organs)

(D)  Karmendriyas (Motor Organs)

Answer: (A; B)

24. Which of the following are meant by Kant’s notion of autonomy of will?

(A)  A recognition of the will as duty-bound.

(B)  The will is not bound by empirical laws.

(C)  The will is not bound by material objects of desire.

(D)  The will is only determined by the material principle of self-love.

Answer: (A; B; C)

25. On which of the following, Plato and Aristotle DISAGREE concerning the realm of the political?

(A)  Women, in principle, are barred from participation in the political realm.

(B)  The best form of government entails the concentration of power in a limited few.

(C)  Manual labourers, traders, and businessmen are not fit for political powers.

(D)  The ethical and the political are intricately connected.

Answer: (A; B; C)

26. Which among the following are part of yama in Patanjali’s Aṣṭānga-Yoga?

(A)  Ahimsā (Non-violence)

(B)  Satya (Truthfulness)

(C)  Aparigraha (Detachment)

(D)  Iśvara-praṇidhāna (Devotion to God)

Answer: (A; B; C)

27. Progress of the modern sciences and reflection on method have led to the development of new fields of analysis in Renaissance Philosophy. Which among the following correctly trace the influence of a particular science on a particular philosopher’s thought?

(A)  Mathematics on Rene Descartes

(B)  Mechanics on Thomas Hobbes

(C)  Historical science on G.W.F. Hegel

(D)  Biology and the evolutionary hypothesis on Francis Bacon

Answer: (A; B; C)

28. Gottlob Frege, in his Sense and Reference, discusses the identity relation between the statements “a=a” and “a=b”. Which of the following are his conclusions?

(A)  Identity relation is between names or signs of objects.

(B)  They are statements of differing cognitive value.

(C)  The two ensuing judgments of the statements are different.

(D)  Sense expressed in the two statements are the same.

Answer: (A; B; C)

29. If Descartes’ Meditations is credited for a modern version of mind-body dualism, which statements among the following hold true in accordance with it?

(A)  Descartes is a substance dualist.

(B)  Mind is essentially a thinking thing.

(C)  Essential property of matter is determined by the form.

(D)  Both, mind and body are indivisible.

Answer: (A; B)

30. John Stuart Mill, in his Utilitarianism, proposes the conception of Utility or Happiness as the directive rule of human conduct. Which of the following are drawn from his conception of Happiness to form the utilitarian standard?

(A)  Happiness of all concerned is overriding.

(B)  The agent acts as a disinterested spectator.

(C)  The agent’s own happiness is paramount.

(D)  Impartiality cannot be maintained in action.

Answer: (A; B)

31. Which among the following statements does W.V.O. Quine REJECT in his work, Two Dogmas of Empiricism?

(A)  The distinction between analytic and synthetic truths.

(B)  Every meaningful statement can be reduced to a statement about immediate experience.

(C)  Truths which are grounded in meanings are dependent on truths which are grounded in fact.

(D)  The verification theory of meaning is not a possible key to resolve the problem of meaning.

Answer: (A; B; C)

32. Read the following statements carefully and answer the following question.

i. Greater welfare of others is to be valued more than the individual freedom.

ii. Only when the conception of justice is on hand, the ideas of respect and human dignity can be given a more definite meaning.

iii. Principles of justice are derived from the ideas of respect and human dignity.

iv. The loss of freedom for some is not made right by a greater welfare of others.

In light of the theory of justice as fairness, as proposed by John Rawls, which of following pairs of statement DO NOT agree with Rawl’s position?

(A)  i and iii

(B)  iii and iv

(C)  ii and iv

(D)  i and ii

Answer: (A; B; C)

33. George Berkeley, in his Principles of Human Knowledge, reflects on the nature of thought and attacks abstract ideas. Which among the following hold true to his view?

(A)  There cannot be an idea of anything essentially independent of mind.

(B)  One cannot conceive of the unperceived.

(C)  Any idea is essentially independent of mind.

(D)  One can conceive of the unperceived.

Answer: (A; B)

34. In his An Enquiry Concerning Human Understanding, Hume relies on a basic distinction between two forms of perception. Which among the following are true about it?

(A)  Perceptions are understood as the items of our mental world.

(B)  Impressions and ideas are two categories of perceptions.

(C)  Ideas are derived from impressions.

(D)  Impressions include sensations, desires, and passions.

Answer: (A; B; C)

35. In Martin Heidegger’s Being and Time, which among the following correctly describe Dasein?

(A)  Inquiring is one of the possibilities of Dasein’s Being.

(B)  Understanding of Being is a definite characteristic of Dasein’s Being.

(C)  Dasein always understands itself in terms of its existence.

(D)  Dasein is closest to us but it is not we ourselves.

Answer: (A; B; C)

36. Read the passage carefully and answer the question.

“There is … a subtler domination exercised in the sphere of ideas by one culture on another, a domination all the more serious in the consequence, because it is not ordinarily felt… Slavery begins when one ceases to feel the evil and it deepens when the evil is accepted as a good. Cultural subjection is ordinarily of an unconscious character and it implies slavery from the very start. When I speak of cultural subjection, I do not mean the assimilation of an alien culture. That assimilation need not be an evil; it may be positively necessary for healthy progress and in any case it does not mean a lapse of freedom. There is cultural subjection only when one’s traditional cast of ideas and sentiments is superseded without comparison or competition by a new cast representing an alien culture which possesses one like a ghost.” (K.C.Bhattacharyya, Swaraj in Ideas, p.13)

In the light of the passage above, cultural subjection amounts to

(A)  an uncritical assimilation of foreign culture.

(B)  an inability to accurately distinguish the good from the evil.

(C)  an uncritical discarding of one’s tradition.

(D)  a complete rejection of foreign ideas.

Answer: (A; B; C)

37. Read the following statements carefully and answer the following question.

i. Rahul is not what he is and is what he is not.

ii. The book is a book and can be nothing more.

iii. Of course, a book is a book, but it can always be something more.

iv. Rahul is what he is and must always be so.

Which of the following pairs of statements given below is NOT compatible with Jean-Paul Sartre’s Existential Philosophy?

(A)  iii and iv

(B)  i and iii

(C)  ii and iv

(D)  i and ii

Answer: (A OR A; B; C)

38. Which of the following philosophical tenets are admissible in Cārvāka philosophy?

(A)  The soul is nothing but the conscious body.

(B)  Consciousness arises from matter.

(C)  Death alone is liberation.

(D)  Earth, water, fire, air, and ether are elements.

Answer: (A; B; C)

39. Read the passage carefully and answer the following question.

‘While I condemn a religion of rules, I must not be understood to hold theopinion that there is no necessity for a religion. On the contrary, I agree with Burke when he says that “True religion is the foundation of society, the basis on which all true Civil Government rests, and both their sanction.”Consequently, when I urge that these ancient rules of life be annulled, I amanxious that their place shall be taken by a religion of principles, which alone can lay claim to being a true religion.’ (B. R. Ambedkar, Annihilation of Caste,24.1)

From the above passage, which among the following accurately represents Ambedkar’s view on foundation of society?

(A)  Religion of principles should provide the foundation of society.

(B)  Traditional religion should provide the foundation of society.

(C)  Religion of rules should provide a foundation of society.

(D)  Religion is not necessary at all for the foundation of society.

Answer: (A)

40. Which among the following statements are justifiably held from Thomas Hobbes’ political theory on the social contract, in his book Leviathan?

(A)  It is founded on the hypothetical State of Nature.

(B)  All men are made by nature to be equals, therefore, no one has a natural right togovern others.

(C)  All are to submit to the authority of an absolute sovereign power.

(D)  People can live together only by submitting their individual, particular wills tothe collective will.

Answer: (A; B; C)

Psychology (XH-C5)

Q.1 – Q.19 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. According to the Path-Goal theory of leadership, a style of leadership in which the leader consults with subordinates, involving them in the decision making process is _________.

(A)  participative

(B)  directive

(C)  supportive

(D)  achievement oriented

Answer: (A)

2. A process to test reliability that involves creating a large ‘bank’ of items and then dividing it into different versions or creating two tests with items of similar difficulty is called _________.

(A)  alternate and parallel form reliability

(B)  measure of test homogeneity

(C)  test-retest

(D)  inter-rater reliability

Answer: (A)

3. Delusion of ‘reference’ is a symptom of schizophrenia in which people _______.

(A)  believe that random events or comments are directed at them

(B)  believe that their thoughts are being broadcasted

(C)  believe they have special powers

(D)  have sensory experiences in the absence of stimulus

Answer: (A)

4. A student who has prepared inadequately for an exam attributes his failing grade to an unfair test, cheating by other students or a professor whotaught badly, is expressing __________.

(A)  projection

(B)  reaction formation

(C)  repression

(D)  rationalization

Answer: (A)

5. Which of the following theories of emotion best fits with the statement that perception of an environmental situation results in emotions and both, felt emotion and bodily reactions in emotions are independent of each other, but triggered simultaneously?

(A)  Cannon-Bard Theory

(B)  Lazarus’s Cognitive Appraisal Theory

(C)  Schachter-Singer Theory

(D)  James-Lange Theory

Answer: (A)

6. The perceived fairness of the distribution of resources and rewards is described as _____.

(A)  distributive justice

(B)  procedural justice

(C)  interactional justice

(D)  informational justice

Answer: (A)

7. According to Bandura’s theory of personality, which one of the following is the most important person variables in determining personality?

(A)  Self-efficacy

(B)  Self-concept

(C)  Self-esteem

(D)  Self-determination

Answer: (A)

8. Match the events in the first column with the different categories of stress in the second column.

(A)  P-(iv), Q-(i), R-(ii), S-(iii)

(B)  P-(iv), Q-(iii), R-(i), S-(ii)

(C)  P-(ii), Q-(i), R-(iii), S-(iv)

(D)  P-(i), Q-(iv), R-(ii), S-(iii)

Answer: (A)

9. Which of the following types of colour blindness denotes blue-yellow colourdeficiency?

(A)  Tritanopia

(B)  Protanopia

(C)  Dueteranopia

(D)  Ritalin

Answer: (A)

10. Which of the following properties of sound is similar to the hue of light?

(A)  Pitch

(B)  Timbre

(C)  Loudness

(D)  Purity

Answer: (A)

11. _______ is a reinforcement schedule, where a person or animal receives the reinforcement based on varying amount of time.

(A)  Variable-interval

(B)  Fixed-ratio

(C)  Fixed-interval

(D)  Variable-ratio

Answer: (A)

12. ________ is a loss of memory of events that occurred prior to the trauma.

(A)  Retrograde amnesia

(B)  Anterograde amnesia

(C)  Infantile amnesia

(D)  Posthypnotic amnesia

Answer: (A)

13. Phobias and Obsessive Compulsive Disorder fall in the category of _________.

(A)  anxiety disorders

(B)  mood disorders

(C)  somatoform disorders

(D)  psychotic disorders

Answer: (A)

14. The smallest unit of speech perception that has meaning is _______.

(A)  morpheme

(B)  syntax

(C)  semantics

(D)  phoneme

Answer: (A)

15. In adolescence, with the development of the stage of ‘formal operations’, weare likely to see the development of ________.

(A)  post-conventional morality

(B)  pre-conventional morality

(C)  bodily-kinesthetic intelligence

(D)  transference

Answer: (A)

16. Which technique allows researchers to conduct an integrative statistical analysis of multiple independent studies addressing the same question?

(A)  Meta-analysis

(B)  Correlational analysis

(C)  Regression analysis

(D)  Bootstrapping

Answer: (A)

17. The role of culture and ‘scaffolding’ are emphasized in _________.

(A)  Vygotsky’s theory of cognitive development

(B)  Piaget’s theory of cognitive development

(C)  Atkinson-Shiffrin’s information-processing model

(D)  Kamiloff-Smith’s theory of cognitive development

Answer: (A)

18. Most people tend NOT to consider situational factors while judging others’ behaviour because _______.

(A)  people are inclined to commit the fundamental attribution error

(B)  of the frustration-aggression relationship

(C)  people are influenced by the laws of reinforcement

(D)  of the overjustification effect

Answer: (A)

19. Using archival analysis, scientists describe a culture by _______.

(A)  examining documents like magazines, diaries and newspapers

(B)  surveying a representative sample of members of the society

(C)  observing the behaviour of members of the society

(D)  comparing the direct observations of behaviour from different cultures

Answer: (A)

Q.20 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).

20. Which is/are the component(s) of Gardner’s theory of multiple intelligences?

(A)  Logical-Mathematical intelligence

(B)  Linguistic intelligence

(C)  Spatial intelligence

(D)  Insight

Answer: (A; B; C)

Q.21 – Q.23 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

21. Match the neurotransmitter in the first column with its effect in the second column.

(A)  P-(iv), Q-(i), R-(ii), S-(iii)

(B)  P-(iii), Q-(i), R-(ii), S-(v)

(C)  P-(i), Q-(ii), R-(iv), S-(iii)

(D)  P-(iv), Q-(i), R-(v), S-(iii)

Answer: (A)

22. Match the depth cues in the first column with their description in the second column.

(A)  P-(ii), Q-(iv), R-(i), S-(iii)

(B)  P-(ii), Q-(iii), R-(iv), S-(i)

(C)  P-(iv), Q-(i), R-(ii), S-(iii)

(D)  P-(iii), Q-(iv), R-(i), S-(ii)

Answer: (A)

23. Match the concepts in the first column with the description in the second column.

(A)  P-(iii), Q-(i), R-(iv), S-(ii)

(B)  P-(i), Q-(ii), R-(iii), S-(iv)

(C)  P-(ii), Q-(i), R-(iv), S-(iii)

(D)  P-(iii), Q-(iv), R-(i), S-(ii)

Answer: (A)

Q.24 – Q.40 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).

24. Which of the following will hold true for a learning acquisition curve drawn for a classical conditioning experiment on eye blinking as conditioned response that plots the learning over a number of trials?

(A)  The rate of learning on earlier trials is more than that on later trials.

(B)  The learning curve is negatively accelerated.

(C)  The rate of learning in later trials will be more than that on earlier trials.

(D)  The rate of learning is proportionally increasing with increasing number of trials.

Answer: (A; B)

25. In the situation where ‘A teenager who hates studying science but is also not able to tell his parents fearing their reaction’, what is the conflict he is facing and which of these may be his way of dealing with this situation?

(A)  Avoidance-Avoidance conflict, he will keep vacillating between telling his parents and continuing to study science.

(B)  Avoidance-Avoidance conflict, he may contemplate running away from his home.

(C)  Approach-Avoidance conflict, he will experience some emotional turmoil.

(D)  Multiple Approach-Avoidance conflict, he will be guided by internal values.

Answer: (A; B)

26. Which of these is true about individuals high on n-achievement motivation?

(A)  High n-achievement individuals like to work on situations where they have control and can get feedback.

(B)  High n-achievement individuals persistently work on tasks they perceive as, either reflecting their personal characteristics like intelligence or are career-related.

(C)  High n-achievement individuals prefer working on extremely challenging tasksfor bigger gains.

(D)  High n-achievement individuals avoid changing their aspiration levels.

Answer: (A; B)

27. Which of the following is/are Allport’s basic assumption(s) concerning human nature?

(A)  Human growth as an active process of “becoming”.

(B)  Personality cannot be fully understood by examining each trait separately, though some system of conceptual schemata are essential for personality study and a trait must be related to the total pattern of personality.

(C)  Personality is organized in a topographical model.

(D)  All human events are determined by powerful instinctual forces.

Answer: (A; B)

28. Which of the following aspects are characteristics of the group structure in an organizational context?

(A)  Task-oriented role (the activities of an individual that involve helping the group reach the goal).

(B)  Socio-emotional role (the activities of an individual that involve being supportive and nurturing of other group members).

(C)  Prescriptive norms (expectations within groups regarding what has to be done).

(D)  Monitoring (observing work performance).

Answer: (A; B; C)

29. Which of the following needs/motives are proposed by Abraham Maslow?

(A)  Deficit needs.

(B)  Metaneeds.

(C)  Self-actualization needs.

(D)  Need-achievement.

Answer: (A; B; C)

30. A researcher is conducting a study involving two independent variables. Which of the following Analysis of Variance (ANOVA) is/are available to him/her?

(A)  2 × 2 ANOVA.

(B)  4 × 3 ANOVA.

(C)  3 × 2 × 2 ANOVA.

(D)  One-way ANOVA.

Answer: (A; B)

31. Which of the following statements is true about personal space?

(A)  It is silent and invisible.

(B)  It is a geographic component of interpersonal relations.

(C)  Invasions of personal space are a matter of degree.

(D)  There are no across culture variations.

Answer: (A; B; C)

32. If a person got a score of 75 on a test, which of the following distributions allow(s) for the most favourable interpretation of that score? (assuming higher values are more favourable)

(A)  Mean = 55, Standard Deviation = 4

(B)  Mean = 60, Standard Deviation = 3

(C)  Mean = 65, Standard Deviation = 5

(D)  Mean = 50, Standard Deviation = 10

Answer: (A; B)

33. A man’s wife is dying. She is in dire need of a drug. The only place to get the drug is at the store of a pharmacist who is known to overcharge people for drugs. The man can only pay Rs. 20000 but the pharmacist wants Rs. 50000, and refuses to sell it to him for less, or to let him pay later. What will the man do

if he is at the conventional stage of morality as per Kohlberg’s theory ofmoral reasoning?

(A)  He would not steal the drug, as everyone will see him as a thief, and his wife would not approve of his stealing or accept the stolen drug.

(B)  No matter what, he would obey the law because stealing is a crime.

(C)  The man would not steal the drug, as he may get caught and go to jail.

(D)  The man would steal the drug to cure his wife and then tell the authorities what he has done. He may have to pay a penalty, but at least he would have saved ahuman life.

Answer: (A; B)

34. According to Erik Erikson, identity versus role confusion is the fifth stage of life span development. Which of the following outcomes may emerge as a result of identity crisis?

(A)  Identity diffusion

(B)  Identity moratorium

(C)  Identity foreclosure

(D)  Identity perception

Answer: (A; B)

35. Life span experts argue that biological aging begins at birth. Which of the following is/are explanation/s of aging?

(A)  Cells can divide to a maximum of about 75 to 80 times and that as people age, cells become less capable of dividing.

(B)  People age because when cells metabolize energy, the by-products include unstable oxygen molecules known as free radicals.

(C)  Aging is due to the decay of mitochondria.

(D)  Cell division increases as people age.

Answer: (A; B; C)

36. Which of the following are involved in sympathetic nervous system activation?

(A)  Inhibited salivation

(B)  Increased heart rate

(C)  Inhibited digestion

(D)  Constricted pupils

Answer: (A; B; C)

37. How is/are genetic theories of psychopathology tested?

(A)  Using twin studies

(B)  Using family history studies

(C)  Using adoption studies

(D)  Using psychodynamic studies

Answer: (A; B; C)

38. An investigator approached college students who initially believed that water should be purified and asked them to compose and recite a videotaped speech against the use of water purifiers. To do this, some were offered large

incentives and others were offered small incentives. Later their attitudes towards water purifiers were tested. Which of the following will be the expected finding(s)?

(A)  The smaller the incentive, the greater will be the attitude change.

(B)  All the students will change their attitudes towards water purifiers.

(C)  All the students will continue to feel favourably about water purifiers.

(D)  The larger the incentive, the greater will be the attitude change.

Answer: (A)

39. In which attachment style(s), do children tend to show clingy behaviour but then reject the attachment figure’s attempt to interact with them?

(A)  Resistant attachment

(B)  Avoidant attachment

(C)  Secure attachment

(D)  Disorganized attachment

Answer: (A)

40. A study is conducted to see the effectiveness of volume levels of commercials. In the graph given below, values of mean effectiveness (dependent variable) are presented on the Y axis, and three levels of volume, namely, soft, medium and loud are presented on the X axis. The graph shows the relationship between volume and mean effectiveness for males in the continuous line and for females in the dashed line. Which of the following interpretation(s) is/are correct from the graph?

(A)  A linear relationship exists for males and a nonlinear relationship for females.

(B)  The effect of increasing volume on effectiveness depends on whether theparticipant is a male or a female.

(C)  No interaction effect is seen.

(D)  A linear relationship exists for both males and females.

Answer: (A; B)

SOCIOLOGY (XH-C6)

Q.1 – Q.12 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. The term kulak refers to

(A)  a type of hoe used in agriculture.

(B)  a form of property right over agrarian produce.

(C)  a rich farmer.

(D)  the Russian word for peasant uprising.

Answer: (C)

2. M.N. Srinivas’ principal work was built around the method of

(A)  conjectural history.

(B)  archival research.

(C)  fieldwork.

(D)  content analysis.

Answer: (C)

3. In an experimental design, the dependent variable is

(A)  the one that is not manipulated and in which any changes are observed.

(B)  the one that is manipulated in order to observe any effects on the other.

(C)  the unknown variable that emerges from the analysis of the data.

(D)  the variable whose meaning depends on how informants perceive it.

Answer: (A)

4. The avunculate refers to the relationship between

(A)  virilocal and neolocal families.

(B)  matrilateral cross cousins.

(C)  members of a matrilocal tharavad.

(D)  mother’s brother and sister’s son.

Answer: (D)

5. Who among the following Indian sociologists argued against Verrier Elwin’s proposal of preserving the ‘tribal way of life’ on the grounds that the Indian tribes are not ‘aborigines’ but are “imperfectly integrated classes of Hindu society” or are ‘Backward Hindus’?

(A)  Irawati Karve

(B)  A.R. Desai

(C)  G.S. Ghurye

(D)  D.D. Kosambi

Answer: (C)

6. M. N. Srinivas called his work on Rampura ‘The Remembered Village’ because

(A)  ‘collective memory’ is the concept he used to understand Rampura.

(B)  his experience in Rampura was memorable.

(C)  the village Headman had forbidden Srinivas from taking any notes forcing him to write this account solely from memory.

(D)  he lost his field material in a fire and had to rely on his memory to write thebook.

Answer: (D)

7. “An ideal society should be mobile, should be full of channels for conveying a change taking place in one part to other parts. In an ideal society there should be many interests consciously communicated and shared. There should be varied and free points of contact with other modes of association. In other words there must be social endosmosis.”

On the basis of the above statement, which one of the following can beasserted?

(A)  This is M.K. Gandhi describing his vision of Rama Rajya in ‘Hind Swaraj’.

(B)  This is V.D. Savarkar describing caste equality in ‘Essentials of Hindutva’.

(C)  This is Jawaharlal Nehru describing socialist society in ‘The Discovery of India’.

(D)  This is B.R. Ambedkar describing fraternity in ‘The Annihilation of Caste’.

Answer: (D)

8. ‘The City and the Grassroots’ authored by _____________ is among the most important books published on urban social movements.

(A)  Michel Foucault

(B)  Charles Tilly

(C)  Manuel Castells

(D)  Veena Das

Answer: (C)

9. A fisherman in southwest Sri Lanka has received a warning that a cyclone may hit his coastal region and he has to decide whether to evacuate or stay put. He knows that the probability of the cyclone striking is 70%. He has the means to evacuate and his property is worth three times the cost of evacuation. He calculates accurately that his best chance to protect himself and his assets lies in evacuation. At a later meeting of the whole community, the village elders decide that no one will evacuate because the village shrines cannot be left unattended indefinitely. Hence in deference to the elders, the fisherman decides to stay put.

In Max Weber’s terms, his decision is closest to

(A)  value rational action.

(B)  instrumental rational action.

(C)  traditional action.

(D)  affective action.

Answer: (C)

10. The Jonestown massacre of 1978 in the United States saw the death of 900persons including children. Reverend Jones, leader of an American cult, ordered his followers ‘The Peoples Temple’ to kill a US Congressman and several journalists and then commit mass suicide by drinking fruit punchlaced with cyanide. In Durkheim’s view, this would be a case of

(A)  anomic suicide.

(B)  altruistic suicide.

(C)  egoistic suicide.

(D)  fatalistic suicide.

Answer: (B)

11. Pierre Bourdieu defined ____________ as “Systems of durable dispositions, structured structures predisposed to function as structuring structures … collectively orchestrated without being the product of the

orchestrating action of a conductor.”

Which of the following completes the above sentence?

(A)  social capital

(B)  culture

(C)  habitus

(D)  field

Answer: (C)

12. Read the following statements:

(1) Throughout the developing world, poverty rates among householdsheaded by women are higher than those headed by men.

(2) The greater ‘investment value’ associated with the survival of boys in a household in comparison with girls leads to discrimination against girl children and adult women.

(3) The unequal allocation of resources within households results in differential allotments of nutrition and healthcare that reflect the perceived inferior short-term and long-term value of females.

(4) In all transitional economies, an increase in prostitution and trafficking of women has been observed.

The above statements are all examples of

(A)  the ‘feminisation of poverty’ thesis.

(B)  labour market informalisation.

(C)  the ‘culture of poverty’ thesis.

(D)  differences in bargaining power between advanced and transitional economies.

Answer: (A)

Q.13 – Q.20 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).

13. In which of the following ways did the founding scholars usually distinguish New Social Movements (NSMs) from Old Social Movements?

(A)  NSMs are devoted to changing cultural norms concerning individual dignity rather than bringing about structural transformation.

(B)  NSMs are based in social class and not on social identities.

(C)  NSMs reject hierarchical organisational structures and prefer flexible, horizontal participation.

(D)  NSMs are all revolutionary in their mode of action.

Answer: (A; C)

14. Which of the following option(s) correctly applies/apply to a key information sociological research?

(A)  One who intentionally restricts a researcher’s access to participants.

(B)  One with in-depth knowledge of the community.

(C)  One who refers the researcher to those knowledgeable about the subject of theresearch.

(D)  One who because of her social position provides a deeper understanding of hersociety.

Answer: (B; C; D)

15. For Karl Marx, which statement(s) below define(s) absolute surplus value?

(A)  It is value extracted by using technology in the labour process.

(B)  It is value saved by technology.

(C)  It is value created over and above worker subsistence.

(D)  It is value extracted by means of extending the working day.

Answer: (D)

16. Who among the following sociologist(s) use(s) a Marxist framework tounderstand Indian society and history?

(A)  Yogendra Singh

(B)  A.K. Saran

(C)  Leela Dube

(D)  A. R. Desai

Answer: (D)

17. Which of the following reverse(s) the process of primitive accumulation in India?

(A)  NREGA

(B)  The Land Acquisition Act of 1894

(C)  Special Economic Zones

(D)  Microfinance lending

Answer: (A; D)

18. Which of the following applies/apply to Lévi-Strauss’ fundamental unit ofkinship?

(A)  It is constituted by the father and mother and their children.

(B)  It is constituted by the nuclear family and the wife’s brother.

(C)  It is the basis of alliance theory.

(D)  It is based on the universal incest taboo.

Answer: (B; C; D)

19. Which statement(s) correctly explain(s) why feminists and women’s rights activists are uncomfortable with the term ‘honour killings’?

(A)  It has been defined variously across disciplines from law to sociology to philosophy.

(B)  It has become associated with the ‘uniqueness’ of Asian societies and cultures.

(C)  The idea that women embody male honour makes violence against them and even their murder justifiable.

(D)  It has become associated with communities that retain archaic patriarchal practices and refuse to modernise.

Answer: (B; C; D)

20. Which of the following is/are Louis Dumont’s formulation(s)?

(A)  Indian sociology must lie at the confluence of Indology and anthropology.

(B)  The ideological principle that religion is always superior to power is at all times found exhibited at the empirical level in India.

(C)  Equality runs contrary to the general tendencies of societies.

(D)  Traditional Indian ideology allows only ‘surreptitious’ entry of economic andpolitical power.

Answer: (A; C; D)

Q.21 – Q.28 Multiple Choice Question (MCQ), carry TWO mark each (for each wronganswer: – 2/3).

21. The Latin American system of compadraz go or ‘god parenthood’ is one in which, at the time of baptism of a child into the Christian church, a relationship is set up between the child’s biological mother and father and possibly unrelated persons who become the child’s spiritual parents. This may be understood as a form of

(A)  fictive kinship.

(B)  cognatic kinship.

(C)  mystical kinship.

(D)  bilateral kinship.

Answer: (A)

  1. The Self-Employed Women’s Association (SEWA) is

(A)  a trade union for self-employed women workers in the informal economy.

(B)  not a trade union as its members have no employer.

(C)  an association of all home-based women workers across India.

(D)  a trade union for all self-employed women workers outside the agrarian sector.

Answer: (A)

23. Match statements (P), (Q), (R), (S) to names (1), (2), (3), (4):

(P) “Today, Indians no longer idealise hierarchy. What they … idealise is equality.”

(Q) “[We] do not argue that non-dalit feminists can ‘speak as’ or ‘for the’ dalit women but they can ‘reinvent themselves as dalit feminists’.”

(R) “[From] the point of view of people at the lowest end of the scale, caste has functioned (and continues to function) as a very effective system of economic exploitation.”

(S) “The pure hierarchy that Louis Dumont wrote so compellingly about a

few decades ago … now stands bereft of empirical support from practically every quarter of Hindu India.”

(1) Dipankar Gupta

(2) Sharmila Rege

(3) André Béteille

(4) Joan P. Mencher

(A)  (P)-(3), (Q)-(2), (R)-(4), (S)-(1)

(B)  (P)-(4), (Q)-(2), (R)-(3), (S)-(1)

(C)  (P)-(3), (Q)-(1), (R)-(4), (S)-(2)

(D)  (P)-(4), (Q)-(1), (R)-(2), (S)-(3)

Answer: (A)

24. Match statements (P), (Q), (R), (S) to names (1), (2), (3), (4):

(P) “The executive of the modern state is but a committee for managing the common affairs of the whole bourgeoisie.”

(Q) The state is “an institutional association of rule, which within a given territory has succeeded in gaining a monopoly of legitimate physical force as a means of ruling.”

(R) “It is only through the State that individualism is possible, although it cannot be the means of making it a reality, except in

certain precise conditions. We might say that in the State we have the prime mover. It is the State that has rescued the child from

patriarchal domination and from family tyranny; it is the State that has freed the citizen from feudal groups and later from communal

groups; it is the State that has liberated the craftsman and his master from guild tyranny.”

(S) “The family is indeed a fiction, a social arte fact, an illusion in the most ordinary sense of the word, but a ‘well-founded illusion’, because, being produced and reproduced with the guarantee of the state, it receives from the state at every moment the means to exist and persist.”

(1) Pierre Bourdieu

(2) Emile Durkheim

(3) Karl Marx and Friedrich Engels

(4) Max Weber

(A)  (P)-(3), (Q)-(4), (R)-(2), (S)-(1)

(B)  (P)-(3), (Q)-(4), (R)-(1), (S)-(2)

(C)  (P)-(3), (Q)-(1), (R)-(2), (S)-(4)

(D)  (P)-(4), (Q)-(2), (R)-(3), (S)-(1)

Answer: (A)

25. Read the abstract of the article titled ‘Taming’ Arab social movements: Exporting neoliberal governmentality” (2013).

“In the wake of the recent Arab revolutions, the European Union (EU) has sought to provide genuine and substantial support to a range of Arab social movements in the region’s emerging polities…We argue, however, that the EU’s attempts at democracy promotion in the Middle East and North Africa (MENA) region may be understood through a governmentality frame work, despite the limitations of such an approach. Specifically, theEU is actively promoting neoliberal policies in the aftermath of the Arab

Spring in order to foster a mode of subjectivity that is conducive to the EU’s own norms and interests. What we observe are not just innocent attempts at democracy promotion, but a form of politics and economics that seeks to subject the agency on the ‘Arab street’ to EU standards. We conclude by going over the radical plurality of the Arab street, and show how it was in fact earlier neoliberal reforms by their former regimes that created the conditions of possibility for the recent revolutions in Tunisia and Egypt.”

On the basis of the above statement, which of the following can be asserted?

(1) Social movements can no longer be understood as a purely intra-national phenomenon.

(2)Local social movements for democratisation have little to do with the transnationalisation of the practices of neoliberal governmentality.

(A)  Both the statements are correct

(B)  Both the statements are incorrect

(C)  Only (1) can be asserted

(D)  Only (2) can be asserted

Answer: (C)

26. According to Karl Marx, the socially necessary labour time to produce acommodity will directly vary with

(A)  the particular time period and place.

(B)  the annual rainfall.

(C)  the average productivity of agrarian workers.

(D)  the output of natural resources.

Answer: (A)

27. Imagine there is a spiritual leader from any religion who has a huge estate, organisation, publications etc. In Weberian terms, this could be considered an example of

(A)  patrimonial power.

(B)  bureaucratised patrimonial power.

(C)  charismatic power.

(D)  bureaucratised charismatic power.

Answer: (D)

28. Which of the following is a proposed explanation for a group of facts orphenomena that provides the basis for empirical testing?

(A)  An ideal type

(B)  A logical framework matrix

(C)  A hypothesis

(D)  A sampling procedure

Answer: (C)

Q.29 – Q.40 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).

29. To which of the following option(s) does C. Wright Mills’ ‘Grand Theory’ NOT apply?

(A)  A theory proposed by one of classical sociological theorists.

(B)  A highly abstract theory making broad generalisations about the social world.

(C)  An accurate theoretical explanation of observed empirical regularities.

(D)  An intellectually satisfying theory of social knowledge.

Answer: (A; C; D)

30. Which statement(s) about contemporary India is/are endorsed by recent sociological research?

(A)  The skewed sex ratio at birth is enabling cross-regional marriages that may breach caste boundaries.

(B)  The skewed sex ratio at birth means that women are valued more for their roles in reproduction, domestic and care work.

(C)  The skewed sex ratio at birth reduces the supply of women and improves their life chances throughout society.

(D)  The skewed sex ratio at birth is causing a male marriage squeeze due to the female deficit.

Answer: (A; B; D)

31. Which of the following statements is/are representation(s) of the ‘modernisation theory’ of the mid-twentieth century?

(A)  All versions of this theory could be summarised as the attempt to under standhow traditional societies modernise.

(B)  This theory saw the developmental efforts of all decolonised nations through the binary of communist or capitalist.

(C)  Ashis Nandy termed this theory as a “secular theory of salvation”.

(D)  The theory seeks to understand macro changes in terms of ‘development’ andnot how to make individuals develop modern values and sensibilities.

Answer: (A; B; C)

32. “We demanded changes that would make the law more sensitive to the cultural and economic contexts of women’s lives. Women’s groups investigating ‘dowry deaths’ demonstrated how the designation of the family as the private domain restricted women’s access to protection against domestic violence. They exposed the collusion of the law, police, medical system, and the family in classifying these deaths as suicides. Feminist scholars worked to salvage gender and women’s issues from being subsumed by class analysis, sought to extend the Marxist understanding of labour to include domestic production, and pointed out the marginality and vulnerability of women in the workforce”.

(Susie Tharu and Tejaswini Niranjana (1996), ‘Problems for a Contemporary Theory of Gender’)

Which among the following statements can be asserted from the aboveexcerpt?

(A)  Women’s lives have contexts that are peculiar/unique.

(B)  The division of domains into public and private allows women’s specific concerns to be fore grounded.

(C)  Marxist understanding of labour is not gender-sensitive.

(D)  The classification of dowry deaths as suicide lowers the institutional and social protection of women against violence.

Answer: (A; C; D)

33. “The claim, made by structuralism and dependency theory, that subordination to the world market seals the fate of nations is wrong. Inequality, poverty, low productivity and sluggish growth in the periphery, their propensity to import luxury goods and transfer profits to the centre, and the lack of coordination of economic activity in many countries, are due primarily to the social structures prevailing in the periphery, rather than their international trade relations.”

(Alfredo Saad-Filho (2005), ‘The Rise and Decline of Latin American Structuralism and Dependency Theory’)

Which among the following statements can be asserted from the above excerpt?

(A)  Underdevelopment is mainly due to the balance of political forces within theperiphery.

(B)  Trade patterns between core and periphery follow from “the social structures prevailing in the periphery”.

(C)  Unequal exchange between core and periphery inhibits development of thelatter.

(D)  There is a pathway to development through the world market.

Answer: (A; B; D)

34. There is scholarly controversy over the role of the middle peasants inpeasant movements in India. In this regard, which of the following statements is/are true?

(A)  Hamza Alavi argued that the middle peasants are more likely to initiate and actively participate in peasant movements.

(B)  Dhanagare argued that the middle peasants are weaker and more heterogeneous than other agrarian classes.

(C)  Kathleen Gough argued that poor peasants and agricultural labourers have the potential for organising peasant movements.

(D)  Gail Omvedt argued that caste is the basis of peasant mobilisation, not class.

Answer: (A; B; C)

35. In ‘The Nation and its Fragments’ (1993), Partha Chatterjee observes that“ By the 1940s, the dominant argument of nationalism against colonial rule was that the latter was impeding the…development of India….A developmental ideology…was a constituent part of the self-definition of the postcolonial state. The state was connected to the people not simply through the procedural forms of representative government; it also acquired its representativeness by directing a program of economic development on behalf of the nation.”

In what way(s) was the connection between development and the representativeness of the Indian state achieved, for Chatterjee?

(A)  Colonialism had demonstrated the benefits of free trade and globalisation.

(B)  Colonialism stood for economic exploitation, therefore liberty meant thereverse.

(C)  The procedural forms of government would by themselves be insufficient todrive development.

(D)  The procedural forms of government would inevitably fall to corruption.

Answer: (B; C)

36. Which of the following statement(s) correctly represent(s) A.M. Shah’sviews in his ‘The Household Dimension of the Family in India’?

(A)  Indological conceptions of the ‘Indian joint family’ have become an obstacle tosociological investigation of the familial structure and transformation.

(B)  Household and family are two different, though related, categories.

(C)  The process of modernisation will break the traditional Indian joint family into nuclear families.

(D)  The classification of the households into ‘simple’ and ‘complex’ resolves theexisting confusing classification of ‘elementary’ and ‘joint’ family.

Answer: (A; B)

37. See the diagram and identify which option(s) below applies/apply to it

(A)  The diagram shows parallel cousin marriage which is a form of restricted exchange.

(B)  The diagram shows cross cousin marriage which is a form of generalized exchange.

(C)  This form of marriage creates a distinction between bride-givers and bride-takers.

(D)  This form of marriage conforms to the ideal of kanyadana.

Answer: (B; C; D)

38. Which of the following statement(s) correctly applies/apply to reflexivity in sociological research?

(A)  A researcher can take a bird’s eye perspective of research subjects.

(B)  A researcher reflects on how her position impacts her research and findings.

(C)  A researcher considers how her biases and values bear on her interpretations and analyses.

(D)  A researcher reflects on how she in turn can help the community she is studying.

Answer: (B; C)

39. “If we make abstraction from its use value, we make abstraction at the same time from the material elements and shapes that make the product a use value; we see in it no longer a table, a house, yarn, or any other useful thing. Its existence as a material thing is put out of sight. Neither can it any longer be regarded as the product of the labour of the joiner, the mason, the spinner, or of any other definite kind of productive labour. Along with the useful qualities of the products themselves, we put out of sight both the useful character of the various kinds of labour embodied in them, and the concrete forms of that labour; there is nothing left but what is common to them all; all are reduced to one and the same sort of labour, human labour in the abstract.” (Karl Marx, ‘Capital’)

Which statement(s) can be asserted from the above excerpt?

(A)  Abstraction refers to a material process that occurs in production.

(B)  Abstraction refers to an analytical operation.

(C)  Abstraction refers to the reduction of material products to their commonelement.

(D)  Abstraction refers to a mathematical operation.

Answer: (B; C)

40. “The capitalistic economy of the present day is an immense cosmos into which the individual is born, and which presents itself to him, at least as an individual, as an unalterable order of things in which he must live…In order that a manner of life so well adapted to the peculiarities of capitalism could be selected at all, i.e. should come to dominate others, it had to originate somewhere, and not in isolated individuals alone, but as a way of life common to whole groups of men. This origin is what really needs explanation…The question of the motive forces in the expansion of modern capitalism is not in the first instance a question of the origin of the capital sums which were available for capitalistic uses, but, above all, of the development of the spirit of capitalism. Where it appears and is able to work itself out, it produces its own capital and monetary supplies as the means to its ends, but the reverse is not true.” (Max Weber, ‘The Protestant Ethic and the Spirit of Capitalism’)

Which among the following is/are Weber’s argument(s) in the above excerpt?

(A)  The origins of capitalism cannot be explained by purely material factors.

(B)  Before it is mature, capitalism does not drive individual behaviour.

(C)  Before it is fully functional, capitalism needed the support of an ethic.

(D)  Capitalism requires greed to be adopted by all as “a manner of life”.

Answer: (A; B; C)

GATE Exam 2021 Engineering Sciences (XE) Question Paper With Answer Key

GATE-2021

XE: Engineering Sciences

GA-General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Gauri said that she can play the keyboard __________ her sister.

(A)  as well as

(B)  as better as

(C)  as nicest as

(D)  as worse as

Answer: (A)

2. A transparent square sheet shown above is folded along the dotted line. The folded sheet will look like ________.

Answer: (B)

3. If θ is the angle, in degrees, between the longest diagonal of the cube and any one of the edges of the cube, then, cos θ =

(A)  1/2

(B)  1/√3

(C)  1/√2

(D)  √3/2

Answer: (B)

4. If  then the value of x is:

(A)  2

(B)  4

(C)  6

(D)  8

Answer: (B)

5. Pen : Write :: Knife : _________

Which one of the following options maintains a similar logical relation in the above?

(A)  Vegetables

(B)  Sharp

(C)  Cut

(D)  Blunt

Answer: (C)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

6. Listening to music during exercise improves exercise performance and reduces discomfort. Scientists researched whether listening to music while studying can help students learn better and the results were inconclusive. Students who needed external stimulation for studying fared worse while students who did not need any external stimulation benefited from music.

Which one of the following statements is the CORRECT inference of the above passage?

(A)  Listening to music has no effect on learning and a positive effect on physical exercise.

(B)  Listening to music has a clear positive effect both on physical exercise and on learning.

(C)  Listening to music has a clear positive effect on physical exercise. Music has a positive effect on learning only in some students.

(D)  Listening to music has a clear positive effect on learning in all students. Music has a positive effect only in some students who exercise.

Answer: (C)

7. A jigsaw puzzle has 2 pieces. One of the pieces is shown above. Which one of the given options for the missing piece when assembled will form a rectangle? The piece can be moved, rotated or flipped to assemble with the above piece.

Answer: (A)

8. The number of students in three classes is in the ratio 3:13:6. If 18 students are added to each class, the ratio changes to 15:35:21.

The total number of students in all the three classes in the beginning was:

(A)  22

(B)  66

(C)  88

(D)  110

Answer: (C)

9. The number of units of a product sold in three different years and the respective net profits are presented in the figure above. The cost/unit in Year 3 was ` 1, which was half the cost/unit in Year 2. The cost/unit in Year 3 was one-third of the cost/unit in Year 1. Taxes were paid on the selling price at 10%, 13% and 15% respectively for the three years. Net profit is calculated as the difference between the selling price and the sum of cost and taxes paid in that year.

The ratio of the selling price in Year 2 to the selling price in Year 3 is ________.

(A)  4:3

(B)  1:1

(C)  3:4

(D)  1:2

Answer: (A)

10. Six students P, Q, R, S, T and U, with distinct heights, compare their heights and make the following observations.

Observation I: S is taller than R.

Observation II: Q is the shortest of all.

Observation III: U is taller than only one student.

Observation IV: T is taller than S but is not the tallest.

The number of students that are taller than R is the same as the number of students shorter than ______.

(A)  T

(B)  R

(C)  S

(D)  P

Answer: (C)

Engineering Mathematics (XE-A)

Q.1 – Q.3 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Let  If  

(A)  −4

(B)  −2

(C)  2

(D)  4

Answer: (D)

2. Let C be the boundary of the region R ∶ 0 ≤ x ≤ π, 0 ≤ y ≤ sin x in the xy-plane and α be the area of the region R. If C traverses once in the counter clockwise direction, then the value of the line integral ∮C(2ydx + 5xdy) is equal to

(A)  α

(B)  2α

(C)  3α

(D)  4α

Answer: (C)

3. Given that i = √−1. The value of  is

(A)    

(B)   

(C)    

(D)   

Answer: (B)

Q.4 – Q.7 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

4. Let f(x) be a non-negative continuous function of real variable x. If the area under the curve y = f(x) from x = 0 to x = a is  then the of f(π/2) is ________ (round off to one decimal place).

Answer: (0.5 to 0.5)

5. If the numerical approximation of the value of the integral  using the Trapezoidal rule with two subintervals is 9, then the value of the real constant α is _________ (round off to one decimal place).

Answer: (0.5 to 0.5)

6. Let the transformation y(x) = exv(x) reduce the ordinary differential equation  x > 0 to  where α, β, γ are real constants. Then, the arithmetic mean of α, β, γ is __________ (round off to three decimal places).

Answer: (0.665 to 0.668)

7. A person, who speaks the truth 3 out of 4 times, throws a fair dice with six faces and informs that the outcome is 5. The probability that the outcome is really 5 is _________ (round off to three decimal places).

Answer: (0.375 to 0.375)

Q.8 – Q. 9 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

8. Let f(x, y) = x4 + y4 − 2x2 + 4xy − 2y2 + α be a real valued function. Then, which one of the following statements is TRUE for all α ?

(A)  (0, 0) is not a stationary point of f

(B)  f has a local maxima at (0, 0)

(C)  f has a local minima at (0, 0)

(D)  f has a saddle point at (0, 0)

Answer: (D)

9. Let u(x, y) = (x2 − y2)v(x, y) be such that both u(x, y) and v(x, y) satisfy the Laplace equation in a domain Ω of the xy-plane. Then, which one of the following is TRUE in Ω ?

Answer: (A)

Q.10 – Q. 11 Numerical Answer Type (NAT), carry TWO marks each (no negative marks).

10. Let I denote the identity matrix of order 7, and A be a 7 × 7 real matrix having characteristic polynomial CA (λ) = λ2(λ − 1)α (λ + 2)β, where α and β are positive integers. If A is diagonalizable and rank(A) = rank(A + 2I), then rank(A − I) is ____________ (in integer).

Answer: (4 to 4)

11. Let C1 be the line segment from (0, 1) to (4/5, 3/5) and let C2 be the arc of the circle x2 + y2 = 1 from (0, 1) to (4/5, 3/5). If  and  where  then the value of α2 + β2 is _________ (round off to two decimal places).

Answer: (0.32 to 0.32)

Fluid Mechanics (XE-B)

Q.1 – Q.8 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. The general relationship between shear stress, τ, and the velocity gradient (du/dy) for a fluid is given by where k is a constant with appropriate units. The fluid is Newtonian if

(A)  n > 1

(B)  n < 1

(C)  n = 1

(D)  n = 0

Answer: (C)

2. Which one of the following options is TRUE?

(A)  Pathlines and streaklines are the same in an unsteady flow, and streamlines are tangential to the local fluid velocity at a point.

(B)  Streamlines are perpendicular to the local fluid velocity at a point, and streamlines and streaklines are the same in a steady flow.

(C)  Pathlines and streaklines are the same in an unsteady flow, and streamlines and streaklines are the same in a steady flow.

(D)  Streamlines are tangential to the local fluid velocity at a point, and streamlines and streaklines are the same in a steady flow.

Answer: (D)

3. If Pin = 1.2 Pa and Pout = 1.0 Pa are the average pressures at inlet and outlet respectively for a fully-developed flow inside a channel having a height of 50 cm, then the absolute value of average shear stress (in Pa) acting on the walls of the channel of length 5 m is

(A)  0.005

(B)  0.02

(C)  0.01

(D)  0.05

Answer: (C)

4. Consider the fully-developed flow of a Newtonian fluid (density ρ; viscosity μ) through a smooth pipe of diameter D and length L. The average velocity of the flow is V. If the length of the pipe is doubled, keeping V, D, ρ, μ constant, the friction factor

(A)  increases by two times

(B)  remains the same

(C)  decreases by two times

(D)  increases by four times

Answer: (B)

5. The absolute value of pressure difference between the inside and outside of a spherical soap bubble of radius, R, and surface tension, γ, is :

(A)  2γ/B

(B)  γ/R

(C)  γ/2R

(D)  4γ/R

Answer: (D)

6. Which one of the following statements is TRUE about the continuity equation  (where u, v, w are the velocity components along the x, y and z coordinates respectively):

(A)  The equation is valid only for steady incompressible flows.

(B)  The equation is valid for both steady and unsteady incompressible flows.

(C)  The equation is valid only for steady compressible flows.

(D)  The equation is valid only for unsteady compressible flows.

Answer: (B)

7. The head loss (KL) associated with the flow entry of water to an internal passage depends on the shape of the entry. The following figure shows three different types of flow entry into a pipe. Which one of the following relationships correctly represents the head loss associated with the three different flow entries?

(A)  (KL)a > (KL)b > (KL)c

(B)  (KL)b > (KL)a > (KL)c

(C)  (KL)b ≤ (KL)a = (KL)c

(D)  (KL)b < (KL)a < (KL)c

Answer: (B)

8. The form and friction drags together contribute to the total drag when flow of air occurs past any object. Two orientations of a finite flat plate are shown in the figure. In Orientation-1, the plate is placed perpendicular to the flow while in Orientation-2, the plate is placed parallel to the flow. If the velocity (V) of air in both orientations is the same, which one of the following options is TRUE?

(A)  Orientation-1 has higher form drag and lower friction drag and Orientation-2 has lower form drag and higher friction drag

(B)  Orientation-1 has lower form drag and lower friction drag and Orientation-2 has higher form drag and higher friction drag

(C)  Orientation-1 has lower form drag and higher friction drag and Orientation-2 has higher form drag and lower friction drag

(D)  Orientation-1 has higher form drag and higher friction drag and Orientation-2 has lower form drag and lower friction drag

Answer: (A)

Q.9 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

9. A spherical ball is steadily supported against gravity by an upward air jet as shown in the figure. Take acceleration due to gravity to be g =10 m/s2. The mass flow rate of air, reaching the ball, is 0.01 kg/s and the air reaches the ball at an upward velocity of 3 m/s. Neglecting the buoyancy force, and using the principle of integral momentum balance, the mass (in grams, up to one decimal place) of the ball is ____.

Answer: (2.9 to 3.1)

Q.10 – Q. 12 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

10. The incompressible flow of air over a curved surface having possible flow separation is schematically shown in the figure. Two zones P and Q are indicated in the figure. Which one of the following combinations is TRUE for zones P and Q?

(a) Acceleration of flow, (b) Deceleration of flow, (c) Adverse pressure gradient, (d) Favorable pressure gradient, (e) No flow separation (f) Possible flow separation.

(A)  P: (a), (d), (e) and Q: (b), (c), (f)

(B)  P: (a), (d), (f) and Q: (b), (d), (f)

(C)  P: (a), (c), (f) and Q: (a), (d), (e)

(D)  P: (a), (c), (e) and Q: (a), (d), (f)

Answer: (A)

11. A spherical metal ball (of density ρx and diameter D), attached to a string, is exposed to a crossflow (of velocity U) of a viscous fluid (of viscosity μ and density ρf). Due to the crossflow, the string makes an angle of inclination, θ, , with the top surface as shown in the figure. The acceleration due to gravity is denoted by g. For this flow, Reynolds number,   and buoyancy force in the fluid is negligible compared to viscous force. Assuming the string to be weightless and offering negligible drag, the expression for θ is

Answer: (D)

12. In a Cartesian coordinate system, a steady, incompressible velocity field of a Newtonian fluid is given by V = μ0 (1 – ay2) i

Here, V is the velocity vector in m/s, i is the unit vector in the x-direction, u0 is a positive, real constant (in m/s), and a is a positive, real constant (in m2). The viscosity of the fluid is μ (in Pa-s). The absolute value of the pressure gradient (in Pa/m) is

(A)  aμu0

(B)  2aμu0

(C)  3aμu0

(D)  4aμu0

Answer: (B)

Q.13 – Q. 22 Numerical Answer Type (NAT), carry TWO marks each (no negative marks).

13. In a laminar, incompressible, fully-developed pipe flow of a Newtonian fluid, as shown in the figure, the velocity profile over a cross-section is given by  where U is a constant. The pipe length is L and the fluid viscosity is μ. The power P required to sustain the flow is expressed as P = cμLU2, where c is a dimensionless constant. The value of the constant c (up to one decimal place) is _________.

Answer: (6.0 to 6.5)

14. The two-dimensional velocity field V of a flow in a Cartesian coordinate system is given in dimensionless form by  Here, i and j are the unit vectors along the x and y directions respectively, a and b are independent of x, y and time. If the flow is incompressible, then  the value of (a−b), up to one decimal place, is ______.

Answer: (0.9 to 1.1)

15. For the configuration shown in the figure, oil of density 800 kg/m3 lies above water of density 1000 kg/m3. Assuming hydrostatic conditions and acceleration due to gravity g =10 m/s2, the length L (in meters, up to one decimal place) of water in the inclined tube is _____.

Answer: (1.7 to 1.9)

16. A two-dimensional Eulerian velocity field is given (in m/s) by V = [(√5)x] i − [(√12)y] j, where x and y are the coordinates (in meters) in a Cartesian coordinate system. The magnitude of the acceleration (in m/s2, up to one decimal place) of a fluid particle at x = 1 m and y = −1 m is ______.

Answer: (12.9 to 13.1)

17. A large pump is to deliver oil at an average velocity (V) of 1.5 m/s. The pump has an impeller diameter (D) of 40 cm and the pressure rise across the pump is 400 kPa. To design this pump, a lab-scale model pump with an impeller diameter of 4 cm is to be used with water as the fluid. The viscosity (μ) of the oil is 100 times that of water, and the densities (ρ) of oil and water are identical. A complete geometric similarity is maintained between the model and prototype. If the pressure rise is a function only of V, D, ρ and μ, the pressure rise (in kPa, up to one decimal place) across the model pump is ______.

Answer: (3.9 to 4.1)

18. Water (density = 103 kg/m3) enters steadily into a horizontal pipe bend, which is part of a larger piping system, as shown in the figure. The volumetric flow rate of water is 0.1 m3/s. The gage pressure at the inlet is 500 kPa, while the exit is open to atmosphere. The x -component of the force on the support is Fx. The absolute value of Fx (in kN, up to one decimal place) is _______.

Answer: (10.5 to 12.0)

19. Air (of density 0.5 kg/m3) enters horizontally into a jet engine at a steady speed of 200 m/s through an inlet area of 1.0 m2. Upon entering the engine, the air passes through the combustion chamber and the exhaust gas exits the jet engine horizontally at a constant speed of 700 m/s. The fuel mass flow rate added in the combustion chamber is negligible compared to the air mass flow rate. Also neglect the pressure difference between the inlet air and the exhaust gas. The absolute value of the horizontal force (in kN, up to one decimal place) on the jet engine is__________.

Answer: (48.0 to 52.0)

20. Water discharges from a cylindrical tank through an orifice, as shown in the figure. The flow is considered frictionless. Initially, the water level in the tank was h1 = 2 m. The diameter of the tank is D = 1 m, while the diameter of the jet is d = 10 cm, and the acceleration due to gravity is g = 10 m/s2. The time taken (in seconds, up to one decimal place) for the water level in the tank to come down to h2 = 1 m is _______.

Answer: (17.5 to 19.5)

21. Water discharges steadily from a large reservoir through a long pipeline, as shown in the figure. The Darcy friction factor in the pipe is 0.02. The pipe diameter is 20 cm and the discharge of water is 360 m3/h. Water level in the reservoir is 10 m and acceleration due to gravity g = 10 m/s2. If minor losses are negligible, the length L (in meters, up to one decimal place) of the pipeline is ____ .

Answer: (182.0 to 192.0)

22. Water is flowing with a flow rate Q in a horizontal circular pipe. Due to the low pressure created at the venturi section (Section-1 in the figure), water from a reservoir is drawn upward using a connecting pipe as shown in the figure. Take acceleration due to gravity g = 10 m/s2. The flow rate Q = 0.1 m3/s, D1 = 8 cm, and D2 = 20 cm. The maximum height (h, in meters, up to one decimal place) of the venturi from the reservoir just sufficient to raise the liquid upto Section-1 is __________.

Answer: (18.5 to 20.0)

Materials Science (XE-C)

Q.1 – Q.7 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Condition to be satisfied for α and β phases to be in equilibrium in a two-component (A and B) system at constant temperature and pressure is

(Given: μ is the chemical potential)

(A)  entropy of the system should be maximum

(B)  Gibbs energy of the system should be minimum and   

(C)  Gibbs energy of the system should be minimum and  

(D)  Helmholtz energy should be minimum

Answer: (C)

2. Amino acids react to form peptides and proteins. This process is known as

(A)  addition polymerization

(B)  nucleophilic substitution

(C)  condensation polymerization

(D)  hydration

Answer: (C)

3. The most favoured slip system in face centered cubic metal is

Answer: (D)

4. The dielectric constant of a material at ultraviolet frequencies is mainly due to

(A)  dipolar polarizability

(B)  ionic polarizability

(C)  electronic polarizability

(D)  interfacial polarizability

Answer: (C)

5. Match the different transformations/reactions in Column I with the most suitable information in Column II.

(A)  P-2; Q-3; R-1

(B)  P-1; Q-2; R-3

(C)  P-2; Q-1; R-3

(D)  P-3; Q-2; R-1

Answer: (C)

6. In scanning electron microscopy, the resolution of backscattered electron (BSE) image is poorer compared to that of secondary electron (SE) image, because

(A)  energy of BSE is lower

(B)  sampling volume of BSE is larger

(C)  yield of BSE is lower

(D)  sampling volume of SE is larger

Answer: (B)

7. Which of the following deposition conditions favour the formation of larger grains in thin film?

(A)  Low deposition rate and low substrate temperature

(B)  Low deposition rate and high substrate temperature

(C)  High deposition rate and low substrate temperature

(D)  High deposition rate and high substrate temperature

Answer: (B)

Q.8 Multiple Select Question (MSQ), Carry ONE mark each (no negative marks).

8. A metal has a melting point of 600 °C. By rapid cooling, liquid metal can be made to solidify either at 500 °C or 400 °C or 300 °C. Critical size of the solid nuclei is

(A)  same for solidification at 400 °C and 500 °C

(B)  smaller for solidification at 400 °C as compared to solidification at 500 °C

(C)  larger for solidification at 400 °C as compared to solidification at 500 °C

(D)  the smallest for solidification at 300 °C

Answer: (B; D)

Q.9 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

9. A magnet of mass 50 g has a magnetic moment of 4.2 × 10−7 A m2. The density of the magnet is 7.2 g cm−3. The intensity of magnetization in A m−1 is _________ (round off to 3 decimal places)

Answer: (0.058 to 0.063)

Q.10 – Q. 12 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

10. In the context of scanning electron microscopy, match the information in Column I with most appropriate information in Column II.

(A)  P-3; Q-2; R-1; S-4

(B)  P-2; Q-4; R-3; S-1

(C)  P-1; Q-3; R-2; S-4

(D)  P-4; Q-2; R-1; S-3

Answer: (B)

11. Match the heat treatment processes given in Column I with the most suitable outcomes in Column II.

(A)  P-3; Q-2; R-1; S-4

(B)  P-2; Q-4; R-3; S-1

(C)  P-1; Q-2; R-3; S-4

(D)  P-1; Q-3; R-4; S-2

Answer: (C)

12. A co-joined cross-ply laminate composite, as shown in figure, is distorted upon heating. What are the resultant shapes of edges XY and YZ ?

Answer: (C)

Q.13 Multiple Select Question (MSQ), Carry TWO marks each (no negative marks).

13. X-ray diffraction peak broadening enables the estimation of

(A)  X-ray diffraction peak broadening enables the estimation of

(B)  microstrain in the material

(C)  precise lattice parameter

(D)  residual macrostress acting on the material

Answer: (A; B)

Q.14 – Q. 22 Numerical Answer Type (NAT), carry TWO marks each (no negative marks).

14. Fe – 10 atom % C austenite (fcc), having no Fe vacancies, has a lattice parameter of 4 Å. The density of austenite in g cm−3 is _________ (round off to 2 decimal places)

(Given: atomic weight of Fe = 55.8; atomic weight of C = 12.0; Avogadro’s number = 6.023 × 1023)

Answer: (5.85 to 6.00)

15. An element transforms from α to β at 773 K and 1 atm pressure with 912 J mol−1 as enthalpy of transformation. The molar volumes of α and β phases are 7.377 cm3 and 7.317 cm3, respectively. Assume that the difference in molar volumes of α and β is independent of pressure. The pressure (in atm) required for α to β transformation to occur at 723 K is _________ (round off to nearest integer) (Given: 1 atm = 1.01325 × 105 Pa)

Answer: (9600 to 9800)

16. A binary A-B alloy has α and β phases at equilibrium. The ratio of weight percentages (wt.%) of α to β is 4. The wt.% of A in α and β phases is 70 and 20, respectively. The wt.% of B in the alloy is _________ (round off to nearest integer)

Answer: (38 to 42)

17. During heating, Ti undergoes allotropic transformation from hcp to bcc at 882 °C. The percent volume change accompanying this transformation is _________ (round off to 1 decimal place)

(Given: atomic weight of Ti = 47.9; lattice parameter of bcc Ti = 0.332 nm; density of hcp Ti = 4.51 g cm−3; Avogadro’s number = 6.023 × 1023)

Answer: (3.4 to 4.8)

18. Vickers hardness test is performed with an indenter of square-base diamond pyramid having an included angle of 136° between the opposite faces of the pyramid. If the applied load is 10 kg and the average length of diagonals of square indentation is 0.5 mm, the Vickers hardness in kg mm−2 is_______ (round off to nearest integer)

Answer: (71 to 77)

19. The drift mobility of electron in an n-type Si crystal doped with 1016 cm−3 phosphorous atoms is 1350 cm2 V−1 s−1. The electrical conductivity in Ω−1 m−1 is _________ (round off to nearest integer)

(Given: Intrinsic charge concentration of Si = 1.45 × 1010 cm−3;

Charge of an electron, e = 1.6 × 10−19 C)

Answer: (210 to 220)

20. At 1000 K, the linear thermal expansion coefficients of graphite, parallel and perpendicular to the graphite layers, are 0.8 × 10−6 K−1 and 29 × 10−6 K−1, respectively. The percentage increase in the volume of graphite when heated from 900 K to 1100 K is _________ (round off to 2 decimal places)

Answer: (0.60 to 0.62)

21. A certain ceramic has a theoretical density and sintered density of 6.76 g cm−3 and 6.60 g cm−3, respectively. The green compact has 18 volume percent porosity. For a sintered cube of side 2 cm, the required side of the cubic green compact in cm is _________ (round off to 2 decimal places)

Answer: (2.10 to 2.14)

22. When a metal (M) is immersed in de-aerated acid electrolyte, it polarizes anodically by 0.4 V. The M/Mn+ exchange current density is 10−5 A m−2 and Tafel slope is 0.1 V/decade for the anodic reaction. Assume that corrosion is uniform and, anodic and cathodic reactions are under activation control. The rate of metal dissolution in A m−2 is _________ (round off to 1 decimal place)

Answer: (0.1 to 0.1)

Solid Mechanics (XE-D)

Q.1 – Q.8 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. A force F = 40 kN is applied on the hook as shown. The equivalent force-couple system at B is

(A)  40 kN in +y direction and M = 0

(B)  40 kN in –y direction and M = 0

(C)  40 kN in +y direction and M =4000 Nm counter clockwise

(D)  40 kN in -y direction and M = 4000 Nm clockwise

Answer: (D)

2. A rigid rod OA rotates clockwise at an angular velocity of 10 rad/s. A bead B (OB = 1 m) translates outward on the rod at a speed of 5 m/s and acceleration 2.5 m/s2 (both quantities with respect to the rod). The Coriolis component of acceleration is

(A)  2.5 m/s2 in +x direction

(B)  100 m/s2 in +x direction

(C)  100 m/s2 in –y direction

(D)  25 m/s2 in + y direction

Answer: (B)

3. A two force member in equilibrium is one in which

(A)  Forces act at two points and forces are collinear

(B)  Forces act at two points and member is always straight

(C)  Forces act at two points but the member is free to carry moment at any point

(D)  Force acts at one point and moment acts at second point

Answer: (A)

4. If the yield point shear stress obtained from the torsion test of a cylindrical specimen is τy, then what is the maximum value of principal strain at yielding? (μ is Poisson’s ratio and E is Young’s modulus)

Answer: (B)

5. If the ratio of Young’s modulus to bulk modulus of a material is 3/2, then the ratio of shear modulus to the Young’s modulus of the material is

(A)  1

(B)  2/5

(C)  1/3

(D)  3/5

Answer: (B)

6. With respect to the plane of maximum shear stress, which of the following statements is INCORRECT?

(A)  The normal stress on this plane is zero.

(B)  The maximum shear stress is equal to the largest of the one half the difference of principal stresses

(C)  The plane of maximum shear stress occurs at 45° to the principal planes.

(D)  The magnitude of the maximum shear stress is equal to the largest of the radius of the Mohr’s circles.

Answer: (A)

7. A simply supported beam of length L is loaded by two symmetrically applied point loads P at L/3 from each support. Both the loads are then shifted to new points which are at a distance L/4 from each support. The bending moments at the mid-section of the beam in both the cases are same. The magnitude of P1 in terms of P is

(A)  P/4

(B)  8P/3

(C)  4P/3

(D)  P/3

Answer: (C)

8. A beam having rectangular cross section is subjected to transverse loading. The ratio of maximum shear stress developed in the beam to the average shear stress is

(A)  1.50

(B)  1.25

(C)  1.33

(D)  1.66

Answer: (A)

Q.9 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

9. During an earthquake, a structure vibrates and the vibration can be assumed to be in simple harmonic motion at 5 Hz. At a measurement point, the RMS value of acceleration is 10 m/s2. The approximate amplitude of motion (in mm) at this point (rounded off to two decimal places) is ___________

Answer: (14.30 to 14.35)

Q.10–Q. 15 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

10. For the state of plane stress shown, the components of normal and shear stresses are given in terms of stress σ and unknown constants m and n. If the normal and shear components of stress on a 45o plane are 2σ and zero, the values of m and n would be:

(A)  m = 1, n = 2

(B)  m = 2, n = 1

(C)  m = 1, n = 1

(D)  m = 2, n = 2

Answer: (C)

11. For a state of plane strain, the normal strains are given by εxx = 1000 × 106, εyy = 200 × 10-6 and the maximum shear strain is γmax = 1000 × 106. The value of shear strain γxy for this strain state is

(A)  600 × 106

(B)  183 × 106

(C)  1000 × 106

(D)  800 × 106

Answer: (A)

12. A thin cylinder (closed at its ends) of radius r and thickness t ( r ≫ t ) is subjected to internal pressure p. The maximum shear stress in the wall of the cylinder is

(A)  pr/t

(B)  pr/2t

(C)  pr/4t

(D)  3pr/2t

Answer: (B)

13. The truss shown is subjected to a force P. All members of the truss have the same length L. The reaction at A and force in member AB are

Answer: (A)

14. The figure shows a structure with supports. The correct free body diagram when the supports are removed is

Answer: (A)

15. A hammer of mass 1 kg is used to break an almond shell. The velocity time graph of the hammer during the impact duration is shown in the figure. The shape of force time graph is also given, which can be approximated as a triangle. A force of 300 N is required for breaking the shell, while a force of 200 N will not be able to break it, but just introduce a crack. Which one of the following events will happen?

(A)  The almond shell will crack but not break

(B)  The almond shell will not crack.

(C)  The almond shell will break

(D)  Cannot be determined from the given data

Answer: (A)

16. A rigid circular disc of radius 0.2 m and mass 10 kg rolls without slip on the ground at A. The coefficient of static friction μ between ground and disc is 0.7. A torque T of 9 Nm acts on the disc as shown. Given acceleration due to gravity g = 10 m/s2. The friction force (in N) acting on the disc (in integer) is _________

Answer: (30 to 30)

17. A prismatic solid circular rod of diameter d is bent to introduce an offset s = d as shown. The rod is further subjected to an axial load P. If the maximum longitudinal stress at a section A-B in the rod (with offset) is n times the longitudinal stress in the straight rod, the value of n (in integer) would be ________

Answer: (9 to 9)

18. A naturally curved steel beam AB having Young’s modulus 208 GPa, area moment of inertia I = 26.7 cm4 and radius R = 2 m is subjected to a vertical load P = 1000 N at B. The end A at θ = 900 is rigidly fixed. The bending strain energy of the beam (in Nm, rounded off to two decimal places) is ___________

Answer: (56.50 to 56.60)

19. At room temperature of 25°C, a gap of 1 mm exists between the ends of the rods 1 and 2 as shown. Given the cross section area A of the rods is 1500 mm2, Young’s modulus E = 75 GPa and the coefficient of thermal expansion α = 23 × 106/° When the temperature has reached 150°C, the magnitude of normal stress in each of the rods (in MPa, rounded off to two decimal places) is _________

Answer: (90.60 to 90.65)

20. A tube of inner radius 4 cm and outer radius 5 cm can carry a maximum torque of T. This tube is now replaced by a solid circular shaft of the same material. The minimum radius of the solid circular shaft (in cm, rounded off to two decimal places) to carry the same amount of torque T is ___________

Answer: (4.17 to 4.21)

21. In System A, a rectangular block of mass M is centrally supported on a spring of stiffness K as shown. In the System B, the mass is hinged at one of its ends and is supported centrally by the spring. The ratio of natural frequency of System B to that of System A (rounded off to two decimal places) is __________

Answer: (0.80 to 0.90)

22. A coronavirus droplet of mass 1 microgram ejects from the mouth of a patient with a velocity of 0.7 m/s and travels through air. The gravitational force experienced by it can be neglected due to the buoyancy effect. However, the droplet experiences air drag force proportional to its velocity and the drag coefficient is given as 1.0 μN-s/m. The distance travelled by the droplet before its velocity drops to 10% of its initial velocity (in m, rounded off to two decimal places) is _____________.

Answer: (0.00 to 0.01)

Thermodynamics (XE-E)

Q.1 – Q.7 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. A refrigerator working on a reversed Carnot cycle has a Coefficient of Performance (COP) of 4. If it works as a heat pump and consumes work input of 1 kW, the heating effect will be:

(A)  1 kW

(B)  4 kW

(C)  5 kW

(D)  6 kW

Answer: (C)

2. The liquid phase of a pure substance is termed as _________, if its temperature is lower than the saturation temperature corresponding to its pressure P.

(A)  super-heated liquid

(B)  sub-cooled liquid

(C)  metastable liquid

(D)  flashing liquid

Answer: (B)

3. Two air streams of mass flow rates ṁ 1 and ṁ 2 enter a mixing chamber and exit after perfect mixing. The corresponding temperatures of the inlet streams are T1 and T2, respectively. Heat loss rate from the mixing chamber to the surrounding is Q̇. Assume that the process is steady, specific heat capacity is constant, and air behaves as an ideal gas. Identify the correct expression for the final exit temperature T3 after mixing. The mass specific heat capacities of the gas at constant volume and constant pressure are cv and cp, respectively. Neglect the bulk kinetic and potential energies of the streams.

Answer: (C)

4. If

h is the mass specific enthalpy,

s is the mass specific entropy,

P is the pressure,

T is the temperature,

CV is the mass specific heat at constant volume,

CP is the mass specific heat at constant pressure,

β is the coefficient of thermal expansion,

v is the mass specific volume,

κ is the isothermal compressibility,

then the partial derivative   

Answer: (D)

5. If

v is the mass specific volume,

s is the mass specific entropy,

P is the pressure,

T is the temperature,

then using Maxwell relations,  

Answer: (B)

6. A closed system consists of a solution of liquid water and ethanol in equilibrium with its vapours. Using the Gibbs phase rule, the degree of freedom of the system is:

(A)  0

(B)  1

(C)  2

(D)  3

Answer: (C)

7. For a real gas passing through an insulated throttling valve, the outlet temperature of the gas __________ with respect to the inlet temperature.

(A)  is always higher

(B)  is always lower

(C)  may be higher, lower or same

(D)  is always same

Answer: (C)

Q.8 Multiple Select Question (MSQ), Carry ONE mark each (no negative marks).

8. Atmospheric air with Dry Bulb Temperature (DBT) of 24°C and Relative Humidity of 35%, entering in a circular duct (assume no pressure drop in the duct) is heated by an electrical resistance arrangement inside the duct. The DBT of air measured at the outlet of the duct is equal to 30°C. Considering the flow to be steady, which of the following statement(s) is (are) correct as regards to the outlet air, with respect to the inlet air?

(A)  There is no change in the Relative Humidity

(B)  There is no change in the Dew Point Temperature

(C)  There is no change in the Specific Humidity

(D)  There is no change in the Specific Enthalpy

Answer: (B; C)

Q.9 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

9. A cylinder of volume 1 m3 contains a mixture of CO2 (20% by mol) and O2 (80% by mol) at 100 kPa and 300 K. This cylinder is connected to a 1 MPa pressure line carrying N2 at 300 K. The cylinder is filled isothermally till the pressure of gas mixture inside it becomes 500 kPa, and then the filling is stopped. The amount of N2 gas that has entered the cylinder is _________ (in mole, 2 decimal places).

The universal gas constant is 8.3145 J/(mol K).

Answer: (159.00 to 162.00)

Q.10 – Q. 13 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

10. The saturation pressure Psat of a pure liquid is represented by an equation of the form:

ln Psat = A – (B/T),

where, A and B are constants, and T is the absolute temperature. For this substance, which of the following expression for specific entropy difference between the saturated vapour and the saturated liquid phase (sfg) is correct?

Note: Subscripts f and g refer to saturated liquid and saturated vapour phases, respectively, and vfg is the specific volume difference between the saturated vapour and the saturated liquid phases.

Answer: (B)

11. For a refrigeration cycle, the ratio of actual COP to the COP of a reversible refrigerator operating between the same temperature limits is 0.8. The condenser and evaporator temperatures are 51°C and −30°C, respectively. If the cooling capacity of the plant is 2.4 kW, then the power input to the refrigerator is:

(COP: Coefficient of Performance)

(A)  1.00 kW

(B)  1.33 kW

(C)  1.25 kW

(D)  2.08 kW

Answer: (A)

12. Two identical pressure cookers, Cooker A and Cooker B, each having a total internal capacity of 6 litres are available. Cooker A is filled with 2 litres of liquid water at 110°C and Cooker B is filled with 4 litres of liquid water at 110°C. The remaining space in both the cookers is filled with saturated water vapour in equilibrium with the liquid water. If g represents the specific Gibbs free energy, and subscripts v and l represent the saturated vapour and the saturated liquid phases, respectively, which of the following expressions is correct?

(A)  gv,A > gl,B

(B)  gv,A < gl,B

(C)  gv,A = gl,B

(D)  gl,B = 2 gl,A

Answer: (C)

13. Four different Entropy (S) – Temperature (T) diagrams, representing liquid to vapour phase transition process of a pure substance in a closed system under constant pressure are shown. The diagram, which correctly represents the process, is:

(A)  1

(B)  2

(C)  3

(D)  4

Answer: (A)

Q.14 – Q. 22 Numerical Answer Type (NAT), carry TWO marks each (no negative marks).

14. Air having a mass flow rate of 2 kg/s enters a diffuser at 100 kPa and 30°C, with a velocity of 200 m/s. Exit area of the diffuser is 400 cm2 while the exit temperature of the air is 45°C. The rate of heat loss from the diffuser to the surrounding is 8 kJ/s. The pressure at the diffuser exit is ____________ kPa (2 decimal places).

For air, the characteristic gas constant is 287 J/(kgK) and specific heat capacity at constant pressure is 1005 J/(kgK). Assume air to be an ideal gas and the flow in the diffuser is steady.

Answer: (100.79 to 111.39)

15. For the Refrigerant R-134 (at 1 MPa and 50°C), the difference between the specific volume computed by assuming it to be an ideal gas and its actual specific volume is: videal − vactual = 4.529 × 10−3 m3/kg. If the compressibility factor associated with this state is Z = 0. 84, then vcom − vactual =_________ ×10−3 m3/kg (3 decimal places).

Here vcom is the specific volume calculated using the compressibility factor.

For Refrigerant R-134 (at 1 MPa and 50°C):

The characteristic gas constant: 0.0815 kJ/(kgK), The critical pressure and temperature are, respectively, Pcr = 4.059 MPa and Tcr = 374.2 K.

Answer: (0.300 to 0.330)

16. A mixture of air and water vapour enters a steady-flow adiabatic saturator at 50°C and 100 kPa. It leaves the saturator in a completely saturated state at temperature of 25°C and pressure of 100 kPa. Liquid water enters the saturator at 25°C. If air is considered to be an ideal gas, with constant specific heat capacity, the relative humidity of the air entering the saturator is ______ % (1 decimal place).

Use the following data:

at 25°C hf = 104.87 kJ/kg, hg = 2547.17 kJ/kg, Psat=3.161 kPa

at 50°C hf = 209.31 kJ/kg, hg = 2592.06 kJ/kg, Psat=12.335 kPa

Specific heat capacity of air at constant pressure CP=1.005 kJ/(kgK)

Answer: (12.1 to 13.0)

17. Air at a pressure of 1 MPa and 300 K is flowing in a pipe. An insulated evacuated rigid tank is connected to this pipe through an insulated valve. The volume of the tank is 1 m3. The valve is opened and the tank is filled with air until the pressure in the tank is 1 MPa. Subsequently, the valve is closed. Consider air to be an ideal gas and neglect bulk kinetic and potential energy. The final temperature of air in the tank is _______ K (1 decimal place).

Specific heat capacity of air at constant pressure CP=1.005 kJ/(kgK) and characteristic gas constant for air = 0.287 kJ/(kgK)

Answer: (418.0 to 422.0)

18. A cylinder of volume 0.1 m3 is filled with 100 mol of propane (C3H8) at 2 MPa. If propane is assumed to obey the van der Waals equation of state, then its temperature is ______ K (1 decimal place).

The van der Waals constants for propane are: a = 939. 2 kPa (m3/kmol)2 and b = 0.0905 m3/kmol. The universal gas constant is 8.3145 J/(mol K).

Answer: (320.0 to 323.0)

19. A frictionless piston cylinder device contains 1 kg of an ideal gas. The gas is compressed according to Pv3 = constant (P is pressure and v is mass specific volume), from 100 kPa, 250 K, till it reaches a temperature of 500 K. The heat transfer from the piston cylinder device to its surroundings is __________ kJ (2 decimal places).

The characteristic gas constant is 287 J/(kgK) and the ratio of specific heat capacities is 1.4.

Answer: (56.80 to 62.78)

20. A 0.8 m3 insulated rigid tank contains 1.5 kg of an ideal gas at 100 kPa. Electric work is done on the system until the pressure in the tank rises to 135 kPa. The loss in availability (exergy) associated with the process is __________ kJ (2 decimal places).

For the ideal gas, the characteristic gas constant is 188.9 J/(kgK) and the specific heat capacity at constant volume is 680 J/(kgK). The temperature of the dead state is 298 K.

Answer: (86.66 to 95.78)

21. A rigid tank contains 1.0 kg of pure water consisting of liquid and vapour phases in equilibrium at 10 bar. If the liquid and vapour phase each occupies one half of the volume of the tank, then the net enthalpy of the contents of the tank is ________ kJ (1 decimal place).

For saturated liquid and vapour at 10 bar, the thermodynamic data table provides the following values:

vf = 1. 127 × 10−3 m3/kg, vg = 194. 3 × 10−3 m3

hf = 762. 6 kJ/kg, hg = 2776. 2 kJ/kg

/kg,

Answer: (773.0 to 775.0)

22. An air-standard Diesel cycle with a compression ratio of 16 takes air at 1 bar and 300 K. If the maximum temperature in the cycle is 2100 K, then the thermal efficiency of the cycle is _______ % (1 decimal place). The ratio of the specific heat capacities of air is 1.4.

Answer: (59.0 to 61.0)

Polymer Science and Engineering (XE-F)

Q.1 – Q.9 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Linear low density polyethylene (LLDPE) is a copolymer of ethylene and a small fraction of _______.

(A)  butadiene

(B)  isoprene

(C)  butene

(D)  hexadiene

Answer: (C)

2. Binary polymer blends of polypropylene and polyamide 6 are immiscible. From a thermodynamic viewpoint this is due to _________.

(A)  low enthalpy of mixing

(B)  high entropy of mixing

(C)  high enthalpy of mixing

(D)  low entropy of mixing

Answer: (D)

3. Which one of the following is an elastomer?

(A)  Polyamide 6,6

(B)  Poly(ethylene terepthalate)

(C)  Vulcanized polybutadiene

(D)  High density polyethylene

Answer: (C)

4. Compression moulded isotropic polypropylene film exhibits _______ in X-ray diffraction analysis.

(A)  spot pattern

(B)  circular ring pattern

(C)  circular ring and spot pattern

(D)  arc pattern

Answer: (B)

5. Which one of the following is an example of a biodegradable polymer?

(A)  Polyethylene

(B)  Polyamide 6,6

(C)  Polypropylene

(D)  Polylactic acid

Answer: (D)

6. Polymer crystals show a range of melting points in contrast to single melting point of crystals of small molecules, because ________.

(A)  there is an absence of intermolecular interactions

(B)  there is an absence of long range ordering

(C)  the polymer chains are not in thermodynamic equilibrium in a metastable state

(D)  the melting behavior of polymer crystal is independent of sample thermal history

Answer: (C)

7. When the rate of cooling is increased during the solidification process, the glass transition temperature of a polymer ______.

(A)  decreases

(B)  increases

(C)  stays unaltered

(D)  shows a non-monotonic dependence

Answer: (B)

8. Equal and opposite forces of a constant magnitude F are applied at the two ends of a thin elastomeric rod, which is held at a temperature T1 (Tg < T1 < Tm), where Tg and Tm are the glass transition temperature and melting temperature respectively. If the temperature is increased to T2 (Tg < T2 < Tm and T2 > T1), the rod will ____________.

(A)  expand along the loading direction and the transverse direction

(B)  shrink along the loading direction

(C)  remain dimensionally unaltered

(D)  expand only along the loading direction

Answer: (B)

9. The size of a coiled polymer chain in a dilute solution is RG in a good solvent, RI in an ideal solvent and RP in a poor solvent. Select the correct ordering of sizes.

(A)  RG > RI > RP

(B)  RG < RI < RP

(C)  RP > RG > RI

(D)  RP < RG < RI

Answer: (A)

Q.10 – Q. 12 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

10. Match the Additive to its Function.

(A)  P-3, Q-2, R-1, S-4

(B)  P-3, Q-1, R-4, S-2

(C)  P-4, Q-1, R-3, S-2

(D)  P-1, Q-2, R-4, S-3

Answer: (B)

11. Match the polymer processing operation with respect to its typical range of shear rate.

(A)  P-3, Q-4, R-2, S-1

(B)  P-1, Q-3, R-2, S-4

(C)  P-2, Q-4, R-3, S-1

(D)  P-3, Q-2, R-1, S-4

Answer: (A)

12. Shear stress (σ) and shear viscosity (η) are plotted as functions of the shear rate, γ̇, for idealized “solid-like with yielding (1)” and “liquid-like (2)” materials.

Associate the shear stress and viscosity plots with the appropriate material responses.

(A)  P-2, Q-1, R-2, S-1

(B)  P-1, Q-2, R-1, S-2

(C)  P-1, Q-2, R-2, S-1

(D)  P-2, Q-1, R-1, S-2

Answer: (B)

Q.13 – Q. 22 Numerical Answer Type (NAT), carry TWO marks each (no negative marks).

13. The plateau modulus of polystyrene has a value of 0.2 × 106 Pa at 150°C. Given, the density of polystyrene is 1.05 g/cm3, the universal gas constant, R = 8.3 J K1 mol1, and the monomer molecular weight is 104 g/mol. The molecular weight between entanglements (rounded off to the nearest integer) of polystyrene chains is __________ g/mol.

Answer: (18000 to 19000)

14. A unidirectional composite of epoxy and carbon fiber of 50% by volume is made. The elastic modulus of epoxy and carbon fiber are 3.5 GPa and 350 GPa, respectively. The ratio (rounded off to one decimal place) of the modulus of the composite to the matrix modulus is __________.

Answer: (50.4 to 50.6)

15. A single screw extruder is operating at a rotational speed of 2 revolutions per second for the extrusion of a Newtonian polymer under open-discharge conditions (in absence of a die, the pressure drop, ∆p = 0). The extruder has a screw diameter, D = 5 cm, a channel depth, H = 0.4 cm, distance between flights, W = 1 cm, and a helix angle, θ = 20°. Assume the value of π = 3.14. The volumetric flow rate (rounded off to 2 decimal places) is _________ cm3/s.

Answer: (5.00 to 7.00)

16. At 215°C, the viscosity of a polystyrene of molecular weight 250 × 103 g/mol is 8.0 × 103 Pa.s. The critical molecular weight of polystyrene, Mc = 35 × 103 g/mol. For a similar polystyrene of molecular weight 500 × 103 g/mol, the viscosity (rounded off to nearest integer) will be __________ × 103 s.

Answer: (62 to 99)

17. There are two different PTFE polymer specimens of the following density (ρ) and % crystallinity. For PTFE-specimen-1, ρ is 2.144 g/cm3 and % crystallinity is 50. For PTFE- specimen-2, ρ is 2.215 g/cm3 and % crystallinity is 75. Assuming the polymer is pure and defect free, the density (rounded off to 3 decimal places) of 100% amorphous PTFE specimen will be _______ g/cm3.

Answer: (1.980 to 2.040)

18. The behavior of a polymer is described by a Maxwell model consisting of a spring element of modulus 1010 Pa in series with a dashpot of viscosity 1012s. In the solid, 50 s after the sudden application of a fixed strain of 1%, the stress (rounded off to 2 decimal places) will be _________ × 107 Pa.

Answer: (6.00 to 7.00)

19. A particular free radical polymerization process yields a polymer with a number averaged degree of polymerization,  The monomer concentration is doubled and the initiator concentration is increased by four times. Assuming that all rate coefficients and other parameters remain unchanged, the value of  (rounded off to the nearest integer) is ________.

Answer: (100 to 100)

20. A polymer is synthesized from 2 moles of terephthalic acid (molecular weight of the repeat unit, (−OCC6H4CO−), is 132 g/mol), 1 mol of ethylene glycol (molecular weight of the repeat unit, (−OCH2CH2O−), is 60 g/mol), and 1 mol of butylene glycol (molecular weight of the repeat unit, (−O(CH2)4O−), number averaged molecular weight,   (rounded off to the nearest integer) is _______ g/mol.

Answer: (10000 to 10500)

21. A sample of natural rubber (cis-1,4-polyisoprene) is vulcanized such that one of every 240 chain carbon atoms is cross-linked. The formula unit of the isoprene monomer is C5H8 (molecular weight = 68 g/mol). The average molecular weight (rounded off to the nearest integer) between cross-links is ________ g/mol.

Answer: (4000 to 4200)

22. A sample of an oriented semi-crystalline polymer is subjected to uniaxial tensile stress, σ, in an X-ray diffractometer. The wavelength of X-ray radiation (Cu Kα) is λ = 1.542 Å. The position of the (002) peak, which was found initially at a Bragg angle of 37.50° at σ = 0 MPa shifted to 37.45° at σ = 160 MPa. Assuming elastic deformation, the strain (rounded off to three decimal places) in the sample along the direction of applied stress is ________ × 10−3.

Answer: (1.000 to 1.500)

Food Technology (XE-G)

Q.1 – Q.9 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. In a typical bacterial growth curve, the first order kinetics for growth rate is observed in

(A)  Lag phase

(B)  Log phase

(C)  Stationary phase

(D)  Death phase

Answer: (B)

2. Which one of the following microorganism is NOT a causative agent for food borne diseases?

(A)  Campylobacter jejuni

(B)  Clostridium perfingens

(C)  Norovirus

(D)  Borrelia burgdorferi

Answer: (D)

3. Which of the followings is NOT a fermented food product?

(A)  Tofu

(B)  Vinegar

(C)  Sauerkraut

(D)  Tempeh

Answer: (A)

4. The Protein Efficiency Ratio (PER) is defined as

(A)  Percentage of absorbed nitrogen retained in the body

(B)  Weight gain in body mass (in gram) per gram protein intake

(C)  Ratio of essential and non-essential amino acids in a protein

(D)  Percent in vitro digestibility of a protein

Answer: (B)

5. Which one of the following enzymes sequentially releases maltose from starch?

(A)  α−Amylase

(B)  β−Amylase

(C)  Glucoamylase

(D)  Pullulanase

Answer: (B)

6. Which one of the following enzymes is involved in proteolysis of casein in cheese during aging?

(A)  Myrosinase

(B)  Alliinases

(C)  Cathepsin

(D)  Plasmin

Answer: (D)

7. Which one of the following compounds is present in soybean and acts as phytoesterogen?

(A)  Tangeretin

(B)  Lutin

(C)  Quercetin

(D)  Genistein

Answer: (D)

8. Ultra high temperature (UHT) process of pasteurization of milk is achieved by Heating at

(A)  145°F for 30 minutes

(B)  161°F for 15 seconds

(C)  280°F for 2 seconds

(D)  400°F for 15 seconds

Answer: (C)

9. Bittering agent in grape fruit formed after juice extraction under acidic conditions is

(A)  Quinine

(B)  Theobromine

(C)  Isohumulone

(D)  Limonin

Answer: (D)

Q.10–Q. 12 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

10. The conversion of pyruvate to lactic acid in homolactic fermentation is catalyzed by

(A)  Lactate dehydrogenase

(B)  Pyruvate dehydrogenase

(C)  Lactase

(D)  Pyruvate decarboxylase

Answer: (A)

11. Which one of the following statements is INCORRECT with respect to Controlled Atmosphere Package (CAP) and Modified Atmosphere Package (MAP) of agro-produce?

(A)  CAP and MAP limit microbial as well as biochemical activities.

(B)  Gas composition inside a MAP during the storage is continuously monitored and regulated.

(C)  CAP implies a greater degree of precision than MAP in maintaining specific levels of the gas composition.

(D)  Modification of the atmosphere inside a MAP is achieved by natural interplay between respiration of products and permeation of gases through the packaging film.

Answer: (B)

12. Match unit operation in Column I with its application in food processing in Column II.

(A)  P-2, Q-4, R-2, S-I

(B)  P-2, Q-3, R-4, S-1

(C)  P-4, Q-1, R-2, S-3

(D)  P-4, Q-2, R-1, S-3

Answer: (B)

Q.13 – Q.19 Multiple Select Question (MSQ), Carry TWO marks each (no negative marks).

13. Which of the followings are correct pair of GRAS chemical food preservative, affected organism and given food matrix?

(A)  Sodium lactate-Bacteria-Pre-cooked meats

(B)  Caprylic acid-Insects-Cheese wraps

(C)  Dehydroacetic acid-Molds-Squash

(D)  Sodium nitrite-Clostridia-Meat curing preparations

Answer: (A; D)

14. Choose the correct pair of pigment and their corresponding color in given plant product.

(A)  Carotene – Yellow-orange-Peppers

(B)  Betanin – Purple/red-Cactus pear

(C)  Lycopene – Red-Red beets

(D)  Flavanols – Orange-Cauliflower

Answer: (A; B)

15. Which of the following compounds act as anti-nutritional factors?

(A)  Phytate

(B)  Isoflavones

(C)  Trypsin Inhibitor

(D)  Resveratrol

Answer: (A; C)

16. Which of the followings is/are commonly used medium/media in the supercritical fluid extraction of spices and tea?

(A)  Water

(B)  Carbon dioxide

(C)  Dichloromethane

(D)  Carbon dioxide with Ethanol

Answer: (A; B; D)

17. Which of the following expressions represent the Reynolds number of a fluid flowing through a uniform circular cross section pipe?

Answer: (A; B)

18. Which of the following combinations of analytical equipment, property measured and food property are correct?

(A)  Particle size analyzer – particle size distribution – span value

(B)  Texture profile analyzer – morphology – chewiness

(C)  Differential scanning calorimeter – glass transition temperature – degree of caking

(D)  Capillary viscometer – viscosity – sensory

Answer: (A; C)

19. Choose the correct pair(s) of Governing Law and corresponding application(s)

(A)  Hagen Poiseuille law – Pressure drop

(B)  Rittinger’s law – Vapour pressure

(C)  Stefan Boltzmann law – Radiation heat transfer

(D)  Raoult’s law – Size reduction

Answer: (A; C)

Q.20 – Q. 22 Numerical Answer Type (NAT), carry TWO marks each (no negative marks).

20. An orange juice sample is concentrated from 10% to 40% (by weight) total soluble solids in a single effect evaporator with a feed rate of 3600 kg hr1 at 25°C. The evaporator operates at sufficient vacuum to allow the product moisture to evaporate at 55°C. The specific heat of both feed and concentrated juice is 4.0 kJ kg1 °C1. If enthalpy of water vapour at 55°C is 2600 kJ kg1, heat transfer rate through the heating surface area of the evaporator in kilowatt (in integer) will be________.

Answer: (1900 to 1910)

21. Dry air is fed into a tray dryer. The percentage relative humidity of the air leaving the dryer is 60% at 70°C and 101.35 kPa. If, saturated vapour pressure of water at 70°C is 31.2 kPa, the humidity of the air leaving the dryer in kg water per kg dry air (round off to 3 decimal places) will be __________.

(Given : Molecular weight of water and air are 18.02 g mol1 and 28.97 g mol1 respectively)

Answer: (0.135 to 0.150)

22. In a cold storage plant, 5000 kg potato having a constant specific heat capacity of 3.65 kJ kg1 °C1 are cooled from 28°C to 2°C in 24 hours. The heat of respiration of potato per 24 hour is 3.12 kJ kg1 during the storage. Assuming the efficiency of the storage plant to be 70%, the capacity of the plant in ton of refrigeration (round off to 2 decimal places) is __________.

(Given: 1 ton of refrigeration = 3.517 kilowatt)

Answer: (2.20 to 2.40)

Atmospheric and Oceanic Sciences (XE-H)

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Western Boundary Current in the ocean is primarily due to

(A)  Ekman pumping.

(B)  rotation of the earth.

(C)  river water forcing.

(D)  ocean floor topography.

Answer: (B)

2. The relevant nondimensional number in deciding deepening of the thermocline driven by instability of ocean currents is

(A)  Rossby number.

(B)  Reynolds number.

(C)  Richardson number.

(D)  Ekman number.

Answer: (C)

3. During July-August, the highest number of monsoon low pressure systems form over

(A)  Arabian Sea.

(B)  Bay of Bengal.

(C)  South India.

(D)  Himalayan foothills.

Answer: (B)

4. CO2 concentration in the Earth’s atmosphere is increasing because 50% of the annual anthropogenic emissions are retained in the atmosphere. If nations agree to reduce annual CO2 emissions by one Giga ton every year starting from 2021, then in which year will the CO2 concentration in the atmosphere stop rising due to anthropogenic emissions?

Take the anthropogenic CO2 emissions in 2020 as 40 Giga tons.

(A)  2020

(B)  2050

(C)  2060

(D)  2100

Answer: (C)

5. The figure shows a schematic of Indian Ocean surface circulation. This pattern is representative of the circulation in which month of the year?

(A)  January

(B)  July

(C)  May

(D)  November

Answer: (C)

Q.6–Q. 7 Multiple Select Question (MSQ), Carry ONE mark each (no negative marks).

6. Over the open ocean, if the air sea temperature difference is zero, then which of the following statements is/are always true?

(A)  Sensible heat flux is zero.

(B)  Latent heat flux is zero.

(C)  Momentum flux is zero.

(D)  Net energy flux is zero.

Answer: (A)

7. The psychrometric equation, which is useful in measuring humidity, is derived assuming the following process(es).

(A)  Isobaric process

(B)  Isothermal process

(C)  Adiabatic process

(D)  Isentropic process

Answer: (A; C)

Q.8 – Q.9 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

8. The water vapour mixing ratio of an air parcel increases from 10 g kg1 to 20 g kg1 at a constant pressure of 1010 hPa and temperature of 300 K. The change in virtual temperature is _____ K (to one decimal place).

Answer: (1.7 to 1.9)

9. The Ekman layer thickness, if turbulent diffusivity is 0.01 m2 s1, is _____ m. Take Coriolis parameter to be 104s1. Calculate to the nearest integer.

Answer: (0 to 11)

Q.10 – Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

10. The figure shows vertical variation of two chemicals P and Q measured in the Pacific Ocean. Identify the correct combination showing (P, Q) pair from the list below.

(A)  Oxygen, Nitrate

(B)  Oxygen, Neon

(C)  Nitrate, Oxygen

(D)  Neon, Nitrate

Answer: (C)

Q.11 –Q. 15 Multiple Select Question (MSQ), Carry TWO marks each (no negative marks).

11. Consider tropical high-level clouds and low-level stratus clouds with bases at 12 km and 1 km above the surface of the Earth, respectively. Which of the following statement(s) is/are correct?

(A)  High clouds are composed of ice crystals.

(B)  High clouds have a larger albedo than low clouds.

(C)  High clouds have a net warming effect on climate.

(D)  Low clouds have a net warming effect on climate.

Answer: (A; C)

12. Which of the following statement(s) is/are correct in the context of Sverdrup transport?

(A)  Sverdrup transport is always in the meridional direction.

(B)  Sverdrup transport is always orthogonal to the wind direction.

(C)  Sverdrup transport depends on the variation of the Coriolis parameter.

(D)  Sverdrup transport is only due to ageostrophic currents.

Answer: (A; C)

13. Which of the following statement(s) is/are true with regard to the Hadley circulation?

(A)  The ascending branch is narrower than its descending branch.

(B)  Thunderstorms are more frequent in the subsiding region of the Hadley cell than in its ascending region.

(C)  The lower level winds between the ascending and descending branches of the Hadley cell are north-westerly.

(D)  Latent heat is transported from the subsiding to the ascending region of the Hadley cell.

Answer: (A; D)

14. Which of the following statement(s) is/are true about the ocean circulation?

(A)  Large-scale ocean surface currents are driven by winds.

(B)  Cold, dense and salty water forms in the North Atlantic Ocean.

(C)  Upwelling currents bring warm nutrient deficient water to the surface of the ocean.

(D)  Thermohaline circulation does not transport energy in the meridional direction.

Answer: (A; B)

15. Coral reefs are found primarily in tropical and subtropical shallow seawaters. Which of the following statement(s) is/are correct?

(A)  Corals require plenty of sunlight for photosynthesis and sunlight is abundant in the tropical and subtropical latitudes.

(B)  Corals grow optimally in seawater unsaturated in carbonate, which is found only in the tropical and subtropical oceans.

(C)  Corals grow optimally in fresh low-salinity water.

(D)  Corals grow optimally in water temperatures between 23°C and 29°C.

Answer: (A; D)

Q.16 – Q. 22 Numerical Answer Type (NAT), carry TWO marks each (no negative marks).

16. In an incompressible fluid, the horizontal divergence is −0.01 s1. Then, the vertical velocity at 50 m above a flat surface is ____ m s1. Round off to one decimal place.

Answer: (0.4 to 0.6)

17. In an atmosphere, temperature (T) decreases linearly with height above the ground (z), i.e., T(z) = To – γz, where γ is a constant. Surface pressure is 900 hPa. If the atmosphere is at rest, then the value of z at which the pressure decreases to half of that at the surface is _____ m (round off to the nearest integer).

Take acceleration due to gravity g = 10 m s2, gas constant R = 300 J kg1 K1 To = 300 K and γ = 1/30 K m1, and the atmosphere behaves as an ideal gas.

Answer: (4450 to 4550)

18. In a local Cartesian system, a zonal jet has a form u(y) = uo (1 – y2/L2), for −L ≤ y ≤ L. Here, y is the meridional distance measured from the axis of the jet and is positive northward. The vertical component of vorticity of this flow at y=L/2 is _____ s1. Round off to 3 decimal places.

Take uo = 50 m s1 and L = 5 km.

Answer: (0.009 to 0.011)

19. An eastward flow with a speed of 10 m s1 goes from station M to station N, which are separated by a distance of 1 km. The temperature at station N is always higher than that at station M by 10 K. The absolute change in temperature due to advection at the mid-point between the stations in 50 s is _______ K (round off to nearest integer).

Answer: (4 to 6)

20. Suppose, because of the doubling of atmospheric CO2 concentration, an ocean water column receives an additional net energy input of 4 Wm2. If the entire water column of depth 1 km heats up uniformly, the water temperature will increase by 1 K in ____ years (round off to the nearest integer).

Assume all the additional heat added is retained and not lost. Take density of seawater = 1000 kg m3; specific heat capacity of seawater = 4200 J kg1K1.

Answer: (32 to 34)

21. Consider a layer of atmosphere between 5 and 6 km height. The downwelling longwave radiation at 5 and 6 km is 240 and 230 Wm2, respectively. The upwelling longwave radiation at these heights is 260 and 240 Wm2, respectively. The longwave heating rate in this layer is___ K per day. (Round off to one decimal place.)

Take the average density of air in this layer to be 0.5 kg m3; Specific heat capacity of air at constant pressure = 1000 J kg1 K1.

Answer: (1.6 to 1.8)

22. A spherical asteroid, revolving around the sun in a circular orbit, is in radiative balance. Suddenly, the asteroid enters the shadow of a planet and solar radiation is cut off. Assuming that the asteroid emits as a blackbody in the longwave regime, the time taken to reduce the average temperature of the asteroid by 0.5 K is ______ seconds (round off to the nearest integer). Ignore the temporal change in radiation emitted by the asteroid during this cooling period.

The physical properties of the asteroid are: diameter = 2 m, density = 3000 kg m−3, specific heat = 2000 J kg-1 K−1 and albedo = 0.8 in shortwave radiation. Take the solar constant = 500 W m−2, Stefan-Boltzmann constant = 5.67 x 10-8 W m−2 K−4.

Answer: (39990 to 40010)

GATE Exam 2021 Textile Engineering and Fibre Science (TF) Question Paper With Answer Key

GATE-2021

TF: Textile Engineering and Fibre Science

GA- General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. The ratio of boys to girls in a class is 7 to 3.

Among the options below, an acceptable value for the total number of students in the class is:

(A)  21

(B)  37

(C)  50

(D)  73

Answer: (C)

2. A polygon is convex if, for every pair of points, P and Q belonging to the polygon, the line segment PQ lies completely inside or on the polygon.

Which one of the following is NOT a convex polygon?

Answer: (A)

3. Consider the following sentences:

(i) Everybody in the class is prepared for the exam.

(ii) Babu invited Danish to his home because he enjoys playing chess.

Which of the following is the CORRECT observation about the above two sentences?

(A)  (i) is grammatically correct and (ii) is unambiguous

(B)  (i) is grammatically incorrect and (ii) is unambiguous

(C)  (i) is grammatically correct and (ii) is ambiguous

(D)  (i) is grammatically incorrect and (ii) is ambiguous

Answer: (C)

4. A circular sheet of paper is folded along the lines in the directions shown. The paper, after being punched in the final folded state as shown and unfolded in the reverse order of folding, will look like _______.

Answer: (A)

5. _____ is to surgery as writer is to ________

Which one of the following options maintains a similar logical relation in the above sentence?

(A)  Plan, outline

(B)  Hospital, library

(C)  Doctor, book

(D)  Medicine, grammar

Answer: (C)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

6. We have 2 rectangular sheets of paper, M and N, of dimensions 6 cm × 1 cm each. Sheet M is rolled to form an open cylinder by bringing the short edges of the sheet together. Sheet N is cut into equal square patches and assembled to form the largest possible closed cube. Assuming the ends of the cylinder are closed, the ratio of the volume of the cylinder to that of the cube is _______

(A)  π/2

(B)  3/π

(C)  9/π

(D)  3π

Answer: (C)

7. 

Details of prices of two items P and Q are presented in the above table. The ratio of cost of item P to cost of item Q is 3:4. Discount is calculated as the difference between the marked price and the selling price. The profit percentage is calculated as the ratio of the difference between selling price and cost, to the cost

The discount on item Q, as a percentage of its marked price, is ______

(A)  25

(B)  12.5

(C)  10

(D)  5

Answer: (C)

8. There are five bags each containing identical sets of ten distinct chocolates. One chocolate is picked from each bag.

The probability that at least two chocolates are identical is ___________

(A)  0.3024

(B)  0.4235

(C)  0.6976

(D)  0.8125

Answer: (C)

9. Given below are two statements 1 and 2, and two conclusions I and II.

Statement 1: All bacteria are microorganisms.

Statement 2: All pathogens are microorganisms.

Conclusion I: Some pathogens are bacteria.

Conclusion II: All pathogens are not bacteria.

Based on the above statements and conclusions, which one of the following options is logically CORRECT?

(A)  Only conclusion I is correct

(B)  Only conclusion II is correct

(C)  Either conclusion I or II is correct.

(D)  Neither conclusion I nor II is correct.

Answer: (C OR D)

10. Some people suggest anti-obesity measures (AOM) such as displaying calorie information in restaurant menus. Such measures sidestep addressing the core problems that cause obesity: poverty and income inequality.

Which one of the following statements summarizes the passage?

(A)  The proposed AOM addresses the core problems that cause obesity.

(B)  If obesity reduces, poverty will naturally reduce, since obesity causes poverty.

(C)  AOM are addressing the core problems and are likely to succeed.

(D)  AOM are addressing the problem superficially.

Answer: (D)

TF: Textile Engineering and Fibre Science (TF)

Q.1 – Q.13 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Let the function f(x, y) be defined as 

Then  is equal to

(A)  √2

(B)  √3

(C)  0

(D)  1

Answer: (B)

2. If a continuous random variable X has the following probability density function  then the value of k is

(A)  1

(B)  2

(C)  3

(D)  4

Answer: (C)

3. The smallest positive real number λ, for which the following problem

y′′(x) + λ y(x) = 0,

y′(0) = 0, y(1) = 0

has non-zero solution, is

(A)  π2

(B)  π2/2

(C)  π2/4

(D)  π2/8

Answer: (C)

4. The gummy substance present in raw silk fibre is

(A)  Serine

(B)  Fibroin

(C)  Keratin

(D)  Sericin

Answer: (D)

5. The technique used for producing viscose rayon is

(A)  Melt spinning

(B)  Wet spinning

(C)  Dry spinning

(D)  Dry-jet wet spinning

Answer: (B)

6. The yarn manufacturing technology that uses perforated drums for twisting is

(A)  Ring spinning

(B)  Rotor spinning

(C)  Friction spinning

(D)  Air-jet spinning

Answer: (C)

7. In roving frame, the distance between top and bottom aprons at the exit point is maintained by

(A)  Spacer

(B)  Trumpet

(C)  Condenser

(D)  Pressure-bar

Answer: (A)

8. Fabric structure related to weft knitting is

(A)  Locknit

(B)  Reverse locknit

(C)  Double tricot

(D)  1×1 Rib

Answer: (D)

9. The nonwoven technology which uses high-pressure water jets is

(A)  Needlepunching

(B)  Spunlacing

(C)  Spunbonding

(D)  Meltblowing

Answer: (B)

10. Cotton fibre length variation can be expressed by

(A)  Uniformity index

(B)  Limit irregularity

(C)  U%

(D)  Index of irregularity

Answer: (A)

11. A high value of drape coefficient indicates

(A)  Limp fabric

(B)  Stiff fabric

(C)  Compressible fabric

(D)  Smooth fabric

Answer: (B)

12. The process for removal of protruding fibres from fabric surface is

(A)  Desizing

(B)  Scouring

(C)  Souring

(D)  Singeing

Answer: (D)

13. Dimethylol dihydroxy ethylene urea (DMDHEU) is a

(A)  Crease-resist agent

(B)  Flame retardant

(C)  Softener

(D)  Soil repellent

Answer: (A)

Q.14 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

14. Suppose  is a solution of the following initial value problem of the wave equation utt = 9 uxx, u(x, 0) = g(x), ut(x, 0) = 0. Then the value of c2 is ___________.

Answer: (9 to 9)

15. If the numerical solution of the initial value problem  is obtained by the Euler’s method with step size of 0. 2, then the value of y(0. 4), (rounded off to two decimal places), is __________.

Answer: (0.98 to 1.10)

16. Assuming the atomic mass of H=1, C=12, N=14 and O=16, the molecular mass of a repeat unit of Nylon 6 fibre is ______________.

Answer: (113 to 113)

17. A textile filament records a tensile stress of 0.3 GPa at a tensile strain of 0.04. Assuming Hookean behavior, the tensile modulus (GPa) of the filament, (rounded off to one decimal place), is ___________.

Answer: (7.5 to 7.5)

18. Number of fibres, each of 40 mm length and 0.16 tex fineness, in a tuft of 24 mg mass is __________.

Answer: (3745 to 3755)

19. Twist (turns per inch) of a cotton yarn of 36 Ne count produced with a twist multiplier of 3.5 inch−1Ne−0.5 is __________.

Answer: (21 to 21)

20. In winding, if traverse speed and package surface speed are the same, the angle of wind (in degree) is ________.

Answer: (45 to 45)

21. During air-jet weft insertion, if the diameter of the yarn increases by 20 % then the percentage increase in drag force acting on the yarn would be ___________.

Answer: (20 to 20)

22. If the ratio of the linear densities (denier) of two circular fibers is 3, the corresponding ratio of their diameters, (rounded off to two decimal places), is _______.

Answer: (1.70 to 1.75)

23. If the sample size (n) is 25 and the standard deviation (σ) of population is 2, then the standard error (SE) of sample mean, (rounded off to one decimal place), is _______.

Answer: (0.4 to 0.4)

24. The wet expression for a padding mangle is set at 80 %. If the add-on of a flame retardant chemical required on the fabric is 2 % then the concentration (g/L) of the chemical in the pad bath is ________.

Answer: (25 to 25)

25. Assuming Beer-Lambert law is applicable for dilute solutions, if the molar concentration of dye in the solution is doubled then the percentage increase in absorbance would be __________.

Answer: (100 to 100)

Q.26 – Q.41 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

26. The value of a, for which the following system of equations

2x + y + 3z = a, x + z = 2,         y + z = 2

is consistent, is

(A)  6

(B)  4

(C)  3

(D)  2

Answer: (A)

27. If the function f(x, y) is defined by  then

(A)  Neither (0, 0) nor (1, 1) is a critical point

(B)  (0, 0) is a critical point but (1, 1) is NOT a critical point

(C)  (0, 0) is NOT a critical point but (1, 1) is a critical point

(D)  (0, 0) and (1, 1) are both critical points

Answer: (D)

28. Determine the correctness or otherwise of the following Assertion [a] and Reason [r]

Assertion: Draw texturing of isotactic polypropylene (POY) at a relatively high speed is possible despite high crystallinity of the feeder yarn.

Reason: Isotactic polypropylene (POY) has majorly smectic mesomorphic phase.

(A)  Both [a] and [r] are true and [r] is the correct reason for [a]

(B)  Both [a] and [r] are true but [r] is not the correct reason for [a]

(C)  Both [a] and [r] are false

(D)  [a] is true but [r] is false

Answer: (A)

29. Group I gives a list of fibres and Group II contains their applications. Match the fibre with its application.

(A)  P-1, Q-4, R-2, S-3

(B)  P-4, Q-3, R-1, S-2

(C)  P-4, Q-2, R-1, S-3

(D)  P-1, Q-3, R-4, S-2

Answer: (B)

30. Techniques used for determination of orientation in fibres from amongst the followings are

P Birefringence measurement

Q Scanning electron microscopy

R X-ray diffraction

S Differential scanning calorimetry

(A)  P and Q

(B)  P and R

(C)  Q and R

(D)  Q and S

Answer: (B)

31. In a modern high performance blowroom line, the correct sequence of machines is

(A)  Automatic bale opener → Blender → Coarse cleaner → Fine cleaner

(B)  Automatic bale opener → Blender → Fine cleaner → Coarse cleaner

(C)  Automatic bale opener → Coarse cleaner → Fine cleaner → Blender

(D)  Automatic bale opener → Coarse cleaner → Blender → Fine cleaner

Answer: (D)

32. As compared to cylinder, doffer has

(A)  Lower rotational speed and lower wire point density

(B)  Lower rotational speed and higher wire point density

(C)  Higher rotational speed and lower wire point density

(D)  Higher rotational speed and higher wire point density

Answer: (A)

33. Assuming no fibre loss in draw frame, if draft is equal to doubling then the delivered sliver, as compared to fed sliver, will exhibit

(A)  Decreased mass variation and higher linear density

(B)  Increased mass variation and lower linear density

(C)  Improved fibre orientation without change in linear density

(D)  Poor fibre orientation without change in linear density

Answer: (C)

34. Group I gives a list of loom motions and Group II contains loom systems. Match the motion from Group I with the corresponding system from Group II.

(A)  P-1, Q-3, R-4, S-2

(B)  P-4, Q-3, R-2, S-1

(C)  P-4, Q-3, R-1, S-2

(D)  P-3, Q-4, R-1, S-2

Answer: (C)

35. Group I gives a list of terms related to woven fabrics and Group II contains equivalent terms related to knitted fabrics. Match the term from Group I with the equivalent term from Group II.

(A)  P-3, Q-1, R-4, S-2

(B)  P-3, Q-1, R-2, S-4

(C)  P-1, Q-3, R-2, S-4

(D)  P-1, Q-3, R-4, S-2

Answer: (B)

36. Determine the correctness or otherwise of the following Assertion [a] and Reason [r]

Assertion: In shuttle loom, late shedding is preferred for filament weaving.

Reason: In late shedding, the timing of shed dwell matches with the timing of shuttle travel through the shed, and therefore, it minimises the rubbing of warp yarns.

(A)  Both [a] and [r] are true and [r] is the correct reason for [a]

(B)  Both [a] and [r] are true and [r] is not the correct reason for [a]

(C)  Both [a] and [r] are false

(D)  [a] is true but [r] is false

Answer: (A)

37. The typical shapes of comb sorter diagram and fibrogram of polyester fibres of equal cut length will be

(A)  Triangular and rectangular respectively

(B)  Rectangular and triangular respectively

(C)  Rectangular and S-shaped respectively

(D)  S-shaped and triangular respectively

Answer: (B)

38. In Classimat system, the yarn fault H2, as compared to yarn fault C3, is

(A)  Thicker and longer

(B)  Thicker and shorter

(C)  Thinner and longer

(D)  Thinner and shorter

Answer: (C)

39. Determine the correctness or otherwise of the following Assertion [a] and Reason [r]

Assertion: Application of an optical brightening agent makes the white fabrics appear brighter.

Reason: Optical brightening agents absorb energy in the visible region and radiate back in the UV region.

(A)  Both [a] and [r] are true and [r] is the correct reason for [a]

(B)  Both [a] and [r] are true and [r] is not the correct reason for [a]

(C)  Both [a] and [r] are false

(D)  [a] is true but [r] is false

Answer: (D)

40. Determine the correctness or otherwise of the following Assertion [a] and Reason [r]

Assertion: Nylon is dyed with acid dyes in the acidic medium.

Reason: Nylon assumes positive charge in the acidic medium and thus, attracts the negatively charged acid dye molecules.

(A)  Both [a] and [r] are true and [r] is the correct reason for [a]

(B)  Both [a] and [r] are true and [r] is not the correct reason for [a]

(C)  Both [a] and [r] are false

(D)  [a] is true but [r] is false

Answer: (A)

41. Determine the correctness or otherwise of the following Assertion [a] and Reason [r]

Assertion: Discharge printing of dyed polyester fabric is not possible.

Reason: The discharging agents damage the polyester fibres significantly.

(A)  Both [a] and [r] are true and [r] is the correct reason for [a]

(B)  Both [a] and [r] are true and [r] is not the correct reason for [a]

(C)  Both [a] and [r] are false

(D)  [a] is true but [r] is false

Answer: (C)

Q.42 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

42. If 3 and 6 are eigenvalues of the matrix  then the value of μ is _______.

Answer: (5 to 5)

43. If y(x) is a solution of x2y′′ − 4 x y ′ + 6 y 0,   y(−1) = 1,        y ′ (−1) = 0. Then the value of y(2) is _______.

Answer: (28 to 28)

44. In melt spinning, the mass throughput rate of polymer is 210 g/min, the winding speed is 3000 m/min, and the linear density of the yarn produced is 200 denier. The effective draw ratio, (rounded off to two decimal places), is___________.

Answer: (3.00 to 3.30)

45. The molecular weight (M) of a polymer is determined from Mark-Houwink Equation by using coefficient K = 11.5×10−3 ml/g and exponent a = 0.73. If the measured intrinsic viscosity [η] of the solution is 6.0×102 ml/g then the value of M×10−6, (rounded off to two decimal places), is _________.

Answer: (2.70 to 3.10)

46. A roving of 2 Ne count is fed to a ringframe set with a mechanical draft of 30. If the length of the drafted strand delivered from the nip of the front rollers is reduced by 3 % due to twist then the count (Ne) of the yarn, (rounded off to one decimal place), is ___________.

Answer: (58.0 to 58.4)

47. In a 3 over 3 drafting arrangement, the diameter of all bottom rollers is 28 mm. The back zone draft is 1.3 and the front zone draft is 6. If the back bottom roller is eccentric then the wavelength (mm) of the resulting fault in the drawn sliver, (rounded off to two decimal places), is ___________.

Answer: (685.00 to 687.00)

48. For a given woven fabric, fractional cover is 0.5 for both warp and weft. The fractional cover of the fabric, (rounded off to two decimal places), is _________.

Answer: (0.75 to 0.75)

49. For a shuttle loom, producing plain woven fabric, if each of the dwell periods of the shedding cam corresponds to one-third of crank shaft rotation, the sum of the two dwell periods of the cam (in degree) is _______.

Answer: (120 to 120)

50. If the moisture regain (%) and moisture content (%) of a fibre are the same then the value of moisture regain (%) is _______.

Answer: (0 to 0)

51. Mass of 120 yards of cotton yarn is 3 g. The count (Ne) of yarn, (rounded off to one decimal place), is __________.

Answer: (21.0 to 22.0)

52. A woven fabric with areal density of 300 g/m2 is tested by strip tensile test method, keeping the specimen width as 5 cm and gauge length as 25 cm. If the breaking load is 900 N, the tenacity (cN/tex) of the fabric is __________.

Answer: (6 to 6)

53. A 50 tex yarn with mass CV of 12.5 % is produced from staple polyester fibres each of 4.5 denier fineness. The index of irregularity of the yarn, (rounded off to two decimal places), is ____________.

Answer: (1.25 to 1.25)

54. A counter-flow heat exchanger is attached to a stenter for waste heat recovery.

Consider the following data:

Ambient temperature                                                         : 30°C

Temperature of exhaust from stenter                             : 150 °C

Temperature of exhaust at exit of heat exchanger       : 100°C

Specific heat of exhaust                                                     : 0.42 kcal·deg−1 ·kg−1

Specific heat of air                                                              : 0.24 kcal·deg−1 ·kg−1

At steady state, if the mass flow rates of the exhaust gas and the incoming air are the same, assuming heat loss as zero, the temperature (°C) of the air at the exit of the heat exchanger (towards the stenter), (rounded off to one decimal place), is_________.

Answer: (117.0 to 118.0)

55. Consider the following isotherms at equilibrium for two disperse dyes D1 and D2 dyed on polyester. If the partition coefficients of these are K1 and K2, respectively, the value of K2/K1­ is _______.

Answer: (4 to 4)

GATE Exam 2021 Stastics (ST) Question Paper With Answer Key

GATE-2021

ST: Statistics

GA-General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. The current population of a city is 11,02,500. If it has been increasing at the rate of 5% per annum, what was its population 2 years ago?

(A)  9,92,500

(B)  9,95,006

(C)  10,00,000

(D)  12,51,506

Answer: (C)

2. p and q are positive integers and 

(A)  3

(B)  7

(C)  9

(D)  11

Answer: (B)

3. 

The least number of squares that must be added so that the line P-Q becomes the line of symmetry is ________

(A)  4

(B)  3

(C)  6

(D)  7

Answer: (C)

4. Nostalgia is to anticipation as _______ is to ________

Which one of the following options maintains a similar logical relation in the above sentence?

(A)  Present, past

(B)  Future, past

(C)  Past, future

(D)  Future, present

Answer: (C)

5. Consider the following sentences:

(i) I woke up from sleep.

(ii) I woked up from sleep.

(iii) I was woken up from sleep.

(iv) I was wokened up from sleep.

Which of the above sentences are grammatically CORRECT?

(A)  (i) and (ii)

(B)  (i) and (iii)

(C)  (ii) and (iii)

(D)  (i) and (iv)

Answer: (B)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

6. Given below are two statements and two conclusions.

Statement 1: All purple are green.

Statement 2: All black are green.

Conclusion I: Some black are purple.

Conclusion II: No black is purple.

Based on the above statements and conclusions, which one of the following options is logically CORRECT?

(A)  Only conclusion I is correct.

(B)  Only conclusion II is correct.

(C)  Either conclusion I or II is correct.

(D)  Both conclusion I and II are correct.

Answer: (C)

7. Computers are ubiquitous. They are used to improve efficiency in almost all fields from agriculture to space exploration. Artificial intelligence (AI) is currently a hot topic. AI enables computers to learn, given enough training data. For humans, sitting in front of a computer for long hours can lead to health issues.

Which of the following can be deduced from the above passage?

(i) Nowadays, computers are present in almost all places.

(ii) Computers cannot be used for solving problems in engineering.

(iii) For humans, there are both positive and negative effects of using computers.

(iv) Artificial intelligence can be done without data.

(A)  (ii) and (iii)

(B)  (ii) and (iv)

(C)  (i), (iii) and (iv)

(D)  (i) and (iii)

Answer: (D)

8. Consider a square sheet of side 1 unit. In the first step, it is cut along the main diagonal to get two triangles. In the next step, one of the cut triangles is revolved about its short edge to form a solid cone. The volume of the resulting cone, in cubic units, is ________

(A)  π/3

(B)  2π/3

(C)  3π/2

(D)  3π

Answer: (A)

9. 

The number of minutes spent by two students, X and Y, exercising every day in a given week are shown in the bar chart above.

The number of days in the given week in which one of the students spent a minimum of 10% more than the other student, on a given day, is

(A)  4

(B)  5

(C)  6

(D)  7

Answer: (C)

10. 

Corners are cut from an equilateral triangle to produce a regular convex hexagon as shown in the figure above.

The ratio of the area of the regular convex hexagon to the area of the original equilateral triangle is

(A)  2 : 3

(B)  3 : 4

(C)  4 : 5

(D)  5 : 6

Answer: (A)

Statistics (ST)

Q.1 – Q.9 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Let X be a non-constant positive random variable such that E(X) = 9. Then which one of the following statements is true?

Answer: (A)

2. Let {W(t)}t≥0 be a standard Brownian motion. Then the variance of W(1)W(2) equals

(A)  1

(B)  2

(C)  3

(D)  4

Answer: (C)

3. Let X1,X2, … ,Xn be a random sample of size n (≥ 2) from a distributionhaving the probability density function

where θ ∈ (0, ∞). Then the method of moments estimator of θ equals

Answer: (A)

4. Let {x1, x2, … , xn} be a realization of a random sample of size n (≥ 2) from a N(μ,σ2) distribution, where −∞ < μ < ∞ and σ > 0. Which of the following statements is/are true?

P : 95% confidence interval of μ based on {x1, x2, … , xn} is unique when σ is known.

Q : 95% confidence interval of μ based on {x1, x2, … , xn} is NOT unique when σ is unknown.

(A)  P only

(B)  Q only

(C)  Both P and Q

(D)  Neither P nor Q

Answer: (B)

5. Let X1, X2, … , Xn be a random sample of size n (≥ 2) from a N(0, σ2) distribution. For a given σ > 0, let fσ denote the joint probability density function of (X1,X2, … ,Xn) and S = {fσ: σ > 0}. Let  For any positive integer ν and any α ∈ (0, 1), let  denote the (1 − α)-th quantile of the central chi-square distribution with ν degrees of freedom. Consider testing H0: σ = 1 against H1: σ > 1 at level α. Then which one of the following statements is true?

(A)  S has a monotone likelihood ratio in T1 and H0 is rejected if   

(B)  S has a monotone likelihood ratio in T1 and H0 is rejected if   

(C)  S has a monotone likelihood ratio in T2 and H0 is rejected if   

(D)  S has a monotone likelihood ratio in T2 and H0 is rejected if  

Answer: (A)

6. Let X and Y be two random variables such that p11 + p10 + p01 + p00 = 1, where pij = P(X = i, Y = j), i,j = 0, 1. Suppose that a realization of a random sample of size 60 from the joint distribution of (X, Y) gives

n11 = 10, n10 = 20, n01 = 20 and n00 = 10,

where nij denotes the frequency of (i, j) for i, j = 0, 1. If the chi-square test of independence is used to test

H0: pij = pi⋅pj for i, j = 0, 1 against H1: pij ≠ pi⋅pj for at least one pair

where pi = pi0 + pi1 and pj = p0j + p1j, then which one of the following statements is true?

(i,j),

(A)  Under H0, the test statistic follows central chi-square distribution with one degree of freedom and the observed value of the test statistic is 20/3

(B)  Under H0, the test statistic follows central chi-square distribution with three degrees of freedom and the observed value of the test statistic is 20/3

(C)  Under H0, the test statistic follows central chi-square distribution with one degree of freedom and the observed value of the test statistic is 16/3

(D)  Under H0, the test statistic follows central chi-square distribution with three degrees of freedom and the observed value of the test statistic is 16/3

Answer: (A)

7. Let the joint distribution of (X, Y) be bivariate normal with mean vector  and variance-covariance matrix   where −1 < ρ < 1. Let Φρ(0, 0) = P(X ≤ 0, Y ≤ 0). Then the Kendall’s τ coefficient between X and Y equals

(A)  4Φρ(0,0) − 1

(B)  4Φρ(0,0)

(C)  4Φρ(0,0) + 1

(D)  Φρ(0,0)

Answer: (A)

8. Consider the simple linear regression model

Yi = β0 + β1xi + εi, i = 1, 2, … , n (n ≥ 3),

where β0 and β1 are unknown parameters and εi’s are independent and identically distributed random variables with mean zero and finite variance σ2 > 0. Suppose that  are the ordinary least squares estimators of β0 and β1, respectively. Define  and  , where yi 0 is the observed value of Yi, , i = 1, 2, … , n. Then for a real constant c, the variance of  is

Answer: (B)

9. Let X1, X2, X3, Y1, Y2, Y3 and Y4 be independent random vectors such that Xi follows N4(0, Σ1) distribution for i = 1, 2, 3, and Yj follows N4(0, Σ2) distribution for j = 1, 2, 3, 4, where Σ1 and Σ2 are positive definite matrices. Further, let

where X = [X1 X2 X3] is a 4 × 3 matrix, Y = [Y1 Y2 Y3 Y4] is a 4 × 4 matrix and XT and YT denote transposes of X and Y, respectively. If Wm(n, Σ) denotes a Wishart distribution of order m with n degrees of  freedom and variance-covariance matrix Σ and In denotes the n × n identity matrix, then which one of the following statements is true?

(A)  Z follows W4(7,I4) distribution

(B)  Z follows W4(4,I4) distribution

(C)  Z follows W7 (4,I7 ) distribution

(D)  Z follows W7 (7,I7) distribution

Answer: (A)

Q.10 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

10. 

Answer: (2 to 2)

11. Let 

Then the value of e I1+ π equals __________ (round off to 2 decimal places).

Answer: ()

12. Let  and I3 be the 3 × 3 identity matrix. Then the nullity of 5A(I3 + A  2) equals __________

Answer: (33.50 to 34.50)

13. Let A be the 2 × 2 real matrix having eigenvalues 1 and − 1, with corresponding eigenvectors  respectively. If  then a + b + c + d equals __________ (round off to 2 decimal places).

Answer: (2 to 2)

14. Let A and B be two events such that P(B) = 3/4 and P(A ⋃ BC) = 1/2. If A and B are independent, then P(A) equals __________ (round off to 2 decimal places).

Answer: (1.70 to 1.75)

15. A fair die is rolled twice independently. Let X and Y denote the outcomes of the first and second roll, respectively. Then E(X + Y | (X − Y)2 = 1) equals ________

Answer: (7 to 7)

16. Let X be a random variable having distribution function

where a and c are appropriate constants. Let  n ≥ 1, and  If P(X ≤ 1) = 1/2 and E(X) = 5/3, then P(X ∈ A) equals __________ (round off to 2 decimal places).

Answer: (0.32 to 0.35)

17. If the marginal probability density function of the kth order statistic of a random sample of size 8 from a uniform distribution on [0, 2] is then k equals __________

Answer: (7 to 7)

18. For α > 0, let  be a sequence of independent random variables such that 

Let S = {α > 0 ∶ Xn(a) converges to 0 almost surely as n → ∞}. Then the infimum of S equals __________ (round off to 2 decimal places).

Answer: (0.50 to 0.50)

19. Let {Xn}n≥1 be a sequence of independent and identically distributed random variables each having uniform distribution on [0, 2]. For n ≥ 1, let

Then, as n → ∞, the sequence {Zn}n≥1 converges almost surely to _______ (round off to 2 decimal places).

Answer: (0.27 to 0.35)

20. Let {Xn}n≥0 be a time-homogeneous discrete time Markov chain with state space {0, 1} and transition probability matrix  If P(X0 = 0) = P(X0 = 1) = 0. 5, then  equals ______

Answer: (50 to 50)

21. Let {0, 2} be a realization of a random sample of size 2 from a binomial distribution with parameters 2 and p, where p ∈ (0, 1). To test H0: p = 1/2 against H1: p ≠ 1 the observed value of the likelihood ratio test statistic equals _________ (round off to 2 decimal places).

Answer: (0.98 to 1.00)

22. Let X be a random variable having the probability density function

Then  equals __________ (round off to 2 decimal places).

Answer: (8.60 to 8.75)

23. Let (Y, X1,X2) be a random vector with mean vector and variance-covariance matrix  Then the value of the multiple correlation coefficient between Y and its best linear predictor on X1 and X2 equals _________ (round off to 2 decimal places).

Answer: (0.14 to 0.18)

24. Let  be a random sample from a bivariate normal distribution with unknown mean vector μ and unknown variance-covariance matrix Σ, which is a positive definite matrix. The p-value corresponding to the likelihood ratio  test for testing  based on the realization  of the random sample equals __________ (round off to 2 decimal places).

Answer: (1.00 to 1.00)

25. Let Yi = α + βxi + εi, i = 1, 2, 3, where xi’s are fixed covariates, α and β are unknown parameters and εi’s are independent and identically distributed random variables with mean zero and finite variance. Let  be the ordinary least squares estimators of α and β, respectively. Given the following observations

the value of  equals ________ (round off to 2 decimal places).

Answer: (6.31 to 6.35)

Q.26 – Q.43 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

26. Let f: ℝ → ℝ be defined by

where ℝ denotes the set of all real numbers, ℤ denotes the set of all integers, ℕ denotes the set of all positive integers and gcd(p, q) denotes the greatest common divisor of p and q. Then which one of the following statements is true?

(A)  f is not continuous at 0

(B)  f is not differentiable at 0

(C)  f is differentiable at 0 and the derivative of f at 0 equals 0

(D)  f is differentiable at 0 and the derivative of f at 0 equals 1

Answer: (C)

27. Let f:[0, ∞) → ℝ be a function, where R denotes the set of all real numbers. Then which one of the following statements is true?

(A)  If f is bounded and continuous, then f is uniformly continuous

(B)  If f is uniformly continuous, then   exists

(C)  If f is uniformly continuous, then the function g(x) = f(x) sin x is also uniformly continuous

(D)  If f is continuous and  is finite, then f is uniformly continuous

Answer: (D)

28. Let f: ℝ → ℝ be a differentiable function such that f(0) = 0 and f′ (x) + 2f(x) > 0 for all x ∈ R, where f′ denotes the derivative of f and R denotes the set of all real numbers. Then which one of the following statements is true?

(A)  f(x) > 0, for all x > 0 and f(x) < 0, for all x < 0

(B)  f(x) < 0, for all x ≠ 0

(C)  f(x) > 0, for all x ≠ 0

(D)  f(x) < 0, for all x > 0 and f(x) > 0, for all x < 0

Answer: (A)

29. Let M be the collection of all 3 × 3 real symmetric positive definite matrices. Consider the set  where 0 denotes the 3 × 3 zero matrix. Then the number of elements in S equals

(A)  0

(B)  1

(C)  8

(D)  ∞

Answer: (B)

30. Let A be a 3 × 3 real matrix such that I3 + A is invertible and let B = (I3 + A)1(I3 – A), where I3 denotes the 3 × 3 identity matrix. Then which one of the following statements is true?

(A)  If B is orthogonal, then A is invertible

(B)  If B is orthogonal, then all the eigenvalues of A are real

(C)  If B is skew-symmetric, then A is orthogonal

(D)  If B is skew-symmetric, then the determinant of A equals −1

Answer: (C)

31. Let X be a random variable having Poisson distribution such thatE(X2) = 110. Then which one of the following statements is NOT true?

(A)  E(Xn) = 10 E[(X + 1)n−1], for all n = 1, 2, 3, …

(B)   

(C)  P(X = k) < P(X = k + 1), for k = 0, 1, … , 8

(D)  P(X = k) > P(X = k + 1), for k = 10, 11, …

Answer: (B)

32. Let X be a random variable having uniform distribution on  Then which one of the following statements is NOT true?

(A)  Y = cot X follows standard Cauchy distribution

(B)  Y = tan X follows standard Cauchy distribution

(C)    has moment generating function  

(D)    follows central chi-square distribution with one degree of freedom

Answer: (D)

33. Let Ω = {1, 2, 3, … } represent the collection of all possible outcomes of a random experiment with probabilities P({n}) = αn for n ∈ Ω. Then which one of the following statements is NOT true?

(A)   

(B)   

(C)  For any positive integer k, there exist k disjoint events A1, A2, … , Ak such that  

(D)  There exists a sequence {Ai}i≥1 of strictly increasing events such that   

Answer: (B)

34. Let (X, Y) have the joint probability density function

Then which one of the following statements is NOT true?

(A)  The probability density function of X + Y is   

(B)  P(X + Y > 4) = 3/4

(C)  E(X + Y) = 4 loge 2

(D)  E(Y | X = 2) = 4

Answer: (C)

35. Let X1, X2 and X3 be three uncorrelated random variables with common variance σ2 < ∞. Let Y1 = 2X1 + X2 + X3, Y2 = X1 + 2X2 + X3 and Y3 = X1 + X2 + 2X3. Then which of the following statements is/are true?

P : The sum of eigenvalues of the variance covariance matrix of (Y1, Y2, Y3) is 18σ2.

Q : The correlation coefficient between Y1 and Y2 equals that between Y2 and Y3.

(A)  P only

(B)  Q only

(C)  Both P and Q

(D)  Neither P nor Q

Answer: (C)

36. Let {Xn}n≥0 be a time-homogeneous discrete time Markov chain with either finite or countable state space S. Then which one of the following statements is true?

(A)  There is at least one recurrent state

(B)  If there is an absorbing state, then there exists at least one stationary distribution

(C)  If all the states are positive recurrent, then there exists a unique stationary distribution

(D)  If {Xn}n≥0 is irreducible, S = {1, 2} and [π1 π2] is a stationary distribution, then  for i = 1, 2

Answer: (B)

37. Let customers arrive at a departmental store according to a Poisson process with rate 10. Further, suppose that each arriving customer is either a male or a female with probability 1/2 each, independent of all other arrivals. Let N(t) denote the total number of customers who have arrived by time t. Then which one of the following statements is NOT true?

(A)  If S2 denotes the time of arrival of the second female customer, then   

(B)  If M(t) denotes the number of male customers who have arrived by time t, then  

(C)  E [(N(t))2] = 100t2 + 10t

(D)  E[N(t)N(2t)] = 200t2 + 10t

Answer: (B)

38. Let X(1) < X(2) < X(3) < X(4) < X(5)be the order statistics corresponding to a random sample of size 5 from a uniform distribution on [0, θ], where θ ∈ (0, ∞). Then which of the following statements is/are true?

P : 3X(2) is an unbiased estimator of θ.

Q : The variance of E[2X(3) | X(5)] is less than or equal to the variance of 2X(3).

(A)  P only

(B)  Q only

(C)  Both P and Q

(D)  Neither P nor Q

Answer: (C)

39. Let X1, X2, … , Xn be a random sample of size n (≥ 2) from a distribution having the probability density function

where θ ∈ (0, ∞). Let X(1) = min{ X1, X2, … , Xn} and  Then E(X(1)| T ) equals

(A)  T/n2

(B)  T/n

(C)   

(D)   

Answer: (A)

40. Let X1, X2, … , Xn be a random sample of size n (≥ 2) from a uniform distribution on [−θ, θ], where θ ∈ (0, ∞). Let X(1) = min{X1, X2, … , Xn} and X(n) = max{X1, X2, … ,Xn}. Then which of the following statements is/are true?

P : (X(1), X(n)) is a complete statistic.

Q : X(n) − X(1) is an ancillary statistic.

(A)  P only

(B)  Q only

(C)  Both P and Q

(D)  Neither P nor Q

Answer: (D)

41. Let {Xn}n≥1 be a sequence of independent and identically distributed random variables having common distribution function F(⋅). Let a < b be two real numbers such that F(x) = 0 for all x ≤ a, 0 < F(x) < 1 for all a < x < b and F(x) = 1 for all x ≥ b. Let Sn(x) be the empirical distribution function at x based on X1, X2, … ,Xn, n ≥ 1. Then which one of the following statements is NOT true?

(A)    

(B)  For fixed x ∈ (a, b) and t ∈ (− ∞, ∞),  where Z is the standard normal random variable

(C)  The covariance between Sn(x) and Sn(y) equals  for all n ≥ 2 and for fixed −∞ < x, y < ∞

(D)  If  then {4n Yn}n≥1 converges in distribution to a central chi-square random variable with 2 degrees of freedom

Answer: (C)

42. Let the joint distribution of random variables X1,X2,X3 and X4 be  where

Then which one of the following statements is true?

(A)   follows a central chi-square distribution with 2 degrees of freedom

(B)   follows a central chi-square distribution with 2 degrees of freedom

(C)   is NOT finite

(D)   is NOT finite

Answer: (D)

43. Let  distribution, where I8 is the 8 × 8 identity matrix. Let  be independent and follow central chi-square distributions with 3 and 4 degrees of freedom, respectively, where Σ1 and Σ2 are 8 × 8 matrices and  denotes transpose of  Then which of the following statements is/are true?

P : Σ1 and Σ2 are idempotent.

Q : Σ1Σ2 = 0, where 0 is the 8 × 8 zero matrix.

(A)  P only

(B)  Q only

(C)  Both P and Q

(D)  Neither P nor Q

Answer: (C)

Q.44 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

44. Let (X, Y) have a bivariate normal distribution with the joint probability density function

Then 8 E(XY) equals ________

Answer: (3 to 3)

45. Let f: ℝ × ℝ → ℝ be defined by f(x, y) = 8x2 − 2y, where ℝ denotes the set of all real numbers. If M and m denote the maximum and minimum values of f, respectively, on the set {(x, y) ∈ ℝ × ℝ ∶ x2 + y2 = 1}, then M − m equals ________ (round off to 2 decimal places).

Answer: (10.10 to 10.15)

46. Let A = [a u1 u2 u3], B = [b u1 u2 u3] and C = [u2 u3 u1 a + b] be three 4 × 4 real matrices, where a, b, u1, u2 and u3 are 4 × 1 real column vectors. Let det(A), det(B) and det(C) denote the determinants of the matrices A, B and C, respectively. If det(A) = 6 and det(B) = 2, then det(A + B) − det(C) equals _________

Answer: (72 to 72)

47. Let X be a random variable having the moment generating function 

Then P(X > 1) equals __________ (round off to 2 decimal places).

Answer: (0.60 to 0.66)

48. Let {Xn}n≥1 be a sequence of independent and identically distributed random variables each having uniform distribution on [0, 3]. Let Y be a random variable, independent of {Xn}n≥1, having probability mass function

Then P(max{X1,X2, … ,XY} ≤ 1) equals __________ (round off to 2 decimal places).

Answer: (0.20 to 0.26)

49. Let {Xn}n≥1 be a sequence of independent and identically distributed random variables each having probability density function

Let X(n) = max{X1,X2, … ,Xn} for n ≥ 1. If Z is the random variable to which {X(n) − loge n}n≥1converges in distribution, as n → ∞, then the median of Z equals __________ (round off to 2 decimal places).

Answer: (0.32 to 0.42)

50. Consider an amusement park where visitors are arriving according to a Poisson process with rate 1. Upon arrival, a visitor spends a random amount of time in the park and then departs. The time spent by the visitors are independent of one another, as well as of the arrival process, and have common probability density function

If at a given time point, there are 10 visitors in the park and p is the probability that there will be exactly two more arrivals before the next departure, then 1/p equals ________

Answer: (143 to 143)

51. Let {0. 90, 0. 50, 0. 01, 0. 95} be a realization of a random sample of size 4 from the probability density function

where 0. 5 ≤ θ < 1. Then the maximum likelihood estimate of θ based on the observed sample equals __________ (round off to 2 decimal places).

Answer: (0.50 to 0.50)

52. Let a random sample of size 100 from a normal population with unknown mean μ and variance 9 give the sample mean 5. 608. Let Φ(⋅) denote the distribution function of the standard normal random variable. If Φ(1. 96) = 0. 975, Φ(1. 64) = 0. 95 and the uniformly most powerful unbiased test based on sample mean is used to test H0: μ = 5. 02 against H1: μ ≠ 5. 02, then the p-value equals __________ (round off to 3 decimal places).

Answer: (0.045 to 0.055)

53. Let X be a discrete random variable with probability mass function p ∈ {p0, p1}, where

To test H0: p = p0 against H1: p = p1, the power of the most powerful test of size 0. 05, based on X, equals __________ (round off to 2 decimal places).

Answer: (0.20 to 0.22)

54. Let X1, X2, … , X10 be a random sample from a probability density function fθ(x) = f(x − θ), −∞ < x < ∞, where −∞ < θ < ∞ and f(−x) = f(x) for −∞ < x < ∞. For testing H0: θ = 1. 2 against H1: θ ≠ 1. 2, let T+ denote the Wilcoxson Signed-rank test statistic. If η denotes the probability of the event {T+ < 50} under H0, then 32 η equals __________ (round off to 2 decimal places).

Answer: (31.60 to 31.80)

55. Consider the multiple linear regression model Yi = β0 + β1x1,i + β2x2,i + ⋯ + β22x22,i + ϵi, i = 1, 2, … , 123, where, for j = 0, 1, 2, … , 22, βj’s are unknown parameters and ϵi’s are independent and identically distributed N(0, σ2), σ > 0, random variables.

If the sum of squares due to regression is 338. 92, the total sum of squares is 522. 30 and R2adj denotes the value of adjusted R2 then 100 R2adj, equals __________ (round off to 2 decimal places).

Answer: (57.00 to 57.40)

GATE Exam 2021 Production and Industrial Engineering (PI) Question Paper With Answer Key

GATE-2021

PI: Production and Industrial Engineering

GA-General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. The current population of a city is 11,02,500. If it has been increasing at the rate of 5% per annum, what was its population 2 years ago?

(A)  9,92,500

(B)  9,95,006

(C)  10,00,000

(D)  12,51,506

Answer: (C)

2. p and q are positive integers and 

(A)  3

(B)  7

(C)  9

(D)  11

Answer: (B)

3. 

The least number of squares that must be added so that the line P-Q becomes the line of symmetry is ________

(A)  4

(B)  3

(C)  6

(D)  7

Answer: (C)

4. Nostalgia is to anticipation as _______ is to ________

Which one of the following options maintains a similar logical relation in the above sentence?

(A)  Present, past

(B)  Future, past

(C)  Past, future

(D)  Future, present

Answer: (C)

5. Consider the following sentences:

(i) I woke up from sleep.

(ii) I woked up from sleep.

(iii) I was woken up from sleep.

(iv) I was wokened up from sleep.

Which of the above sentences are grammatically CORRECT?

(A)  (i) and (ii)

(B)  (i) and (iii)

(C)  (ii) and (iii)

(D)  (i) and (iv)

Answer: (B)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

6. Given below are two statements and two conclusions.

Statement 1: All purple are green.

Statement 2: All black are green.

Conclusion I: Some black are purple.

Conclusion II: No black is purple.

Based on the above statements and conclusions, which one of the following options is logically CORRECT?

(A)  Only conclusion I is correct.

(B)  Only conclusion II is correct.

(C)  Either conclusion I or II is correct.

(D)  Both conclusion I and II are correct.

Answer: (C)

7. Computers are ubiquitous. They are used to improve efficiency in almost all fields from agriculture to space exploration. Artificial intelligence (AI) is currently a hot topic. AI enables computers to learn, given enough training data. For humans, sitting in front of a computer for long hours can lead to health issues.

Which of the following can be deduced from the above passage?

(i) Nowadays, computers are present in almost all places.

(ii) Computers cannot be used for solving problems in engineering.

(iii) For humans, there are both positive and negative effects of using computers.

(iv) Artificial intelligence can be done without data.

(A)  (ii) and (iii)

(B)  (ii) and (iv)

(C)  (i), (iii) and (iv)

(D)  (i) and (iii)

Answer: (D)

8. Consider a square sheet of side 1 unit. In the first step, it is cut along the main diagonal to get two triangles. In the next step, one of the cut triangles is revolved about its short edge to form a solid cone. The volume of the resulting cone, in cubic units, is ________

(A)  π/3

(B)  2π/3

(C)  3π/2

(D)  3π

Answer: (A)

9. 

The number of minutes spent by two students, X and Y, exercising every day in a given week are shown in the bar chart above.

The number of days in the given week in which one of the students spent a minimum of 10% more than the other student, on a given day, is

(A)  4

(B)  5

(C)  6

(D)  7

Answer: (C)

10. 

Corners are cut from an equilateral triangle to produce a regular convex hexagon as shown in the figure above.

The ratio of the area of the regular convex hexagon to the area of the original equilateral triangle is

(A)  2 : 3

(B)  3 : 4

(C)  4 : 5

(D)  5 : 6

Answer: (A)

Production & Industrial Engineering (PI)

Q.1 – Q.17 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. A product has an exponential time-to-failure distribution with a constant failure rate of 0.00006 per hour. The reliability of the product after 4000 hours of operation is

(A)  0.5866

(B)  0.6866

(C)  0.7866

(D)  0.8866

Answer: (C)

2. In a typical product development process under concurrent engineering approach, all elements of product life cycle from conception to disposal are considered at

(A)  Product design stage

(B)  Process design stage

(C)  Manufacturing stage

(D)  Disposal stage

Answer: (A)

3. When acceptance number of a single sampling plan under attribute category is zero with sample size less than or equal to 10, the Operating Characteristic (OC) curve is

(A)  A horizontal line

(B)  A vertical line

(C)  A convex function

(D)  An inverted S-shaped curve

Answer: (C)

4. Which one of the following is an improvement type heuristic algorithm for computerized layout design technique?

(A)  Systematic layout planning (SLP)

(B)  Computerized relative allocation of facilities technique (CRAFT)

(C)  Computerized relationship layout planning (CORELAP)

(D)  Plant layout analysis and evaluation technique (PLANET)

Answer: (B)

5. Which one of the following is NOT a measure of forecast error?

(A)  Mean absolute deviation (MAD)

(B)  Mean squared error (MSE)

(C)  Mean absolute percent error (MAPE)

(D)  Mean sum product error (MSPE)

Answer: (D)

6. Pearlite microstructure in an eutectoid steel consists of alternating layers of two phases, namely α ferrite and

(A)  Martensite

(B)  Austenite

(C)  Cementite

(D)  Bainite

Answer: (C)

7. Which one of the following defects is NOT associated with welding processes?

(A)  Angular distortion

(B)  Hot tear

(C)  Hydrogen embrittlement

(D)  Earring

Answer: (D)

8. Match the component with the corresponding manufacturing process in the table below.

(A)  P-3, Q-2, R-1, S-4

(B)  P-3, Q-4, R-2, S-1

(C)  P-2, Q-3, R-4, S-1

(D)  P-1, Q-3, R-2, S-4

Answer: (B)

9. In a turning operation, doubling the cutting speed (V) reduces the tool life (T) to 1/8th of the original tool life. The exponent n in the Taylor’s tool life equation, VTn = C is

(A)  1/2

(B)  1/3

(C)  1/4

(D)  1/8

Answer: (B)

10. Which one among the following mechanisms is NOT used for transforming rotation to translation in machine tools?

(A)  Screw-nut system

(B)  4-bevel gear type differential mechanism

(C)  Cam and cam follower system

(D)  Whitworth mechanism

Answer: (B)

11. Match the measuring feature with the corresponding measuring instrument in the table below.

(A)  P-4, Q-1, R-2, S-3

(B)  P-1, Q-3, R-4, S-2

(C)  P-2, Q-4, R-3, S-1

(D)  P-4, Q-3, R-1, S-2

Answer: (B OR D)

12. The frequency of pulsing in a die-sinking electric discharge machine (EDM) is 10 kHz. The pulse off-time is set at 40 micro-seconds. The duty factor at this setting is

(A)  0.40

(B)  0.60

(C)  0.67

(D)  2.50

Answer: (B)

13. A cantilever beam of length 0.3 m is subjected to a uniformly distributed load C = 10 kN/m, as shown in the figure. The bending (flexural) rigidity of the beam is 5000 Nm2. Neglecting the self-weight of the beam, the magnitude of beam curvature in m1 at the fixed end is

(A)  1.10

(B)  0.02

(C)  0.09

(D)  0.05

Answer: (C)

14. A circular rod of length l = 2 m is subjected to a compressive load P, as shown in the figure. The bending (flexural) rigidity of the rod is 2000 Nm2. If both ends are pinned, then the critical load Pcr in N (rounded to the nearest integer) at which the rod buckles elastically is

(A)  4935

(B)  2000

(C)  5167

(D)  1238

Answer: (A)

15. Two cylindrical parts of equal length l, as shown in the figure, made of steel having Young’s modulus E = 200 GPa and Poisson’s ratio v = 0.33 are press fitted upon one another. If radial interference δ = 0.05 mm, and radii R = 25 mm and R0 = 40 mm, then the contact pressure P in MPa at the interface upon press fit is

(A)  10.7

(B)  60.9

(C)  121.9

(D)  1005.3

Answer: (C)

16. The dimensionless number defined by the ratio of inertial force to viscous force is called

(A)  Mach number

(B)  Froude number

(C)  Weber number

(D)  Reynolds number

Answer: (D)

17. A small capillary tube of 3 mm inner diameter is inserted into a fluid having density 900 kg/m3, surface tension 0.1 N/m, and contact angle 300. The rise in the height of fluid in the capillary tube due to surface tension is

(A)  111.4 mm

(B)  128.3 mm

(C)  89.1 mm

(D)  154.1 mm

Answer: (MTA)

Q.18 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

18. A given steel has identical yield strength of 700 MPa in uni-axial tension and uni-axial compression. If the steel is subjected to pure shear stress such that the three principal stresses are σ1 = σ, σ2 = 0, σ3 = − σ with σ1 ≥ σ2 ≥ σ3, then the stress σ in MPa for the initiation of plastic yielding in the steel as per von Mises yield criterion is ________. [round off to 2 decimal places]

Answer: (404.00 to 405.00)

19. A cylindrical mild steel tensile test specimen of gauge length 50 mm and diameter 10 mm is extended in two stages at a deformation speed of 4 mm/min. The specimen is extended from 50 mm to 55 mm in the first stage, and from 55 mm to 60 mm in the second stage. Neglecting elastic deformation, the total longitudinal true strain is _________. [round off to2 decimal places]

Answer: (0.17 to 0.19)

20. A M30 bolt needs to be subjected to pretension Fi = 350 kN. If the torque coefficient K of the bolt is 0.2, then the torque in Nm needed to achieve this pretension is _________. [in integer]

Answer: (2100 to 2100)

21. A 150 mm wide polyamide flat belt is transmitting 15 kW power through a belt-pulley system. The driving pulley of 150 mm pitch diameter is rotating at 200 RPM. If F1 is the belt tension on high tension side, and F2 is the belt tension on low tension side, then the difference in belt tensions ∆F = F1 – F2 in N is _________. [round off to one decimal place]

Answer: (9545.0 to 9555.0)

22. Heat is being removed from a refrigerator at a rate of 300 kJ/min to maintain its inside temperature at 2° If the input power to the refrigerator is 2 kW, the coefficient of performance of the refrigerator is ________. [round off to one decimal place]

Answer: (2.4 to 2.6)

23. In an ideal Otto cycle, 800 kJ/kg is transferred to air during the constant volume heat addition process and 381 kJ/kg is removed during the constant volume heat rejection process. The thermal efficiency in % of the cycle is __________. [round off to one decimal place]

Answer: (52.2 to 52.5)

24. If (3i +1)x + (4i + 4)y + 5 = 0 with x, y being real and i = √−1, then x = ________. [correct up to one decimal place]

Answer: (2.4 to 2.6)

25. The minimum value of function f defined by f(x, y, z) = x2 + 5y2 + 5z2 − 4x + 40y − 40z + 300 is ____________. [in integer]

Answer: (136 to 136)

Q.26 – Q.36 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

26. For a given process control chart, there are four rules for determining out-of-control state of the process which are being used simultaneously. The probability of Type-I error for the four rules are 0.005, 0.02, 0.03, and 0.05. Assuming independence of the rules, the probability of overall Type-I error when all the four rules are used simultaneously is

(A)  0.101

(B)  0.201

(C)  0.001

(D)  0301

Answer: (A)

27. An in-control process has an estimated standard deviation of 2 mm. The specification limits of the component being processed are 120 ± 8 mm. When the process mean shifts to 118 mm, the values of the process capability indices, Cp and Cpk, respectively are,

(A)  1.000, 1.667

(B)  1.333, 1.667

(C)  1.333, 1.000

(D)  1.000, 1.000

Answer: (C)

28. There are a number of identical components in a parallel system. When the system reliability is 0.97 and the reliability of each individual component is 0.68, the number of identical components in the system is (if actual value is a fraction, it may be rounded up to the next higher integer).

(A)  2

(B)  4

(C)  6

(D)  8

Answer: (B)

29. A retail chain company has identified four sites A, B, C and D to open a new retail store. The company has selected four factors as the basis for evaluation of these sites. The factors, their weights, and the score for each site are given in the following table.

The site that should be selected to open the new retail store is

(A)  Site A

(B)  Site B

(C)  Site C

(D)  Site D

Answer: (C)

30. In the classical economic order quantity (EOQ) model, let Q and C denote the optimal order quantity and the corresponding minimum total annual cost (the sum of the inventory holding and ordering costs). If the order quantity is estimated incorrectly as Q′ = 2Q, then the corresponding total annual cost C′ is

(A)  C′ = 1.25C

(B)  C′ = 1.5C

(C)  C′ = 1.75C

(D)  C′ = 2C

Answer: (A)

31. The eigenvalues of matrix  are 5 and 10. For matrix B = A + α I, where α is a constant and I is 2×2 identity matrix, its eigenvalues are

(A)  5, 10

(B)  5 + α, 10 + α

(C)  5 – α, 10 – α

(D)  5α, 10α

Answer: (B)

32. A company manufactures two products P and Q with unit profit of 4 and 5, respectively. The production requires manpower and two kinds of raw materials R1 and R2. The following table summarizes the requirement and availability of resources.

The maximum profit the company can make is

(A)  45

(B)  48

(C)  42

(D)  54

Answer: (B)

33. A tool of an NC machine has to move along a circular arc from (20,20) to (10,10), while performing an operation. The center of the arc is at (20,10). Which one of the following NC tool commands performs the above mentioned operation?

(A)  N020 G03 X20 Y20 X10 Y10 R10

(B)  N020 G02 X20 Y20 X10 Y10 R10

(C)  N020 G02 X10 Y10 X20 Y20 R10

(D)  N020 G01 X20 Y20 X10 Y10 R10

Answer: (A)

34. In a shaft-hole assembly, the hole is specified as  The mating shaft has a clearance fit with minimum clearance of 0.01 mm. The tolerance on the shaft is 0.03 mm. The maximum clearance in mm between the hole and the shaft is

(A)  0.04

(B)  0.05

(C)  0.08

(D)  0.10

Answer: (C)

35. ‘GO’ and ‘NO GO’ snap gauges are to be designed for a shaft  Gauge tolerance can be taken as 5% of the hole tolerance. Following the ISO system of gauge design, the respective sizes of ‘GO’ and ‘NO GO’ gauges are

(A)  36.013 mm and 36.067 mm

(B)  36.015 mm and 36.065 mm

(C)  36.018 mm and 36.062 mm

(D)  36.020 mm and 36.060 mm

Answer: (A)

36. A circular tank of 4 m diameter is filled up to a height of 3 m. Assuming almost steady flow and neglecting losses, the time taken in seconds to empty the tank through a 5 cm diameter hole located at the center of the tank bottom (take acceleration due to gravity g = 9.81 m/s2) is [round off to the nearest integer]

(A)  5005

(B)  1807

(C)  8097

(D)  3154

Answer: (A)

Q.37 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

37. The probability mass function P(x) of a discrete random variable X is given by  where x = 1, 2, ⋯ , ∞. The expected value of X is _______. [in integer]

Answer: (2 to 2)

38. The time to pass through a security screening at an airport follows an exponential distribution. The mean time to pass through the security screening is 15 minutes. To catch the flight, a passenger must clear the security screening within 15 minutes. The probability that the passenger will miss the flight is __________. [round off to 3 decimal places]

Answer: (0.365 to 0.370)

39. A machine shop has received four jobs A, B, C and D for processing on a single CNC machine. All jobs are available for processing on the first day of the production schedule calendar, and processing times and due dates as applicable on the first day are given below. Using earliest due date rule, the average tardiness (in days) is ________. [in integer]

Answer: (4 to 4)

40. A time study is carried out for a spot welding operation which is being performed by an operator. The time taken (in seconds) for five observations are recorded as 40, 35, 45, 37 and 43, respectively. If the standard time and the allowance for this operation are 45 seconds and 9 seconds, respectively, then the performance rating (in percentage) of the operator is ________. [in integer]

Answer: (90 to 90)

41. The initial cost of a machine is INR 10,00,000 and its salvage value after 10 years of use is INR 50,000. Using the straight line depreciation method, the book value in INR of the machine at the end of 7th year is ________. [in integer]

Answer: (335000 to 335000)

42. A project consists of eight activities. The time required for each activity and its immediate predecessor(s) are given in the table below.

If the project completion time using critical path method (CPM) is 15 days, then the value of X (in days) is ________. [in integer]

Answer: (5 to 5)

43. A wire of 5 mm diameter is drawn into a wire of 4 mm diameter through a conical die at a constant pulling speed of 5 m/s. Neglecting the coefficient of friction and redundant work, the drawing stress (σd) in MPa for the above process is given by  where  is the mean flow strength of wire material in MPa, and r is the ratio of decrease in area of cross-section to initial area of cross-section of the wire. If the mean flow strength of wire material is 600 MPa, then the power required in kW in the above wire drawing process is ________.

[round off to 2 decimal places]

Answer: (16.80 to 16.84)

44. In an arc welding process, the DC power source characteristic is linear with an open circuit voltage of 60 V and short circuit current of 600 A. The heat required for melting a metal during the welding is 10 J/mm3, and the heat transfer and melting efficiencies are 80% and 25%, respectively. If the weld cross-sectional area of 20 mm2 is made using the maximum arc power, then the required welding speed in mm/s is ________. [round off to one decimal place]

Answer: (8.8 to 9.2)

45. A company is producing a disc-shaped product of 50 mm thickness and 1.0 m diameter using sand casting process. The solidification time of the above casting process is estimated by Chvorinov’s equation  where B is the mold constant, and V and A are the volume and surface area of the casting, respectively. It is decided to modify both the thickness and diameter of the disc to 25 mm and 0.5 m, respectively, maintaining the same casting condition. The percentage reduction in solidification time of the modified disc as compared to that of the bigger disc is _________.[round off to one decimal place]

Answer: (74.5 to 75.5)

46. A single point cutting tool with 150 orthogonal rake angle is used to machine a mild steel plate under orthogonal machining condition. The depth of cut (uncut thickness) is set at 0.9 mm. If the chip thickness is 1.8 mm, then the shear angle in degree is ________. [round off to one decimal place]

Answer: (28.0 to 30.0)

47. The top layer of a flat 750 mm × 300 mm rectangular mild steel plate is to be machined with a single depth of cut using a shaping machine. The plate hasbeen fixed by keeping 750 mm side along the tool travel direction. If the approach and the over-travel are 25 mm each, average cutting speed is 10 m/min, feed rate is 0.4 mm/stroke, and the ratio of return time to cutting time of the tool is 1:2, the time (in minutes) required to complete the machining operation is _______. [round off to one decimal place]

Answer: (89.0 to 91.0)

48. A 3 mm thick steel sheet, kept at room temperature of 30 °C, is cut by a fiber laser beam. The laser spot diameter on the top surface of the sheet is 0.2 mm. The laser absorptivity of the sheet is 50%. The properties of steel are density = 8000 kg/m3, specific heat = 500 J/kg.°C, melting temperature = 1530 °C, and latent heat of fusion = 3 × 105 J/kg. Assume that melting efficiency is 100% and that the kerf width is equal to the laser spot diameter. The maximum speed (in m/s) at which the sheet can be fully cut at 2 kW laser power is ________.

[round off to 3 decimal places]

Answer: (0.193 to 0.203)

49. In a point-to-point open-loop NC drive, a stepper motor with 1.80 step angle is coupled to a leadscrew through a gear reduction of 4:1 (4 rotations of the motor enables 1 rotation of leadscrew). The single-start leadscrew has a pitch of 4 mm. The worktable of the system is driven by the leadscrew. If the table moves at a uniform speed of 10 mm/s, the pulse frequency (in Hz) required to drive the stepper motor is ________. [round off to one decimal place]

Answer: (1999.0 to 2001.0)

50. A 30 kg smooth, solid sphere rests on two frictionless inclines as shown in the figure. The magnitude of contact force in N acting at the point A is (take acceleration due to gravity g = 9.81 m/s2 and consider both sphere and inclines to be rigid) _________. [round off to 2 decimal places]

Answer: (147.00 to 147.30)

51. Consider the truss shown in the figure. The members AB, BC, and CA are all rigid and form an equilateral triangle. The contact between roller and ground at C is frictionless. If the self-weight of members is neglected, the force in member BC in N is (negative sign should be used if the force is compressive and positive if the force in the member is tensile) _________. [round off to one decimal place]

 

Answer: (-5773.7 to -5773.4)

52. A fluid with dynamic viscosity μ = 1 Pa.s is flowing through a circular pipe with diameter 1 cm. If the flow rate (discharge) in the pipe is 0.2 liter/s, the maximum velocity in m/s of the fluid in the pipe is (assume fully developed flow and take fluid density ρ = 1000 kg/m3) ________. [round off to one decimal place]

Answer: (5.0 to 5.2)

53. Values of function y(x) at discrete values of x for 0 ≤ x ≤ 10 are given in table. Using trapezoidal rule, 

[round off to one decimal place]

Answer: (33.4 to 33.6)

54. Temperature field inside a sphere of radius R = 1 m with origin at its center is T(x, y, z) = 100 – 70x + 51y – 80z – 10x2 – 20y2 – 20z2. If thermal conductivity of the sphere material is K = 50 W/m.K and Fourier law of heat conduction is valid, net heat leaving the sphere per unit time in W is _________. [round off to one decimal place]

Answer: (20.943.8 to 20944.1)

55. A 3.5 mm thick sheet is rolled using a two high rolling mill to reduce the thickness under plane strain condition. Both rolls have a diameter of 500 mm and are rotating at 200 RPM. The coefficient of friction at the sheet and roll interface is 0.08, and the elastic deflection of the rolls is negligible. If the mean flow strength of the sheet material is 400 MPa, then the minimum possible thickness (in mm) of sheet that can be produced in a single pass is _________. [round off to 2 decimal places]

Answer: (1.85 to 1.95)

GATE Exam 2021 Physics (PH) Question Paper With Answer Key

GATE-2021

PH: Physics

GA – General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. (i) Arun and Aparna are here.

(ii) Arun and Aparna is here.

(iii) Arun’s families is here.

(iv) Arun’s family is here.

Which of the above sentences are grammatically CORRECT?

(A)    (i) and (ii)

(B)    (i) and (iv)

(C)    (ii) and (iv)

(D)    (iii) and (iv)

Answer: (B)

2. 

Answer: (B)

3. Two identical cube shaped dice each with faces numbered 1 to 6 are rolled simultaneously. The probability that an even number is rolled out on each dice is:

(A)    1/36

(B)    1/12

(C)    1/8

(D)    1/4

Answer: (D)

4. ⊕ and ⊙ are two operators on numbers p and q such that p ⊙ q = p – q, and p ⊕ q – p × q

Then, (9 ⊙ (6 ⊕ 7)) ⨀ (7 ⊕ (6 ⊙ 5) =

(A)    40

(B)    -26

(C)    -33

(D)    -40

Answer: (D)

5. Four persons P, Q, R and S are to the seated in a row, R should not be seated at the second position from the left end of the row. The number of distinct seating arrangement possible is:

(A)    6

(B)    9

(C)    18

(D)    24

Answer: (C)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

6. On a planar field, you travelled 3 units East from a point O. Next you travelled 4 units South to arrive at point P. Then you travelled from P in the North-East direction such that you arrive at a point that is 6 units East of point O. Next, you travelled in the North-West direction, so that  you arrive at point Q that is 18 units North of Point P.

The distance of point Q to point O, in the same units, should be_____

(A)    3

(B)    4

(C)    5

(D)    6

Answer: (C)

7. The author said, “Musicians rehearse before their concerts. Actors rehearse their roles before the opening of a new play, On the other hand, I find it strange that many public speakers think key can just walk on to the stage and start speaking. In my opinion, it is no less important for public speakers to rehearse their talks.”

Based on the above passage, which one of the following is TRUE?

(A)    The author is of the opinion that rehearsing is important for musicians, actors and public speakers.

(B)    The author is of the opinion that rehearsing is  less important for public speakers than for musicians and actors.

(C)    The author is of the opinion that rehearsing is more important only for musicians than public speakers.

(D)    The author is of the opinion that rehearsal is more important for actors than musicians.

Answer: (A)

8. (1) Some football players play cricket.

(2) All cricket players play hockey.

Among the options given below, the statement that logically follows from the two statements 1 and 2 above, is:

(A)    No football player plays hockey.

(B)    Some football players play hockey.

(C)    All football players play hockey.

(D)    All hockey players play football.

Answer: (B)

9. In the figure shown above, PQRS is a square. The shaded portion is formed by the intersection of sectors of circles with radius equal to the side of the square and centers at S and Q.

The probability that any point picked randomly within the square falls in the shaded area is______

(A)  

(B)    1/2

(C)    π/2

(D)    π/4

Answer: (C)

10. In an equilateral triangle PQR, side PQ is divided into four equal parts, side QR is divided into six equal parts and side PR is divided into eight equal parts. The length of each subdivided part in cm is an integer.

The minimum area of the triangle PQR possible, in cm2, is

(A)    18

(B)    24

(C)    48√3

(D)    144√3

Answer: (D)

Physics (PH)

Q.1 – Q.9 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Choose the graph that best describes the variation of dielectric constant (ϵr) with temperature (T) in a ferroelectric material.

(TC is the Curie temperature)

Answer: (A)

2. A matter wave is represented by the wave function

Ψ(x, y, z, t) = Aei(4x+3y+5z−10πt)

where A is a constant. The unit vector representing the direction of propagation of this matter wave is

Answer: (A)

3. As shown in the figure, X-ray diffraction pattern is obtained from a diatomic chain of atoms P and Q. The diffraction condition is given by a cos θ = nλ, where n is the order of the diffraction peak. Here, a is the lattice constant and λ is the wavelength of the X-rays. Assume that atomic form factors and resolution of the instrument do not depend on θ. Then, the intensity of the diffraction peaks is

(A)  lower for even values of n, when compared to odd values of n

(B)  lower for odd values of n, when compared to even values of n

(C)  zero for odd values of n

(D)  zero for even values of n

Answer: (B)

4. As shown in the figure, two metal-semiconductor junctions are formed between an n-type semiconductor S and metal M. The work functions of S and M are φS and φM, respectively with φM > φS.

The I − V characteristics (on linear scale) of the junctions is best represented by

Answer: (A)

5. Consider a tiny current loop driven by a sinusoidal alternating current. If the surface integral of its time-averaged Poynting ector is constant, then the magnitude of the time-averaged magnetic field intensity, at any arbitrary position is proportional to

(A)  1/r3

(B)  1/r2

(C)  1/r

(D)  r

Answer: (C)

6. Consider a solenoid of length L and radius R, where R ≪ A steady-current flows through the solenoid. The magnetic field is uniform inside the solenoid and zero outside.

Among the given options, choose the one that best represents the variation in the magnitude of the vector potential, (0,Aφ, 0) at z = L/2, as a function

of the radial distance (r) in cylindrical coordinates.

Useful information: The curl of a vector   in cylindrical coordinates is

Answer: (C)

7. Assume that 13N (Z = 7) undergoes first forbidden β+ decay from its ground state with spin-parity Jπi, to a final state Jπf. The possible values for Jπi and Jπf, respectively, are

Answer: (A)

8. In an experiment, it is seen that an electric-dipole (E1) transition can connect an initial nuclear state of spin-parity Jπi = 2+ to a final state Jπf. All possible values of Jπf are

(A)  1+, 2+

(B)  1+, 2+, 3+

(C)  1, 2

(D)  1, 2, 3

Answer: (D)

9. Choose the correct statement from the following.

(A)  Silicon is a direct band gap semiconductor.

(B)  Conductivity of metals decreases with increase in temperature.

(C)  Conductivity of semiconductors decreases with increase in temperature.

(D)  Gallium Arsenide is an indirect band gap semiconductor.

Answer: (B)

Q.10 – Q.16 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).

10. A two-dimensional square lattice has lattice constant a.

k represents the wavevector in reciprocal space. The coordinates (kx, ky) of reciprocal space where band gap(s) can occur, are

Answer: (B; C; D)

11. As shown in the figure, an electromagnetic wave with intensity II is incident at the interface of two media having refractive indices n1 = 1 and n2 = √3. The wave is reflected with intensity IR and transmitted with intensity IT. Permeability of each medium is the same. (Reflection coefficient R = IR/II and Transmission coefficient T = IT/II).

Choose the correct statement(s).

(A)  R = 0 if θI = 0° and polarization of incident light is parallel to the plane of incidence.

(B)  T = 1 if θI = 60° and polarization of incident light is parallel to the plane of incidence.

(C)  R = 0 if θI = 60° and polarization of incident light is perpendicular to the plane of incidence.

(D)  T = 1 if θI = 60° and polarization of incident light is perpendicular to the plane of incidence.

Answer: (B)

12. A material is placed in a magnetic field intensity H. As a result, bound current density Jb is induced and magnetization of the material is M. The magnetic flux density is B. Choose the correct option(s) valid at the surface of the material.

(A)  ∇. M = 0

(B)  ∇. B = 0

(C)  ∇. H = 0

(D)  ∇. Jb = 0

Answer: (B; D)

13. For a finite system of Fermions where the density of states increases with energy, the chemical potential

(A)  decreases with temperature

(B)  increases with temperature

(C)  does not vary with temperature

(D)  corresponds to the energy where the occupation probability is 0.5

Answer: (A; D)

14. Among the term symbols

4S1, 2D7/2, 3S1 and 2D5/2

choose the option(s) possible in the LS coupling notation.

(A)  4S1

(B)  2D7/2

(C)  3S1

(D)  2D5/2

Answer: (C; D)

15. To sustain lasing action in a three-level laser as shown in the figure, necessary condition(s) is(are)

(A)  lifetime of the energy level 1 should be greater than that of energy level 2

(B)  population of the particles in level 1 should be greater than that of level 0

(C)  lifetime of the energy level 2 should be greater than that of energy level 0

(D)  population of the particles in level 2 should be greater than that of level 1

Answer: (A; B)

16. If yn(x) is a solution of the differential equation

y′′ − 2xy′ + 2ny = 0

where n is an integer and the prime ( ′ ) denotes differentiation with respect to x, then acceptable plot(s) of  is (are)

Answer: (B; C)

Q.17 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

17. The donor concentration in a sample of n-type silicon is increased by a factor of 100. Assuming the sample to be non-degenerate, the shift in the Fermi level (in meV) at 300 K (rounded off to the nearest integer) is ______.

(Given: kBT= 25 meV at 300 K)

Answer: (115 to 116)

18. Two observers O and Oʹ observe two events P and Q. The observers have a constant relative speed of 0.5c. In the units, where the speed of light, c, is taken as unity, the observer O obtained the following coordinates:

Event P: x = 5, y = 3, z = 5, t = 3

Event Q: x = 5, y = 1, z = 3, t = 5

The length of the space-time interval between these two events, as measured by Oʹ, is L. The value of |L| (in integer) is ______.

Answer: (2 to 2)

19. A light source having its intensity peak at the wavelength 289.8 nm is calibrated as 10,000 K which is the temperature of an equivalent black body radiation. Considering the same calibration, the temperature of light source (in K) having its intensity peak at the wavelength 579.6 nm (rounded off to the nearest integer) is ______.

Answer: (5000 to 5000)

20. A hoop of mass M and radius R rolls without slipping along a straight line on a horizontal surface as shown in the figure. A point mass m slides without friction along the inner surface of the hoop, performing small oscillations about the mean position. The number of degrees of freedom of the system (in integer) is ______.

Answer: (2 to 2)

21. Three non-interacting bosonic particles of mass m each, are in a one-dimensional infinite potential well of width a. The energy of the third excited state of the system is The value of x (in integer) is ______.

Answer: (5 to 6)

22. The spacing between two consecutive S-branch lines of the rotational Raman spectra of hydrogen gas is 243. 2 cm−1. After excitation with a laser of wavelength 514. 5 nm, the Stoke’s line appeared at 17611. 4 cm−1 for a particular energy level. The wavenumber (rounded off to the nearest integer), in cm−1, at which Stoke’s line will appear for the next higher energy level is ______.

Answer: (17367 to 17371)

23. The transition line, as shown in the figure, arises between 2D3/2 and 2P1/2 states without any external magnetic field. The number of lines that will appear in the presence of a weak magnetic field (in integer) is _______.

Answer: (6 to 6)

24. Consider the atomic system as shown in the figure, where the Einstein A coefficients for spontaneous emission for the levels are A2→1 = 2 × 107s–1 and A1→0 = 108s–1. If 1014 atoms/cm3 are excited from level 0 to level 2 and a steady state population in level 2 is achieved, then the steady state population at level 1 will be x × 1013 cm–3. The value of x (in integer) is ______.

Answer: (2 to 2)

25. If  are constant vectors,  are generalized positions and conjugate meomenta, respectively, then for the transformation  to be canonical, the value of  (in integer) is ______.

Answer: (-1 to -1)

Q.26 – Q.41 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

26. 

The above combination of logic gates represents the operation

(A)  OR

(B)  NAND

(C)  AND

(D)  NOR

Answer: (B)

27. In a semiconductor, the ratio of the effective mass of hole to electron is 2:11 and the ratio of average relaxation time for hole to electron is 1:2. The ratio of the mobility of the hole to electron is

(A)  4:9

(B)  4:11

(C)  9:4

(D)  11:4

Answer: (D)

28. Consider a spin S = ħ⁄2 particle in the state  The probability that a measurement finds the state with Sx = +ħ⁄2 is

(A)  5/18

(B)  11/18

(C)  15/18

(D)  17/18

Answer: (D)

29. An electromagnetic wave having electric field E = 8 cos(kz − ωt) ŷ V cm−1 is incident at 90°(normal incidence) on a square slab from vacuum (with refractive index n0 = 1. 0) as shown in the figure. The slab is composed of two different materials with refractive indices n1and n2. Assume that the permeability of each medium is the same. After passing through the slab for the first time, the electric field amplitude, in V cm−1, of the electromagnetic wave, which emerges from the slab in region 2, is closest to

(A)  11/1.6

(B)  11/3.2

(C)  11/13.8

(D)  11/25.6

Answer: (A)

30. Consider a point charge +Q of mass m suspended by a massless, inextensible string of length l in free space (permittivity ε0) as shown in the figure. It is placed at a height d (d > l) over an infinitely large, grounded conducting plane. The gravitational potential energy is assumed to be zero at the position of the conducting plane and is positive above the plane.

If θ represents the angular position and pθ its corresponding canonical momentum, then the correct Hamiltonian of the system is

Answer: (D)

31. Consider two concentric conducting spherical shells as shown in the figure. The inner shell has a radius a and carries a charge +Q. The outer shell has a radius b and carries a charge −Q. The empty space between them is half-filled by a hemispherical shell of a dielectric having permittivity ε1. The remaining space between the shells is filled with air having the permittivity ε0.

The electric field at a radial distance r from the center and between the shells (a < r < b) is

Answer: (A)

32. 

For the given sets of energy levels of nuclei X and Y whose mass numbers are odd and even, respectively, choose the best suited interpretation.

(A)  Set I: Rotational band of X

Set II: Vibrational band of Y

(B)  Set I: Rotational band of Y

        Set II: Vibrational band of X        

(C)  Set I: Vibrational band of X

        Set II: Rotational band of Y

(D)  Set I: Vibrational band of Y

        Set II: Rotational band of X

Answer: (D)

33. Consider a system of three distinguishable particles, each having spin S = 1/2 such that Sz = ±1/2 with corresponding magnetic moments μz = ±μ. When the system is placed in an external magnetic field H pointing along the z-axis, the total energy of the system is μH. Let x be the state where the first spin has Sz = 1/2. The probability of having the state x and the mean magnetic moment (in the +z direction) of the system in state x are

Answer: (A)

34. Consider a particle in a one-dimensional infinite potential well with its walls at x = 0 and x = L. The system is perturbed as shown in the figure.

The first order correction to the energy eigenvalue is

(A)  V0/4

(B)  V0/3

(C)  V0/2

(D)  V0/5

Answer: (C)

35. Consider a state described by ψ(x, t) = ψ2(x, t) + ψ4(x, t), where ψ2(x, t) and ψ4(x, t) are respectively the second and fourth normalized harmonic oscillator wave functions and ω is the angular frequency of the harmonic oscillator. The wave function ψ(x, t = 0) will be orthogonal to ψ(x, t) at time t equal to

(A)  π/2ω

(B)  π/ω

(C)  π/4ω

(D)  π/6ω

Answer: (A)

36. Consider a single one-dimensional harmonic oscillator of angular frequency ω, in equilibrium at temperature T = (kBβ)−1. The states of the harmonic oscillator are all non-degenerate having energy  with equal probability, where n is the quantum number. The Helmholtz free energy of the oscillator is

Answer: (B)

37. A system of two atoms can be in three quantum states having energies 0, ε and 2ε. The system is in equilibrium at temperature T = (kBβ)−1. Match the following Statistics with the Partition function.

(A)  CD:Z1, CI:Z2, FD:Z3, BE:Z4

(B)  CD:Z2, CI:Z3, FD:Z4, BE:Z1

(C)  CD:Z3, CI:Z4, FD:Z1, BE:Z2

(D)  CD:Z4, CI:Z1, FD:Z2, BE:Z3

Answer: (C)

38. The free energy of a ferromagnet is given by F = F0 + a0(T − TC)M2 + bM4, where F0, a0, and b are positive constants, M is the magnetization, T is the temperature, and TC is the Curie temperature. The relation between M2 and T is best depicted by

Answer: (B)

39. Consider a spherical galaxy of total mass M and radius R, having a uniform matter distribution. In this idealized situation, the orbital speed v of a star of mass m (m ≪ M) as a function of the distance r from the galactic centre is best described by

(G is the universal gravitational constant)

Answer: (A)

40. Consider the potential U(r) defined as  where α and U0 are real constants of appropriate dimensions. According to the first Born approximation, the elastic scattering amplitude calculated with U(r) for a (wave-vector) momentum transfer q and α → 0, is proportional to

((Useful integral:  

(A)  q2

(B)  q1

(C)  q

(D)  q2

Answer: (A)

41. As shown in the figure, inverse magnetic susceptibility (1/χ) is plotted as a function of temperature (T) for three different materials in paramagnetic states.

(Curie temperature of ferromagnetic material =TC

Néel temperature of antiferromagnetic material= TN)

Choose the correct statement from the following

(A)  Material 1 is antiferromagnetic (T < TN), 2 is paramagnetic, and 3 is ferromagnetic (T < TC).

(B)  Material 1 is paramagnetic, 2 is antiferromagnetic (T < TN), and 3 is ferromagnetic (T < TC).

(C)  Material 1 ferromagnetic (T < TC), 2 is antiferromagnetic (T < TN), and 3 is paramagnetic.

(D)  Material 1 is ferromagnetic (T < TC), 2 is paramagnetic, and 3 is antiferromagnetic (T < TN).

Answer: (A)

Q.42 – Q.46 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).

42. A function f(t) is defined only for t ≥ 0. The Laplace transform of f(t) is

whereas the Fourier transform of f(t) is

The correct statement(s) is(are)

(A)  The variable s is always real.

(B)  The variable s can be complex.

(C)  L(f; s) and  can never be made connected.

(D)  L(f; s) and  can be made connected.

Answer: (B; D)

43. P and Q are two Hermitian matrices and there exists a matrix R, which diagonalizes both of them, such that RPR−1 = S1 and RQR−1 = S2 , where S1 and S2 are diagonal matrices. The correct statement(s) is(are)

(A)  All the elements of both matrices S1 and S2 are real.

(B)  The matrix PQ can have complex eigenvalues.

(C)  The matrix QP can have complex eigenvalues.

(D)  The matrices P and Q commute.

Answer: (A; D)

44. A uniform block of mass M slides on a smooth horizontal bar. Another mass m is connected to it by an inextensible string of length l of negligible mass, and is constrained to oscillate in the X-Y plane only. Neglect the sizes of the masses. The number of degrees of freedom of the system is two and the generalized coordinates are chosen as x and θ, as shown in the figure.

If px and pθ are the generalized momenta corresponding to x and θ, respectively, then the correct option(s) is(are)

(A)   

(B)   

(C)  px is conserved

(D)  pθ is conserved

Answer: (A; C)

45. The Gell-Mann – Okuba mass formula defines the mass of baryons as where M0, a and b are constants, I represents the isospin and Y represents the hypercharge. If the mass of Σ hyperons is same as that of Λ hyperons, then the correct option(s) is(are)

(A)  M ∝ I(I + 1)

(B)  M ∝ Y

(C)  M does not depend on I

(D)  M does not depend on Y

Answer: (B; C)

46. The time derivative of a differentiable function g(qi, t) is added to a Lagrangian L(qi, q , t) such that  where qi, q̇i, t are the generalized coordinates, generalized velocities and time, respectively. Let pi be the generalized momentum and H the Hamiltonian associated with L(qi, q̇i, t). If p’i and H’ are those associated with L′, then the correct option(s) is(are)

(A)  Both L and L′ satisfy the Euler-Lagrange’s equations of motion

(B)    

(C)  If pi is conserved, then p’i is necessarily conserved

(D)   

Answer: (A; B)

Q.47 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

47. A linear charged particle accelerator is driven by an alternating voltage source operating at 10 MHz. Assume that it is used to accelerate electrons. After a few drift-tubes, the electrons attain a velocity 2. 9 × 108 m s–1. The minimum length of each drift-tube, in m, to accelerate the electrons further (rounded off to one decimal place) is______.

Answer: (14.0 to 15.0)

48. The Coulomb energy component in the binding energy of a nucleus is 18.432 MeV. If the radius of the uniform and spherical charge distribution in the nucleus is 3 fm, the corresponding atomic number (rounded off to the nearest integer) is _______.

Answer: (8 to 8 OR 9 to 9)

49. For a two-nucleon system in spin singlet state, the spin is represented through the Pauli matrices σ1, σ2 for particles 1 and 2, respectively.

The value of (σ1 ⋅ σ2) (in integer) is ________.

Answer: (-3 to -3)

50. A contour integral is defined as  where n is a positive integer and C is the closed contour, as shown in the figure, consisting of the line from −100 to 100 and the semicircle traversed in the counter-clockwise sense.

The value of  (in integer) is ______.

Answer: (5 to 5)

51. The normalized radial wave function of the second excited state of hydrogen atom is 

where a is the Bohr radius and r is the distance from the center of the atom. The distance at which the electron is most likely to be found is y × a. The

value of y (in integer) is ______.

Answer: (4 to 4)

52. Consider an atomic gas with number density n = 1020 m−3, in the ground state at 300 K. The valence electronic configuration of atoms is f7. The paramagnetic susceptibility of the gas χ = m × 1011. The value of m (rounded off to two decimal places) is ______.

(Given: Magnetic permeability of free space μ0 = 4π × 10−7 H m−1

Bohr magneton μB = 9. 274 × 10−24A m2

Boltzmann constant kB = 1. 3807 × 10−23 J K−1)

Answer: (5.40 to 5.50)

53. Consider a cross-section of an electromagnet having an air-gap of 5 cm as shown in the figure. It consists of a magnetic material (μ = 20000μ0) and is driven by a coil having NI = 104A, where N is the number of turns and I is the current in Ampere.

Ignoring the fringe fields, the magnitude of the magnetic field  (in Tesla, rounded off to two decimal places) in the air-gap between the magnetic poles is ______.

Answer: (0.24 to 0.26)

54. The spin  and orbital angular momentum total angular momentum.   precesses about an axis fixed by a magnetic field  where B0 is a constant. Now the magnetic field is changed to  Given the orbital angular momentum quantum number l = 2 and spin quantum number s = 1⁄2, θ is the angle between  for the largest possible values of total angular quantum number j and its z-component jz. The value of θ (in degree, rounded off to the nearest integer) is______.

Answer: (27 to 93)

55. The spin-orbit effect splits the 2P → 2S transition (wavelength, λ = 6521 Å) in Lithium into two lines with separation of ∆λ = 0. 14 Å. The corresponding positive value of energy difference between the above two lines, in eV, is m × 10−5. The value of m (rounded off to the nearest integer) is ______.

(Given: Planck’s constant, h = 4. 125 × 10−15eV s

Speed of light, c = 3 × 108 m s−1)

Answer: (3 to 5)

GATE Exam 2021 Petroleum Engineering (PE) Question Paper With Answer Key

GATE-2024

PE-Petroleum Engineering

GA – General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. The current population of a city is 11,02,500. If it has been increasing at the rate of 5% per annum, what was its population 2 years ago?

(A)  9,92,500

(B)  9,95,006

(C)  10,00,000

(D)  12,51,506

Answer: (C)

2. p and q are positive integers and 

(A)  3

(B)  7

(C)  9

(D)  11

Answer: (B)

3. 

The least number of squares that must be added so that the line P-Q becomes the line of symmetry is ________

(A)  4

(B)  3

(C)  6

(D)  7

Answer: (C)

4. Nostalgia is to anticipation as _______ is to ________

Which one of the following options maintains a similar logical relation in the above sentence?

(A)  Present, past

(B)  Future, past

(C)  Past, future

(D)  Future, present

Answer: (C)

5. Consider the following sentences:

(i) I woke up from sleep.

(ii) I woked up from sleep.

(iii) I was woken up from sleep.

(iv) I was wokened up from sleep.

Which of the above sentences are grammatically CORRECT?

(A)  (i) and (ii)

(B)  (i) and (iii)

(C)  (ii) and (iii)

(D)  (i) and (iv)

Answer: (B)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

6. Given below are two statements and two conclusions.

Statement 1: All purple are green.

Statement 2: All black are green.

Conclusion I: Some black are purple.

Conclusion II: No black is purple.

Based on the above statements and conclusions, which one of the following options is logically CORRECT?

(A)  Only conclusion I is correct.

(B)  Only conclusion II is correct.

(C)  Either conclusion I or II is correct.

(D)  Both conclusion I and II are correct.

Answer: (C)

7. Computers are ubiquitous. They are used to improve efficiency in almost all fields from agriculture to space exploration. Artificial intelligence (AI) is currently a hot topic. AI enables computers to learn, given enough training data. For humans, sitting in front of a computer for long hours can lead to health issues.

Which of the following can be deduced from the above passage?

(i) Nowadays, computers are present in almost all places.

(ii) Computers cannot be used for solving problems in engineering.

(iii) For humans, there are both positive and negative effects of using computers.

(iv) Artificial intelligence can be done without data.

(A)  (ii) and (iii)

(B)  (ii) and (iv)

(C)  (i), (iii) and (iv)

(D)  (i) and (iii)

Answer: (D)

8. Consider a square sheet of side 1 unit. In the first step, it is cut along the main diagonal to get two triangles. In the next step, one of the cut triangles is revolved about its short edge to form a solid cone. The volume of the resulting cone, in cubic units, is ________

(A)  π/3

(B)  2π/3

(C)  3π/2

(D)  3π

Answer: (A)

9. 

The number of minutes spent by two students, X and Y, exercising every day in a given week are shown in the bar chart above.

The number of days in the given week in which one of the students spent a minimum of 10% more than the other student, on a given day, is

(A)  4

(B)  5

(C)  6

(D)  7

Answer: (C)

10. 

Corners are cut from an equilateral triangle to produce a regular convex hexagon as shown in the figure above.

The ratio of the area of the regular convex hexagon to the area of the original equilateral triangle is

(A)  2 : 3

(B)  3 : 4

(C)  4 : 5

(D)  5 : 6

Answer: (A)

Petroleum Engineering (PE)

Q.1 – Q.13 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. MOPU (in the context of offshore drilling and production systems) stands for

(A)  Mobile Offshore Process Unit

(B)  Mobile Offshore Piping Unit

(C)  Mobile Offshore Production Unit

(D)  Mobile Oil Production Unit

Answer: (C)

2. Which ONE of the following statements is INCORRECT?

(A)  Conductor is the outer casing of a well

(B)  Riser is used for transporting fluid

(C)  Conductor and riser have the same functions

(D)  Conductor is used for shielding the well flow lines from external forces

Answer: (C)

3. Which ONE of the following offshore installations uses Dynamic Positioning System (DPS) for station keeping?

(A)  Jacket

(B)  Jack-up

(C)  Semi-submersible

(D)  Tension Leg Platform

Answer: (C)

4. Which ONE of the following is NOT a primary safety system for offshore installations?

(A)  Emergency Shut Down

(B)  Isolation

(C)  Fire Protection

(D)  Blowdown

Answer: (C)

5. The primary function of the thruster in the Dynamic Positioning System (DPS) of an offshore installation is

(A)  To apply thrust in the direction opposite to the resultant environmental force

(B)  To apply thrust in the same direction as the resultant environmental force

(C)  To apply thrust in the direction opposite to the motion

(D)  To apply thrust in the same direction as the motion

Answer: (A OR C)

6. Select the CORRECT firefighting system for electrical switchgear room in an offshore facility.

(A)  Wet chemical

(B)  Halon system

(C)  Foam

(D)  Water sprinklers

Answer: (B)

7. Which ONE of the following options can be used to quantify secondary porosity?

(A)  Sonic and Gamma Ray Logs

(B)  Sonic and Neutron Logs

(C)  Sonic and Caliper Logs

(D)  Density and Neutron Logs

Answer: (B)

8. Among the options given below, what is the typical temperature range for significant oil generation in a source rock associated with conventional crude-oil reservoirs?

(A)  10 °C – 40 °C

(B)  60 °C – 175 °C

(C)  225 °C – 325 °C

(D)  350 °C – 425 °C

Answer: (B)

9. In the original Darcy’s law as proposed by Henry Darcy, which of the following drives the fluid flow through a fully saturated sand column?

(A)  Pressure-gradient or hydraulic-gradient

(B)  Viscous force per unit volume

(C)  Capillary force per unit volume

(D)  Inertial force per unit volume

Answer: (A)

10. At which ONE of the following scales is Darcy’s law for fluid flow through a porous medium applicable?

(A)  Nano-scale

(B)  Molecular-scale

(C)  Microscopic-scale

(D)  Macroscopic-scale

Answer: (D)

11. Pressure – Temperature phase diagram of CO2 is shown below. Identify the correct phases from the given options.

(A)  I = Solid Phase, II = Liquid Phase, III = Gas Phase, IV = Supercritical Phase

(B)  I = Gas Phase, II = Supercritical Phase, III = Solid Phase, IV = Liquid Phase

(C)  I = Supercritical Phase, II = Liquid Phase, III = Solid Phase, IV = Gas Phase

(D)  I = Gas Phase, II = Solid Phase, III = Liquid Phase, IV = Supercritical Phase

Answer: (D)

12. A measure of the potential of crude oil to form surfactants for Enhanced Oil Recovery (EOR) is given by the Total Acid Number (TAN). TAN is the mass of _________ (in milligrams) that is required to neutralize one gram of crude oil.

(A)  Ca(OH)2

(B)  NaCl

(C)  KOH

(D)  NaOH

Answer: (C)

13. In Water-Alternating-Gas (WAG) injection, the purpose of the injection is to _____I_____ the “relative permeability” of gas and to ____II_____ the “mobility” of the gas.

(A)  I = reduce, II = enhance

(B)  I = reduce, II = reduce

(C)  I = enhance, II = reduce

(D)  I = enhance, II = enhance

Answer: (B)

Q.14 – Q.19 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).

14. Solids that may possibly form in the offshore pipelines during the production of oil and gas from deep-water reservoirs are

(A)  Wax

(B)  Char

(C)  Hydrates

(D)  Asphaltenes

Answer: (A; C; D)

15. Oil and gas pipelines, which are at an elevated pressure (about 3 MPa) and sub-ambient temperature (below 298 K), may get blocked by the formation of solid hydrates. One of the strategies adopted to inhibit the formation of hydrates is the injection of Thermodynamic Hydrate Inhibitors (THIs) into the reservoir fluid.

Identify all suitable chemicals that are commonly used as THIs.

(A)  Sodium Chloride

(B)  Methanol

(C)  Polyvinylpyrrolidone

(D)  Sodium Dodecyl Sulphate

Answer: (A; B)

16. When CO2 and liquid water are brought in contact with each other, they may form solid hydrates. The three-phase hydrate boundary is shown in the Pressure -Temperature plot given below.

Identify the correct statements.

G = Gas Phase, H = Hydrate Phase, L = Liquid Phase

(A)  Hydrates are stable in region I

(B)  Hydrates are stable in region II

(C)  Hydrates are stable in region III

(D)  Hydrates are stable in region IV

Answer: (B; D)

17. Heavy oil recovered from reservoirs can be represented by CXH5X. Suitable processes to reduce the density of heavy oil are

(A)  Carbon Rejection

(B)  Pyrolysis

(C)  Hydrogenation

(D)  Filtration

Answer: (A; C OR A; B; C)

18. Identify the CORRECT statements for a n × n matrix.

(A)  Under elementary row operations, the rank of the matrix remains invariant

(B)  Under elementary row operations, the eigenvalues of the matrix remain the same

(C)  If the elements in a row can be written as a linear combination of two or more rows, then the matrix is singular.

(D)  The rank of the matrix is equal to n if the determinant of the matrix is zero.

Answer: (A; C)

19. During a drilling operation, kick occurs if

(A)  the shear ram in the Blow Out Preventer (BOP) does not work.

(B)  the formation pressure is equal to the drilling fluid pressure.

(C)  the volume of the mud used to fill the hole is less than that of the pipe being pulled out.

(D)  the formation pressure is more than the drilling fluid pressure.

Answer: (C; D OR D)

Q.20 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

20. The value of  is __________ (correct up to one decimal place).

Answer: (0.5 to 0.5)

21. Given two complex numbers, z1 = 4 + 3i and z2 = 2 − 5i, the real part of is _____.

Answer: (-7 to -7)

22. The number of ‘three-digit numbers’ that can be formed using the digits from 1 to 9 without the repetition of each digit is ________.

Answer: (504 to 504)

23. The estimate for the root of the function f(x) = e2x + 2x after one iteration with an initial guess of x0 = 0, using the Newton-Raphson method is________ (correct up to two decimal places).

Answer: (-0.25 to -0.25)

24. A saturated oil reservoir has an average reservoir pressure of 3000 psia tested for flowing bottom-hole pressure (BHP) of 2000 psia and production rate of 500 STB/day. The maximum reservoir deliverability based on Vogel’s equation for two-phase flow is ________ STB/day.

Answer: (960 to 990)

25. If the specific heat ratio of natural gas is 1.28, the critical pressure ratio (ratio of outlet pressure to upstream pressure) through a choke is ________ (round off to two decimal places).

Answer: (0.52 to 0.57)

Q.26 – Q.37 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

26. Match the suitable artificial lift methods (GROUP I) to meet the requirements (GROUP II) given in the table.

(A)  P – I, Q – II, R – IV, S – III

(B)  P – II, Q – I, R – IV, S – III

(C)  P – I, Q – II, R – III, S – IV

(D)  P – II, Q – I, R – III, S – IV

Answer: (D)

27. Match the Enhanced Oil Recovery (EOR) methods (GROUP I) with the corresponding laboratory tests (GROUP II).

(A)  P – III, Q – II, R – I, S – IV

(B)  P – II, Q – IV, R – I, S – III

(C)  P – III, Q – IV, R – II, S – I

(D)  P – III, Q – II, R – IV, S – I

Answer: (C)

28. Identify the following well test methods corresponding to the transient pressure profiles in the figures given below. (BHP: Bottom-hole pressure, BOPD: Barrels of oil per day)

(P) Flow-after-flow test

(Q) Interference test

(R) Fall-off test

(S) Modified isochronal test

(A)  P – IV, Q – II, R – I, S – III

(B)  P – II, Q – III, R – IV, S – I

(C)  P – II, Q – III, R – I, S – IV

(D)  P – IV, Q – I, R – III, S – II

Answer: (C)

29. Match the following wire-line logging methods (GROUP I) based on the physical principles of measurements (GROUP II).

(A)  P – II, Q – I, R – IV, S – III

(B)  P – II, Q – I, R – IV, S – III

(C)  P – III, Q – II, R – IV, S – I

(D)  P – II, Q – I, R – III, S – IV

Answer: (B)

30. Match the following rock types (GROUP I) with their respective chemical compositions (GROUP II) from the given options.

(A)  P – III, Q – II, R – IV, S – I

(B)  P – II, Q – III, R – I, S – IV

(C)  P – III, Q – I, R – IV, S – II

(D)  P – III, Q – I, R – II, S – IV

Answer: (C)

31. The following equations describe the transient fluid flow in a typical petroleum reservoir system. Here, p is pressure, x and r are the spatial coordinates in rectangular and cylindrical systems respectively, and t is time. Also, ϕ (porosity), μ (viscosity), cf (formation compressibility), ct (total compressibility) and k(permeability) are constant coefficients.

Match the equations (GROUP I) with their corresponding descriptions (GROUP II).

(A)  P – IV, Q – I, R – II, S – III

(B)  P – IV, Q – III, R – II, S – I

(C)  P – III, Q – IV, R – II, S – I

(D)  P – III, Q – IV, R – I, S – II

Answer: (A)

32. Select the INCORRECT statement related to Enhanced Oil Recovery (EOR) techniques from the following options.

(A)  Alkaline flooding recovers crude oil by reduction of interfacial tension (IFT) and reversal of wettability of rocks.

(B)  In-situ combustion recovers crude oil by the application of heat, thus lowering the viscosity of the crude oil.

(C)  Nitrogen flue gas flooding recovers crude oil by vaporizing the lighter components of the crude oil.

(D)  Polymer flooding recovers crude oil by reducing the viscosity and increasing the mobility of water.

Answer: (D)

33. Match the petroleum reservoir forming traps (GROUP I) with their general classifications (GROUP II).

(A)  P – III, Q – II, R – IV, S – I

(B)  P – II, Q – III, R – IV, S – I

(C)  P – III, Q – I, R – II, S – IV

(D)  P – II, Q – III, R – I, S – IV

Answer: (B)

34. An Ideal Pressure Buildup Test yields a single straight line for all times, when shut-in Bottom-Hole Pressure (Pws) is plotted against  . Here tp is the well production time and Δt is the time elapsed since shut-in. However, in an actual Pressure Buildup Test, a non-linear curve is obtained which can be logically divided into distinct regions.

Choose the INCORRECT option from the following.

(A)  A late-time region, in which the radius of investigation has reached the well’s drainage boundaries.

(B)  A middle-time region during which the pressure transient has moved away from the wellbore and into the bulk formation.

(C)  An early-time region during which a pressure transient is moving through the formation nearest the wellbore.

(D)  An early-time region during which a pressure transient is moving away from the drainage boundary.

Answer: (D)

35. When two immiscible fluid phases are placed in contact with a solid surface, one phase usually is attracted to solid more strongly than the other phase. The more strongly attracted phase is called the ‘wetting phase’.

The inter-molecular interaction of the non-wetting phase with the solid is ___I___ than its intra-molecular interaction. Due to this, the non-wetting phase tends to occupy the ____II_____ of the reservoir.

(A)  I = stronger, II = smaller pores

(B)  I = stronger, II = larger pores

(C)  I = weaker, II = smaller pores

(D)  I = weaker, II = larger pores

Answer: (D)

36. Coal bed methane is methane gas adsorbed in coal seams. To desorb the methane from the coal seam it should be exposed to CO2 and (or) N2. Which ONE of the following is an appropriate reason to enhance the desorption process?

(A)  N2 is used because it has low kinetic energy compared to CH4

(B)  CO2 is used as it has high kinetic energy compared to CH4

(C)  CO2 is used as it strongly binds with coal compared to CH4

(D)  N2 is used as it strongly binds with coal compared to CH4

Answer: (C)

37. Match the platforms (GROUP I) with appropriate support systems (GROUP II).

(A)  P – IV, Q – III, R – I, S – II

(B)  P – II, Q – III, R – I, S – IV

(C)  P – III, Q – I, R – IV, S – II

(D)  P – I, Q – IV, R – II, S – III

Answer: (A)

Q.38 – Q.39 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).

38. Select the CORRECT statements from the following.

Well testing operations on a typical crude oil reservoir

(A)  do not measure rock and fluid properties of the reservoir when the well is flowing or shut-in.

(B)  measure variation in pressure response of the reservoir with time when the well is flowing or shut-in.

(C)  measure productivity index and partial well completion.

(D)  do not measure length and conductivity of hydraulic fractures.

Answer: (B; C; OR A; B; C)

39. Crude oil from oil sands contains bitumen and asphaltene and this crude is heavy and viscous at room temperature. Assume that one such crude oil is represented by CXH2XOY. For easier transportation through pipelines it should be processed further. Identify the processes which help in transportation of this crude oil.

(A)  Drying

(B)  Vis-breaking

(C)  Coking process

(D)  Hydro-treating

Answer: (B; C; D)

Q.40 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

40. Given matrix  The eigenvalue corresponding to the eigenvector  is ________.

Answer: (3 to 3)

41. The maximum value of the function f(x) = x4 − 8x2 + 2 for −2 ≤ x ≤ 2 is ________.

Answer: (2 to 2)

42. Given the second order ordinary differential equation: y′′ + 3y′ − 4y = 0with the initial conditions y(0) = 3, and y′(0) = −7, the value of y(1) is ________ (round off to two decimal places).

Answer: (2.71 to 2.79)

43. The directional derivative of f(x, y, z) = x2 + 3y2 + z2, at point (2, 1, 0) along the unit vector in x-direction, î, is _________.

Answer: (4 to 4)

44. A productivity test conducted on a crude oil well indicates a stabilized flow rate of 150 STB/day (water-free oil production) at a bottom-hole flowing pressure of 935 psig. After shutting the well for 24 hours, the bottom-hole pressure reached a static value of 1250 psig.

The Absolute Open Flow (AOF) potential of the well is __________STB/day.

Answer: (580 to 610)

45. A porous medium (shown schematically in the figure) has the following properties.

Length L = 600 m, Width W = 8 m, Height h = 0.5 m,

Permeability k = 100 mD, Porosity ϕ = 15%.

An incompressible fluid having a viscosity of 2 cP is flowing through a porous medium at the inlet and exit pressures of 7 × 106 Pa and 6 × 106 Pa, respectively.

The actual fluid velocity through the porous medium is _______× 107 m/s.

(1 Darcy = 1012 m2)

Answer: (5 to 6)

46. A tubing with an inner diameter of 2.259 inch delivers oil from a well at the rate of 1000 bbl/day. The API gravity and viscosity of the oil are 40o and 1.2 cP, respectively. The tubing makes an angle of 15o with the vertical. Assuming a fanning friction factor of 0.006, the pressure-drop over a length of 1000 ft tubing is _________ psi (round off to nearest integer).

[1 bbl = 5.615 ft3]

Answer: (340 to 360)

47. A cylindrical crude oil reservoir with a radius of 3000 ft is under water influx from a cylindrical aquifer with an estimated radius of 9000 ft. The reservoir has the following properties.

Aquifer thickness, h = 40 ft

Porosity, ϕ = 15%

Formation compressibility, Cf = 4.5 × 106 psi1

Water compressibility, Cw = 4.0 × 10-6 psi1

Assuming a pot reservoir model with fractional encroachment angle as unity, the water influx into the reservoir for a pressure drop of 700 psi is ________ MMbbl (million barrels) (round off to two decimal places).

(π = 3.14, 1 bbl = 5.615 ft3)

Answer: (1.36 to 1.50)

48. A heavy oil reservoir with an initial oil recovery of 10% has the following properties.

Confined area A = 1.5 acres, thickness of the reservoir h = 15 ft,

effective porosity ϕ = 15%, irreducible water saturation Swr = 25%,

oil formation volume factor Bo = 1.10 bbl/STB.

An in-situ combustion test was conducted in the above reservoir. Oil recovery due to the combustion process at the well is observed to be 12000 bbl.

The total (overall) oil recovery at the end of the in-situ combustion process is __________% (round off to nearest integer) of the original oil in place.

(1 acre = 43560 ft2, 1 bbl = 5.615 ft3)

Answer: (68 to 78)

49. A double acting duplex pump with a rod diameter of 2.5 inch and a stroke of 20 inch is to be operated at 60 strokes per minute for drilling down to 10000 ft. The flow rate is 600 gpm. If the volumetric efficiency of the pump is 80%, the liner size is_________ inch (round off to one decimal place).

[1 gallon = 231 inch3]

Answer: (6.5 to 7.5)

50. The fluid flow through an under-saturated oil reservoir is driven by solution gas drive mechanism. The reservoir parameters are as given below.

Compressibility of water, cw = 1 × 10−6 psi−1

Compressibility of formation, cf = 1 × 10−5 psi−1

Connate water saturation, Swc = 0. 2

Initial reservoir pressure, pi = 4000 psi

Reservoir pressure at bubble-point, pb = 3000 psi

Oil formation volume factor, Boi = 1. 24 rb/STB

Formation volume factor at bubble point pressure, Bob = 1. 26 rb/STB.

The percentage of oil recovered as a fraction of the Original Oil in Place (OOIP) is ________% (round off to one decimal place).

Answer: (2.6 to 3.0)

51. During drilling, a well is damaged out to a radial distance of 5 ft from the periphery of the wellbore so that the permeability within the damaged zone is reduced to 1/50th of the undamaged effective permeability. After completion, the well is stimulated so that the permeability out to a radial distance of 15 ft from the periphery of the wellbore is increased to twenty times the permeability of the undamaged zone.

The radial inflow equation for stabilized flow conditions under semi-steady state conditions is given by

where pe is effective pressure, pwf is flowing bottom-hole pressure, q is flow-rate, μ is viscosity, ke is average effective permeability, h is reservoir thickness, re is drainage radius, rw is wellbore radius and S is skin factor.

If rw = 0. 5 ft and re = 500 ft, then the increase in Productivity Index ratio   is ___________ (round off to one decimal place).

Answer: (32 to 42)

52. A depleted and shut-in oil reservoir originally contained 25 × 106 STB of oil with a formation volume factor of 1.35 res bbl/STB and a connate water saturation of 0.25. Cumulative oil production to date has been 2. 5 × 106 STB of oil. The oil formation volume factor is now 1.25 res bbl/STB. Assuming no water influx, the gas saturation in the reservoir is ___________ %(round off to one decimal place).

Answer: (11 to 14)

53. Surface tension of liquid A in a capillary is being measured in the laboratory using capillary rise (refer the figure given below). The capillary radius (r) is 100 μm, the height of liquid column (h) is 10 cm and Ө = 38°. Density of air can be neglected. Assume liquid A to have the same density as water.

Surface tension of liquid A at room temperature is ___________dynes/cm (round off to one decimal place).

Answer: (61 to 65)

54. Miscible displacement process is one of the EOR techniques. The performance of this process depends on fluid physical properties that affect flow behavior in a reservoir. Two of the important properties are density and viscosity. Consider the use of CO2 for one such process. The density of CO2 at the reservoir condition is ____________ lb/ft3 (round off to one decimal place).

Relevant data for this calculation are given below.

Reservoir temperature = 300 °F (422 K)

Reservoir pressure = 1470 psig (100 atm)

Compressibility factor (z) at the reservoir condition = 0.5

Values of Universal Gas Constant (R) in different units are listed below.

Universal Gas Constant (R) = 8.314 m3.Pa.K−1mol−1

= 10.731 psi. ft3.lb. mol−1 °R−1

= 0.082 L. atm. K−1 mol−1

Answer: (15.7 to 16.1)

55. In a counter current heat exchanger, the hot fluid enters at 175 °F and exits at 100 ° The cold fluid enters at 75 °F and exits at 85 °F. For the calculation of heat transfer rate, consider the tube surface area (per unit length) to be 0.26 ft2/ft and a tube length of 40 ft. The overall heat transfer coefficient of the exchanger is 100 BTU/hr-ft2. The minimum number of tubes required in the exchanger for a heat duty of 15 × 105 BTU/hr is____________ (round off to nearest integer).

Answer: (MTA)

GATE Exam 2021 Metallurgical Engineering (MT) Question Paper With Answer Key

GATE-2021

MT-Metallurgical Engineering

GA – General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Five persons P, Q, R, S and T are to be seated in a row, all facing the same direction, but not necessarily in the same order. P and T cannot be seated at either end of the row. P should not be seated adjacent to S. R is to be seated at the second position from the left end of the row. The number of distinct seating arrangements possible is:

(A)  2

(B)  3

(C)  4

(D)  5

Answer: (B)

2. Consider the following sentences:

(i) The number of candidates who appear for the GATE examination is staggering.

(ii) A number of candidates from my class are appearing for the GATE examination.

(iii) The number of candidates who appear for the GATE examination are staggering.

(iv) A number of candidates from my class is appearing for the GATE examination.

Which of the above sentences are grammatically CORRECT?

(A)  (i) and (ii)

(B)  (i) and (iii)

(C)  (ii) and (iii)

(D)  (ii) and (iv)

Answer: (A)

3. A digital watch X beeps every 30 seconds while watch Y beeps every 32 seconds. They beeped together at 10 AM.

(A)  10.08 AM

(B)  10.42 AM

(C)  11.00 AM

(D)  10.00 PM

Answer: (A)

4. If ⊕÷⊙= 2 ; ⊕÷ Δ = 3; ⊙ +Δ = 5; Δ ×⊗ =10,

Then, the value of (⊗ − ⊕)2, is:

(A)  0

(B)  1

(C)  4

(D)  16

Answer: (B)

5. The front door of Mr. X’s house faces East. Mr. X leaves the house, walking 50 m straight from the back door that is situated directly opposite to the front door. He then turns to his right, walks for another 50 m and stops. The direction of the point Mr. X is now located at with respect to the starting point is ______

(A)  South-East

(B)  North-East

(C)  West

(D)  North-West

Answer: (D)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

6. Given below are two statements 1 and 2, and two conclusions I and II.

Statement 1: All entrepreneurs are wealthy.

Statement 2: All wealthy are risk seekers.

Conclusion I: All risk seekers are wealthy.

Conclusion II: Only some entrepreneurs are risk seekers.

Based on the above statements and conclusions, which one of the following options is CORRECT?

(A)  Only conclusion I is correct

(B)  Only conclusion II is correct

(C)  Neither conclusion I nor II is correct

(D)  Both conclusions I and II are correct

Answer: (C)

7. A box contains 15 blue balls and 45 black balls. If 2 balls are selected randomly, without replacement, the probability of an outcome in which the first selected is a blue ball and the second selected is a black ball, is _____

(A)  3/16

(B)  45/236

(C)  1/4

(D)  3/4

Answer: (B)

8. 

The ratio of the area of the inscribed circle to the area of the circumscribed circle of an equilateral triangle is____

(A)  1/8

(B)  1/6

(C)  1/4

(D)  1/2

Answer: (C)

9. Consider a square sheet of side 1 unit. The sheet is first folded along the main diagonal. This is followed by a fold along its line of symmetry. The resulting folded shape is again folded along its line of symmetry. The area of each face of the final folded shape, in square units, equal to _______

(A)  1/4

(B)  1/8

(C)  1/16

(D)  1/32

Answer: (B)

10. The world is going through the worst pandemic in the past hundred years. The air travel industry is facing a crisis, as the resulting quarantine requirement for travelers led to weak demand.

In relation to the first sentence above, what does the second sentence do?

(A)  Restates an idea from the first sentence.

(B)  Second sentence entirely contradicts the first sentence.

(C)  The two statements are unrelated.

(D)  States an effect of the first sentence.

Answer: (D)

Metallurgical Engineering (MT)

Q.1 – Q.13 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. For the matrix given below, the eigenvalues are:

(A)  0, 2, 2

(B)  1, 1, 2

(C)  0, 1, 2

(D)  0, 1, 3

Answer: (C)

2. Which one of the following is a homogeneous function of degree three?

(A)  x3 + 2x2y2

(B)  y2x + 2yx2

(C)  y3 + 2x2

(D)  xy2 + 3xy

Answer: (B)

3. The divergence of a vector field  where its three components (Vx, Vy, Vz) are functions of x, y, z, is:

Answer: (A)

4. Which one of the following is ‘center split’ defect in rolling operation?

Answer: (D)

5. Single crystal turbine blades of nickel-based superalloys for aero-engines are manufactured using:

(A)  Investment casting

(B)  Die casting

(C)  Squeeze casting

(D)  Directional solidification

Answer: (D)

6. Elements A and B have the same crystal structure. For a dilute solution of B in A, which one of the following is true?

(Given: ∆Hmix – Mixing enthalpy, aB – Activity of B and XB – Mole fraction of B)

(A)  If ∆Hmix = 0, then aB < XB

(B)  If ∆Hmix = 0, then aB > XB

(C)  If ∆Hmix > 0, then aB < XB

(D)  If ∆Hmix < 0, then aB < XB

Answer: (D)

7. For uniaxial tensile stress-strain behaviour of polycrystalline aluminium, which one of the following statements is FALSE?

(A)  True stress is always higher than the engineering stress.

(B)  At the ultimate tensile stress point on the true stress – strain curve,  

(C)  Resilience is the area under the elastic region of the engineering stress – strain curve.

(D)  Maximum true stress does not correspond to the maximum load.

Answer: (B)

8. Which one of the following is FALSE for creep deformation?

(A)  The minimum creep rate is obtained in the primary stage (stage I).

(B)  Creep resistance decreases with decrease in grain size.

(C)  Coble creep occurs via grain boundary diffusion.

(D)  Nabarro-Herring creep occurs via lattice diffusion.

Answer: (A)

9. Which one of the following elements alloyed with iron is a ferrite stabilizer?

(A)  Nickel

(B)  Manganese

(C)  Carbon

(D)  Silicon

Answer: (D)

10. Which one of the following is the correct decreasing sequence of Quenching Power for quenchants used in heat treatment of steels?

(A)  Oil > Water > Brine > Air

(B)  Brine > Oil > Water > Air

(C)  Brine > Water > Oil > Air

(D)  Water > Brine > Oil > Air

Answer: (C)

11. For a zeroth order chemical reaction, which one of the following is FALSE?

(A)  Concentration versus time plot is a straight line.

(B)  Increase in concentration of reacting species increases the rate of reaction.

(C)  Half-life depends on the initial concentration and zero-order rate constant.

(D)  Rate of reaction depends on temperature.

Answer: (B)

12. Which one of the following elements oxidizes first in basic oxygen steel making process?

(A)  Silicon

(B)  Carbon

(C)  Manganese

(D)  Phosphorus

Answer: (A)

13. Which one of the following is a hydrometallurgical operation?

(A)  Roasting

(B)  Leaching

(C)  Zone refining

(D)  Smelting

Answer: (B)

Q.14 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

14. The value of  is: ____________ (round off to nearest integer).

Answer: (25 to 25)

15. The grain size (X) of annealed specimens follows a symmetric distribution with a mean (μ) of 5 μm and a standard deviation (σ) of 0.5 μm. The percentage of specimens with grain size in the range 5 to 6 μm is expected to be: __________ (round off to nearest integer).

Given: For the symmetric distribution: Probability P(X ≤ μ + 2σ) = 0. 98

Answer: (48 to 48)

16. If  the value of  (in J mol1) at 298 K is: ________ (round off to nearest integer).

Given: F = 96500 C mol1

Answer: (-48251 to -48240)

17. Melting point of Cu is 1358 K and its enthalpy of melting is 13400 J mol1The value of free energy change (in J mol1) for liquid to solid transformation at 1058 K is: _____________ (round off to nearest integer).

Answer: (-2962 to -2958)

18. A body is subjected to a state of stress given by the following stress tensor:

If yielding is predicted by the Tresca Criterion, the uniaxial tensile yield stress (in MPa) of the body should be less than or equal to: ___________ (round off to nearest integer).

Answer: (150 to 150)

19. Consider homogeneous nucleation of a spherical solid in liquid. For a given undercooling, if surface energy of a nucleus increases by 20 %, the corresponding increase (in percent) in the critical radius of the nucleus is: ________ (round off to nearest integer).

Answer: (20 to 20)

20. If saturation magnetization of iron at room temperature is 1700 kA m-1, the magnetic moment (in A m2) per iron atom in the crystal is: _______ × 1023 (round off to 1 decimal place).

(Given: Lattice parameter of iron at room temperature = 0.287 nm)

Answer: (1.7 to 2.3)

21. In the X-ray diffraction pattern of a FCC crystal, the first reflection occurs at a Bragg angle (θ) of 30°. The Bragg angle (in degree) for the second reflection will be: __________ (round off to 1 decimal place).

Answer: (34.8 to 36.1)

22. A 0.6 wt.% C steel sample is slowly cooled from 900°C to room temperature. The fraction of proeutectoid ferrite in the microstructure is: ___________ (round off to 2 decimal places).

Given: Eutectoid composition: 0.8 wt.% C

Maximum solubility of carbon in α-Fe: 0.025 wt.% C

Answer: (0.22 to 0.30)

23. If the degree of polymerization of polyethylene is 30000, the average molecular weight (in g mol1) is: _____________ (round off to nearest integer).

(Given: Atomic weights of carbon and hydrogen are 12 and 1, respectively)

Answer: (840000 to 840000)

24. Water flows over a plate of finite length. At x = x1 from the leading edge, the velocity of the flow is Vx = 0. 5y – 0. 5y3. The thickness, δ (in meter) of the boundary layer at x = x1 is: _________ (round off to 2 decimal places).

Given: V is the free stream velocity.

Answer: (0.53 to 0.59)

25. The vacancy concentration in a crystal doubles upon increasing the temperature from 27 °C to 127 ° The enthalpy (in kJ mol1) of vacancy formation is: ________ (round off to 2 decimal places).

Given: R = 8.314 J mol1 K1

Answer: (6.85 to 7.00)

Q.26 – Q.36 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

26. The minimum value of y for the equation y = x2 − 2x + 4 is ______.

(A)  3

(B)  1

(C)  4

(D)  6

Answer: (A)

27. Match the forming process (in Column I) with its name (in Column II):

(A)  P−1, Q−2, R−3, S−4

(B)  P−3, Q−1, R−4, S−2

(C)  P−3, Q−4, R−1, S−2

(D)  P−1, Q−4, R−3, S−2

Answer: (B)

28. Match the nondestructive technique (in Column I) with its underlying phenomenon (in Column II):

(A)  P−4, Q−3, R−2, S−1

(B)  P−2, Q−1, R−3, S−4

(C)  P−2, Q−1, R−4, S−3

(D)  P−3, Q−2, R−1, S−4

Answer: (C)

29. Number of degrees of freedom for the following reacting system is: M (s) + CO2 (g) = MO (s) + CO (g)

(A)  0

(B)  1

(C)  2

(D)  3

Answer: (C)

30. The condition for getting the binary phase diagram of A-B (shown below) is:

Answer: (B)

31. In the absence of any external stress, which one of the following statements related to the interaction of point defect and a dislocation is FALSE:

(A)  An oversized solute atom would preferentially migrate below the slip plane of an edge dislocation.

(B)  A spherically symmetric point defect can interact with both the hydrostatic and shear stress fields of a dislocation.

(C)  A point defect can locally modify the elastic modulus and thereby can change the interaction energy.

(D)  Vacancies are attracted towards the compressive region of dislocation.

Answer: (B)

32. A single crystal aluminium sample is subjected to uniaxial tension along [112] direction. If the applied tensile stress is 100 MPa and the critical resolved shear stress (CRSS) is 25 MPa, which one of the following slip systems will be activated?

Answer: (A)

33. One-dimensional steady-state temperature distribution in two adjacent refractory blocks (with thermal conductivities, k1 and k2) of unit cross-sectional area are shown below. The temperature T1 and thermal contact resistance of the interface, respectively, are:

(A)  200 K, 0.5 K W1

(B)  400 K, 1.0 K W1

(C)  200 K, 0.25 K W1

(D)  500 K, 0.5 K W1

Answer: (A)

34. For a fully developed 1-D flow of a Newtonian fluid through a horizontal pipe of radius R (see figure), the axial velocity (vz) is given by:

where, ∆P is the pressure difference (P1 –P2), μ is the viscosity, r is the radial distance from the axis and L is the length of the tube. The shear stress exerted by the fluid on the tube wall is:

(A)  ∆PR/2L

(B)  ∆PR/L

(C)  3∆PR/2L

(D)  2∆PR/L

Answer: (A)

35. Match the terms (in Column I) with the unit process (in Column II)

(A)  P−2, Q−1, R−4, S−3

(B)  P−4, Q−1, R−2, S−3

(C)  P−4, Q−3, R−1, S−2

(D)  P−2, Q−3, R−4, S−1

Answer: (A)

36. A blast furnace uses hematite ore with 80% Fe2O3 and 20% gangue materials. It uses 600 kg coke per ton of hot metal. The coke contains 85% C and 15% ash. The composition of hot metal is 95.5% Fe and 4.5% C.

The weight of iron ore used and slag produced per ton of hot metal respectively, are:

Given: Atomic weight: O = 16, C = 12, N = 14, Fe = 56

All the compositions are in wt.%.

1 ton = 1000 kg

Assume that the gangue materials of the ore and ash content of coke form slag while Fe2O3 in the ore is consumed in making hot metal.

(A)  1705 kg, 431 kg

(B)  2131 kg, 546 kg

(C)  1705 kg, 331 kg

(D)  1500 kg, 431 kg

Answer: (A)

Q.37 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

37. Consider the function f(x) = x − cos x. Using Newton-Raphson method, the estimated root of f(x) after the first iteration is: ______ (round off to 3 decimal places).

Assume: Initial guess of the root = 0.5 radians.

Answer: (0.745 to 0.770)

38. The work done by a force  along a straight line from point (0, 0) to (1, 2) is: ____________ (round off to nearest integer).

Answer: (7 to 7)

39. A coin is tossed three times. Given that there are more heads than tails, the probability of getting exactly one tail is: ___________ (round off to 2 decimal places).

Answer: (0.75 to 0.75)

40. A continuous fillet weld is made using a 3000 W welding machine. At a travel speed of 6 mm s1, the cross-sectional area (in mm2) of the weld is: _________ (round off to nearest integer).

Given: The unit energy required to melt the metal is 6 J mm3

Heat transfer factor = 0.6

Melting factor = 0.5

Answer: (25 to 25)

41. Liquid iron is cast into a spherical sand mold (6 cm radius) and a cubical sand mold (12 cm edge length). If solidification time is 60 minutes in the spherical casting, the time (in minutes) required to solidify in the cubical casting is: ____________ (round off to nearest integer).

Answer: (58 to 62)

42. True strain for 60% height reduction of a sample subjected to hot forging is: ___________ (round off to 2 decimal places).

Answer: (0.90 to 0.94 OR -0.94 to -0.90)

43. For the equilibrium reaction: 2Cu (s) + SO2(g) = Cu2S (s) + O2 (g), the value of ln  at 973 K is: ________ (round off to 2 decimal places).

Given: 2Cu (s) + 0. 5S2(g) = Cu2S (s) ΔG° at 973 K = −100 kJ

SO2(g) = 0. 5S2(g) + O2(g) ΔG° at 973 K = 292 kJ

R = 8.314 J mol1 K1

Assume: Cu and Cu2S are pure solids.

Answer: (-24.00 to -23.50)

44. One mole of an ideal gas at 10 atm. and 300 K undergoes reversible adiabatic expansion to a pressure of one atm. The work done (in Joule) by the gas is: ________ (round off to nearest integer).

Given: R = 8.314 J mol-1 K1; 1 atm. = 101325 Pa; Cp = 2.5R

Answer: (2230 to 2270)

45. The figure shows the entropy versus temperature (S-T) plot of a reversible cycle of an engine. If T1 = 200 K and T2 = 600 K, the efficiency of the engine (in percent) is: ___________ (round off to 2 decimal places).

Answer: (63.00 to 71.00)

46. Two dislocation lines parallel to z-axis lying in the x-z plane are shown in the figure. The glide force (in Newton) exerted by the edge dislocation on the screw dislocation is: __________ (round off to nearest integer)

For the edge, the shear stress component is given by:

Given:Shear modulus, G = 28 GPa

Poisson’s ratio, v = 0.3

Burgers vector, b = 0.29 nm

Distance between the two dislocations = 0.5 nm

Answer: (0 to 0)

47. In a material, a shear stress of 100 MPa is required to bow a dislocation line between precipitates with a spacing of 0.2 μm. If the spacing between the precipitates is increased to 0.5 μm, the shear stress (in MPa) to bow the dislocation would be: _________ (round off to nearest integer).

Answer: (40 to 40)

48. A metal plate is in a state of plane strain (εzz = 0) with σxx = σyy ≠ 0 and τxy = τxz = τyz = 0. If the Poisson’s ratio is 0.3, the ratio, σzz/ σxx is ___________ (round off to 1 decimal place).

Answer: (0.6 to 0.6)

49. An infinite metal plate has a central through-thickness crack of length 80/π The maximum applied stress (in MPa) that the plate can sustain in mode I is: _________ (round off to nearest integer).

Assume: Linear elastic fracture mechanics is valid

Given: Fracture toughness, KIC= 20 MPa m1/2

Answer: (98 to 102)

50. A hypothetical binary eutectic phase diagram of A – B is shown below. An alloy with 5 wt.% B solidifies with no convection. Assuming steady state, the critical temperature gradient (in K mm1) required to maintain planar solidification front is: ___________ (round off to nearest integer).

Given: Diffusivity of B in liquid = 109 m2s1

Velocity of solidification front = 4 μm s1

Answer: (298 to 302)

51. A thick steel plate containing 0.1 wt.% C is carburized at 950 ° The plate’s surface carbon concentration is maintained at 1.1 wt.% C. After 9 hours, the depth (in mm) below the surface at which the carbon concentration is 0.6 wt.% C will be: _________ (round off to 2 decimal places).

Given: Diffusivity of carbon in γ-Fe at 950 °C = 1.6 x 1011 m2s1

Error function table:

Answer: (0.65 to 0.75)

52. At 25 °C, iron corrodes in a deaerated acid of pH 3 with a corrosion current density of 4 μA cm2 . The corrosion potential (V) is: ________ (round off to 2 decimal places).

Given: βc = 0.1 V per decade of current density

Exchange current density of hydrogen on iron surface = 109 A cm2

R = 8.314 J mol-1 K1, F = 96500 C mol1

All potentials are with reference to standard hydrogen electrode.

Answer: (-0.60 to -0.50)

53. The radius of an interstitial atom which just fits (without distorting the structure) inside an octahedral void of a bcc-iron crystal (in nm) is: ________ (round off to 3 decimal places).

Assume the radius of Fe atom to be 0.124 nm.

Answer: (0.017 to 0.023)

54. Nickel undergoes isothermal oxidation at 800 K for a duration of 400 s resulting in a weight gain of 2 mg cm2. The weight gain (mg cm2) after a duration of 1600 s is: __________ (round off to nearest integer).

Assume: Weight gain is proportional to square root of time.   

Answer: (4 to 4)

55. A solid sphere (0.5 m radius) is enclosed within a larger hollow sphere (1 m radius), as shown in figure. The radiation exchange takes place between the outer surface (surface 1) of the small sphere and the inner surface (surface 2) of the bigger sphere. The value of the view factor, F22 is: _________ (round off to 2 decimal places).

Given: View factor (Fij) is the fraction of the radiation leaving surface i that is intercepted by surface j.

Answer: (0.74 to 0.76)

GATE Exam 2021 Mining Engineering (MN) Question Paper With Answer Key

GATE-2021

MN-Mining Engineering

GA-General Aptitude

Q 1 – Q5 Carry one mark each. ( for each wrong answer: 1/3)

1. (i) Arun and Aparna are here.

(ii) Arun and Aparna is here.

(iii) Arun’s families is here.

(iv) Arun’s family is here.

Which of the above sentences are grammatically CORRECT?

(A)    (i) and (ii)

(B)    (i) and (iv)

(C)    (ii) and (iv)

(D)    (iii) and (iv)

Answer: (B)

2.

Answer: (B)

3. Two identical cube shaped dice each with faces numbered 1 to 6 are rolled simultaneously. The probability that an even number is rolled out on each dice is:

(A)    1/36

(B)    1/12

(C)    1/8

(D)    1/4

Answer: (D)

4. ⊕ and ⊙ are two operators on numbers p and q such that p ⊙ q = p – q, and p ⊕ q – p × q

Then, (9 ⊙ (6 ⊕ 7)) ⨀ (7 ⊕ (6 ⊙ 5) =

(A)    40

(B)    -26

(C)    -33

(D)    -40

Answer: (D)

5. Four persons P, Q, R and S are to the seated in a row, R should not be seated at the second position from the left end of the row. The number of distinct seating arrangement possible is:

(A)    6

(B)    9

(C)    18

(D)    24

Answer: (C)

Q.6-Q. 10 carry two marks (for each wrong answer: 2/3)

6. On a planar field, you travelled 3 units East from a point O. Next you travelled 4 units South to arrive at point P. Then you travelled from P in the North-East direction such that you arrive at a point that is 6 units East of point O. Next, you travelled in the North-West direction, so that  you arrive at point Q that is 18 units North of Point P.

The distance of point Q to point O, in the same units, should be_____

(A)    3

(B)    4

(C)    5

(D)    6

Answer: (C)

7. The author said, “Musicians rehearse before their concerts. Actors rehearse their roles before the opening of a new play, On the other hand, I find it strange that many public speakers think key can just walk on to the stage and start speaking. In my opinion, it is no less important for public speakers to rehearse their talks.”

Based on the above passage, which one of the following is TRUE?

(A)    The author is of the opinion that rehearsing is important for musicians, actors and public speakers.

(B)    The author is of the opinion that rehearsing is  less important for public speakers than for musicians and actors.

(C)    The author is of the opinion that rehearsing is more important only for musicians than public speakers.

(D)    The author is of the opinion that rehearsal is more important for actors than musicians.

Answer: (A)

8. (1) Some football players play cricket.

(2) All cricket players play hockey.

Among the options given below, the statement that logically follows from the two statements 1 and 2 above, is:

(A)    No football player plays hockey.

(B)    Some football players play hockey.

(C)    All football players play hockey.

(D)    All hockey players play football.

Answer: (B)

9. In the figure shown above, PQRS is a square. The shaded portion is formed by the intersection of sectors of circles with radius equal to the side of the square and centers at S and Q.

The probability that any point picked randomly within the square falls in the shaded area is______

(A)   

(B)    1/2

(C)    π/2

(D)    π/4

Answer: (C)

10. In an equilateral triangle PQR, side PQ is divided into four equal parts, side QR is divided into six equal parts and side PR is divided into eight equal parts. The length of each subdivided part in cm is an integer.

The minimum area of the triangle PQR possible, in cm2, is

(A)    18

(B)    24

(C)    48√3

(D)    144√3

Answer: (D)

Mining Engineering (MN)

Q.1 – Q.19 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Tricone roller bit is used with

(A)  down-the-hole hammer.

(B)  Jack hammer.

(C)  rotary-percussive drill.

(D)  rotary drill.

Answer: (D)

2. Resuing method of mining is practiced for

(A)  thick vein deposit.

(B)  massive shallow deposit.

(C)  narrow vein deposit.

(D)  massive deep-seated deposit.

Answer: (C)

3. The equipment used for both drop cut and terrace cut in surface mining is

(A)  surface miner.

(B)  shovel.

(C)  dragline.

(D)  bucket wheel excavator.

Answer: (D)

4. Surface miner does NOT have a

(A)  differential gear for turning.

(B)  tensioning arrangement for crawler.

(C)  scraper plate behind the drum.

(D)  pick cooling system.

Answer: (A)

5. Induced blasting enhances production in

(A)  sublevel stoping.

(B)  block caving.

(C)  cut and fill mining.

(D)  shrinkage stoping.

Answer: (B)

6. The measures of dispersion of a dataset are

(A)  standard deviation, range and mode.

(B)  standard deviation, range and interquartile range.

(C)  variance, range and median.

(D)  interquartile range, median and mode.

Answer: (B)

7. NONEL is used as down-the-hole initiator to

(A)  avoid generation of air overpressure.

(B)  provide precise delay.

(C)  avoid deflagration of column charge.

(D)  reduce ground vibration.

Answer: (C)

8. The vectors  act in a plane as shown below. The magnitude of the vector  is

(A)  zero.

(B)  half to the area bounded by the vectors   

(C)  equal to the area bounded by the vectors

(D)  twice the area bounded by the vectors

Answer: (D)

9. As per MMDR Act 1957, for the allocation of lease of minor minerals

(A)  the State Government is authorised to give the permit.

(B)  the Central Government is authorised to give the permit.

(C)  the State Government is authorised to give permit but with the consent of Central Government.

(D)  the Central Government is authorised to give permit but with the consent of State Government.

Answer: (A)

10. In photogrammetry, the ‘Tilt of a photograph’ refers to the angle between the

(A)  lines joining the opposite fiducial marks of a photograph.

(B)  normal to the plane of photograph and optical axis.

(C)  vertical and the axis of the flight.

(D)  vertical and optical axis of the camera.

Answer: (D)

11. The hydraulic sand stowing pipeline layout should be such that

(A)  the geometric profile must coincide with the hydraulic gradient line.

(B)  the hydraulic profile should always be below the hydraulic gradient line.

(C)  the hydraulic profile should always be above the hydraulic gradient line.

(D)  the geometric profile should always be above the hydraulic gradient line.

Answer: (B)

12. For a “positive definite” square matrix, the TRUE statement is

(A)  the matrix is singular.

(B)  all the eigen values of the matrix are greater than zero.

(C)  all the eigen values of the matrix are zero.

(D)  some of the eigen values can be less than zero.

Answer: (B)

13. The standard normal distribution is a

(A)  non-parametric distribution.

(B)  single parameter distribution.

(C)  two-parameter distribution.

(D)  three-parameter distribution.

Answer: (C)

14. Variance of the sum of two statistically independent random variables X and Y, σ2X+Y, is

Answer: (A)

15. The difference between depreciation and amortization allowances in tax calculation is that

(A)  depreciation is for a tangible asset applicable on its declared life; whereas amortization is for an intangible asset applicable on a specified period.

(B)  depreciation is for an intangible asset applicable on its declared life; whereas amortization is for a tangible asset applicable on a specified period.

(C)  depreciation is for a tangible asset applicable on a specified period; whereas amortization is for an intangible asset applicable on its declared life.

(D)  depreciation is for an intangible asset applicable on a specified period; whereas amortization is for a tangible asset applicable on its declared life.

Answer: (A)

16. Owning cost of a machine does NOT include

(A)  purchase price.

(B)  insurance.

(C)  interest.

(D)  operating cost.

Answer: (D)

17. Folds are the structural features resulting from

(A)  ductile deformation of earth crust.

(B)  brittle deformation of earth crust.

(C)  high impact tectonic stresses of earth crust.

(D)  fracturing of earth crust.

Answer: (A)

18. The CORRECT curve showing the relationship between vertical stress on a coal pillar and extraction ratio of a bord and pillar panel in a horizontal seam is

(A)  Curve A.

(B)  Curve B.

(C)  Curve C.

(D)  Curve D.

Answer: (C)

19. Given impeller diameter D, speed of rotation n and air density ρ, for geometrically similar fans, the fan pressure is proportional to

(A)  nD2ρ.

(B)  n2D2ρ.

(C)  n2D5ρ2.

(D)  n3D5ρ.

Answer: (B)

Q.20 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

20. A coal sample having moisture content of 8.0% has unit weight 15.6 kN/m3. The dry unit weight of the sample, in kN/m3 is _____.

Answer: (14.00 to 15.00)

21. The value of the integral  computed using Simpson’s 1/3 rule with 2 subintervals is_______.

[round off to 3 decimal places]

Answer: (5.000 to 5.200)

22. In the context of sound frequency analysis, the lower and upper frequencies of a 1/1 octave band are 710 Hz and 1420 Hz respectively. The corresponding centre frequency of the band in Hz, is_______. [round off to the nearest integer]

Answer: (999 to 1005)

23. In Battle Environmental Evaluation System (BEES) of Environmental Impact Assessment (EIA), “air pollution” has a Parameter Importance Unit (PIU) value of 52. The Environmental Quality (EQ) score of a project with respect to air pollution was 0.8 before the project implementation and it becomes 0.6 after the project implementation. The difference in the “Environmental Impact Unit (EIU)”, before and after the project implementation is______.

[round off to 2 decimal places]

Answer: (10.40 to 10.40)

24. A system consists of four components connected functionally in a parallel configuration. The reliability of the individual components is 0.40, 0.60, 0.50 and 0.40. The system reliability, is________. [round off to 3 decimal places]

Answer: (0.918 to 0.938)

25. A vehicle is moving at a speed of 12 m/s on a level road. It applies emergency brakes and starts to skid without rolling in a straight path. The deceleration of the vehicle is constant after braking and it comes to rest at a distance of 15 m. Assuming, g = 10 m/s2, the coefficient of kinetic friction between the tyres and road is _______. [round off to 2 decimal places]

Answer: (0.45 to 0.50)

Q.26 – Q.36 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

26. In a bord and pillar panel six shuttle cars, each of 10 tonne capacity, are deployed to transport coal produced by two continuous miners to a belt conveyor. Each shuttle car on an average carries 80% of its rated capacity and makes 7 round trips in an hour. The belt conveyor has a capacity such that the effective material cross section area is of 0.09 m2 and runs at a speed 1.1 m/s. The broken coal has a bulk density of 1.2 tonne/m3. The ratio between the production and the capacity of the belt conveyor, in percent is

(A)  65.46

(B)  71.42

(C)  78.56

(D)  82.46

Answer: (C)

27. With reference to the figure related to rock cutting by point attack tool, match the angle with corresponding name.

(A)  P-2, Q-4, R-1, S-3.

(B)  P-4, Q-2, R-1, S-3.

(C)  P-2, Q-4, R-3, S-1.

(D)  P-4, Q-2, R-3, S-1.

Answer: (A)

28. The pit bottom in a correlation survey is shown in the figure. Points C and D represent two suspended wires. The bearing of line CD is 286o00′00′′ and its length is 4.64 m. The angle CED is measured as 00o00′40′′. The length of line DE is 5.46 m. Considering the Weisbach triangle method, the bearing of the line CE is

(A)  286°00’47”

(B)  285°59’12.9″

(C)  286°00’40”

(D)  285°00’47.1″

Answer: (B)

29. A dump truck moves up an incline of 50 with constant tractive force of 800 kN. The gross mass of the truck is 250 tonne and its rolling resistance is 545 kN. The acceleration due to gravity is 10 m2/s. The time required, in s, to reach a speed of 3.3 m/s from 1.0 m/s is

(A)  22.0

(B)  15.5

(C)  3.3

(D)  0.2

Answer: (B)

30. In a longwall panel, face is supported with shields of yield capacity 460 tonne per shield. The distance from the canopy tip to coal face is 0.15 m when the support is fully advanced. The depth of web is 0.60 m. The shields are set skin to skin at the face. Length of the canopy of the shield is 3.25 m and width 1.5 m. Setting capacity is 80% of the yield capacity. The setting resistance at the maximum and minimum span of the coal face, in tonne/m2, respectively are

(A)  61.33 and 72.15.

(B)  63.72 and 75.48.

(C)  76.66 and 90.19.

(D)  91.99 and 108.22.

Answer: (A)

31. A 10 ml sample of wastewater is diluted with water having no BOD, to fill a 300 ml BOD bottle. The initial DO of the diluted waste water is 9.0 mg/l. If the BOD5 of the waste water sample is 60 mg/l, the final DO of the diluted waste water in mg/l, is

(A)  5.0

(B)  6.0

(C)  7.0

(D)  8.0

Answer: (C)

32. The Mohr circle of stress of a dry porous rock is shown in the figure. If the rock is fully saturated with a pore pressure p, then the Mohr circle takes the form of

Answer: (A)

33. The straight line shown depicts the failure criterion of a rock type. The values of stress at points A and B are as shown. The safety factor at the points A and B respectively are

(A)  1.175 and 0.755

(B)  1.324 and 0.851

(C)  0.851 and 1.324

(D)  0.755 and 1.175

Answer: (D)

34. Figure shown relates to the manufacture of roof bolts. With respect to the cost/revenue vs production level, match the appropriate trend line with corresponding description.

(A)  (P)-(1); (R)-(3); (S)-(2).

(B)  (P)-(2); (R)-(1); (S)-(3).

(C)  (P)-(1); (R)-(2), (S)-(3).

(D)  (P)-(3); (R)-(1); (S)-(2).

Answer: (D)

35. The value of  is

(A)  0

(B)  b2/2

(C)  ∞

(D)  b2

Answer: (B)

36. In order to check whether iron ore is supplied to the specification of 62% Fe, a steel company has conducted a hypothesis test with the null hypothesis as H0: μFe = 62% and alternative hypothesis Ha: μFe < 62%. A random sample of 5 observations reveal the following grade values of the lot, 58%, 56%, 60%, 64%, 62%. The t-test statistic for the hypothesis is

(A)  – 3.000

(B)  1.414

(C)  – 1.414

(D)  3.000

Answer: (C)

Q.37 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks)

37. Production planning of a small quarry having 3 years of life is shown in the figure. The following information of revenue and cost data are available.

Selling price of ore = Rs. 1500/tonne

Ore mining cost = Rs. 500/tonne

Waste mining cost = Rs. 500/m3

Initial capital = Rs. 1000 million

Discount rate = 10 %

By neglecting depreciation, salvage value and corporate tax, the NPV of the mining project, in million Rs., is_______. [round off to 2 decimal places]

Answer: (35.50 to 38.30)

38. A triangular distributed load is applied on top of a beam as shown in the figure. The value of maximum bending moment in kN-m is______.

[round off to 2 decimal places]

Answer: (1.20 to 1.35)

39. For a dumpy level, the bubble tube has sensitivity of 40″ for one division. While taking a staff reading at a distance of 60 m, the bubble is out of centre by 2 divisions. The error in staff reading in mm is______. [round off to one decimal place]

Answer: (225 to 24.0)

40. On an old plan of scale 1:1000, leasehold area of a mine is now measured as 802 cm2 using a planimeter. The plan is found to have shrunk, such that the original line of 10 cm is now measured as 9.8 cm on the plan. True lease hold mine area, in m2, is _______. [round off to the nearest integer]

Answer: (83450 to 83550)

41. CO is released from a point source on a level ground at a rate of 25 g/s. The average wind speed is 5 m/s. The dispersion coefficients are 150 m and 200 m in horizontal and vertical directions, respectively, at a receiver station located on the ground along the downwind direction. Assuming the plume follows Gaussian dispersion model, the concentration of CO, in μg/m3, at the station is______.

[round off to 2 decimal places]

Answer: (50.00 to 55.00)

42. Assume that COVID-19 growth rate of number of infections per day (c) in a certain population is represented by the following differential equation.

Where, t stands for time in days. Time taken for the number of infections per day to double, in days, is______. [round off to the nearest integer]

Answer: (9 to 11)

43. Ore is hoisted from 620 m depth using a single skip of 7 tonne pay load. The skip winding system has constant acceleration/deceleration of 1 m/s2 and a constant speed of 10 m/s. The skip loading time and unloading time are 120 s and 60 s, respectively. Considering the overall utilization of the skip as 70 %, the maximum daily capacity of the winding system, in tonne, is ______. [round off to the nearest integer]

Answer: (1250 to 1350)

44. In an analysis of fragmented blast muck, the mean fragment size is found to be 60 cm with uniformity index of 1.25. Considering Rosin-Ramler equation, the cumulative mass fraction, in percent, to pass the grizzly screen size of 100 cm is______. [round off to 2 decimal places]

Answer: (71.00 to 75.00)

45. A single-acting reciprocating ram pump, while running at 120 rpm, delivers water at a rate of 10 litres per second. Considering the ram diameter is 150 mm and stroke length is 300 mm, the volumetric efficiency of the pump, in percent is _______.

[round off to one decimal place]

Answer: (92.0 to 96.0)

46. In a sand stowing arrangement, the slurry has a sand concentration of 35% by volume. The specific gravity of sand grain is 2.6. The concentration of sand by weight, in percent, in the slurry is _____. [round off to one decimal place]

Answer: (57.00 to 59.80)

47. In a surface mine, third bench from the pit bottom is blasted, as shown in the figure. The width, height and slope angle of each bench are 8 m, 6 m, and 800, respectively. A fly rock is projected at an angle of 450 with the horizontal with initial velocity, v. If the acceleration due to gravity is 10 m/s2 then the minimum velocity (v) in m/s required for the fly rock to reach just beyond toe of the pit slope is ______.

[round off to 2 decimal places]

Answer: (9.00 to 11.00)

48. Injury experience is studied in an underground coal mine with a random sample of 132 workers. The results of the study are tabulated below.

The odds ratio of experiencing an injury by the roof-bolter operators when compared to the loader operators is______. [round off to 2 decimal places]

Answer: (2.20 to 2.30)

49. A random variable X is defined by

The value of E(X2) is ______. [round off to one decimal place]

Answer: (6.0 to 6.0)

50. A project network consists of the following activities

If the project completion time is 30 days, then the value of ‘X’, in days, is_______.

[in integer]

Answer: (5 to 5)

51. Rate of fuel consumption fc (litres per hour) of a truck varies with truck speed x, (kmph) as given below 

The fuel price is Rs. 70 per litre. Other costs amount to Rs. 500 per hour. If the truck travels 100 km from a coal mine to a thermal plant, the speed of the truck, in kmph, that minimizes the total cost is_______. [round off to one decimal place]

Answer: (35.0 to 38.0)

52. A cement company has three factories which transport cement to four distribution centres. The daily production of each factory, the demand at each distribution centre, and the associated transportation cost per tonne from factory to distribution centre are given in the Table.

The initial basic feasible solution using the least-cost rule is _____. [in integer]

Answer: (112000 to 112000)

53. The grade-tonnage distribution for the ultimate pit of a mine is given below.

The mill cut-off grade is 0.5 % Cu. The annual mining capacity (ore + waste) is 4.5 million tonne and milling capacity is 1.0 million tonne. Excavation is planned in such a way that either of the mine or the mill runs at full capacity throughout. The planned life of the mine, in years, is _______. [round off to one decimal place]

Answer: (6.0 to 6.0)

54. A coal mine operating in three shifts produces 400 tonnes of coal per day with a face OMS of 1.0 from panel A, and 200 tonnes of coal with face OMS of 1.0 from panel B. The panel A and panel B are in parallel with resistance 0.6 Ns−2m−8 and 0.5 Ns−2m−8, respectively. If the panels are supplied with minimum permissible quantity as per CMR 2018, the requisite regulator resistance to meet the conditions in Ns−2m−8 [round off to 2 decimal places]

Answer: (1.80 to 2.00)

55. A set of three steel bars of equal cross-sectional area of 0.01 m2 are loaded, as shown in the figure. The elastic modulus of steel is 200 GPa. The overall change of length of the complete set of bars, in mm, is_______. [round off to 3 decimal places]

Answer: (0.045 to 0.055)

GATE Exam 2021 Mechanical Engineering (ME-2) Question Paper With Answer Key

GATE-2021

ME-2: Mechanical Engineering

GA – General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Five persons P, Q, R, S and T are to be seated in a row, all facing the same direction, but not necessarily in the same order. P and T cannot be seated at either end of the row. P should not be seated adjacent to S. R is to be seated at the second position from the left end of the row. The number of distinct seating arrangements possible is:

(A)  2

(B)  3

(C)  4

(D)  5

Answer: (B)

2. Consider the following sentences:

(i) The number of candidates who appear for the GATE examination is staggering.

(ii) A number of candidates from my class are appearing for the GATE examination.

(iii) The number of candidates who appear for the GATE examination are staggering.

(iv) A number of candidates from my class is appearing for the GATE examination.

Which of the above sentences are grammatically CORRECT?

(A)  (i) and (ii)

(B)  (i) and (iii)

(C)  (ii) and (iii)

(D)  (ii) and (iv)

Answer: (A)

3. A digital watch X beeps every 30 seconds while watch Y beeps every 32 seconds. They beeped together at 10 AM.

(A)  10.08 AM

(B)  10.42 AM

(C)  11.00 AM

(D)  10.00 PM

Answer: (A)

4. If ⊕÷⊙= 2 ; ⊕÷ Δ = 3; ⊙ +Δ = 5; Δ ×⊗ =10,

Then, the value of (⊗ − ⊕)2, is:

(A)  0

(B)  1

(C)  4

(D)  16

Answer: (B)

5. The front door of Mr. X’s house faces East. Mr. X leaves the house, walking 50 m straight from the back door that is situated directly opposite to the front door. He then turns to his right, walks for another 50 m and stops. The direction of the point Mr. X is now located at with respect to the starting point is ______

(A)  South-East

(B)  North-East

(C)  West

(D)  North-West

Answer: (D)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

6. Given below are two statements 1 and 2, and two conclusions I and II.

Statement 1: All entrepreneurs are wealthy.

Statement 2: All wealthy are risk seekers.

Conclusion I: All risk seekers are wealthy.

Conclusion II: Only some entrepreneurs are risk seekers.

Based on the above statements and conclusions, which one of the following options is CORRECT?

(A)  Only conclusion I is correct

(B)  Only conclusion II is correct

(C)  Neither conclusion I nor II is correct

(D)  Both conclusions I and II are correct

Answer: (C)

7. A box contains 15 blue balls and 45 black balls. If 2 balls are selected randomly, without replacement, the probability of an outcome in which the first selected is a blue ball and the second selected is a black ball, is _____

(A)  3/16

(B)  45/236

(C)  1/4

(D)  3/4

Answer: (B)

8. 

The ratio of the area of the inscribed circle to the area of the circumscribed circle of an equilateral triangle is____

(A)  1/8

(B)  1/6

(C)  1/4

(D)  1/2

Answer: (C)

9. Consider a square sheet of side 1 unit. The sheet is first folded along the main diagonal. This is followed by a fold along its line of symmetry. The resulting folded shape is again folded along its line of symmetry. The area of each face of the final folded shape, in square units, equal to _______

(A)  1/4

(B)  1/8

(C)  1/16

(D)  1/32

Answer: (B)

10. The world is going through the worst pandemic in the past hundred years. The air travel industry is facing a crisis, as the resulting quarantine requirement for travelers led to weak demand.

In relation to the first sentence above, what does the second sentence do?

(A)  Restates an idea from the first sentence.

(B)  Second sentence entirely contradicts the first sentence.

(C)  The two statements are unrelated.

(D)  States an effect of the first sentence.

Answer: (D)

Mechanical Engineering (ME, Set-2)

Q.1 – Q.19 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Consider an n × n matrix A and a non-zero n × 1 vector p. Their product Ap = α 2p, where α ∈ ℜ and α ∉ {−1, 0, 1}. Based on the given information, the eigen value of A2 is:

(A)  a

(B)  a2

(C)  √α

(D)  α4

Answer: (D)

2. If the Laplace transform of a function f(t) is given by  then f(0) is

(A)  0

(B)  1/2

(C)  1

(D)  3/2

Answer: (C)

3. The mean and variance, respectively, of a binomial distribution for n independent trials with the probability of success as p, are

(A)  √np , np(1 − 2p)

(B)   

(C)  np, np

(D)  np, np(1 – p)

Answer: (D)

4. The Cast Iron which possesses all the carbon in the combined form as cementite is known as

(A)  Grey Cast Iron

(B)  Spheroidal Cast Iron

(C)  Malleable Cast Iron

(D)  White Cast Iron

Answer: (D)

5. The size distribution of the powder particles used in Powder Metallurgy process can be determined by

(A)  Laser scattering

(B)  Laser reflection

(C)  Laser absorption

(D)  Laser penetration

Answer: (A)

6. In a CNC machine tool, the function of an interpolator is to generate

(A)  signal for the lubrication pump during machining

(B)  error signal for tool radius compensation during machining

(C)  NC code from the part drawing during post processing

(D)  reference signal prescribing the shape of the part to be machined

Answer: (D)

7. The machining process that involves ablation is

(A)  Abrasive Jet Machining

(B)  Chemical Machining

(C)  Electrochemical Machining

(D)  Laser Beam Machining

Answer: (D)

8. A PERT network has 9 activities on its critical path. The standard deviation of each activity on the critical path is 3. The standard deviation of the critical path is

(A)  3

(B)  9

(C)  27

(D)  81

Answer: (B)

9. The allowance provided in between a hole and a shaft is calculated from the difference between

(A)  lower limit of the shaft and the upper limit of the hole

(B)  upper limit of the shaft and the upper limit of the hole

(C)  upper limit of the shaft and the lower limit of the hole

(D)  lower limit of the shaft and the lower limit of the hole

Answer: (C)

10. In forced convective heat transfer, Stanton number (St), Nusselt number (Nu), Reynolds number (Re) and Prandtl number (Pr) are related as

Answer: (A)

11. For a two-dimensional, incompressible flow having velocity components u and v in the x and y directions, respectively, the expression  can be simplified to

Answer: (D)

12. Which of the following is responsible for eddy viscosity (or turbulent viscosity) in a turbulent boundary layer on a flat plate?

(A)  Nikuradse stresses

(B)  Reynolds stresses

(C)  Boussinesq stresses

(D)  Prandtl stresses

Answer: (B)

13. A two dimensional flow has velocities in x and y directions given by u = 2xyt and v = −y2t, where t denotes time. The equation for streamline passing through x = 1, y = 1 is

(A)  x2y = 1

(B)  xy2 = 1

(C)  x2 y2 = 1

(D)  x/y2 = 1

Answer: (B)

14. A plane truss PQRS (PQ = RS, and ∠PQR = 90°) is shown in the figure.

The forces in the members PR and RS, respectively, are _____________

(A)  F√2 (tensile) and F (tensile)

(B)  F√2 (tensile) and F (compressive)

(C)  F (compressive) and F√2 (compressive)

(D)  F (tensile) and F√2 (tensile)

Answer: (B)

15. Consider the mechanism shown in the figure. There is rolling contact without slip between the disc and ground.

Select the correct statement about instantaneous centers in the mechanism.

(A)  Only points P, Q, and S are instantaneous centers of mechanism

(B)  Only points P, Q, S and T are instantaneous centers of mechanism

(C)  Only points P, Q, R, S, and U are instantaneous centers of mechanism

(D)  All points P, Q, R, S, T and U are instantaneous centers of mechanism

Answer: (D)

16. The controlling force curves P, Q and R for a spring controlled governor are shown in the figure, where r1 and r2 are any two radii of rotation.

The characteristics shown by the curves are

(A)  P – Unstable; Q – Stable; R – Isochronous

(B)  P – Unstable; Q – Isochronous; R – Stable

(C)  P– Stable; Q – Isochronous; R – Unstable

(D)  P – Stable; Q – Unstable; R – Isochronous

Answer: (B)

17. The von Mises stress at a point in a body subjected to forces is proportional to the square root of the

(A)  total strain energy per unit volume

(B)  plastic strain energy per unit volume

(C)  dilatational strain energy per unit volume

(D)  distortional strain energy per unit volume

Answer: (D)

18. Value of  using Simpson’s one-third rule with interval size 0.3 is

(A)  1.83

(B)  1.60

(C)  1.51

(D)  1.06

Answer: (A)

19. Value of (1 + i)8, where i = √−1 , is equal to

(A)  4

(B)  16

(C)  4i

(D)  16i

Answer: (B)

Q.20 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

20. Consider adiabatic flow of air through a duct. At a given point in the duct, velocity of air is 300 m/s, temperature is 330 K and pressure is 180 kPa. Assume that the air behaves as a perfect gas with constant cp =1.005 kJ/kg.K. The stagnation temperature at this point is _________ K (round off to two decimal places).

Answer: (373.00 to 377.00)

21. Consider an ideal vapour compression refrigeration cycle working on R-134a refrigerant. The COP of the cycle is 10 and the refrigeration capacity is 150 kJ/kg. The heat rejected by the refrigerant in the condenser is __________ kJ/kg (round off to the nearest integer).

Answer: (165 to 165)

22. A rigid tank of volume 50 m3 contains a pure substance as a saturated liquid vapour mixture at 400 kPa. Of the total mass of the mixture, 20% mass is liquid and 80% mass is vapour. Properties at 400 kPa are: Tsat = 143.61 °C, vf = 0.001084 m3/kg, vg = 0.46242 m3/kg. The total mass of liquid vapour mixture in the tank is ___________kg (round off to the nearest integer).

Answer: (134 to 136)

23. An object is moving with a Mach number of 0.6 in an ideal gas environment, which is at a temperature of 350 K. The gas constant is 320 J/kg.K and ratio of specific heats is 1.3. The speed of object is ____________m/s (round off to the nearest integer).

Answer: (228 to 230)

24. A column with one end fixed and one end free has a critical buckling load of 100 N. For the same column, if the free end is replaced with a pinned end then the critical buckling load will be ___________N (round off to the nearest integer).

Answer: (800 to 840)

25. A steel cubic block of side 200 mm is subjected to hydrostatic pressure of 250 N/mm2. The elastic modulus is 2 × 105 N/mm2 and Poisson ratio is 0.3 for steel. The side of the block is reduced by _________ mm (round off to two decimal places).

Answer: (0.08 to 0.12)

Q.26 – Q.34 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

26. The value of  is

(A)  0

(B)  1/6

(C)  4/3

(D)  π

Answer: (B)

27. Let the superscript T represent the transpose operation. Consider the function  where x and r are n × 1 vectors and Q is a symmetric n × n matrix. The stationary point of f(x) is

(A)  QTr

(B)  Q1r

(C)  r/rTr

(D)  r

Answer: (B)

28. Consider the following differential equation 

The solution of the equation that satisfies the condition y(1) = 1 is

(A)  2yey = ex + e

(B)  y2ey = ex

(C)  yey = ex

(D)  (1 + y)ey = 2ex

Answer: (C)

29. A factory produces m (i = 1, 2, … , m) products, each of which requires processing on n (j = 1, 2, … , n) workstations. Let aij be the amount of processing time that one unit of the ith product requires on the jth Let the revenue from selling one unit of the ith product be ri and hi be the holding cost per unit per time period for the ith product. The planning horizon consists of T (t = 1, 2, …, T) time periods. The minimum demand that must be satisfied in time period t is dit, and the capacity of the jth workstation in time period t is cjt. Consider the aggregate planning formulation below, with decision variables Sit (amount of product i sold in time period t), Xit (amount of product i manufactured in time period t) and Iit (amount of product i held in inventory at the end of time period t.

Answer: (A)

30. Ambient pressure, temperature, and relative humidity at a location are 101 kPa, 300 K, and 60%, respectively. The saturation pressure of water at 300 K is 3.6 kPa. The specific humidity of ambient air is _________ g/kg of dry air.

(A)  1.4

(B)  35.1

(C)  21.9

(D)  13.6

Answer: (D)

31. A plane frame PQR (fixed at P and free at R) is shown in the figure. Both members (PQ and QR) have length, L, and flexural rigidity, EI. Neglecting the effect of axial stress and transverse shear, the horizontal deflection at free end, R, is

Answer: (B)

32. A power transmission mechanism consists of a belt drive and a gear train as shown in the figure.

Diameters of pulleys of belt drive and number of teeth (T) on the gears 2 to 7 are indicated in the figure. The speed and direction of rotation of gear 7, respectively, are

(A)  255.68 rpm; clockwise

(B)  255.68 rpm; anticlockwise

(C)  575.28 rpm; clockwise

(D)  575.28 rpm; anticlockwise

Answer: (A)

33. A machine of mass 100 kg is subjected to an external harmonic force with a frequency of 40 rad/s. The designer decides to mount the machine on an isolator to reduce the force transmitted to the foundation. The isolator can be considered as a combination of stiffness (K) and damper (damping factor, ξ ) in parallel. The designer has the following four isolators:

(1) K = 640 kN/m, ξ = 0.70

(2) K = 640 kN/m, ξ = 0.07

(3) K = 22.5 kN/m, ξ = 0.70

(4) K = 22.5 kN/m, ξ = 0.07

Arrange the isolators in the ascending order of the force transmitted to the foundation.

(A)  1-3-4-2

(B)  1-3-2-4

(C)  4-3-1-2

(D)  3-1-2-4

Answer: (C)

34. Consider the system shown in the figure. A rope goes over a pulley. A mass, m, is hanging from the rope. A spring of stiffness, k, is attached at one end of the rope. Assume rope is inextensible, massless and there is no slip between pulley and rope.

The pulley radius is r and its mass moment of inertia is J. Assume that the mass is vibrating harmonically about its static equilibrium position. The natural frequency of the system is

Answer: (B)

Q.35 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

35. Find the positive real root of x3 − x − 3 = 0 using Newton-Raphson method. If the starting guess (x0) is 2, the numerical value of the root after two iterations (x2) is _____________ (round off to two decimal places).

Answer: (1.66 to 1.68)

36. Daily production capacity of a bearing manufacturing company is 30000 bearings. The daily demand of the bearing is 15000. The holding cost per year of keeping a bearing in the inventory is ₹ 20. The setup cost for the production of a batch is ₹ 1800. Assuming 300 working days in a year, the economic batch quantity in number of bearings is ______________ (in integer).

Answer: (40200 to 40300)

37. A cast product of a particular material has dimensions 75 mm × 125 mm × 20 mm. The total solidification time for the cast product is found to be 2.0 minutes as calculated using Chvorinov’s rule having the index, n = 2. If under the identical casting conditions, the cast product shape is changed to a cylinder having diameter = 50 mm and height = 50 mm, the total solidification time will be ____________ minutes (round off to two decimal places).

Answer: (2.60 to 3.00)

38. A spot welding operation performed on two pieces of steel yielded a nugget with a diameter of 5 mm and a thickness of 1 mm. The welding time was 0.1 s. The melting energy for the steel is 20 J/mm3. Assuming the heat conversion efficiency as 10%, the power required for performing the spot welding operation is ____________ kW (round off to two decimal places).

Answer: (39.00 to 40.00)

39. A surface grinding operation has been performed on a Cast Iron plate having dimensions 300 mm (length) × 10 mm (width) × 50 mm (height). The grinding was performed using an alumina wheel having a wheel diameter of 150 mm and wheel width of 12 mm. The grinding velocity used is 40 m/s, table speed is 5 m/min, depth of cut per pass is 50 μm and the number of grinding passes is 20. The average tangential and average normal force for each pass is found to be 40 N and 60 N respectively. The value of the specific grinding energy under the aforesaid grinding conditions is ______________ J/mm3 (round off to one decimal place).

Answer: (38.0 to 39.0)

40. In a pure orthogonal turning by a zero rake angle single point carbide cutting tool, the shear force has been computed to be 400 N. The cutting velocity, Vc = 100 m/min, depth of cut, t = 2.0 mm, feed, s0 = 0.1 mm/revolution and chip velocity, Vf = 20 m/min, the shear strength, τs of the material will be ___________ MPa (round off to two decimal places).

Answer: (388.00 to 400.00)

41. The thickness, width and length of a metal slab are 50 mm, 250 mm and 3600 mm, respectively. A rolling operation on this slab reduces the thickness by 10% and increases the width by 3%. The length of the rolled slab is __________ mm (round off to one decimal place).

Answer: (3880.0 to 3886.0)

42. A 76.2 mm gauge block is used under one end of a 254 mm sine bar with roll diameter of 25.4 mm. The height of gauge blocks required at the other end of the sine bar to measure an angle of 30° is __________ mm (round off to two decimal places).

Answer: (200.00 to 206.00)

43. The demand and forecast of an item for five months are given in the table.

The Mean Absolute Percent Error (MAPE) in the forecast is ___________ % (round off to two decimal places)

Answer: (6.00 to 10.00)

44. A shell and tube heat exchanger is used as a steam condenser. Coolant water enters the tube at 300 K at a rate of 100 kg/s. The overall heat transfer coefficient is 1500 W/m2.K, and total heat transfer area is 400 m2. Steam condenses at a saturation temperature of 350 K. Assume that the specific heat of coolant water is 4000 J/kg.K. The temperature of the coolant water coming out of the condenser is _________ K (round off to the nearest integer).

Answer: (337 to 341)

45. Ambient air flows over a heated slab having flat, top surface at y = 0. The local temperature (in Kelvin) profile within the thermal boundary layer is given by T(y) = 300 + 200 exp(−5y), where y is the distance measured from the slab surface in meter. If the thermal conductivity of air is 1.0 W/m.K and that of the slab is 100 W/m.K, then the magnitude of temperature gradient |dT/dy| within the slab at y = 0 is __________ K/m (round off to the nearest integer).

Answer: (10 to 10)

46. Water flows out from a large tank of cross-sectional area At = 1 m2 through a small rounded orifice of cross-sectional area Ao = 1 cm2, located at y = 0. Initially the water level, measured from y = 0, is H = 1 m. The acceleration due to gravity is 9.8 m/s2.

Neglecting any losses, the time taken by water in the tank to reach a level of y = H/4 is __________ seconds (round off to one decimal place).

Answer: (2257.0 to 2259.0)

47. Consider the open feed water heater (FWH) shown in the figure given below:

Specific enthalpy of steam at location 2 is 2624 kJ/kg, specific enthalpy of water at location 5 is 226.7 kJ/kg and specific enthalpy of saturated water at location 6 is 708.6 kJ/kg. If the mass flow rate of water entering the open feed water heater (at location 5) is 100 kg/s then the mass flow rate of steam at location 2 will be __________ kg/s (round off to one decimal place).

Answer: (25.0 to 25.4)

48. A high velocity water jet of cross section area = 0.01 m2 and velocity = 35 m/s enters a pipe filled with stagnant water. The diameter of the pipe is 0.32 m. This high velocity water jet entrains additional water from the pipe and the total water leaves the pipe with a velocity 6m/s as shown in the figure.

The flow rate of entrained water is ___________ litres/s (round off to two

decimal places).

Answer: (130.00 to 134.00)

49. A vertical shaft Francis turbine rotates at 300 rpm. The available head at the inlet to the turbine is 200 m. The tip speed of the rotor is 40 m/s. Water leaves the runner of the turbine without whirl. Velocity at the exit of the draft tube is 3.5 m/s. The head losses in different components of the turbine are: (i) stator and guide vanes: 5.0 m, (ii) rotor: 10 m, and (iii) draft tube: 2 m. Flow rate through the turbine is 20 m3/s. Take g = 9.8 m/s2. The hydraulic efficiency of the turbine is ___________ % (round off to one decimal place).

Answer: (90.0 to 92.0)

50. An adiabatic vortex tube, shown in the figure given below is supplied with 5 kg/s of air (inlet 1) at 500 kPa and 300 K. Two separate streams of air are leaving the device from outlets 2 and 3. Hot air leaves the device at a rate of 3 kg/s from outlet 2 at 100 kPa and 340 K, and 2 kg/s of cold air stream is leaving the device from outlet 3 at 100 kPa and 240 K.

Assume constant specific heat of air is 1005 J/kg.K and gas constant is 287 J/kg.K. There is no work transfer across the boundary of this device. The rate of entropy generation is __________ kW/K (round off to one decimal place).

Answer: (2.1 to 2.3)

51. A block of negligible mass rests on a surface that is inclined at 30° to the horizontal plane as shown in the figure. When a vertical force of 900 N and a horizontal force of 750 N are applied, the block is just about to slide.

The coefficient of static friction between the block and surface is _______ (round off to two decimal places).

Answer: (0.16 to 0.19)

52. The wheels and axle system lying on a rough surface is shown in the figure.

Each wheel has diameter 0.8 m and mass 1 kg. Assume that the mass of the wheel is concentrated at rim and neglect the mass of the spokes. The diameter of axle is 0.2 m and its mass is 1.5 kg. Neglect the moment of inertia of the axle and assume g = 9.8 m/s2. An effort of 10 N is applied on the axle in the horizontal direction shown at mid span of the axle. Assume that the wheels move on a horizontal surface without slip. The acceleration of the wheel axle system in horizontal direction is _________ m/s2 (round off to one decimal place).

Answer: (1.3 to 1.4)

53. A cantilever beam with a uniform flexural rigidity (EI = 200 × 106 N.m2) is loaded with a concentrated force at its free end. The area of the bending moment diagram corresponding to the full length of the beam is 10000 N.m2. The magnitude of the slope of the beam at its free end is _________ micro radian (round off to the nearest integer).

Answer: (48 to 52)

54. The torque provided by an engine is given by T(θ) = 12000 + 2500 sin(2θ) N.m, where θ is the angle turned by the crank from inner dead center. The mean speed of the engine is 200 rpm and it drives a machine that provides a constant resisting torque. If variation of the speed from the mean speed is not to exceed ±0.5%, the minimum mass moment of inertia of the flywheel should be ___________ kg.m2 (round off to the nearest integer).

Answer: (560 to 580)

55. The figure shows the relationship between fatigue strength (S) and fatigue life (N) of a material. The fatigue strength of the material for a life of 1000 cycles is 450 MPa, while its fatigue strength for a life of 106 cycles is 150 MPa.

The life of a cylindrical shaft made of this material subjected to an alternating stress of 200 MPa will then be __________ cycles (round off to the nearest integer).

Answer: (152000 to 165000)

GATE Exam 2021 Mechanical Engineering (ME-1) Question Paper With Answer Key

GATE-2021

ME-1: Mechanical Engineering

GA – General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Consider the following sentences:

(i) After his surgery, Raja hardly could walk.

(ii) After his surgery, Raja could barely walk.

(iii) After his surgery, Raja barely could walk.

(iv) After his surgery, Raja could hardly walk.

Which of the above sentences are grammatically CORRECT?

(A)  (i) and (ii)

(B)  (i) and (iii)

(C)  (iii) and (iv)

(D)  (ii) and (iv)

Answer: (D)

2. X came out of a building through its front door to find her shadow due to the morning sun falling to her right side with the building to her back. From this, it can be inferred that building is facing _________

(A)  North

(B)  East

(C)  West

(D)  South

Answer: (D)

3. 

In the above figure, O is the center of the circle and, M and N lie on the circle.

The area of the right triangle MON is 50 cm2.

What is the area of the circle in cm2 ?

(A)  2π

(B)  50π

(C)  75π

(D)  100π

Answer: (D)

4. If 

then, the value of the expression ∆ 2 ⊕ 3 ∆ ((4 ⨁ 2) ∇ 4)=

(A)  −1

(B)  −0.5

(C)  6

(D)  7

Answer: (D)

5. “The increased consumption of leafy vegetables in the recent months is a clear indication that the people in the state have begun to lead a healthy lifestyle”

Which of the following can be logically inferred from the information presented in the above statement?

(A)  The people in the state did not consume leafy vegetables earlier.

(B)  Consumption of leafy vegetables may not be the only indicator of healthy lifestyle.

(C)  Leading a healthy lifestyle is related to a diet with leafy vegetables.

(D)  The people in the state have increased awareness of health hazards causing by consumption of junk foods.

Answer: (C)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

6. Oxpeckers and rhinos manifest a symbiotic relationship in the wild. The oxpeckers warn the rhinos about approaching poachers, thus possibly saving the lives of the rhinos. Oxpeckers also feed on the parasitic ticks found on rhinos.

In the symbiotic relationship described above, the primary benefits for oxpeckers and rhinos respectively are,

(A)  Oxpeckers get a food source, rhinos have no benefit.

(B)  Oxpeckers save their habitat from poachers while the rhinos have no benefit.

(C)  Oxpeckers get a food source, rhinos may be saved from the poachers.

(D)  Oxpeckers save the lives of poachers, rhinos save their own lives.

Answer: (C)

7. 

A jigsaw puzzle has 2 pieces. One of the pieces is shown above. Which one of the given options for the missing piece when assembled will form a rectangle? The piece can be moved, rotated or flipped to assemble with the above piece.

Answer: (A)

8. The number of hens, ducks and goats in farm P are 65, 91 and 169, respectively. The total number of hens, ducks and goats in a nearby farm Q is 416. The ratio of hens: ducks: goats in farm Q is 5:14:13. All the hens, ducks and goats are sent from farm Q to farm P.

The new ratio of hens: ducks: goats in farm P is_____

(A)  5:7:13

(B)  5:14:13

(C)  10:21:26

(D)  21:10:26

Answer: (C)

9. 

The distribution of employees at the rank of executives, across different companies C1, C2, …, C6 is presented in the chart given above. The ratio of executives with a management degree to those without a management degree in each of these companies is provided in the table above. The total number of executives across all companies is 10,000.

The total number of management degree holders among the executives in companies C2 and C5 together is_____.

(A)  225

(B)  600

(C)  1900

(D)  2500

Answer: (D)

10. Five persons P, Q, R, S and T are sitting in a row not necessarily in the same order. Q and R are separated by one person, and S should not be seated adjacent to Q.

The number of distinct seating arrangements possible is:

(A)  4

(B)  8

(C)  10

(D)  16

Answer: (D)

Mechanical Engineering (ME, Set-1)

Q.1 – Q.19 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. If y(x) satisfies the differential equation  subject to the condition y(π/2) = π/2, then y(π/6) is

(A)  0

(B)  π/6

(C)  π/3

(D)  π/2

Answer: (C)

2. The value of  is

(A)  1/4

(B)  1/3

(C)  1/2

(D)  1

Answer: (C)

3. The Dirac-delta function (δ(t − t0)) for t, t0 ∈ ℝ, has the following property

The Laplace transform of the Dirac-delta function δ(t − a) for a > 0; ℒ(δ(t − a)) = F(s) is

(A)  0

(B)  ∞

(C)  esa

(D)  esa

Answer: (D)

4. The ordinary differential equation  subject to an initial condition y(0) = 1 is solved numerically using the following scheme:

where h is the time step, tn = nh, and n = 0, 1, 2, …. This numerical scheme is stable for all values of h in the interval _________.

(A)  0 < h < 2/π

(B)  0 < h < 1

(C)  0 < h < π/2

(D)  for all h > 0

Answer: (A)

5. Consider a binomial random variable X. If X1,X2, … ,Xn are independent and identically distributed samples from the distribution of X with sum  then the distribution of Y as n → ∞ can be approximated as

(A)  Exponential

(B)  Bernoulli

(C)  Binomial

(D)  Normal

Answer: (D)

6. The loading and unloading response of a metal is shown in the figure. The elastic and plastic strains corresponding to 200 MPa stress, respectively, are

(A)  0.01 and 0.01

(B)  0.02 and 0.01

(C)  0.01 and 0.02

(D)  0.02 and 0.02

Answer: (B)

7. In a machining operation, if a cutting tool traces the workpiece such that the directrix is perpendicular to the plane of the generatrix as shown in figure, the surface generated is

(A)  plane

(B)  cylindrical

(C)  spherical

(D)  a surface of revolution

Answer: (B)

8. The correct sequence of machining operations to be performed to finish a large diameter through hole is

(A)  drilling, boring, reaming

(B)  boring, drilling, reaming

(C)  drilling, reaming, boring

(D)  boring, reaming, drilling

Answer: (A)

9. In modern CNC machine tools, the backlash has been eliminated by

(A)  preloaded balls crews

(B)  rack and pinion

(C)  ratchet and pinion

(D)  slider crank mechanism

Answer: (A)

10. Consider the surface roughness profile as shown in the figure.

The center line average roughness (Ra, in μm) of the measured length (L) is

(A)  0

(B)  1

(C)  2

(D)  4

Answer: (B)

11. In which of the following pairs of cycles, both cycles have at least one isothermal process?

(A)  Diesel cycle and Otto cycle

(B)  Carnot cycle and Stirling cycle

(C)  Brayton cycle and Rankine cycle

(D)  Bell-Coleman cycle and Vapour compression refrigeration cycle

Answer: (B)

12. Superheated steam at 1500 kPa, has a specific volume of 2.75 m3/kmol and compressibility factor (Z) of 0.95. The temperature of steam is______ °C (round off to the nearest integer).

(A)  522

(B)  471

(C)  249

(D)  198

Answer: (C)

13. A hot steel spherical ball is suddenly dipped into a low temperature oil bath.

Which of the following dimensionless parameters are required to determine instantaneous center temperature of the ball using a Heisler chart?

(A)  Biot number and Fourier number

(B)  Reynolds number and Prandtl number

(C)  Biot number and Froude number

(D)  Nusselt number and Grashoff number

Answer: (A)

14. An infinitely long pin fin, attached to an isothermal hot surface, transfers heat at a steady rate of Q̇1 to the ambient air. If the thermal conductivity of the fin material is doubled, while keeping everything else constant, the rate of steady-state heat transfer from the fin becomes Q̇2. The ratio Q̇2/Q̇1 is

(A)  √2

(B)  2

(C)  1/√2

(D)  1/2

Answer: (A)

15. The relative humidity of ambient air at 300 K is 50% with a partial pressure of water vapour equal to pv. The saturation pressure of water at 300 K is psat. The correct relation for the air-water mixture is

(A)  pv = 0.5 psat

(B)  pv = psat

(C)  pv = 0.622 psat

(D)  pv = 2 psat

Answer: (A)

16. Consider a reciprocating engine with crank radius R and connecting rod of length L. The secondary unbalance force for this case is equivalent to primary unbalance force due to a virtual crank of _______

(A)  radius L2/4R rotating at half the engine speed

(B)  radius R/4 rotating at half the engine speed

(C)  radius R2/L rotating at twice the engine speed

(D)  radius L/2 rotating at twice the engine speed

Answer: (C)

17. A cantilever beam of length, L, and flexural rigidity, EI, is subjected to an end moment, M, as shown in the figure. The deflection of the beam at x = L/2 is

(A)  ML2/2EI

(B)  ML2/4EI

(C)  ML2/8EI

(D)  ML2/16EI

Answer: (C)

18. A prismatic bar PQRST is subjected to axial loads as shown in the figure. The segments having maximum and minimum axial stresses, respectively, are

(A)  QR and PQ

(B)  ST and PQ

(C)  QR and RS

(D)  ST and RS

Answer: (D)

19. Shear stress distribution on the cross-section of the coil wire in a helical compression spring is shown in the figure. This shear stress distribution represents

(A)  direct shear stress in the coil wire cross-section

(B)  torsional shear stress in the coil wire cross-section

(C)  combined direct shear and torsional shear stress in the coil wire cross-section

(D)  combined direct shear and torsional shear stress along with the effect of stress concentration at inside edge of the coil wire cross-section

Answer: (C)

Q.20 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

20. Robot Ltd. wishes to maintain enough safety stock during the lead time period between starting a new production run and its completion such that the probability of satisfying the customer demand during the lead time period is 95%. The lead time period is 5 days and daily customer demand can be assumed to follow the Gaussian (normal) distribution with mean 50 units and a standard deviation of 10 units. Using ϕ−1(0. 95) = 1. 64, where φ represents the cumulative distribution function of the standard normal random variable, the amount of safety stock that must be maintained by Robot Ltd. to achieve this demand fulfillment probability for the lead time period is _________ units (round off to two decimal places).

Answer: (331 to 333)

21. A pressure measurement device fitted on the surface of a submarine, located at a depth H below the surface of an ocean, reads an absolute pressure of 4.2 MPa. The density of sea water is 1050 kg/m3, the atmospheric pressure is 101 kPa, and the acceleration due to gravity is 9.8 m/s2. The depth H is ___________ m (round off to the nearest integer).

Answer: (397 to 399)

22. Consider fully developed, steady state incompressible laminar flow of a viscous fluid between two large parallel horizontal plates. The bottom plate is fixed and the top plate moves with a constant velocity of U = 4 m/s. Separation between the plates is 5 mm. There is no pressure gradient in the direction of flow. The density of fluid is 800 kg/m3, and the kinematic viscosity is 1. 25 × 10−4 m2/s. The average shear stress in the fluid is _________ Pa (round off to the nearest integer).

Answer: (79 to 81)

23. A rigid insulated tank is initially evacuated. It is connected through a valve to a supply line that carries air at a constant pressure and temperature of 250 kPa and 400 K respectively. Now the valve is opened and air is allowed to flow into the tank until the pressure inside the tank reaches to 250 kPa at which point the valve is closed. Assume that the air behaves as a perfect gas with constant properties (cp = 1.005 kJ/kg.K, cv = 0.718 kJ/kg.K, R = 0.287 kJ/kg.K). Final temperature of the air inside the tank is __________ K (round off to one decimal place).

Answer: (555 to 565)

24. The figure shows an arrangement of a heavy propeller shaft in a ship. The combined polar mass moment of inertia of the propeller and the shaft is 100 kg.m2. The propeller rotates at ω = 12 rad/s. The waves acting on the ship hull induces a rolling motion as shown in the figure with an angular velocity of 5 rad/s. The gyroscopic moment generated on the shaft due to the motion described is ______________ N.m (round off to the nearest integer).

Answer: (0 to 0)

25. Consider a single degree of freedom system comprising a mass M, supported on a spring and a dashpot as shown in the figure.

If the amplitude of the free vibration response reduces from 8 mm to 1.5 mm in 3 cycles, the damping ratio of the system is ______________ (round off to three decimal places).

Answer: (0.085 to 0.090)

Q.26 – Q. 34 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

26. Consider a vector p in 2-dimensional space. Let its direction (counter- clockwise angle with the positive x-axis) be θ. Let p be an eigenvector of a 2 × 2 matrix A with corresponding eigenvalue λ, λ > 0. If we denote the magnitude of a vector v by ‖v‖, identify the VALID statement regarding p′, where p′ = Ap.

(A)  Direction of p′ = λθ, ||p′|| = ||p||

(B)  Direction of p′ = θ, ||p′|| = λ||p||

(C)  Direction of p′ = λθ, ||p′|| = λ||p||

(D)  Direction of p′ = θ, ||p′|| = ||p||/λ

Answer: (B)

27. Let C represent the unit circle centered at origin in the complex plane, and complex variable, z = x + iy. The value of the contour integral  (where integration is taken counter clockwise) is

(A)  0

(B)  2

(C)  πi

(D)  2πi

Answer: (C)

28. A set of jobs A, B, C, D, E, F, G, H arrive at time t = 0 for processing on turning and grinding machines. Each job needs to be processed in sequence – first on the turning machine and second on the grinding machine, and the grinding must occur immediately after turning. The processing times of the jobs are given below.

If the make span is to be minimized, then the optimal sequence in which these jobs must be processed on the turning and grinding machines is

(A)  A-E-D-F-H-C-G-B

(B)  A-D-E-F-H-C-G-B

(C)  G-E-D-F-H-C-A-B

(D)  B-G-C-H-F-D-E-A

Answer: (A)

29. The fundamental thermodynamic relation for a rubber band is given by dU = TdS + τdL, where T is the absolute temperature, S is the entropy, τ is the tension in the rubber band, and L is the length of the rubber band. Which one of the following relations is CORRECT:

Answer: (B)

30. Consider a two degree of freedom system as shown in the figure, where PQ is a rigid uniform rod of length, b and mass, m.

Assume that the spring deflects only horizontally and force F is applied horizontally at Q. For this system, the Lagrangian, L is

Answer: (B)

31. A right solid circular cone standing on its base on a horizontal surface is of height H and base radius R. The cone is made of a material with specific weight w and elastic modulus E. The vertical deflection at the mid-height of the cone due to self-weight is given by

(A)  wH2/8E

(B)  wH2/6E

(C)  wRH/8E

(D)  wRH/6E

Answer: (A)

32. A tappet valve mechanism in an IC engine comprises a rocker arm ABC that is hinged at B as shown in the figure. The rocker is assumed rigid and it oscillates about the hinge B. The mass moment of inertia of the rocker about B is 10-4 m2. The rocker arm dimensions are a = 3.5 cm and b = 2.5 cm. A pushrod pushes the rocker at location A, when moved vertically by a cam that rotates at N rpm. The pushrod is assumed massless and has a stiffness of 15 N/mm. At the other end C, the rocker pushes a valve against a spring of stiffness 10 N/mm. The valve is assumed massless and rigid.

Resonance in the rocker system occurs when the cam shaft runs at a speed of _________ rpm (round off to the nearest integer).

(A)  496

(B)  4739

(C)  790

(D)  2369

Answer: (B)

33. Customers arrive at a shop according to the Poisson distribution with a mean of 10 customers/hour. The manager notes that no customer arrives for the first 3 minutes after the shop opens. The probability that a customer arrives within the next 3 minutes is

(A)  0.39

(B)  0.86

(C)  0.50

(D)  0.61

Answer: (A)

34. Let f(x) = x2 − 2x + 2 be a continuous function defined on x ∈ [1, 3]. The point x at which the tangent of f(x) becomes parallel to the straight line joining f(1) and f(3) is

(A)  0

(B)  1

(C)  2

(D)  3

Answer: (C)

Q.35 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

35. Activities A, B, C and D form the critical path for a project with a PERT network. The means and variances of the activity duration for each activity are given below. All activity durations follow the Gaussian (normal) distribution, and are independent of each other.

The probability that the project will be completed within 40 days is _________ (round off to two decimal places).

(Note: Probability is a number between 0 and 1).

Answer: (0.5 to 0.5)

36. A true centrifugal casting operation needs to be performed horizontally to make copper tube sections with outer diameter of 250 mm and inner diameter of 230 mm. The value of acceleration due to gravity, g = 10 m/s2. If a G-factor (ratio of centrifugal force to weight) of 60 is used for casting the tube, the rotational speed required is __________________rpm (round off to the nearest integer).

Answer: (660 to 664)

37. The resistance spot welding of two 1.55 mm thick metal sheets is performed using welding current of 10000 A for 0.25 s. The contact resistance at the interface of the metal sheets is 0.0001 Ω. The volume of weld nugget formed after welding is 70 mm3. Considering the heat required to melt unit volume of metal is 12 J/mm3, the thermal efficiency of the welding process is _______ % (round off to one decimal place).

Answer: (30 to 36)

38. An orthogonal cutting operation is performed using a single point cutting tool with a rake angle of 12o on a lathe. During turning, the cutting force and the friction force are 1000 N and 600 N, respectively. If the chip thickness and the uncut chip thickness during turning are 1.5 mm and 0.75 mm, respectively, then the shear force is _____________ N (round off to two decimal places).

Answer: (625 to 750)

39. In a grinding operation of a metal, specific energy consumption is 15 J/mm3. If a grinding wheel with a diameter of 200 mm is rotating at 3000 rpm to obtain a material removal rate of 6000 mm3/min, then the tangential force on the wheel is ______________ N (round off to two decimal places).

Answer: (45.00 to 50.00)

40. A 200 mm wide plate having a thickness of 20 mm is fed through a rolling mill with two rolls. The radius of each roll is 300 mm. The plate thickness is to be reduced to 18 mm in one pass using a roll speed of 50 rpm. The strength coefficient (K) of the work material flow curve is 300 MPa and the strain hardening exponent, n is 0.2. The coefficient of friction between the rolls and the plate is 0.1. If the friction is sufficient to permit the rolling operation then the roll force will be __________ kN (round off to the nearest integer).

Answer: (775 to 784)

41. The XY table of a NC machine tool is to move from P(1,1) to Q(51,1); all coordinates are in mm. The pitch of the NC drive leadscrew is 1 mm. If the backlash between the leadscrew and the nut is 1.8o, then the total backlash of the table on moving from P to Q is ____________ mm (round off to two decimal places).

Answer: (0.20 to 0.30)

42. Consider a single machine workstation to which jobs arrive according to a Poisson distribution with a mean arrival rate of 12 jobs/hour. The process time of the workstation is exponentially distributed with a mean of 4 minutes. The expected number of jobs at the workstation at any given point of time is ___________ (round off to the nearest integer).

Answer: (4 to 4)

43. An uninsulated cylindrical wire of radius 1.0 mm produces electric heating at the rate of 5.0 W/m. The temperature of the surface of the wire is 75°C when placed in air at 25°C. When the wire is coated with PVC of thickness 1.0 mm, the temperature of the surface of the wire reduces to 55°C. Assume that the heat generation rate from the wire and the convective heat transfer coefficient are same for both uninsulated wire and the coated wire. The thermal conductivity of PVC is ___________ W/m.K (round off to two decimal places).

Answer: (0.10 to 0.12)

44. A solid sphere of radius 10 mm is placed at the centroid of a hollow cubical enclosure of side length 30 mm. The outer surface of the sphere is denoted by 1 and the inner surface of the cube is denoted by 2. The view factor F22 for radiation heat transfer is ___________ (rounded off to two decimal places).

Answer: (0.76 to 0.78)

45. Consider a steam power plant operating on an ideal reheat Rankine cycle. The work input to the pump is 20 kJ/kg. The work output from the high pressure turbine is 750 kJ/kg. The work output from the low pressure turbine is 1500 kJ/kg. The thermal efficiency of the cycle is 50 %. The enthalpy of saturated liquid and saturated vapour at condenser pressure are 200 kJ/kg and 2600 kJ/kg, respectively. The quality of steam at the exit of the low pressure turbine is ___________ % (round off to the nearest integer).

Answer: (92 to 96)

46. In the vicinity of the triple point, the equation of liquid-vapour boundary in the P − T phase diagram for ammonia is ln P = 24. 38 − 3063/T, where P is pressure (in Pa) and T is temperature (in K). Similarly, the solid-vapour boundary is given by ln P = 27. 92 − 3754/T. The temperature at the triple point is _________ K (round off to one decimal place).

Answer: (195.1 to 195.3)

47. A cylindrical jet of water (density = 1000 kg/m3) impinges at the center of a flat, circular plate and spreads radially outwards, as shown in the figure. The plate is resting on a linear spring with a spring constant k = 1 kN/m. The incoming jet diameter is D = 1 cm.

If the spring shows a steady deflection of 1 cm upon impingement of jet, then the velocity of the incoming jet is ____________ m/s (round off to one decimal place).

Answer: (11.2 to 11.4)

48. A single jet Pelton wheel operates at 300 rpm. The mean diameter of the wheel is 2 m. Operating head and dimensions of jet are such that water comes out of the jet with a velocity of 40 m/s and flow rate of 5 m3/s. The jet is deflected by the bucket at an angle of 165°. Neglecting all losses, the power developed by the Pelton wheel is ______________ MW (round off to two decimal places).

Answer: (2.50 to 2.80)

49. An air-conditioning system provides a continuous flow of air to a room using an intake duct and an exit duct, as shown in the figure. To maintain the quality of the indoor air, the intake duct supplies a mixture of fresh air with a cold air stream. The two streams are mixed in an insulated mixing chamber located upstream of the intake duct. Cold air enters the mixing chamber at 5°C, 105 kPa with a volume flow rate of 1.25 m3/s during steady state operation. Fresh air enters the mixing chamber at 34 °C and 105 kPa. The mass flow rate of the fresh air is 1.6 times of the cold air stream. Air leaves the room through the exit duct at 24°C.

Assuming the air behaves as an ideal gas with cp = 1.005 kJ/kg.K and R = 0.287 kJ/kg.K, the rate of heat gain by the air from the room is ________ kW(round off to two decimal places).

Answer: (4.90 to 5.10)

50. Two smooth identical spheres each of radius 125 mm and weight 100 N rest in a horizontal channel having vertical walls. The distance between vertical walls of the channel is 400 mm.

The reaction at the point of contact between two spheres is _________ N (round off to one decimal place).

Answer: (124.0 to 126.0)

51. An overhanging beam PQR is subjected to uniformly distributed load 20 kN/m as shown in the figure.

The maximum bending stress developed in the beam is ___________ MPa (round off to one decimal place).

Answer: (249.0 to 251.0)

52. The Whitworth quick return mechanism is shown in the figure with link lengths as follows: OP = 300 mm, OA = 150 mm, AR = 160 mm, RS = 450 mm.

The quick return ratio for the mechanism is _________ (round off to one decimal place).

Answer: (1.9 to 2.1)

53. A short shoe drum (radius 260 mm) brake is shown in the figure. A force of 1 kN is applied to the lever. The coefficient of friction is 0.4.

The magnitude of the torque applied by the brake is ____________ N.m (round off to one decimal place).

Answer: (199.0 to 201.0)

54. A machine part in the form of cantilever beam is subjected to fluctuating load as shown in the figure. The load varies from 800 N to 1600 N. The modified endurance, yield and ultimate strengths of the material are 200 MPa, 500 MPa and 600 MPa, respectively.

The factor of safety of the beam using modified Goodman criterion is ________ (round off to one decimal place).

Answer: (1.9 to 2.1)

55. A cantilever beam of rectangular cross-section is welded to a support by means of two fillet welds as shown in figure. A vertical load of 2 kN acts at free end of the beam.

Considering that the allowable shear stress in weld is 60 N/mm2, the minimum size (leg) of the weld required is _______ mm (round off to one decimal place).

Answer: (6.4 to 6.9)

GATE Exam 2021 Mathematics (MA) Question Paper With Answer Key

GATE-2021

MA: Mathematics

GA-General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. The ratio of boys to girls in a class is 7 to 3.

Among the options below, an acceptable value for the total number of students in the class is:

(A)  21

(B)  37

(C)  50

(D)  73

Answer: (C)

2. A polygon is convex if, for every pair of points, P and Q belonging to the polygon, the line segment PQ lies completely inside or on the polygon.

Which one of the following is NOT a convex polygon?

Answer: (A)

3. Consider the following sentences:

(i) Everybody in the class is prepared for the exam.

(ii) Babu invited Danish to his home because he enjoys playing chess.

Which of the following is the CORRECT observation about the above two sentences?

(A)  (i) is grammatically correct and (ii) is unambiguous

(B)  (i) is grammatically incorrect and (ii) is unambiguous

(C)  (i) is grammatically correct and (ii) is ambiguous

(D)  (i) is grammatically incorrect and (ii) is ambiguous

Answer: (C)

4. A circular sheet of paper is folded along the lines in the directions shown. The paper, after being punched in the final folded state as shown and unfolded in the reverse order of folding, will look like _______.

Answer: (A)

5. _____ is to surgery as writer is to ________

Which one of the following options maintains a similar logical relation in the above sentence?

(A)  Plan, outline

(B)  Hospital, library

(C)  Doctor, book

(D)  Medicine, grammar

Answer: (C)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

6. We have 2 rectangular sheets of paper, M and N, of dimensions 6 cm × 1 cm each. Sheet M is rolled to form an open cylinder by bringing the short edges of the sheet together. Sheet N is cut into equal square patches and assembled to form the largest possible closed cube. Assuming the ends of the cylinder are closed, the ratio of the volume of the cylinder to that of the cube is _______

(A)  π/2

(B)  3/π

(C)  9/π

(D)  3π

Answer: (C)

7. 

Details of prices of two items P and Q are presented in the above table. The ratio of cost of item P to cost of item Q is 3:4. Discount is calculated as the difference between the marked price and the selling price. The profit percentage is calculated as the ratio of the difference between selling price and cost, to the cost 

The discount on item Q, as a percentage of its marked price, is ______

(A)  25

(B)  12.5

(C)  10

(D)  5

Answer: (C)

8. There are five bags each containing identical sets of ten distinct chocolates. One chocolate is picked from each bag.

The probability that at least two chocolates are identical is ___________

(A)  0.3024

(B)  0.4235

(C)  0.6976

(D)  0.8125

Answer: (C)

9. Given below are two statements 1 and 2, and two conclusions I and II.

Statement 1: All bacteria are microorganisms.

Statement 2: All pathogens are microorganisms.

Conclusion I: Some pathogens are bacteria.

Conclusion II: All pathogens are not bacteria.

Based on the above statements and conclusions, which one of the following options is logically CORRECT?

(A)  Only conclusion I is correct

(B)  Only conclusion II is correct

(C)  Either conclusion I or II is correct.

(D)  Neither conclusion I nor II is correct.

Answer: (C OR D)

10. Some people suggest anti-obesity measures (AOM) such as displaying calorie information in restaurant menus. Such measures sidestep addressing the core problems that cause obesity: poverty and income inequality.

Which one of the following statements summarizes the passage?

(A)  The proposed AOM addresses the core problems that cause obesity.

(B)  If obesity reduces, poverty will naturally reduce, since obesity causes poverty.

(C)  AOM are addressing the core problems and are likely to succeed.

(D)  AOM are addressing the problem superficially.

Answer: (D)

Mathematics (MA)

Q.1 – Q.14 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Let A be a 3 × 4 matrix and B be a 4 × 3 matrix with real entries such that AB is non-singular. Consider the following statements:

P: Nullity of A is 0.

Q: BA is a non-singular matrix.

Then

(A)  both P and Q are TRUE

(B)  P is TRUE and Q is FALSE

(C)  P is FALSE and Q is TRUE

(D)  both P and Q are FALSE

Answer: (D)

2. Let f(z) = u(x, y) + i v(x, y) for z = x + iy ∈ ℂ, where x and y are real numbers, be a non-constant analytic function on the complex plane ℂ. Let ux, vx and uy, vy denote the first order partial derivatives of u(x, y) = Re(f(z)) and v(x, y) = Im(f(z)) with respect to real variables x and y, respectively.

Consider the following two functions defined on ℂ:

g1(z) = ux(x, y) − i uy(x, y) for z = x + iy ∈ ℂ,

g2(z) = vx(x, y) + i vy(x, y) for z = x + iy ∈ ℂ.

Then

(A)  both g1(z) and g2(z) are analytic in ℂ

(B)  g1(z) is analytic in C and g2(z) is NOT analytic in ℂ

(C)  g1(z) is NOT analytic in C and g2(z) is analytic in ℂ

(D)  neither g1(z) nor g2(z) is analytic in ℂ

Answer: (B)

3. Let  be the Möbius transformation which maps the points z1 = 0, z2 = −i, z3 = ∞ in the z-plane onto the points w1 = 10, w2 = 5 − 5i, w3 = 5 + 5i in the w-plane, respectively. Then the image of the set S = {z ∈ ℂ ∶ Re(z) < 0} under the map w = T(z) is

(A)  {w ∈ ℂ ∶ |w| < 5}

(B)  {w ∈ ℂ ∶ |w| > 5}

(C)  {w ∈ ℂ ∶ |w − 5| < 5}

(D)  {w ∈ ℂ ∶ |w − 5| > 5}

Answer: (C)

4. Let R be the row reduced echelon form of a 4 × 4 real matrix A and let the third column of R be  Consider the following statements:

P: If  is a solution of Ax = 0, then γ = 0.

Q: For all b ∈ ℝ4, rank[A| b] = rank[R| b].

Then

(A)  both P and Q are TRUE

(B)  P is TRUE and Q is FALSE

(C)  P is FALSE and Q is TRUE

(D)  both P and Q are FALSE

Answer: (D)

5. The eigenvalues of the boundary value problem

are given by

(A)  λ = (nπ)2, n = 1,2,3, …

(B)  λ = n2, n = 1,2,3, …

(C)  λ = kn2, where kn, n = 1,2,3, … are the roots of k − tan(kπ) = 0

(D)  λ = kn2, where kn, n = 1,2,3, … are the roots of k + tan(kπ) = 0

Answer: (C)

6. The family of surfaces given by u = xy + f(x2 − y2), where f: R → R is adifferentiable function, satisfies

Answer: (A)

7. The function u(x, t) satisfies the initial value problem

Then u(5, 5) is

(A)  1 – 1/e100

(B)  1 – e100

(C)  1 – 1/e10

(D)  1 – e10

Answer: (A)

8. Consider the fixed-point iteration

xn+1 = φ(xn), n ≥ 0

with φ(x) = 3 + (x – 3)3, x ∈ (2.5, 3.5),

and the initial approximation x0 = 3.25.

Then, the order of convergence of the fixed-point iteration method is

(A)  1

(B)  2

(C)  3

(D)  4

Answer: (C)

9. Let {en ∶ n = 1, 2, 3, … } be an orthonormal basis of a complex Hilbert space H. Consider the following statements:

P: There exists a bounded linear functional f: H → ℂ such that f(en) = 1/n for n = 1, 2, 3, … .

Q: There exists a bounded linear functional g:H → ℂ such that g(en) = 1/√n for n = 1, 2, 3, … .

Then

(A)  both P and Q are TRUE

(B)  P is TRUE and Q is FALSE

(C)  P is FALSE and Q is TRUE

(D)  both P and Q are FALSE

Answer: (B)

10. Let  be given by   Consider the following statements:

P: |f(x) − f(y)| < |x − y| for all   

Q: f has a fixed point.

Then

(A)  both P and Q are TRUE

(B)  P is TRUE and Q is FALSE

(C)  P is FALSE and Q is TRUE

(D)  both P and Q are FALSE

Answer: (D)

11. Consider the following statements:

Then

(A)  both P and Q are TRUE

(B)  P is TRUE and Q is FALSE

(C)  P is FALSE and Q is TRUE

(D)  both P and Q are FALSE

Answer: (A)

12. Let f: ℝ3 → ℝ be a twice continuously differentiable scalar field such that div(∇f) = 6. Let S be the surface x2 + y2 + z2 = 1 and n̂ be unit outward normal to S. Then the value of  is

(A)  2 π

(B)  4 π

(C)  6 π

(D)  8 π

Answer: (D)

13. Consider the following statements:

P: Every compact metrizable topological space is separable.

Q: Every Hausdorff topology on a finite set is metrizable.

Then

(A)  both P and Q are TRUE

(B)  P is TRUE and Q is FALSE

(C)  P is FALSE and Q is TRUE

(D)  both P and Q are FALSE

Answer: (A)

14. Consider the following topologies on the set ℝ of all real numbers:

T1 = {U ⊂ ℝ ∶ 0 ∉ U or U = ℝ },

T2 = {U ⊂ ℝ ∶ 0 ∈ U or U = ∅} ,

T3 = T1 ∩ T2.

Then the closure of the set {1} in (ℝ, T3) is

(A)  {1}

(B)  {0, 1}

(C)  ℝ

(D)  R\{0}

Answer: (C)

Q.15 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

15. Let f : ℝ2 → ℝ be differentiable. Let Duf(0, 0) and Dvf(0, 0) be the directional derivatives of f at (0, 0) in the directions of the unit vectors u = (1/√5, 2/√5) and v = (1/√2, −1/√2), respectively. If Duf(0, 0) = √5 and Dvf(0, 0) = √2 , then 

Answer: (4 to 4)

16. Let ᴦ denote the boundary of the square region R with vertices (0, 0), (2, 0), (2, 2) and (0, 2) oriented in the counter-clockwise direction. Then 

Answer: (12 to 12)

17. The number of 5-Sylow subgroups in the symmetric group S5 of degree 5 is _______ .

Answer: (6 to 6)

18. Let I be the ideal generated by x2 + x + 1 in the polynomial ring R = ℤ3[x], where ℤ3 denotes the ring of integers modulo 3. Then the number of units in the quotient ring R/I is ________ .

Answer: (6 to 6)

19. Let T: ℝ3 → ℝ3 be a linear transformation such that

Then the rank of T is _____ .

Answer: (2 to 2)

20. Let y(x) be the solution of the following initial value problem

Then y(4) = _________.

Answer: (32 to 32)

21. Let f(x) = x4 + 2x3 − 11x2 − 12x + 36 for x ∈ ℝ.

The order of convergence of the Newton-Raphson method

with x0 = 2. 1, for finding the root α = 2 of the equation f(x) = 0 is _______ .

Answer: (1 to 1)

22. If the polynomial p(x) = α + β (x + 2) + γ (x + 2)(x + 1) + δ (x + 2)(x + 1)x interpolates the data

then α + β + γ + δ = _________.

Answer: (1 to 1)

23. Consider the Linear Programming Problem P:

Maximize 2x1 + 3x2

subject to

2x1 + x2 ≤ 6,

−x1 + x2 ≤ 1,

x1 + x2 ≤ 3,

x1 ≥ 0 and x2 ≥ 0.

Then the optimal value of the dual of P is equal to _________ .

Answer: (8 to 8)

24. Consider the Linear Programming Problem P:

Minimize 2x1 − 5x2

subject to

2x1 + 3x2 + s1 = 12,

−x1 + x2 + s2 = 1,

−x1 + 2x2 + s3 = 3,

x1 ≥ 0, x2 ≥ 0, s1 ≥ 0, s2 ≥ 0, and s3 ≥ 0.

If  is a basic feasible solution of P, then x1 + s1 + s2 + s3 =_______.

Answer: (5 to 5)

25. Let H be a complex Hilbert space. Let u, v ∈ H be such that 〈u, v〉 = 2. Then

Answer: (2 to 2)

Q.26 – Q.43 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

26. Let ℤ denote the ring of integers. Consider the subring

R = {a + b √−17 ∶ a, b ∈ ℤ } of the field ℂ of complex numbers.

Consider the following statements:

P: 2 + √−17 is an irreducible element.

Q: 2 + √−17 is a prime element.

Then

(A)  both P and Q are TRUE

(B)  P is TRUE and Q is FALSE

(C)  P is FALSE and Q is TRUE

(D)  both P and Q are FALSE

Answer: (B)

27. Consider the second-order partial differential equation (PDE)

Consider the following statements:

P: The PDE is parabolic on the ellipse  

Q: The PDE is hyperbolic inside the ellipse  

Then

(A)  both P and Q are TRUE

(B)  P is TRUE and Q is FALSE

(C)  P is FALSE and Q is TRUE

(D)  both P and Q are FALSE

Answer: (A)

28. If u(x, y) is the solution of the Cauchy problem

then u(2, 1) is equal to

(A)  1 − 2 e−2

(B)  1 + 4 e−2

(C)  1 − 4 e−2

(D)  1 + 2 e−2

Answer: (C)

29. Let y(t) be the solution of the initial value problem

obtained by the method of Laplace transform. Then

(A)   

(B)   

(C)   

(D)   

Answer: (A)

30. The critical point of the differential equation  is a

(A)  node and is asymptotically stable

(B)  spiral point and is asymptotically stable

(C)  node and is unstable

(D)  saddle point and is unstable

Answer: (A)

31. The initial value problem

where f(t, y) = −10 y, is solved by the following Euler method

yn+1 = yn + h f(tn, yn), n ≥ 0,

with step-size h. Then yn → 0 as n → ∞, provided

(A)  0 < h < 0.2

(B)  0.3 < h < 0.4

(C)  0.4 < h < 0.5

(D)  0.5 < h < 0.55

Answer: (A)

32. Consider the Linear Programming Problem P:

Maximize c1x1 + c2x2

subject to

a11x1 + a12x2 ≤ b1,

a21x1 + a22x2 ≤ b2,

a31x1 + a32x2 ≤ b3,

x1 ≥ 0 and x2 ≥ 0, where aij, bi and cj are real numbers (i = 1, 2, 3; j = 1, 2).

Let  be a feasible solution of P such that p c1 + q c2 = 6 and let all feasible solutions  of P satisfy −5 ≤ c1x1 + c2x2 ≤ 12.

Then, which one of the following statements is NOT true?

(A)  P has an optimal solution

(B)  The feasible region of P is a bounded set

(C)  If  is a feasible solution of the dual of P, then b1y1 + b2y2 + b3y3 ≥ 6

(D)  The dual of P has at least one feasible solution

Answer: (B)

33. Let L2 [−1, 1] be the Hilbert space of real valued square integrable functions on [−1, 1] equipped with the norm 

Consider the subspace M = {f ∈ L2[−1, 1] :  

For f(x) = x2, define d = inf {‖f − g‖ ∶ g ∈ M }. Then

(A)  d = √2/3

(B)  d = 2/3

(C)  d = 3/√2

(D)  d = 3/2

Answer: (A)

34. Let C[0, 1] be the Banach space of real valued continuous functions on [0, 1] equipped with the supremum norm. Define T: C[0, 1] → C[0, 1] by

Let R(T) denote the range space of T. Consider the following statements:

P: T is a bounded linear operator.

Q: T−1: R(T) → C[0, 1] exists and is bounded.

Then

(A)  both P and Q are TRUE

(B)  P is TRUE and Q is FALSE

(C)  P is FALSE and Q is TRUE

(D)  both P and Q are FALSE

Answer: (B)

35. Let ℓ1 = {x = (x(1), x(2), … , x(n), … )  be the sequence space equipped with the norm  Consider the subspace  and the linear transformation T:X → ℓ1 given by

(Tx)(n) = n x(n) for n = 1, 2, 3, … . Then

(A)  T is closed but NOT bounded

(B)  T is bounded

(C)  T is neither closed nor bounded

(D)  T−1 exists and is an open map

Answer: (A)

36. Let fn:[0, 10] → ℝ be given by fn(x) = n x3 e−nx for n = 1, 2, 3, … .

Consider the following statements:

 P: (fn) is equicontinuous on [0, 10].

 does NOT converge uniformly on [0, 10].

(A)  both P and Q are TRUE

(B)  P is TRUE and Q is FALSE

(C)  P is FALSE and Q is TRUE

(D)  both P and Q are FALSE

Answer: (B)

37. Let f: ℝ2 → ℝ be given by

Consider the following statements:

P: f is continuous at (0, 0) but f is NOT differentiable at (0, 0).

Q: The directional derivative Duf(0, 0) of f at (0, 0) exists in the direction of every unit vector u ∈ ℝ2.

Then

(A)  both P and Q are TRUE

(B)  P is TRUE and Q is FALSE

(C)  P is FALSE and Q is TRUE

(D)  both P and Q are FALSE

Answer: (A)

38. Let V be the solid region in ℝ3 bounded by the paraboloid y = (x2 + z2) and the plane y = 4. Then the value of  is

(A)  128 π

(B)  64 π

(C)  28 π

(D)  256 π

Answer: (A)

39. Let f: ℝ2 → ℝ be given by f(x, y) = 4xy − 2x2 − y4. Then f has

(A)  a point of local maximum and a saddle point

(B)  a point of local minimum and a saddle point

(C)  a point of local maximum and a point of local minimum

(D)  two saddle points

Answer: (A)

40. The equation xy − z log y + exz = 1 can be solved in a neighborhood of the point (0, 1, 1) as y = f(x, z) for some continuously differentiable function f.

Then

(A)  ∇f(0, 1) = (2, 0)

(B)  ∇f(0, 1) = (0, 2)

(C)  ∇f(0, 1) = (0, 1)

(D)  ∇f(0, 1) = (1, 0)

Answer: (A)

41. Consider the following topologies on the set ℝ of all real numbers.

T1 is the upper limit topology having all sets (a, b] as basis.

T2 = {U ⊂ ℝ ∶ ℝ\U is finite} ∪ {∅}.

T3 is the standard topology having all sets (a, b) as basis.

Then

(A)  T2 ⊂ T3 ⊂ T1

(B)  T1 ⊂ T2 ⊂ T3

(C)  T3 ⊂ T2 ⊂ T1

(D)  T2 ⊂ T1 ⊂ T3

Answer: (A)

42. Let ℝ denote the set of all real numbers. Consider the following topological spaces.

X1 = (ℝ, T1), where T1 is the upper limit topology having all sets (a, b] as basis.

X2 = (ℝ, T2), where T2 = {U ⊂ ℝ ∶ ℝ\U is finite} ∪ {∅}.

Then

(A)  both X1 and X2 are connected

(B)  X1 is connected and X2 is NOT connected

(C)  X1 is NOT connected and X2 is connected

(D)  neither X1 nor X2 is connected

Answer: (C)

43. Let 〈∙, ∙〉: ℝn × ℝn → ℝ be an inner product on the vector space ℝn over ℝ. Consider the following statements:

Then

(A)  both P and Q are TRUE

(B)  P is TRUE and Q is FALSE

(C)  P is FALSE and Q is TRUE

(D)  both P and Q are FALSE

Answer: (A)

Q.44 -Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

44. Let G be a group of order 54 with center having 52 Then the number of conjugacy classes in G is ________.

Answer: (145 to 145)

45. Let F be a finite field and F× be the group of all nonzero elements of F under multiplication. If F× has a subgroup of order 17, then the smallest possible order of the field F is _______.

Answer: (103 to 103)

46. Let R = {z = x + iy ∈ 𝕔 ∶ 0 < x < 1 and − 11 π < y < 11 π} and ᴦ be the positively oriented boundary of R. Then the value of the integral  is ______.

Answer: (11 to 11)

47. Let D = {z ∈ ℂ ∶ |z| < 2π} and f: D → ℂ be the function defined by

If  then 6a2 = _______.

Answer: (3 to 3)

48.The number of zeroes (counting multiplicity) of P(z) = 3z5 + 2i z2 + 7i z +1 in the annular region {z ∈ ℂ ∶ 1 < |z| < 7} is ________ .

Answer: (4 to 4)

49. Let A be a square matrix such that det(xI − A) = x4(x − 1)2 (x − 2)3, where det(M) denotes the determinant of a square matrix M.

If rank(A2) < rank(A3) = rank(A4), then the geometric multiplicity of the eigenvalue 0 of A is ________ .

Answer: (MTA)

50. If  is the power series solution of the differential equation   

Answer: (2 to 2)

51. If u(x, t) = A e−t sin x solves the following initial boundary value problem

then πA = _______.

Answer: (MTA)

52. Let V = {p ∶ p(x) = a0 + a1x + a2x2, a0, a1, a2 ∈ R} be the vector space of all polynomials of degree at most 2 over the real field R. Let T: V → V be the linear operator given by T(p) = (p(0) − p(1)) + (p(0) + p(1)) x + p(0) x2.

Then the sum of the eigenvalues of T is _____ .

Answer: (1 to 1)

53. The quadrature formula  is exact for all polynomials of degree ≤ 2. Then 2 β − γ = _______.

Answer: (2 to 2)

54 For each x ∈ (0, 1], consider the decimal representation x = ∙ d1d2d3 ⋯ dn ⋯. Define f:[0, 1] → R by f(x) = 0 if x is rational and f(x) = 18 n if x is irrational, where n is the number of zeroes immediately after the decimal point up to the first nonzero digit in the decimal representation of x. Then the Lebesgue integral 

Answer: (2 to 2)

55. Let  be an optimal solution of the following Linear Programming Problem P:

Maximize 4x1 + x2 − 3x3

subject to

2x1 + 4x2 + ax3 ≤ 10,

x1 − x2 + bx3 ≤ 3,

2x1 + 3x2 + 5x3 ≤ 11,

x1 ≥ 0, x2 ≥ 0 and x3 ≥ 0, where a, b are real numbers.

If  is an optimal solution of the dual of P, then p + q + r = ________ (round off to two decimal places).

Answer: (3.14 to 3.18)

GATE Exam 2021 Instrumentation Engineering (IN) Question Paper With Answer Key

GATE-2021

IN: Instrumentation Engineering

GA-General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Getting to the top is ________________ than staying on top.

(A)  more easy

(B)  much easy

(C)  easiest

(D)  easier

Answer: (D)

2. The mirror image of the above text about the x-axis is

Answer: (B)

3. In a company, 35% of the employees drink coffee, 40% of the employees drink tea and 10% of the employees drink both tea and coffee. What % of employees drink neither tea nor coffee?

(A)  15

(B)  25

(C)  35

(D)  40

Answer: (C)

4. ⊕ and ⨀ are two operators on numbers p and q such that 

If x ⊕ y = 2 ⊙ 2, then x =

(A)  y/2

(B)  y

(C)  3y/2

(D)  2y

Answer: (B)

5. Four persons P, Q, R and S are to be seated in a row, all facing the same direction, but not necessarily in the same order. P and R cannot sit adjacent to each other. S should be seated to the right of Q. The number of distinct seating arrangements possible is:

(A)  2

(B)  4

(C)  6

(D)  8

Answer: (C)

6. Statement: Either P marries Q or X marries Y

Among the options below, the logical NEGATION of the above statement is:

(A)  P does not marry Q and X marries Y.

(B)  Neither P marries Q nor X marries Y.

(C)  X does not marry Y and P marries Q.

(D)  P marries Q and X marries Y.

Answer: (B)

7. Consider two rectangular sheets, Sheet M and Sheet N of dimensions 6 cm × 4 cm each.

Folding operation 1: The sheet is folded into half by joining the short edges of the current shape.

Folding operation 2: The sheet is folded into half by joining the long edges of the current shape.

Folding operation 1 is carried out on Sheet M three times.

Folding operation 2 is carried out on Sheet N three times.

The ratio of perimeters of the final folded shape of Sheet N to the final folded shape of Sheet M is ______.

(A)  13 : 7

(B)  3 : 2

(C)  7 : 5

(D)  5 : 13

Answer: (A)

8. Five line segments of equal lengths, PR, PS, QS, QT and RT are used to form a star as shown in the figure above.

The value of θ, in degrees, is ______

(A)  36

(B)  45

(C)  72

(D)  108

Answer: (A)

9. A function, λ, is defined by

The value of the expression  is:

(A)  −1

(B)  0

(C)  16/3

(D)  16

Answer: (B)

10. Humans have the ability to construct worlds entirely in their minds, which don’t exist in the physical world. So far as we know, no other species possesses this ability. This skill is so important that we have different words to refer to its different flavors, such as imagination, invention and innovation.

Based on the above passage, which one of the following is TRUE?

(A)  No species possess the ability to construct worlds in their minds.

(B)  The terms imagination, invention and innovation refer to unrelated skills.

(C)  We do not know of any species other than humans who possess the ability to construct mental worlds.

(D)  Imagination, invention and innovation are unrelated to the ability to construct mental worlds.

Answer: (C)

Instrumentation Engineering (IN)

Q.1 – Q.8 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Consider the row vectors v = (1, 0) and w = (2, 0). The rank of the matrix M = 2v Tv + 3wTw, where the superscript T denotes the transpose, is

(A)  1

(B)  2

(C)  3

(D)  4

Answer: (A)

2. Consider the sequence xn = 0. 5xn−1 + 1, n = 1, 2, … … with x0 = 0. Then  is

(A)  0

(B)  1

(C)  2

(D)  ∞

Answer: (C)

3. An infinitely long line, with uniform positive charge density, lies along the z- axis. In cylindrical coordinates (r, ∅,z), at any point  not on the z-axis, the direction of the electric field is

Answer: (A)

4. The input-output relationship of an LTI system is given below.

For an input x[n] shown below

the peak value of the output when x[n] passes through h is ____.

(A)  2

(B)  4

(C)  5

(D)  6

Answer: (C)

5. In an ac main, the rms voltage Vac, rms current Iac and power Wac are measured as: Vac = 100 V ± 1%, Iac = 1 A ± 1% and Wac = 50 W ± 2% (errors are with respect to readings). The percentage error in calculating the power factor using these readings is

(A)  1%

(B)  2%

(C)  3%

(D)  4%

Answer: (D)

6. Let u(t) denote the unit step function. The bilateral Laplace transform of the function f(t) = etu(−t) is ____.

Answer: (C)

7. Input-output characteristic of a temperature sensor is exponential for a

(A)  Thermistor

(B)  Thermocouple

(C)  Resistive Temperature Device (RTD)

(D)  Mercury thermometer

Answer: (A)

8. The signal sin(√2πt) is

(A)  periodic with period T√2π

(B)  not periodic

(C)  periodic with period T = 2π

(D)  periodic with period T = 4π2

Answer: (B)

Q.9 – Q.11 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).

9. The step response of a circuit is seen to have an oscillatory behaviour at the output with oscillations dying down after some time. The correct inference(s) regarding the transfer function from input to output is/are

(A)  that it is of at least second order.

(B)  that it has at least one pole-pair that is underdamped.

(C)  that it does not have a real pole.

(D)  that it is a first order system.

Answer: (A; B)

10. For a 4-bit Flash type Analog to Digital Convertor (ADC) with full scale input voltage range “V”, which of the following statement(s) is/are true?

(A)  The ADC requires 15 comparators.

(B)  The ADC requires one 4 to 2 priority encoder and 4 comparators.

(C)  A change in the input voltage by v/16 will always flip MSB of the output.

(D)  A change in the input voltage by v/16 will always flip the LSB of the output.

Answer: (A; D)

11. A 16-bit microprocessor has twenty address lines (A0 to A19) and 16 data lines. The higher eight significant lines of the data bus of the processor are tied to the 8-data lines of a 16 Kbyte memory that can store one byte in each of its 16K address locations. The memory chip should map onto contiguous memory locations and occupy only 16 Kbyte of memory space. Which of the following statement(s) is/are correct with respect to the above design?

(A)  If the 16 Kbyte of memory chip is mapped with a starting address of 80000H, then the ending address will be 83FFFH.

(B)  The active high chip-select needed to map the 16 Kbyte memory with a starting address at F0000H is given by the logic expression (A19 · A18 · A17 · A16).

(C)  The 16 Kbyte memory cannot be mapped with contiguous address locations with a starting address as 0F000H using only A19 to A14 for generating chip select.

(D)  The above chip cannot be interfaced as the width of the data bus of the processor and the memory chip differs.

Answer: (A; C)

Q.12 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

12. A single-phase transformer has a magnetizing inductance of 250 mH and a core loss resistance of 300 Ω, referred to primary side. When excited with a 230 V, 50 Hz sinusoidal supply at the primary, the power factor of the input current drawn, with secondary on open circuit, is ____ (rounded off to two decimal places).

Answer: (0.24 to 0.26)

13. Taking N as positive for clockwise encirclement, otherwise negative, the number of encirclements N of (−1 , 0) in the Nyquist plot of  is _____.

Answer: (-1 to -1)

14. The diode used in the circuit has a fixed voltage drop of 0.6 V when forward biased. A signal vs is given to the ideal OpAmp as shown. When vs is at its positive peak, the output (vOA) of the OpAmp in volts is _______.

Answer: (1 to 1)

15. The transistor Q1 has a current gain β1 = 99 and the transistor Q2 has a current gain β2 = 49. The current IB2 in microampere is _______.

Answer: (10 to 10)

16. A 300 V, 5 A, LPF wattmeter has a full scale of 300 W. The wattmeter can be used for loads supplied by 300 V ac mains with a maximum power factor of ___________ (rounded off to one decimal place).

Answer: (0.2 to 0.2)

17. A 10-bit ADC has a full-scale of 10.230 V, when the digital output is (11 1111 1111)2. The quantization error of the ADC in millivolt is _________.

Answer: (4.9 to 5.1)

18. A strain gage having nominal resistance of 1000 Ω has a gage factor of 2.5. If the strain applied to the gage is 100 μm/m, its resistance in ohm will change to ____________ (rounded off to two decimal places).

Answer: (1000.25 to 1000.25)

19. Given: Density of mercury is 13,600 kg/m3 and acceleration due to gravity is 9.81 m/s2. Atmospheric pressure is 101 kPa. In a mercury U-tube manometer, the difference between the heights of the liquid in the U-tube is 1 cm. The differential pressure being measured in pascal is ______ (rounded off to the nearest integer).

Answer: (1333 to 1360)

20. A piezoresistive pressure sensor has a sensitivity of 1 (mV/V)/kPa. The sensor is excited with a dc supply of 10 V and the output is read using a 3½ digit 200 mV full-scale digital multimeter. The resolution of the measurement set-up, in pascal is ___.

Answer: (10 to 10)

21. An amplitude modulation (AM) scheme uses tone modulation, with modulation index of 0.6. The power efficiency of the AM scheme is ____ % (rounded off to one decimal place).

Answer: (15.0 to 15.5)

22. When the movable arm of a Michelson interferometer in vacuum (n = 1) is moved by 325 μm, the number of fringe crossings is 1000. The wavelength of the laser used in nanometers is ____.

Answer: (650 to 650)

23. Consider the function f(x) = −x2 + 10x + 100. The minimum value of the function in the interval [5, 10] is ___.

Answer: (100 to 100)

24. Let  defined in the complex plane. The integral  over the contour of a circle c with center at the origin and unit radius is _____.

Answer: (0 to 0)

25. The determinant of the matrix M shown below is ____.

Answer: (4 to 4)

Q.26 – Q.36 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

26. f(z) = (z − 1) −1 − 1 + (z − 1) − (z − 1)2 + ⋯ is the series expansion of

Answer: (B)

27. A single-phase transformer has maximum efficiency of 98 %. The core losses are 80 W and the equivalent winding resistance as seen from the primary side is 0.5 Ω. The rated current on the primary side is 25 A. The percentage of the rated input current at which the maximum efficiency occurs is

(A)  35.7%

(B)  50.6%

(C)  80.5%

(D)  100%

Answer: (B)

28. A slip-ring induction motor is expected to be started by adding extra resistance in the rotor circuit. The benefit that is derived by adding extra resistance in the rotor circuit in comparison to the rotor being shorted is

(A)  The starting torque would be higher.

(B)  The power factor at start will be lower.

(C)  The starting current is higher.

(D)  The losses at starting would be lower.

Answer: (A)

29. Consider a unity feedback configuration with a plant and a PID controller as shown in the figure . and  with K being scalar. The closed loop is

(A)  only stable for K > 0

(B)  only stable for K between -1 and +1

(C)  only stable for K < 0

(D)  stable for all values of K

Answer: (A)

30. The output Vo of the ideal OpAmp used in the circuit shown below is 5 V Then the value of resistor RL in kilo ohm (kΩ) is

(A)  2.5

(B)  5

(C)  25

(D)  50

Answer: (C)

31. A Boolean function F of three variables X, Y, and Z is given as

F (X, Y, Z) = (Xʹ + Y + Z)˖(X + Yʹ + Zʹ )˖(Xʹ + Y + Zʹ )˖( Xʹ Yʹ Zʹ + Xʹ Y Zʹ + X Y Zʹ )

Which one of the following is true?

(A)  F (X, Y, Z) = (X + Y + Zʹ)˖( Xʹ + Yʹ +Zʹ )

(B)  F (X, Y, Z) = (Xʹ + Y)˖(X + Y ʹ+ Zʹ )

(C)  F (X, Y, Z) = Xʹ Zʹ + Y Zʹ

(D)  F (X, Y, Z) = Xʹ Yʹ Z + X Y Z

Answer: (C)

32. A 10½ digit Counter-timer is set in the ‘frequency mode’ of operation (with Ts = 1 s). For a specific input, the reading obtained is 1000. Without disconnecting this input, the Counter-timer is changed to operate in the ‘Period mode’ and the range selected is microseconds (μs, with fs = 1 MHz). The counter will then display

(A)  0

(B)  10

(C)  100

(D)  1000

Answer: (D)

33. A J-type thermocouple has an output voltage Vθ = (13650 + 50 θx) μV, where θx is the junction temperature in Celsius (°C). The thermocouple is used with reference junction compensation, as shown in the figure. The Instrumentation amplifier used has a gain G = 20. If If θRef is 1 °C, for an input θx of 100°C, the output Vo of the instrumentation amplifier in millivolt is

(A)  98 mV

(B)  99 mV

(C)  100 mV

(D)  101 mV

Answer: (B)

34. A laser pulse is sent from ground level to the bottom of a concrete water tank at normal incidence. The tank is filled with water up to 2 m below the ground level. The reflected pulse from the bottom of the tank travels back and hits the detector. The round-trip time elapsed between sending the laser pulse, the pulse hitting the bottom of the tank, reflecting back and sensed by the detector is 100 ns. The depth of the tank from ground level marked as x in metre is ____.

(Refractive index of water nwater = 1. 3 and velocity of light in air cair = 3 × 108 m/s)

(A)  9

(B)  10

(C)  11

(D)  12

Answer: (D)

35. A 4 × 1 multiplexer with two selector lines is used to realize a Boolean function F having four Boolean variables X, Y, Z and W as shown below. S0 and S1 denote the least significant bit (LSB) and most significant bit (MSB) of the selector lines of the multiplexer respectively. I0, I1, I2, I3 are the input lines of the multiplexer.

The canonical sum of product representation of F is

(A)  F (X, Y, Z, W) = Σ m( , ,3, 4, 5)

(B)  F (X, Y, Z, W) = Σ m( , ,3,11,14)

(C)  F (X, Y, Z, W) = Σ m( ,5,9, , 4)

(D)  F (X, Y, Z, W) = Σ m(1,3,7,9,15)

Answer: (B)

36. Given below is the diagram of a synchronous sequential circuit with one J-K flip-flop and one T flip-flop with their outputs denoted as A and B respectively, with JA = (Aʹ + Bʹ), KA = (A + B), and TB = A.

Starting from the initial state (AB = 00), the sequence of states (AB) visited by the circuit is

(A)  00 → 01 → 10 → 11 → 00…

(B)  00 → 10 → 01 → 11 → 00…

(C)  00 → 10 → 11 → 01 → 00…

(D)  00 → 01 → 11 → 00…

Answer: (B)

Q.37 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

37. Consider that X and Y are independent continuous valued random variables with uniform PDF given by X ~ U(2, 3) and Y ~ U(1, 4). Then P(Y ≤ X) is equal to __________ (rounded off to two decimal places).

Answer: (0.45 to 0.55)

38. Given The value of the determinant │A4 − 5A3 +6A2 +2 I│= _____.

Answer: (4 to 4)

39. The figure below shows an electrically conductive bar of square cross-section resting on a plane surface. The bar of mass of 1 kg has a depth of 0.5 m along the y direction. The coefficient of friction between the bar and the surface is 0.1. Assume the acceleration due to gravity to be 10 m/s2. The system faces a uniform flux density B = −1 ẑ T. At time t = 0, a current of 10 A is switched onto the bar and is maintained.

When the bar has moved by 1 m, its speed in metre per second is ____ (rounded off to one decimal place).

Answer: (2.7 to 2.9)

40. A toroid made of CRGO has an inner diameter of 10 cm and an outer diameter of 14 cm. The thickness of the toroid is 2 cm. 200 turns of copper wire is wound on the core. μo = 4π × 107 H/m and μR of CRGO is 3000. When a current of 5 mA flows through the winding, the flux density in the core in millitesla is ____.

Answer: (10 to 10)

41. An air cored coil having a winding resistance of 10 Ω is connected in series with a variable capacitor Cx. The series circuit is excited by a 10 V sinusoidal voltage source of angular frequency 1000 rad/s. As the value of the capacitor is varied, a maximum voltage of 30 V was observed across it. Neglecting skin-effect, the value of the inductance of the coil in millihenry is _____.

Answer: (30 to 30)

42. A household fan consumes 60 W and draws a current of 0.3125 A (rms) when connected to a 230 V (rms) ac, 50 Hz single phase mains. The reactive power drawn by the fan in VAr is __________ (rounded off to the nearest integer).

Answer: (39 to 40)

43. Given y(t) = e−3tu(t) ∗ u(t + 3), where * denotes convolution operation. The value of y(t) as t → ∞ is ____________ (rounded off to two decimal places).

Answer: (0.3 to 0.35)

44. The input signal shown below

is passed through the filter with the following taps

The number of non-zero output samples is ____.

Answer: (10 to 10)

45. A sinusoid (√2 sin t) μ(t), where μ(t) is the step input, is applied to a system with transfer-function  The amplitude of the steady state output is ____.

Answer: (0.95 to 1.05)

46. Consider a system with transfer-function  A unit step function μ(t) is applied to the system, which results in an output y(t). If e(t) = y(t) − μ(t), then   is ______.

Answer: (1 to 1)

47. The circuit shown below uses an ideal OpAmp. Output VO in volt is ________ (rounded off to one decimal place).

Answer: (1.0 to 1.1)

48. All the transistors used in the circuit are matched and have a current gain β of 20. Neglecting the Early effect, the current IO4 in milliampere is _____.

Answer: (1 to 1)

49. The power in a 400 V (rms, line-line) three-phase, three-wire RYB sequence system is measured using the two wattmeters, as shown. The R-line current is 5∠60° Wattmeter W1 in the R-line will read (in watt) _________.

Answer: (0 to 0)

50. A 31⁄2 digit, rectifier type digital meter is set to read in its 2000 V range. A symmetrical square wave of frequency 50 Hz and amplitude ±100 V is measured using the meter. The meter will read _____.

Answer: (111 to 111)

51. A bar primary current transformer of rating 1000/1 A, 5VA, UPF has 995 secondary turns. It exhibits zero ratio error and phase error of 30 minutes at 1000 A with rated burden. The watt loss component of the primary excitation current in ampere is __________ (rounded off to one decimal place).

Answer: (4.9 to 5.1)

52. In the bridge circuit shown, the voltmeter V showed zero when the value of the resistors are: R1 = 100 Ω, R2 = 110 Ω, and R3 = 90 Ω. If (R1/R2) = (RA/RB), the value of R4 in ohm is _____.

Answer: (99 to 99)

53. For the full bridge made of linear strain gages with gage factor 2 as shown in the diagram, R1 = R2 = R3 = R4 = 100 Ω at 0°C and strain is 0. The temperature coefficient of resistance of the strain gages used is 0.005 per ° All strain gages are made of same material and exposed to same temperature. While measuring a strain of 0.01 at a temperature of 50 °C, the output VO in millivolt is _____ (rounded off to two decimal places).

Answer: (2.45 to 2.55)

54. A signal having a bandwidth of 5 MHz is transmitted using the Pulse code modulation (PCM) scheme as follows. The signal is sampled at a rate of 50% above the Nyquist rate and quantized into 256 levels. The binary pulse rate of the PCM signal in Mbits per second is ___.

Answer: (120 to 120)

55. In the figure shown, a large multimode fiber with ncore = 1. 5 and nclad = 1. 2 is used for sensing. A portion with the cladding removed passes through a liquid with refractive index nliquid. An LED is used to illuminate the fiber from one end and a paper is placed on the other end, 1 cm from the end of the fiber. The paper shows a spot with radius 1 cm. The refractive index nliquid of the liquid (rounded off to two decimal places) is ________.

Answer: (1.30 to 1.35)

GATE Exam 2021 Geology and Geophysics (GG) Question Paper With Answer Key

GATE-2021

GG-Geology & Geophysics

GA: General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. The people ___________ were at the demonstration were from all sections of society.

(A)  whose

(B)  which

(C)  who

(D)  whom

Answer: (C)

2. A transparent square sheet shown above is folded along the dotted line. The folded sheet will look like ________.

Answer: (C)

3. For a regular polygon having 10 sides, the interior angle between the sides of the polygon, in degrees, is:

(A)  396

(B)  324

(C)  216

(D)  144

Answer: (D)

4. Which one of the following numbers is exactly divisible by (1113 + 1)?

(A)  1126 + 1

(B)  1133 + 1

(C)  1139 – 1

(D)  1152 – 1

Answer: (D)

5. Oasis is to sand as island is to ________

Which one of the following options maintains a similar logical relation in the above sentence?

(A)  Stone

(B)  Land

(C)  Water

(D)  Mountain

Answer: (C)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

6. The importance of sleep is often overlooked by students when they are preparing for exams. Research has consistently shown that sleep deprivation greatly reduces the ability to recall the material learnt. Hence, cutting down on sleep to study longer hours can be counterproductive.

Which one of the following statements is the CORRECT inference from the above passage?

(A)  Sleeping well alone is enough to prepare for an exam. Studying has lesser benefit.

(B)  Students are efficient and are not wrong in thinking that sleep is a waste of time.

(C)  If a student is extremely well prepared for an exam, he needs little or no sleep.

(D)  To do well in an exam, adequate sleep must be part of the preparation.

Answer: (D)

7. 

In the figure shown above, each inside square is formed by joining the midpoints of the sides of the next larger square. The area of the smallest square (shaded) as shown, in cm2 is:

(A)  12.50

(B)  6.25

(C)  3.125

(D)  1.5625

Answer: (C)

8. Let X be a continuous random variable denoting the temperature measured. The range of temperature is [0, 100] degree Celsius and let the probability density function of X be f(x) = 0.01 for 0 ≤ X ≤ 100.

The mean of X is _____

(A)  2.5

(B)  5.0

(C)  25.0

(D)  50.0

Answer: (D)

9. 

The number of students passing or failing in an exam for a particular subject are presented in the bar chart above. Students who pass the exam cannot appear for the exam again. Students who fail the exam in the first attempt must appear for the exam in the following year. Students always pass the

exam in their second attempt.

The number of students who took the exam for the first time in the year 2 and the year 3 respectively, are __________.

(A)  65 and 53

(B)  60 and 50

(C)  55 and 53

(D)  55 and 48

Answer: (D)

10. Seven cars P, Q, R, S, T, U and V are parked in a row not necessarily in that order. The cars T and U should be parked next to each other. The cars S and V also should be parked next to each other, whereas P and Q cannot be parked next to each other. Q and S must be parked next to each other. R is parked to the immediate right of V. T is parked to the left of U.

Based on the above statements, the only INCORRECT option given below is:

(A)  There are two cars parked in between Q and V.

(B)  Q and R are not parked together.

(C)  V is the only car parked in between S and R.

(D)  Car P is parked at the extreme end.

Answer: (A)

Geology (GG)

Q.1 – Q.15 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Which of the given planets has the highest average density?

(A)  Mercury

(B)  Venus

(C)  Earth

(D)  Mars

Answer: (C)

2. In a multi-electrode resistivity tomography (ERT) survey, using equally spaced electrodes, which of the given configurations will provide the maximum number of data points?

(A)  Wenner array

(B)  Axial Dipole-dipole array

(C)  Axial Pole-dipole array

(D)  Schlumberger array

Answer: (C)

3. In Electromagnetic methods of prospecting, which one of the given options is CORRECT about frequency and type of current source for the Primary field used?

(A)  High frequency A.C.

(B)  Low frequency A.C.

(C)  Both high frequency A.C. and D.C.

(D)  Low frequency D.C.

Answer: (B)

4. ‘Group’ is a unit of:

(A)  Lithostratigraphy

(B)  Sequence stratigraphy

(C)  Biostratigraphy

(D)  Chronostratigraphy

Answer: (A)

5. Furongian is an Epoch of:

(A)  Cambrian

(B)  Ordovician

(C)  Triassic

(D)  Cretaceous

Answer: (A)

6. The stage of textural maturity of a clay-rich sandstone containing poorly-sorted and angular framework grains is:

(A)  Mature

(B)  Supermature

(C)  Immature

(D)  Submature

Answer: (C)

7. Which one of the following structures indicates Synsedimentary deformation?

(A)  Festoon bedding

(B)  Flaser bedding

(C)  Tabular bedding

(D)  Convolute bedding

Answer: (D)

8. Low value in SP log as observed in dispersed shales is mainly due to the impeded movement of:

(A)  Na+ ion

(B)  Cl ion

(C)  K+ ion

(D)  OHion

Answer: (B)

9. In Radiometric survey, the g-ray spectrometer count rate depends on:

(A)  Cracks present in the target rock volume

(B)  Solid angle of the target rock about the spectrometer

(C)  Temperature in the target rock

(D)  Pressure in the target rock

Answer: (B)

10. The dimension of radiant emittance of a blackbody as per Stefan-Boltzmann law is:

(A)  M0L1T1

(B)  M1L1T2

(C)  M1L2T2

(D)  M1L0T3

Answer: (D)

11. A surface geological process that can create a landform called Cirque is:

(A)  aeolian deposition

(B)  fluvial deposition

(C)  glacial erosion

(D)  deposition of volcanic ash

Answer: (C)

12. If α and β P- and S-wave velocities, respectively, then α2 – (4/3)β2 is equal to:

(κ is the bulk modulus, μ is shear modulus and ρ is density)

(A)  κ/ρ

(B)  μ/ρ

(C)  κ + μ/ρ

(D)  κ − μ/ρ

Answer: (A)

13. Which one of the following phases is P-wave that converts to S-wave during passage through the solid inner core?

(A)  PKIKP

(B)  PKJKP

(C)  PKiKP

(D)  PKPPcP

Answer: (B)

14. In reduction of gravity data, the latitude correction is maximum at:

(A)  35° latitude

(B)  45° latitude

(C)  55° latitude

(D)  65° latitude

Answer: (B)

15. The most coaliferous unit of the Gondwana Supergroup is:

(A)  Talchir Formation

(B)  Barakar Formation

(C)  Karharbari Formation

(D)  Panchet Formation

Answer: (B)

Q.16 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

16. A vertical borehole encounters a shale bed of uniform thickness occurring at a depth of 5 m and dipping 60°. The borehole pierces through this shale bed for a length of 10 m to reach a sandstone layer below. The true thickness of the shale bed is ________ m. [in integer]

Answer: (5 to 5)

17. The mass and volume of a fully dried soil sample are 2200 gm and 1100 cm3, respectively. If the specific gravity of the soil particles is 2.5 and water density is 1 gm/cm3, the void ratio of the soil is ________. [round off to 2 decimal places]

Answer: (0.25 to 0.25)

18. A constant-head permeability test was performed on a vertical sand column of height 40 cm and cross-sectional area of 25 cm2. During the test, when the loss of head was 50 cm, the volume of water collected in 2 minutes was 300 cm3. Applying Darcy’s law, the calculated coefficient of permeability of the sand column is ________ cm/sec. [round off to 2 decimal places]

Answer: (0.08 to 0.08)

19. The radius (r) of the oblate spheroid at 45° latitude with ellipticity of polar flattening of 1/298.25 and equatorial radius of 6378140 m is ________ km. [round off to 2 decimal places]

Answer: (6367.44 to 6367.46)

20. Light passes through two media with refractive indices of 1.75 and 1.55, respectively. The thickness of both the media is 30 μ The resultant path difference of the yellow light component (λ = 589 nm) is ________ πm. (Take λ = 3.141) [round off to one decimal places]

Answer: (64.0 to 64.0)

21. The water table in an unconfined aquifer at a place near the coast is 1 m above the Mean Sea Level. Given the densities of fresh and saline water as 1.001 and 1.025 g/cc, respectively, the fresh-saline water interface at the same location should be at a depth of _______ m from the water table. [round off to one decimal place]

Answer: (42.6 to 42.7)

22. The volume percentage of galena and quartz in an ore body of Pb are 90 and 10, respectively. The densities of galena and quartz are 7.6 and 2.65 g/cc, respectively. The grade of the ore body in terms of weight percent of Pb is _____. (Atomic weights of Pb = 206 and S = 32) [round off to 2 decimal places]

Answer: (83.30 to 83.34)

23. Normal moveout (NMO) for reflected phase of seismic data is 2 milliseconds. Consider the diffraction source at the edge of the same reflector, where the shot point is directly above diffraction source. In this case, the NMO due to diffraction is ______ milliseconds [in integer].

Answer: (4 to 4)

24. In a 2D seismic survey, first receiver location is at (1000 m, 4000 m), second receiver location is at (2000 m, 4000 m) and the source location is at (2000 m, 1000 m). Consider P-wave velocity as 5000 m/sec. The difference in first arrival time of P-wave phase for the two receivers is ________ seconds. [round off to 2 decimal places].

Answer: (0.03 to 0.03)

25. The potential difference measured between potential electrodes using Wenner array is 500 mV when a current of 2 A is passed through the subsurface between current electrodes. If the computed apparent resistivity is 100 Ωm then the distance between the current electrodes will be ________ m. [round off to 2 decimal places] (Use π = 3.141)

Answer: (190.00 to 192.00)

Q.26 – Q.42 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

26. Which one of the following statements is CORRECT?

(A)  Taphonomy refers to the study of fossilization pathways from death of an organism to its recovery as a fossil.

(B)  Biostratinomy refers to the study of fossilization pathways from burial of an organism under sediments to its recovery as a fossil.

(C)  Biostratinomy is an integral component of biostratigraphy and refers to the characterization of strata based on fossil content.

(D)  Taphonomy refers to the study of fossilization pathways from death of an organism to its burial under the sediments.

Answer: (A)

27. Based on the three statements given below, choose the CORRECT option:

Statement I: Gunderdehi Formation is a stratigraphic unit of the Chattisgarh Supergroup.

Statement II: Raniganj Formation is a coal-bearing Triassic unit of the Gondwana Supergroup.

Statement III: Pitepani Volcanics is a stratigraphic unit of the Dongargarh Supergroup.

(A)  All the statements are correct

(B)  Statement I is correct, but statements II and III are incorrect

(C)  Statements I and III are correct, but statement II is incorrect

(D)  Statements II and III are correct but statement I is incorrect

Answer: (C)

28. Which one of the following equid genera was a one-toed grazer?

(A)  Merychippus

(B)  Parahippus

(C)  Pliohippus

(D)  Mesohippus

Answer: (C)

29. Match the following invertebrate genera in Group I with their corresponding Class/Phylum in Group II:

(A)  P-4, Q-3, R-1, S-2

(B)  P-4, Q-1, R-2, S-3

(C)  P-4, Q-3, R-2, S-1

(D)  P-3, Q-1, R-4, S-2

Answer: (A)

30. Tillite with faceted boulders and green shale with dropstones characterize the lithology of:

(A)  Lameta Formation

(B)  Bagra Formation

(C)  Talchir Formation

(D)  Panchet Formation

Answer: (C)

31. Match the following structures in Group I with the corresponding environment of deposition in Group II:

(A)  P-4, Q-1, R-2, S-3

(B)  P-4, Q-1, R-3, S-2

(C)  P-3, Q-1, R-2, S-4

(D)  P-2, Q-4, R-1, S-3

Answer: (A)

32. Match the items in Group-I with appropriate items in Group-II

(A)  P-4, Q-3, R-1, S-2

(B)  P-2, Q-3, R-4, S-1

(C)  P-4, Q-1, R-2, S-3

(D)  P-3, Q-2, R-1, S-4

Answer: (C)

33. With regard to superposed folding, the stereographic projection represents a geometry of:

(A)  plane cylindrical fold.

(B)  plane non-cylindrical fold.

(C)  non-plane cylindrical fold.

(D)  non-plane non-cylindrical fold.

Answer: (B)

34. The given outcrop pattern of a bed (shaded in grey) with respect to contours (dashed lines) indicates that the bed.

(A)  dips upstream.

(B)  is horizontal.

(C)  dips steeply downstream.

(D)  dips downstream at an angle equal to the valley gradient.

Answer: (A)

35. With regard to occurrence of groundwater in an area, which of the given statements is CORRECT?

(A)  Vadose water occurs in the zone of saturation.

(B)  The zone of aeration lies below the zone of saturation.

(C)  The water table marks the uppermost surface of the vadose zone.

(D)  The depth of the perched water table is less than that of the water table.

Answer: (D)

36. There are indications of presence of a massive tabular multimetal sulfide ore body at a shallow depth from the surface. Which of the following would be the most efficient geophysical method to confirm the presence of the ore body?

(A)  resistivity sounding

(B)  ground geomagnetic survey

(C)  self-potential method of geophysical prospecting

(D)  ground gravity survey

Answer: (C)

37. The following reaction takes place in the amphibolite grade of metamorphism of pelitic rocks:

kyanite + chlorite ⟺ staurolite + quartz +H2O

Which of the following is a CORRECT statement on this reaction?

(A)  The reaction can be represented as a sharp univariant boundary.

(B)  Initially chlorite and staurolite are Fe-rich and will gradually become Mg-rich with increasing temperature.

(C)  With increasing temperature chlorite becomes Mg-rich and staurolite becomes Fe –rich.

(D)  The reaction is independent of fugacity of H2O.

Answer: (B)

38. Match the items in Group-I with corresponding appropriate items in Group-II.

(A)  P-4, Q-1, R-2, S-3

(B)  P-4, Q-3, R-1, S-2

(C)  P-3, Q-1, R-2, S-4

(D)  P-2, Q-1, R-4, S-3

Answer: (A)

39. The symmetry elements of a point group are: 3 crystallographic axes of 2-fold symmetry and 3 mirror planes perpendicular to the crystallographic axes. The Hermann – Mauguin notation of the point group is:

(A)  2m2m2m

(B)  2mm

(C)  2/m2/m2/m

(D)  2/m

Answer: (C)

40. An aqueous polyphase (L + V + solid) inclusion contains a halite daughter crystal at room temperature and pressure. Which of the given statements is CORRECT in relation to this inclusion?

(A)  The salinity of the bulk aqueous fluid can be determined from the temperature of melting of ice.

(B)  The salinity of the bulk aqueous fluid can be determined from the temperature of dissolution of halite.

(C)  The density in all cases can be determined from the temperature of liquid-vapor homogenization.

(D)  The density in all cases can be determined from the temperature of dissolution of the halite daughter crystal.

Answer: (B)

41. Match the rock types in Group-I with their most likely corresponding lithospheric/ tectonic settings of formation in Group-II.

(A)  P-1, Q-3, R-4, S-2

(B)  P-2, Q-4, R-1, S-3

(C)  P-2, Q-1, R-4, S-3

(D)  P-3, Q-2, R-4, S-1

Answer: (C)

42. A mantle source rock melts at a time t0 giving rise to melt (M) and residue (R). Which of the following statements is CORRECT about evolution of the (143Nd/144Nd) and (87Sr/86Sr) isotope ratio in M (that crystallized to form a rock) and R?

(A)  The growth of Nd isotope ratio versus time is faster in R than M and the Sr isotope ratio grows slower in R than M.

(B)  The growth of Nd isotope ratio versus time is slower in R than M and the Sr isotope ratio grows faster in R than M.

(C)  Both the Nd and Sr isotope ratios grow at identical rates in R and M.

(D)  The growth of Nd and Sr isotope ratio in M and R would depend on the initial concentrations of Sm and Rb in the mantle source rock.

Answer: (A)

Q.43 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

43. The mole percentages of SiO2, Al2O3 and K2O in a granitic rock are 84.21, 7.89 and 7.89, respectively. The molar proportion (in %) of K-feldspar in the rock is ______. [ round off to one decimal place]

Answer: (29.9 to 30.1)

44. In a zone of active normal faulting, the maximum and minimum in situ principal stresses (compressive in nature) are 30 MPa (s1) and 10 MPa (s3), respectively. The fault plane striking N-S has a dip amount of 60° towards E. Considering Anderson theory of faulting and using the given information, the calculated normal stress on the fault plane is ________ MPa. [in integer]

Answer: (15 to 15)

45. A circular tunnel is being excavated in a blocky rock mass by drilling and blasting. An excavation disturbed zone (EDZ) around the tunnel extends 0.70 m into the rock from the excavation surface. Considering the unit weight of the rock as 25 kN/m3, the support pressure required at the crown of the tunnel to stabilize the loose blocks of the EDZ is _______ kPa. [round off to one decimal place]

Answer: (17.5 to 17.5)

46. Under uniaxial compression, a cylindrical quartzite specimen (length = 122 mm and diameter = 60 mm) showed linear elastic behaviour. The uniaxial compressive strength and the modulus ratio of the rock are 150 MPa and 500, respectively. The axial strain at 75 MPa during the loading was _________ milli-strain. [in integer]

Answer: (1 to 1)

47. The sketch shows a triangular rock mass (ABC) resting on a joint plane (AC) inclined at 35° with the horizontal. A rockbolt having an inclination of 25° with the horizontal is used to stabilize the slope. If the bolt tension (T) is 110 kN, the absolute value of shear force along the joint plane induced by the bolt tension is _________ kN. [in integer]

Answer: (55 to 55)

48. A stratified confined aquifer consists of three parallel homogeneous and isotropic horizontal layers with thickness of 10 m, 5 m and 5 m. The layers have the same width. The hydraulic conductivities of the strata are 15 m/day, 20 m/day and 30 m/day, respectively. The water flow follows Darcy’s law and is parallel to the strata. Considering the same hydraulic gradient for all the layers, the effective hydraulic conductivity of the aquifer is ________ m/day. [in integer]

Answer: (20 to 20)

49. A drainage basin of fourth order covers an area of 35 km2. Within the basin, the total lengths of the 1st order, 2nd order and 3rd order drainages are 11.5 km, 8.5 km and 4.2 km, respectively. If the drainage density of the basin is 0.8 km1, the total length of the 4th order drainage is ________ km. [round off to one decimal place]

Answer: (3.8 to 3.8)

50. The grade of copper (in wt%) of an ore body determined at locations 1, 2 and 3 are indicated (in parentheses) below. The grade of copper at an unknown location x calculated using Inverse-Square Distance Weighting (IDW) is ________ wt %. [round off to 2 decimal places]

Answer: (1.67 to 1.69)

51. The heat flux at the Earth’s surface is 60 mWm2. If the thermal conductivity at the surface is 2.5 Wm1 °C1, the geothermal gradient is ________ °C/km. [in integer]

Answer: (24 to 24)

52. A rock formed at time t0 = 0 with number of 14C atoms = 105. The number of 14C atoms (in log10) after a time of 8 × 103 years is _______. [round off to 3 decimal places] (Use a decay constant of 1.25 × 10−4 yr−1)

Answer: (4.565 to 4.567)

53. In the given reaction,

2Fe2+ + 3H2O → Fe2O3 + 6H+ + 2e

consider ideal condition, take concentration of Fe2+ as 105 molal, E0 = 0.98 V and pH=6. The value of (2.303 × R × T)/F = 0.059 (where F is the Faraday constant). The value of Eh on the Fe2+ / hematite boundary at 25 °C is ________ V. [round off to 2 decimal places]

Answer: (0.21 to 0.22)

54. The first and second dissociation constants of H2CO3 are 6.761 × 107 and 4.68 × 1011, respectively. If the concentration of H2CO3 is 1 molal and pH = 6, the ∑CO2 in the solution (assuming ideal condition) is _______ molal. [round off to 3 decimal places]

Answer: (1.675 to 1.677)

55. A satellite orbits the earth at an altitude of 700 km on the equatorial plane of the earth and it revolves in the same direction as the direction of rotation of the earth. Considering the radius of a spherical earth as 6300 km and the acceleration due to gravity as 10 m/s2, the tangential velocity of the satellite in the orbit is ____________ km/s. [round off to 2 decimal places]

Answer: (7.52 to 7.53)

Geophysics (GG)

Q.26 – Q.42 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

26. In a horizontally stratified cuboid rock sample (stratified in vertical z direction with various layers of different resistivity), bulk resistivity is measured in three perpendicular directions. If ρ1, ρ2, and ρ3 are the bulk resistivities measured perpendicular to xy, xz and yz planes, respectively, then

(A)  ρ1 < ρ2 = ρ3

(B)  ρ1 > ρ2 = ρ3

(C)  ρ1 = ρ2 ≠ 3

(D)  ρ1 ≠ ρ2 ≠ ρ3

Answer: (B)

27. Which one is the CORRECT sequence of electromagnetic methods in terms of depth of investigation?

P – AFMAG method

Q – VLF method

R – GPR method

S – Magnetotelluric method

(A)  P > Q > S > R

(B)  P > S > R > Q

(C)  S > P > Q > R

(D)  S > Q > R > P

Answer: (C)

28. Which Norm gives the maximum weight to the data points having maximum deviation/outlier from the smoothly fitted curve during linearized inversion?

(A)  L1-Norm

(B)  L2-Norm

(C)  Lp-Norm

(D)  L∞-Norm

Answer: (D)

29. Which one of the following statements is CORRECT for the Quenching agent used in the tube of Geiger-Muller counter?

(A)  It enhances the emission of secondary electrons from the cathode.

(B)  It reduces the emission of secondary electrons from the cathode.

(C)  It enhances the emission of secondary electrons from the anode.

(D)  It reduces the emission of secondary electrons from the anode.

Answer: (B)

30. Which one of the following statements is CORRECT regarding the property of Laplacian operator for vector/scalar fields?

(A)  Laplacian of a vector field is zero if the Laplacian of each of its components are zero.

(B)  Laplacian of a vector field is zero if the Laplacian of any one of its component is zero.

(C)  If the Laplacian of a scalar field is zero then the scalar field is not harmonic.

(D)  If the Laplacian of a scalar field is finite (non-zero) then the scalar field is harmonic.

Answer: (A)

31. The most desirable interaction of γ-ray with matter for γ-ray spectroscopy is

(A)  Photoelectric effect only

(B)  Both Photoelectric effect and Compton scattering

(C)  Both Compton Scattering and Pair production

(D)  Photoelectric effect, Compton scattering and Pair production

Answer: (A)

32. Which one of the following is the CORRECT sequence for a 2D seismic reflection data processing prior to Time-depth conversion?

(A)  Migration → Deconvolution → Filtering → Equalization → Coherency

(B)  Deconvolution → Migration → Filtering → Coherency → Equalization

(C)  Filtering → Deconvolution → Migration → Equalization → Coherency

(D)  Deconvolution → Filtering → Equalization → Migration → Coherency

Answer: (D)

33. Choose the CORRECT procedure to avoid the area of cracked, altered formation in Sonic log.

(A)  Measure interval transit times using long-spacing sonic tools.

(B)  Use more number of sets of sources.

(C)  Measure interval transit times using short-spacing sonic tools.

(D)  Use more number of sets of detectors.

Answer: (A)

34. The factor that DOES NOT influence measurement of Nuclear Magnetic Resonance log is

(A)  mineral composition of the rock.

(B)  bound water (irreducible water).

(C)  free water.

(D)  pore fluid pressure.

Answer: (D)

35. Consider a time-invariant geophysical filter with the given input as:

x(t) = e−αt when t ≥ 0 ; x(t) = 0 when t < 0 and output y(t) = eβt when t ≥ 0 ; y(t) = 0 when t < 0. The transfer function for the given input and output of time-invariant filter will be:

Answer: (B)

36. Which of the given figures is the Hilbert transform of the Dirac delta function δ(ξ) :

(A)  Figure 1

(B)  Figure 2

(C)  Figure 3

(D)  Figure 4

Answer: (A)

37. If a mountain range is 100% isostatically compensated (Airy’s type), what would be the expected nature of the Bouguer anomaly and free air anomaly?

(A)  Bouguer anomaly is very large and negative; free air anomaly is small and positive.

(B)  Bouguer anomaly is very large and negative; free air anomaly is large and positive.

(C)  Bouguer anomaly is exactly zero; free air anomaly is very large and positive.

(D)  Bouguer anomaly is very large and negative; free air anomaly is large and negative.

Answer: (A)

38. Which of the following is INCORRECT for a recorded nuclear explosion event?

(A)  The first P-wave from an explosion to arrive at any seismic station, irrespective of Azimuth, should be compressional.

(B)  Nuclear explosions are not as good as earthquakes at generating surface waves or S-waves.

(C)  In general, earthquakes have Mb values same those for nuclear explosions with same Ms values.

(D)  Nuclear explosions have all been shallower than 2 km depth.

Answer: (C)

39. Focal depth can be determined from measurement of the difference in the travel time between:

(A)  pP and P

(B)  PP and P

(C)  PcP and P

(D)  PPP and P

Answer: (A)

40. Of the following options, at which discontinuity both P-wave and S-wave have maximum velocity drop?

(A)  Conard

(B)  Mohorovicic

(C)  Gutenberg

(D)  Lehman

Answer: (C)

41. In data enhancement techniques, what is the advantage of magnetic anomaly being ‘Reduced to the pole’?

(A)  Enhances the signal to noise ratio.

(B)  Estimates the depth to the basement.

(C)  Takes care of variation of the magnetic anomaly with latitude.

(D)  Helps in pseudo-gravity transformation.

Answer: (C)

42. Match the source in Group – I with their half-width (X1/2) / δgmax and depth (d) relation in Group –II.

(A)  P-1, Q-2, R-4, S-3

(B)  P-1, Q-4, R-3, S-2

(C)  P-3, Q-4, R-1, S-2

(D)  P-3, Q-1, R-4, S-2

Answer: (C)

Q.43 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

43. If a gravity determination is made at an elevation of 150 m above mean sea level, the Bouguer correction required for a density contrast of 250 kg m3 with the surroundings is________ mgal. [round off to 2 decimal places]

Answer: (1.55 to 1.65 OR -1.65 to -1.55)

44. An infinite horizontal cylinder of radius 40 km is buried at a depth of 100 km and yields the same maximum gravity anomaly as that of an infinite horizontal cylinder of radius 1 km, buried at a depth of 1 km having density contrast with the surroundings of 200 kgm3. The density contrast of the deeper cylinder with respect to the surrounding is ________ kg/m3. [round off to one decimal place]

Answer: (12.5 to 12.5)

45. An earthquake causes an average of 25 m strike slip displacement over a 50 km long, 25 km deep portion of a transform fault. Assuming that the rock rigidity is 3 × 1010 Nm2, the moment magnitude (Mw) of the earthquake is ______ . [round off to 2 decimal places]

Answer: (3.24 to 3.26 OR 7.90 to 7.92)

46. Lithological unit X is sandwiched between Y1 above and Y2 below it. Now consider a log across lithology X, where Gamma ray (GR) reading is given by 100API; Y1 lithology, where minimum GR reading is 10API; and Y2 lithology of shale, where GR reading is 200API. Then the shale-free fractional volume in the X lithology will be________. [round off to 2 decimal places]

Answer: (0.52 to 0.53)

47. In a 2D seismic survey, 25 receivers are placed in a group and 25 sources are placed in another group, where random noise is present. The signal to noise ratio for this arrangement will be_______. [in integer]

Answer: (25 to 25)

48. In a VSP survey, the tube wave passage through borehole causes cross-section area change from 0.79 m2 to 1.13 m2. The transmission coefficient will be ______. [round off to 2 decimal places]

Answer: (0.82 to 0.82)

49. In a cratonic region, radioactive heat generation decreases exponentially with depth. Assuming characteristic depth as 10 km and surface heat generation as 3 μWm3 and neglecting mantle heat flow, the heat production per unit volume for a 30 km thick layer will be_______ μWm3. [round off to 2 decimal places]

Answer: (0.95 to 0.95)

50. In an Induced Polarization survey, 50 milliseconds chargeability was measured for steady state voltage (full saturation reached) of 200 V between potential electrodes. When the current was switched off, the voltage across potential electrodes drops instantaneously (time t = 0 s) to a level Va and thereafter decays linearly with time and becomes zero in 10 seconds. The magnitude of instantaneous voltage Va (at time t = 0 s) will be________ mV. [in integer]

Answer: (2000 to 2000)

51. Apparent resistivity sounding data for Schlumberger array is theoretically generated by the teacher for the following 4-layer model as: ρ1 = 100 Ωm, ρ2 = 20 Ωm, ρ3 = 500 Ωm, ρ4 = 10 Ωm and layer thicknesses h1 = 50 m, h2 = 20 m and h3 = 50 m. If the student interprets this theoretical sounding data for ρ3 as 750 Ωm, then according to the Principle of Equivalence, the thickness h3 would be ________ m. [round off to 2 decimal places]

Answer: (33.00 to 34.00)

52. A 3D conducting body is located at a depth of 50 m in a homogeneous medium of resistivity 500 Ω A frequency of f1 Hz is appropriate to detect this conducting body in a plane wave EM survey. When the same conducting body is located in a host medium of resistivity 100 Ωm at the same depth then a frequency of f2 Hz is found to be appropriate. Then the value of f2/f1 will be __________. [round off to 2 decimal places]

Answer: (0.19 to 0.21)

53. The apparent resistivity and phase computed for MT measurement at 103 Hz frequency is 500 Ωm and 30°, respectively. Ratio of Imaginary to Real component of the Impedance tensor is ______. [round off to 2 decimal places]

Answer: (0.57 to 0.59)

54. The diagonal elements of a covariance matrix computed for a linearized inverse problem having model parameters m1, m2, m3, m4, m5 are 49, 15, 3, 200, 40, respectively. The standard deviation (uncertainty) in the estimation of model parameters m4 is ________. [round off to 2 decimal places]

Answer: (14.00 to 15.00)

55. Electric current density incident at an angle 40° from vertical at the horizontal interface between two layers with resistivity ρ1 = 100 Ωm and ρ2 = 500 Ωm (from layer 1 to layer 2). The current density will enter into the second layer at an angle ________ degrees from vertical. [round off to 2 decimal places]

Answer: (9.45 to 9.55)

GATE Exam 2021 Ecology and Evolution (EY) Question Paper With Answer Key

GATE-2021

EY-Ecology and Evolution

GA- General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. The people ___________ were at the demonstration were from all sections of society.

(A)  whose

(B)  which

(C)  who

(D)  whom

Answer: (C)

2. A transparent square sheet shown above is folded along the dotted line. The folded sheet will look like ________.

Answer: (C)

3. For a regular polygon having 10 sides, the interior angle between the sides of the polygon, in degrees, is:

(A)  396

(B)  324

(C)  216

(D)  144

Answer: (D)

4. Which one of the following numbers is exactly divisible by (1113 + 1)?

(A)  1126 + 1

(B)  1133 + 1

(C)  1139 – 1

(D)  1152 – 1

Answer: (D)

5. Oasis is to sand as island is to ________

Which one of the following options maintains a similar logical relation in the above sentence?

(A)  Stone

(B)  Land

(C)  Water

(D)  Mountain

Answer: (C)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

6. The importance of sleep is often overlooked by students when they are preparing for exams. Research has consistently shown that sleep deprivation greatly reduces the ability to recall the material learnt. Hence, cutting down on sleep to study longer hours can be counterproductive.

Which one of the following statements is the CORRECT inference from the above passage?

(A)  Sleeping well alone is enough to prepare for an exam. Studying has lesser benefit.

(B)  Students are efficient and are not wrong in thinking that sleep is a waste of time.

(C)  If a student is extremely well prepared for an exam, he needs little or no sleep.

(D)  To do well in an exam, adequate sleep must be part of the preparation.

Answer: (D)

7. 

In the figure shown above, each inside square is formed by joining the midpoints of the sides of the next larger square. The area of the smallest square (shaded) as shown, in cm2 is:

(A)  12.50

(B)  6.25

(C)  3.125

(D)  1.5625

Answer: (C)

8. Let X be a continuous random variable denoting the temperature measured. The range of temperature is [0, 100] degree Celsius and let the probability density function of X be f(x) = 0.01 for 0 ≤ X ≤ 100.

The mean of X is _____

(A)  2.5

(B)  5.0

(C)  25.0

(D)  50.0

Answer: (D)

9. 

The number of students passing or failing in an exam for a particular subject are presented in the bar chart above. Students who pass the exam cannot appear for the exam again. Students who fail the exam in the first attempt must appear for the exam in the following year. Students always pass the

exam in their second attempt.

The number of students who took the exam for the first time in the year 2 and the year 3 respectively, are __________.

(A)  65 and 53

(B)  60 and 50

(C)  55 and 53

(D)  55 and 48

Answer: (D)

10. Seven cars P, Q, R, S, T, U and V are parked in a row not necessarily in that order. The cars T and U should be parked next to each other. The cars S and V also should be parked next to each other, whereas P and Q cannot be parked next to each other. Q and S must be parked next to each other. R is parked to the immediate right of V. T is parked to the left of U.

Based on the above statements, the only INCORRECT option given below is:

(A)  There are two cars parked in between Q and V.

(B)  Q and R are not parked together.

(C)  V is the only car parked in between S and R.

(D)  Car P is parked at the extreme end.

Answer: (A)

EY: Ecology and Evolution

Q.1 – Q.16 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Animal species can vary in whether dispersal is more likely among male offspring (male-biased), female offspring (female-biased), or similar between the sexes. Dispersal in birds and mammals is most commonly

(A)  female-biased and male-biased, respectively.

(B)  female-biased and similar between the sexes, respectively.

(C)  male-biased and female-biased, respectively.

(D)  similar between the sexes, and female-biased respectively.

Answer: (A)

2. Of the following, which one is the most direct measure of Darwinian fitness?

(A)  Adult body size

(B)  Lifetime reproductive success

(C)  Lifespan

(D)  Maximum sprint speed

Answer: (B)

3. The marginal value theorem in optimal foraging theory examines which one of the following foraging decisions?

(A)  How long to stay in a patch of food

(B)  How to allocate time to foraging versus reproduction

(C)  How to minimise risk while foraging

(D)  How to select between different food types within a patch

Answer: (A)

4. Which one of the following shows the highest degree of endemism?

(A)  Birds of the Himalayas

(B)  Mammals of central India

(C)  Mammals of central India

(D)  Trees of the Gangetic basin

Answer: (C)

5. Which one of the following Mendelian disorders is influenced by diet?

(A)  Cystic fibrosis

(B)  Haemophilia

(C)  Phenylketonuria

(D)  Thalassemia

Answer: (C)

6. Which one of the following mammalian DNA regions exhibits the highest level of sequence variation?

(A)  Homeobox transcription factor binding domain

(B)  Hox genes

(C)  Mitochondrial D-loop region

(D)  Histone protein-encoding genes

Answer: (C)

7. Which one of the following makes a species most vulnerable to extinction?

(A)  Low density throughout a large geographic range and in several habitat types

(B)  Locally common in a restricted geographic range and in several habitat types

(C)  Low density throughout a large geographic range and in a specific habitat type

(D)  Locally common in a restricted geographic range and in a specific habitat type

Answer: (D)

8. The frequency distributions of a trait in two populations, X and Y, are shown in the figure.

Which one of the following statements about the mean and standard deviation (SD) of the two populations is accurate?

(A)  X has higher mean, and Y has higher SD.

(B)  Y has higher mean, and X has higher SD.

(C)  X has higher mean, and X has higher SD.

(D)  Y has higher mean, and Y has higher SD.

Answer: (D)

9. Two sister species of bulbuls have non-overlapping distributions. One is distributed in India and the other in Sri Lanka. Which one of the following modes of speciation is the most parsimonious explanation for this pattern?

(A)  Allopatric speciation

(B)  Sympatric speciation

(C)  Parapatric speciation

(D)  Peripatric speciation

Answer: (A)

10. In an Arctic Ocean food chain, killer whales feed on sea otters, which feed on sea urchins, which in turn feed on kelp (a type of seaweed). An increase in the abundance of killer whales causes sea otter abundance to decline, leading to higher sea urchin densities, which in turn reduces the abundance of kelp. Which one of the following terms describes this phenomenon?

(A)  Trophic cascade

(B)  Prey switching

(C)  Competitive exclusion

(D)  Productivity-stability relationship

Answer: (A)

11. Listed below are hypotheses for the evolution of monogamy. Which one of these is NOT based on the concept of individual selection?

(A)  Food provisioning by both parents is crucial for offspring survival.

(B)  Biparental protection from predators is essential for offspring survival.

(C)  Females are solitary and dispersed, therefore, males cannot effectively mate-guard more than one female at a time.

(D)  Forming monogamous pairs allows individuals to regulate their reproductive output and ensure the survival of the species.

Answer: (D)

12. Rising temperature due to global warming can stimulate decomposition of organic matter and release CO2 into the atmosphere. This is an example of

(A)  positive feedback.

(B)  negative feedback.

(C)  environmental heterogeneity.

(D)  environmental stochasticity.

Answer: (A)

13. Ant-mimic spiders of the genus Myrmarachne are known for which one of the following evolutionary phenomena?

(A)  Aposematism

(B)  Aggressive mimicry

(C)  Batesian mimicry

(D)  Muellerian mimicry

Answer: (B)

14. The probability of local extinction increases with body size when there is forest degradation, loss, and fragmentation. Consider the following hypotheses for the vulnerability of larger-bodied species:

(P) Larger-bodied species tend to have smaller population sizes.

(Q) Larger-bodied species require larger territories/home ranges.

(R) Larger-bodied species have higher absolute resource and energy requirements.

Which one of the following options correctly lists all potential reasons for the vulnerability of larger-bodied species?

(A)  P and Q only

(B)  P only

(C)  P and R only

(D)  P, Q, and R

Answer: (D)

15. Grazing by large mammalian herbivores can have a strong influence on ecosystem structure, and can cause ecosystems to transition between alternative states over decades. Which one of the following transitions can result from grazing?

(A)  Mangrove to coral reef

(B)  Terai grassland to alpine meadow

(C)  Savanna to grassland

(D)  Tropical rainforest to arid desert

Answer: (C)

16. The effective population size of a sexually reproducing, diploid, animal species will be highest when the sex ratio (number of reproducing males /number of reproducing females) is

(A)  1

(B)  0.5

(C)  1.5

(D)  2

Answer: (A)

Q.17 – Q. 22 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).

17. The theory of evolution by natural selection was proposed by which one (or more) of the following?

(A)  Charles Darwin

(B)  Jean Baptiste Lamarck

(C)  Alfred Russel Wallace

(D)  Georges Cuvier

Answer: (A; C)

18. According to the MacArthur – Wilson equilibrium model of island biogeography, which one (or more) of the following factors affect(s) extinction rate on an island?

(A)  Interspecific competition

(B)  Island area

(C)  Intraguild predation

(D)  Species identity

Answer: (B)

19. Which of the following is/are necessary condition(s) for natural selection to shape limb lengths in a population?

(A)  Individuals in a population vary in the length of their limbs.

(B)  Limb length increases in individuals with repeated use.

(C)  Offspring inherit the limb lengths of their parents.

(D)  Limb length influences running speed and thus, their ability to survive and reproduce.

Answer: (A; C; D)

20. Which of the following is/are possible reason(s) for linkage disequilibrium between alleles at two loci?

(A)  Low recombination rate between loci

(B)  High recombination rate between loci

(C)  Natural selection

(D)  Polyploidy

Answer: (A; C)

21. Metabolism includes the processes of catabolism and anabolism. Select the anabolic process(es).

(A)  Growth

(B)  Storage

(C)  Respiration

(D)  Excretion

Answer: (A; B)

22. SARS-CoV-2 is hypothesised to have jumped from bats to pangolins before infecting humans. Which one (or more) of the following methods can be effectively used for testing this hypothesis?

(A)  Comparative genomics

(B)  DNA fingerprinting

(C)  Phylogenetics

(D)  Transgenesis

Answer: (A; C)

Q.23 – Q. 25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

23. A sample of heights of trees follows a normal distribution. In this sample, 68% of height measurements are expected to fall in the interval: mean ± _____ standard deviation. (Round off to the nearest integer.)

Answer: (0.99 to 1.01)

24. A bird species has an annual survival probability of 0.30. While sampling the population of this species, the probability that any individual is captured in a given year is 0.40. A bird is captured, tagged and released in Year one. The probability that it is re-captured in Year two is _____. (Round off to two decimal places.)

Answer: (0.11 to 0.13)

25. Sex ratio at birth is biased towards females in a mongoose population. If the probability of having a daughter is 0.7 in this population, and if sex determination of each offspring is an independent event, then the probability that a female with a litter of four offspring has at least one son is _______. (Round off to two decimal places.)

Answer: (0.74 to 0.77)

Q.26 – Q.46 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

26. In a species of gecko, males are polymorphic such that some males are yellow and other males are white. A student hypothesises that body colour is a signal of aggression. To test this, he measures aggression in yellow and white males. He also measures body size in every individual he tests. He plots the data in the following way (yellow males: solid line and filled dots; white males: dashed line and open dots). Which one of the following statements is correct based on these data?

(A)  All yellow males are more aggressive than white males.

(B)  Body size is correlated with aggression in all males.

(C)  Body size correlates with aggression in yellow males only.

(D)  Small yellow males are more aggressive than small white males.

Answer: (C)

27. Homing pigeons can perceive the pattern of polarized light in the sky (which depends on the position of the sun relative to the earth). This enables homing pigeons to orient and navigate home if released in any location. One can reset their biological clock in captivity by artificially controlling the light conditions. If you acclimatize a pigeon to a new lighting cycle with “sunrise” at 6 PM and “sunset” at 6 AM, instead of 6 AM sunrise and 6 PM sunset that naturally occurs, the bird will be clock- shifted by 12 hours within a few days. Suppose you release two birds, a normal bird (N) and a 12-hr clock-adjusted bird (C), 30 km East of their home at 6 AM. In which direction will each bird fly?

(A)  Both birds will fly West.

(B)  Both birds will fly East.

(C)  Bird N will fly West, bird C will fly East.

(D)  Bird C will fly West, bird N will fly East.

Answer: (C)

28. Demographic stochasticity introduces random variation in population growth because

(A)  changing weather conditions from year-to-year can result in good and bad years for reproduction.

(B)  the discrete nature of births and deaths introduces uncertainty in population parameters.

(C)  per capita birth rate in a population decreases with an increase in population density.

(D)  of predictable time lags between change in population size and reproduction.

Answer: (B)

29. In an island chain, species richness (S) increases with island area (A) according to the equation, S = 4.3 A55.

(A)  (i)

(B)  (ii)

(C)  (iii)

(D)  (iv)

Answer: (B)

30. A researcher measures the abundance of a tree species in 10 plots in each of two habitats. She tests for differences in abundance between the two habitats using an ANOVA. The results from the ANOVA are as follows:

• Mean abundance in habitat A = 30 trees

• Mean abundance in habitat B = 50 trees

• F-statistic (on 1 and 18 degrees of freedom) = 6.04

• P-value = 0.02

Here, a P-value of 0.02 means that

(A)  repeating this study 100 times will provide a result of “no difference” in abundance between the two habitats with a probability of 0.02.

(B)  there is a 2% chance that abundances differ between habitats.

(C)  the probability that an F-statistic with a value of 6.04 or greater falls within theF-distribution for 1 and 18 degrees of freedom is 0.02.

(D)  there is a very large difference in the abundance of the species between the two habitats because the P-value is less than 0.05.

Answer: (C)

31. In the graph shown, the solid line represents the best fit from an ordinary least-squares regression, where X is the predictor variable and Y is the response variable. In this case, which one of the following assumptions of the linear regression is violated?

(A)  Equal variances in Y across values of X

(B)  Normal distribution of residuals

(C)  Independence of data points

(D)  Linear relationship between X and Y

Answer: (A)

32. Consider the following list of bacteria and the infections they cause in humans.

Which one of the following combinations correctly matches these micro-organisms and the infections they cause in humans?

(A)  P-2; Q-1; R-4; S-3

(B)  P-2; Q-3; R-1; S-4

(C)  P-3; Q-4; R-1; S-2

(D)  P-3; Q-4; R-2; S-1

Answer: (C)

33. Which one of the following statements is INCORRECT with respect to the tree of life?

(A)  Ctenophora is more closely related to Cnidaria than it is to Echinodermata.

(B)  Porifera is more closely related to Ctenophora than it is to Echinodermata.

(C)  Arthropoda is more closely related to Tardigrada than it is to Annelida.

(D)  Arthropoda is more closely related to Mollusca than it is to Nematoda.

Answer: (D)

34. Consider a population that shows logistic growth of the form  is the population growth rate, r is the instantaneous rate of increase, K is the carrying capacity and N is the population size.

For such a population (N > 0), which one of the following graphs shows the correct relationship between per capita growth rate  on the y-axis, and population size (N) on the x-axis?

(A)  (i)

(B)  (ii)

(C)  (iii)

(D)  (iv)

Answer: (A)

35. Which one of the following represents the correct chronological order of geological periods (from oldest to most recent)?

(A)  Devonian → Jurassic → Cambrian → Neogene

(B)  Devonian → Cambrian → Neogene → Jurassic

(C)  Cambrian → Devonian → Jurassic → Neogene

(D)  Cambrian → Neogene → Devonian → Jurassic

Answer: (C)

36. Soils undergo weathering over large time-scales (millions of years). Over time, concentration of phosphorus (P) declines monotonically (solid line), while nitrogen (N) shows a unimodal pattern (dotted line) as shown.

Based on this pattern, which one of the following diagrams represents the likely trend in N:P ratio?

(A)  (i)

(B)  (ii)

(C)  (iii)

(D)  (iv)

Answer: (A)

37. A large forest area is fragmented into multiple smaller patches of different sizes. A researcher estimates the number of bird species in these forest fragments immediately following fragmentation, and then again 20 years later. The relationship between fragment size and species richness is shown in the graph for the two sampling events (immediately after fragmentation: closed circles and solid line; 20 years after fragmentation: open circles and dashed line). The best explanation for the differences in species richness with fragment size between the two sampling events is

(A)  Allen’s rule.

(B)  K-selection.

(C)  extinction debt.

(D)  Bergmann’s rule.

Answer: (C)

38. The table shows a list of analysis goals (i, ii, iii) and different statistical tests (P, Q, R).

Match the analysis goal to the most appropriate statistical test.

(A)  (i)-(P), (ii)-(R), (iii)-(Q)

(B)  (i)-(Q), (ii)-(P), (iii)-(R)

(C)  (i)-(Q), (ii)-(R), (iii)-(P)

(D)  (i)-(R), (ii)-(Q), (iii)-(P)

Answer: (C)

39. Shifting cultivation is a form of agricultural practice in the hills of Northeast India, where a forest patch is cleared and cultivated for a few years, after which it is left fallow and allowed to regenerate. Succession occurs on such previously cultivated plots. Over time, the plant community should move towards which region in the graph?

(A)  P

(B)  Q

(C)  R

(D)  S

Answer: (B)

40. Consider 1000 terrestrial species that have geographical ranges of different shapes and sizes. If the Earth were entirely covered by land (no oceans), and the ranges of these species were overlaid on the surface of the Earth at random, which one of the following patterns is expected?

(A)  Highest species richness per unit area in the tropics

(B)  Highest species richness per unit area at higher latitudes

(C)  Roughly equal species richness per unit area at all latitudes

(D)  Geographically restricted species found only near the poles

Answer: (C)

41. The graph below shows how the lower limits of the elevational ranges of bird species on a tropical mountain have changed over 20 years (2000 to 2020) because of climate change. Each point below represents a bird species. Points would cluster on the dashed line if species had the same lower elevational range limits in 2000 and 2020. Given that the mountain summit is at an elevation of 3500 m (solid horizontal line), and assuming that the trend shown by the graph continues over the next 20 years, what would you expect in 2040?

(A)  Low-elevation species will become locally extinct.

(B)  Mid-elevation species will become locally extinct.

(C)  High-elevation species will become locally extinct.

(D)  All species will return to their original elevational ranges.

Answer: (C)

42. Behavioural ecologists exploring a newly discovered island find 20 new species of terrestrial lizards. Males of these species have a dorsal ridge that varies in size from large in some species to entirely lacking in others. The scientists hypothesise that dorsal ridges in males evolved by runaway sexual selection stemming from sensory bias in females. Which one of the following would provide the necessary evidence to support this hypothesis?

(A)  Females of species in which males lack this trait are attracted to males that have a large dorsal ridge artificially attached to them.

(B)  Males without a ridge are more likely to attract females of all species than males with a ridge.

(C)  Males with a larger dorsal ridge win more fights and get more mates than males with a smaller ridge.

(D)  Females of species whose males have a dorsal ridge do not show a preference for this trait.

Answer: (A)

43. The graph shows the relationship between a variable on the x-axis and genetic diversity on the y-axis. Each point represents a species and the trend line describes the relationship across species.

Select the most appropriate variable for the x-axis.

(A)  Evolutionary age of species

(B)  Abundance

(C)  Body size

(D)  Geographic range

Answer: (C)

44. Hunting is a major source of mortality for large frugivorous birds. These birds disperse the seeds of forest trees and are the primary contributors to forest regeneration. The graphs show the distribution of different age-classes of a frugivore-dispersed tree species at two isolated sites.

Based on the graphs, select the most likely conclusion.

(A)  Hunting is higher at site (i) than at site (ii).

(B)  Hunting is higher at site (ii) than at site (i).

(C)  Hunting is similar at both sites.

(D)  Frugivores are not hunted at either site.

Answer: (B)

45. The following phylogeny shows how species P to T are related to each other. The branch lengths indicate the degree of evolutionary change.

The species composition of three areas is given below

Area 1: PQR; Area 2: RST; Area 3: QRS

Given this information, the phylogenetic diversity of

(A)  Area 1 > Area 3 > Area 2

(B)  Area 1 = Area 2 = Area 3

(C)  Area 1 = Area 3 > Area 2

(D)  Area 1 < Area 3 < Area 2

Answer: (A)

46. The IUCN Red List provides information on the conservation status of different species. Match the species to their status in the table below.

(A)  Tiger: NT; Great Indian Bustard: EX; Passenger Pigeon: EN; Blackbuck: CR

(B)  Tiger: EN; Great Indian Bustard: CR; Passenger Pigeon: EX; Blackbuck: NT

(C)  Tiger: EN; Great Indian Bustard: CR; Passenger Pigeon: NT; Blackbuck: EX

(D)  Tiger: NT; Great Indian Bustard: EN; Passenger Pigeon: EX; Blackbuck: CR

Answer: (B)

Q.47 – Q.52 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).

47. A gene duplication event in an organism results in two copies of a gene. Which one (or more) of the following outcomes is/are possible for the duplicated copy?

(A)  It retains the original function.

(B)  It acquires a new function.

(C)  It loses function.

(D)  It gets translated but not transcribed.

Answer: (A; B; C)

48. The egg-laying mammal, platypus, is known for its ability to inject venom by stabbing with spurs on its hindlimbs. Which one (or more) of the following statements supports the hypothesis that venom in this species is used for intrasexual competition?

(A)  Only males produce venom.

(B)  Venom is secreted only during the breeding season.

(C)  Venom is only effective against invertebrates.

(D)  Venom is ineffective against conspecifics.

Answer: (A; B)

49. All octopi dream every night, and sometimes change colour while dreaming. A student hypothesises that octopi change colour only when they dream about the food they ate that day. To test this hypothesis, the student conducts an experiment with two treatments that are randomly ordered, and separated by 2 days. In one treatment, she places 10 octopi in individual tanks in captivity and provides each one with a large crab to eat during the day. She then records the dream state colour of these octopi that night. Which one (or more) of the following would be an appropriate NEGATIVE control to test this hypothesis?

(A)  Provide the same 10 octopi with the same food source (crab), and then record their colour that night when they are dreaming.

(B)  Provide the same 10 octopi with a new food object (e.g. sea stars) and record the colour that night when they are dreaming.

(C)  Provide the same 10 octopi with a non-food object (e.g. rock), and record their colour that night when they are dreaming.

(D)  Provide 10 squid with the same food source (crab) and record the colour that night when they are dreaming.

Answer: (C)

50. Which one (or more) of the following conservation actions would NOT benefit native species?

(A)  Planting Prosopis juliflora in the Thar desert to reduce erosion.

(B)  Stringing rope ladders across roads to connect the canopy for facilitating the movement of arboreal animals in the Western Ghats.

(C)  Increasing lights at night on beaches in Odisha to improve visibility for hatching sea turtles.

(D)  Growing native species in urban gardens of Bengaluru to attract pollinators.

Answer: (A; C)

51. In cooperatively breeding animals, offspring from one year stay back and help their parents to rear offspring born in successive breeding episodes. Kin selection has been used to explain such helping behaviour. Which of the following result(s) support(s) the kin selection hypothesis?

(A)  Helpers provide more care in populations where extra-pair paternity is low, than in populations where extra-pair paternity is high.

(B)  Individuals who choose to stay and help are more likely to inherit their parents’ territory than individuals who stay but do not help.

(C)  Individuals who choose to disperse from their natal territory rather than stay and help have a lower survival because of predation during dispersal, when compared with individuals who stay and help.

(D)  Helpers whose parents continue to form the breeding pair provide more care than helpers whose parents are replaced by a new breeding pair.

Answer: (A; D)

52. Which one (or more) of the following genetic processes is/are likely to be affected by the disruption of codon usage bias in highly expressed genes?

(A)  Translation rate

(B)  Translation accuracy

(C)  Transcription rate

(D)  Transcription accuracy

Answer: (A; B)

Q.53 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

53. Male beetles are of two phenotypes: horned and hornless. Horned males mate with twice as many females compared with hornless males. But females mated to hornless males produce one-third more offspring. The reproductive success of a male (number of offspring fathered) is the number of females he mates with multiplied by the number of offspring each female produces. The reproductive success of horned males is ________ times that of hornless males. (Round off to one decimal place.)

Answer: (1.40 to 1.60)

54. A population shows exponential growth of the form Nt = N0ert where Nt is increase. If r = 0.1, then the doubling time for this population is __________. (Round off to two decimal places.)

Answer: (6.80 to 7.00)

55. At a locus with two alleles A1 and A2, the genotype A1A1 produces white flowers, A2A2 produces red flowers, and A1A2 produces pink flowers. For a population in Hardy-Weinberg equilibrium, the frequency of red flowers is 0.25. If the white flowered plants are removed, and all pink and red flowered-plants in this population are randomly crossed amongst each other, the frequency of white flowered plants in the next generation will be ______. (Round off to two decimal places.)

Answer: (0.10 to 0.12)

GATE Exam 2021 Environmental Science and Engineering (ES) Question Paper With Answer Key

GATE-2021

ES: Environmental Science and Engineering

GA- General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. The current population of a city is 11,02,500. If it has been increasing at the rate of 5% per annum, what was its population 2 years ago?

(A)    9,92,500

(B)    9,95,006

(C)    10,00,000

(D)    12,51,506

Answer: (C)

2. p and q are positive integers and 

(A)    3

(B)    7

(C)    9

(D)    11

Answer: (B)

3. 

The least number of squares that must be added so that the line P-Q becomes the line of symmetry is ________

(A)    4

(B)    3

(C)    6

(D)    7

Answer: (C)

4. Nostalgia is to anticipation as _______ is to ________

Which one of the following options maintains a similar logical relation in the above sentence?

(A)    Present, past

(B)    Future, past

(C)    Past, future

(D)    Future, present

Answer: (C)

5. Consider the following sentences:

(i) I woke up from sleep.

(ii) I woked up from sleep.

(iii) I was woken up from sleep.

(iv) I was wokened up from sleep.

Which of the above sentences are grammatically CORRECT?

(A)    (i) and (ii)

(B)    (i) and (iii)

(C)    (ii) and (iii)

(D)    (i) and (iv)

Answer: (B)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

6. Given below are two statements and two conclusions.

Statement 1: All purple are green.

Statement 2: All black are green.

Conclusion I: Some black are purple.

Conclusion II: No black is purple.

Based on the above statements and conclusions, which one of the following options is logically CORRECT?

(A)    Only conclusion I is correct.

(B)    Only conclusion II is correct.

(C)    Either conclusion I or II is correct.

(D)    Both conclusion I and II are correct.

Answer: (C)

7. Computers are ubiquitous. They are used to improve efficiency in almost all fields from agriculture to space exploration. Artificial intelligence (AI) is currently a hot topic. AI enables computers to learn, given enough training data. For humans, sitting in front of a computer for long hours can lead to health issues.

Which of the following can be deduced from the above passage?

(i) Nowadays, computers are present in almost all places.

(ii) Computers cannot be used for solving problems in engineering.

(iii) For humans, there are both positive and negative effects of using computers.

(iv) Artificial intelligence can be done without data.

(A)    (ii) and (iii)

(B)    (ii) and (iv)

(C)    (i), (iii) and (iv)

(D)    (i) and (iii)

Answer: (D)

8. Consider a square sheet of side 1 unit. In the first step, it is cut along the main diagonal to get two triangles. In the next step, one of the cut triangles is revolved about its short edge to form a solid cone. The volume of the resulting cone, in cubic units, is ________

(A)    π/3

(B)    2π/3

(C)    3π/2

(D)    3π

Answer: (A)

9. 

The number of minutes spent by two students, X and Y, exercising every day in a given week are shown in the bar chart above.

The number of days in the given week in which one of the students spent a minimum of 10% more than the other student, on a given day, is

(A)    4

(B)    5

(C)    6

(D)    7

Answer: (C)

10. 

Corners are cut from an equilateral triangle to produce a regular convex hexagon as shown in the figure above.

The ratio of the area of the regular convex hexagon to the area of the original equilateral triangle is

(A)    2 : 3

(B)    3 : 4

(C)    4 : 5

(D)    5 : 6

Answer: (A)

Environmental Science and Engineering

Q.1 – Q.18 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. A tangent is drawn on the curve of the function y = x2 at the point (x, y) = (3, 9). The slope of the tangent is __________.

(A)  3

(B)  6

(C)  9

(D)  12

Answer: (B)

2.

(A)  0

(B)  1

(C)  2

(D)  −1

Answer: (A)

3. The table below shows the carbon content of four samples of powdered coal. If these four samples are mixed completely, what would be the resultant carbon percentage of the mixture by weight?

(A)  58%

(B)  86%

(C)  87%

(D)  90%

Answer: (B)

4. A sample of air is collected in the morning at an ambient temperature of 25°C. The concentration of carbon monoxide (CO) in this sample is 30 ppmv (ppm by volume). The same sample is analysed later in the afternoon when the sample temperature is 35 °C. The analysis results will show the CO concentration as ___________.

(A)  < 29 ppmv

(B)  > 30 ppmv

(C)  = 30 ppmv

(D)  = 29 ppmv

Answer: (C)

5. In fluid statics, the line of action of the buoyant force always acts through the __________.

(A)  centre of gravity of any submerged body

(B)  centroid of the volume of any floating body

(C)  centroid of the displaced volume of fluid by the body

(D)  centroid of the volume of fluid vertically above the body

Answer: (C)

6. What is the order of preference of the various elements in integrated waste management hierarchy (highest preference to lowest preference)?

(A)  Reduce > Reuse & recycle > Energy recovery > Landfilling

(B)  Reuse & recycle > Reduce > Energy recovery > Landfilling

(C)  Reduce > Energy recovery > Reuse & recycle > Landfilling

(D)  Reduce > Reuse & recycle > Landfilling > Energy recovery

Answer: (A)

7. If d is the depth of an aquifer through which water is flowing, then the relationship between permeability K and transmissibility (also known as transmissivity) T is given by ____________.

(A)  T = Kd

(B)  T = K/d

(C)  T = √Kd

(D)  K = √Td

Answer: (A)

8. Which of the following is the terminal electron acceptor in the electron transport chain of aerobic respiration?

(A)  Water

(B)  NADH

(C)  O2

(D)  Cytochrome-c

Answer: (C)

9. Which of the following causes ‘Type-I’ settling in a sedimentation tank?

(A)  Agglomeration

(B)  Compression

(C)  Force of gravity

(D)  Charge neutralization

Answer: (C)

10. In the context of noise pollution, SPL is the sound pressure level in decibels (dB). The relationship between SPL, the root mean square (rms) sound pressure p, and the reference (hearing threshold) pressure p0 is expressed as

Answer: (A)

11. The following block diagram highlights the typical phases of the life cycle of a product. In the figure, ‘P’, ‘Q’, and ‘R’ represent various possible scopes of analyses in life cycle assessment. Which of the following statements is true?

(A)  ‘R’ represents cradle-to-grave analysis.

(B)  ‘P’ represents cradle-to-gate analysis.

(C)  ‘Q’ represents gate-to-grave analysis.

(D)  ‘R’ represents gate-to-gate analysis.

Answer: (A)

12. The United Nations Conference on Environment and Development was held in 1992 in Rio de Janeiro, Brazil. During this conference, several environmental management principles were adopted by many countries.

Which one of the following principles allows the governments to take mitigation measures on the environmental issues having serious threats or irreversible damage, even if there is scientific uncertainty about such issues?

(A)  Polluters pay principle

(B)  Precautionary principle

(C)  Extended producer responsibility

(D)  Common but differentiated responsibilities

Answer: (B)

13. Choose the correct order of biodegradability (highest to lowest) of the following municipal solid waste components.

(A)  Food waste > Newspaper > Polyvinyl Chloride (PVC)

(B)  Newspaper > Food waste > Polyvinyl Chloride (PVC)

(C)  Food waste > Polyvinyl Chloride (PVC) > Newspaper

(D)  Polyvinyl Chloride (PVC) > Food waste > Newspaper

Answer: (A)

14. In proximate analysis, when a 10 kg moisture-free solid sample is heated in a furnace at 950 °C in the absence of air, its mass is reduced by 6 kg. If the same 10 kg moisture-free solid sample is heated in the furnace at the same temperature in the presence of air, its mass is reduced by 7 kg. The percentage of fixed carbon in the sample is ____________.

(A)  20%

(B)  60%

(C)  10%

(D)  30%

Answer: (C)

15. Chlorine is most effective as a water disinfectant at a pH of ____________.

(A)  6

(B)  8

(C)  10

(D)  12

Answer: (A)

16. The oxidation states of ‘N’ in NH4+, O2, and NO are __________, respectively.

(A)  +2, −3, and +3

(B)  −3, +3, and +2

(C)  −3, +3, and −4

(D)  +4, −2, and +2

Answer: (B)

17. What is the pH of a water sample having H+ concentration of 10 mg/L? The atomic weight of H is 1 g/mol.

(A)  2

(B)  4

(C)  6

(D)  8

Answer: (A)

18. Which of the following pairing of nucleotide bases is present in double helix DNA?

(A)  Thymine – Cytosine

(B)  Adenine – Thymine

(C)  Cytosine – Adenine

(D)  Uracil – Thymine

Answer: (B)

Q.19 – Q.22 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).

19. Which of the following is/are both greenhouse gas(es) and ozone depleting substance(s)?

(A)  CFC-11

(B)  CO2

(C)  HCFC-22

(D)  N2O

Answer: (A; C OR A; C; D)

20. The ordinary differential equation  has y as the dependent variable and x as the independent variable. Which of the following classification(s) is/are applicable to the equation?

(A)  Linear

(B)  Non-linear

(C)  First order

(D)  Second order

Answer: (A; C)

21. Consider the following equation:

x3 − 10x2 + 31x − 30 = 0

Which of the following is/are the root(s) of the above equation?

(A)  1

(B)  2

(C)  3

(D)  4

Answer: (B; C)

22. A wind rose is a representation of meteorological conditions. Which of the following is/are included in this representation?

(A)  Mixing height

(B)  Wind speed

(C)  Wind direction

(D)  Percentage of time

Answer: (B; C; D)

Q.23 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

23. A flocculation tank used for water treatment has a velocity gradient (G) of 800 s1. The volume of the tank is 40 m3. The dynamic viscosity of water is 9×104 N·s/m2. The theoretical power required to maintain the given velocity gradient is ____________ kW (rounded off to the nearest integer).

Answer: (23 to 23)

24. In a sample, the growth of microbial cells started with an initial concentration of 5×104 cells per millilitre (mL) of the sample. After a certain time period, the cell concentration was found to be 1280 × 104 cells per mL of the sample. Assuming binary fission of cells and no cell death, the number of generations of cell growth occurred in this time period is ____________ (answer in integer).

Answer: (8 to 8)

25. A water jet discharging from a 4 cm diameter orifice has a diameter of 3.5 cm at its vena contracta. The coefficient of velocity is defined as the ratio of the actual velocity of the jet at vena contracta to the theoretical velocity of the jet. If the coefficient of velocity is 0.98, the coefficient of discharge for the orifice will be __________ (rounded off to two decimal places).

Answer: (0.74 to 0.76)

Q.26 – Q.34 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

26. The 2×2 matrices P and Q satisfy the following relations:

The matrix Q is equal to ____________.

Answer: (A)

27. A biased die has six faces numbered as k = 1, 2, 3, 4, 5, and 6. On rolling the die, the probability of the number k appearing is proportional to k2. What is the probability that an even number will appear on rolling the die?

(A)  35/91

(B)  56/91

(C)  12/21

(D)  9/21

Answer: (B)

28. Match the entries in Column I with the correct entries in Column II.

(A)  P-(iii), Q-(ii), R-(i)

(B)  P-(ii), Q-(i), R-(iii)

(C)  P-(i), Q-(iii), R-(ii)

(D)  P-(ii), Q-(iii), R-(i)

Answer: (D)

29. Which of the following international multilateral agreements (conventions, protocols) from Column I match with the entries in Column II?

(A)  P-(iv), Q-(iii), R-(ii), S-(i)

(B)  P-(iv), Q-(ii), R-(iii), S-(i)

(C)  P-(iii), Q-(i), R-(ii), S-(iv)

(D)  P-(i), Q-(iii), R-(iv), S-(ii)

Answer: (A)

30. An ideal PFR or an ideal CFSTR may be used to degrade a pollutant with first order reaction kinetics. Both the reactors are fed with the same inlet concentration and the same volumetric flow rate, and are designed to achieve the same outlet concentration. Which of the following statements is true when comparing PFR with CFSTR?

PFR is Plug Flow Reactor.

CFSTR is Continuous Flow Stirred Tank Reactor (also referred to as CSTR).

(A)  PFR will always require less reactor volume than CFSTR.

(B)  PFR will require the same reactor volume as CFSTR.

(C)  CFSTR will always require less reactor volume than PFR.

(D)  CFSTR can sometimes require less reactor volume than PFR.

Answer: (A)

31. A 200 mL sample of water has an initial pH = 9. In order to determine alkalinity, the sample was titrated using 0.02 N H2SO4 acid to an end point of pH = 4.5. In the titration, 25 mL of 0.02 N H2SO4 acid was required. What is the total alkalinity of the sample in ‘mg/L as NaHCO3’?

(A)  20

(B)  125

(C)  210

(D)  305

Answer: (C)

32. A sewage treatment plant (STP) receives sewage at a flow rate of 20000 m3 per day. The sewage has 200 mg/L of suspended solids. Assume 60 % suspended solids are removed in the primary clarifier. The underflow (i.e. sludge) removed from the clarifier contains 5 % solids (by weight).

The daily volume of the sludge generated will be _________ m3 per day.

Assume sludge density = 1000 kg/m3

(A)  48

(B)  80

(C)  480

(D)  800

Answer: (A)

33. In context of municipal solid waste treatment, match the equipment in List I with their function in List II.

(A)  P-(iii), Q-(iv), R-(i), S-(ii)

(B)  P-(iii), Q-(ii), R-(iv), S-(i)

(C)  P-(i), Q-(iv), R-(iii), S-(ii)

(D)  P-(iv), Q-(ii), R-(i), S-(iii)

Answer: (A)

34. The characteristics of a water sample are as follows: Na+ = 92 mg/L, K+ = 19.5 mg/L, Ca2+ = 40 mg/L, and Mg2+ = 24 mg/L. What is the sodium adsorption ratio (SAR) of the water sample which may be considered for irrigation purposes?

[Atomic weight (g/mol): Na = 23, K = 39, Ca = 40, and Mg = 24]

(A)  2.83

(B)  1.94

(C)  2.00

(D)  4.00

Answer: (A)

Q.35 – Q.40 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).

35. Which of the following is true for the nitrifying bacteria belonging to genus Nitrobacter?

(A)  They are autotrophs.

(B)  They are eukaryotes.

(C)  They convert chemical energy to cellular energy using mitochondria.

(D)  They convert NO3 to NO2

Answer: (A)

36. Which of the following is/are the dominant mechanism(s) for the removal of spherical particles with diameter less than 10 μm from a gas stream using a fabric filter?

(A)  Impaction

(B)  Gravitation

(C)  Interception

(D)  Diffusion

Answer: (A; C; D)

37. In air pollution, which of the following is/are classified as primary pollutants?

(A)  Carbon monoxide (CO)

(B)  Sulphur dioxide (SO2)

(C)  Ozone (O3)

(D)  Nitrogen dioxide (NO2)

Answer: (A; B; D)

38. Which of the following is/are correct for the process of glycolysis?

(A)  There is net decrease in standard Gibbs free energy.

(B)  The end product is glyceraldehyde 3-phosphate.

(C)  First phase includes the phosphorylation of the glucose molecule.

(D)  It results in the net gain of NADH.

Answer: (A; C; D)

39. In the context of water quality, which of the following is/are correct for the most probable number (MPN) of a water sample?

(A)  The estimated organisms are gram negative.

(B)  It is based on the assumption of Poisson distribution.

(C)  It measures the exact number of microorganisms present in the sample.

(D)  It includes the quantification of pathogenic virus.

Answer: (A; B)

40. For any particular location, which of the following would influence the solar radiation incident on a rooftop solar water heater?

(A)  Heater surface temperature

(B)  Day of the year

(C)  Hot water temperature

(D)  Sky clearness

Answer: (B; D)

Q.41 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

41. If f(x) + 3f(g(x)) = x − 2,

then the value of the ratio  is _______ (answer in integer).

Answer: (5 to 5)

42. Consider a function y = f(x) which satisfies the following equation:

As x → −∞, y = 1, and at x = 0, y = 2.

The value of  at x = 0 is _______ (answer in integer).

Answer: (1 to 1)

43. The concentration of NO2 in the air at NTP is reported as 0.30 ppmv (ppm by volume). The concentration of NO2 in μg/m3 is __________ (rounded off to the nearest integer).

[At NTP, temperature = 298 K, pressure = 1 atm, and one mole of ideal gas occupies 24.45 L]

[Molecular weight of NO2 = 46 g/mol]

Answer: (562 to 566)

44. In open channel flow, the specific energy is the total energy per unit weight of a liquid, where the component potential energy is measured from the bed of the channel as the datum.

A rectangular channel of 10 m width carries 20 m3/s of water. The depth of flowing water is 1 m. The specific energy for this flow condition is ____________ m (rounded off to one decimal place).

Consider acceleration due to gravity (g) = 10 m/s2.

Answer: (1.1 to 1.3)

45. Two reservoirs are connected by a pipeline consisting of two pipes ‘A’ and ‘B’ in series. The two pipes are of same length and have the same Darcy friction factor. If the internal diameter of pipe ‘B’ is twice as large as the internal diameter of pipe ‘A’, the ratio of the head loss in pipe ‘A’ to that in pipe ‘B’ is ____________ (answer in integer). Neglect all minor losses.

Answer: (32 to 32)

46. In a field test of a geological formation of permeable soil (porosity = 20 %), the hydraulic gradient was found to be 2 %. The actual seepage velocity of the flow was found to be 0.0025 m/s. Assume that the flow is in the laminar regime. The permeability (K) of the aquifer is __________ m/s (rounded off to three decimal places).

Answer: (0.024 to 0.026)

47. An underground hazardous waste storage tank is leaking. The contaminant concentration directly beneath the site is 0.5 mg/L. The contaminant is travelling at an effective rate of 0.4 m per day towards a water well which is 2 km away.

Assume that the degradation of the contaminant follows a first order reaction, and the initial concentration of the contaminant becomes half in 10 years.

In this case, the contaminant concentration expected at the well under steady state conditions is ____________ mg/L (rounded off to two decimal places).

Answer: (0.18 to 0.20)

48. The net profit expected from a manufacturing unit is Rs. 6000 per year. The operational life of the unit is 15 years. Assuming a fixed discount rate of 8% per annum, the net present worth of the profit earned over the operational life is Rs. ____________ (answer in integer).

Answer: (49200 to 53300)

49. A 900 mm internal diameter sewer is laid at a slope of 0.004 and has an actual flow of 0.15 m3/s. Assuming Manning’s roughness coefficient to be 0.013, the ratio of the actual flow to the flow when the sewer is running full is _________ (rounded off to two decimal places).

Take π = 3.14.

Answer: (0.12 to 0.14)

50. A 10 million litres per day (MLD) sewage treatment plant (STP) is based on the Activated Sludge Process (ASP). First, the sewage undergoes primary treatment and the resulting treated sewage has BOD5 of 140 mg/L concentration. This is further passed through a 1500 m3 capacity aeration tank (in ASP), where the mixed liquor volatile suspended solids (MLVSS) concentration is maintained at 3000 mg/L. The concentration of BOD5 of the treated sewage is 5 mg/L.

The Food to Microorganisms ratio (F/M) of the ASP is ____________ day1

(rounded off to two decimal places).

Answer: (0.25 to 0.35)

51. The municipal solid waste (MSW) generated in a community (population = 100000) is disposed on a 12 × 104 m2 landfill site, which can be filled to a total depth of 25 m (including soil cover). Assume that MSW is generated at a rate of 2.5 kg per person per day and its compacted density is 800 kg/m3. If the volumetric ratio of MSW and soil cover is 5:1, the useful life of the landfill site is

Answer: (21 to 22)

52. A mechanized stationary container system is proposed for waste collection from a commercial area. The container unloading time is 0.1 hours per container. There are two containers at each location and the drive time between the two locations is 0.2 hours. The maximum waste ‘pick-up time’ is 2.4 hours per trip.

The ‘pick-up time’ starts at the instant the truck arrives at the first pick-up location and ends when the last container on the route is emptied. The maximum number of locations which can be covered in a trip by the collection vehicle are ____________ (answer in integer).

Answer: (6 to 6)

53. The molar concentrations (M, i.e. mol/L) of some ionic species in a water sample were estimated as follows:

Na+ = 0.25 M; Ca2+ = 0.12 M; Cl = 0.32 M; HCO3 = 0.05 M.

The ionic strength of this water sample is __________ M (correct up to two decimal places).

Answer: (0.50 to 0.68)

54. Excess amount of solid calcium sulphate (CaSO4) was added to a pure water sample (pH = 7) so that some solids remain undissolved at the equilibrium. The solubility product of CaSO4 is 2×10−5 mol2/L2. The molar concentration of SO42− in this water sample at equilibrium will be ____________ mol/L (rounded off to three decimal places).

Answer: (0.004 to 0.006)

55. A facultative pond system for sewage treatment consists of two ponds in series. The hydraulic retention time (HRT) of each pond is 6 days. The total BOD5 reduction through the entire pond system is 90 %. If the ponds are considered to be completely mixed, then the rate constant describing the BOD5 removal is _________ day1 (rounded off to two decimal points). Assume that the rate constant is same for both the ponds.

Answer: (0.34 to 0.38)

GATE Exam 2021 Electrical Engineering (EE) Question Paper With Answer Key

GATE-2021

EE: Electrical Engineering

GA- General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. The people ___________ were at the demonstration were from all sections of society.

(A)  whose

(B)  which

(C)  who

(D)  whom

Answer: (C)

2. A transparent square sheet shown above is folded along the dotted line. The folded sheet will look like ________.

Answer: (C)

3. For a regular polygon having 10 sides, the interior angle between the sides of the polygon, in degrees, is:

(A)  396

(B)  324

(C)  216

(D)  144

Answer: (D)

4. Which one of the following numbers is exactly divisible by (1113 + 1)?

(A)  1126 + 1

(B)  1133 + 1

(C)  1139 – 1

(D)  1152 – 1

Answer: (D)

5. Oasis is to sand as island is to ________

Which one of the following options maintains a similar logical relation in the above sentence?

(A)  Stone

(B)  Land

(C)  Water

(D)  Mountain

Answer: (C)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

6. The importance of sleep is often overlooked by students when they are preparing for exams. Research has consistently shown that sleep deprivation greatly reduces the ability to recall the material learnt. Hence, cutting down on sleep to study longer hours can be counterproductive.

Which one of the following statements is the CORRECT inference from the above passage?

(A)  Sleeping well alone is enough to prepare for an exam. Studying has lesser benefit.

(B)  Students are efficient and are not wrong in thinking that sleep is a waste of time.

(C)  If a student is extremely well prepared for an exam, he needs little or no sleep.

(D)  To do well in an exam, adequate sleep must be part of the preparation.

Answer: (D)

7. 

In the figure shown above, each inside square is formed by joining the midpoints of the sides of the next larger square. The area of the smallest square (shaded) as shown, in cm2 is:

(A)  12.50

(B)  6.25

(C)  3.125

(D)  1.5625

Answer: (C)

8. Let X be a continuous random variable denoting the temperature measured. The range of temperature is [0, 100] degree Celsius and let the probability density function of X be f(x) = 0.01 for 0 ≤ X ≤ 100.

The mean of X is _____

(A)  2.5

(B)  5.0

(C)  25.0

(D)  50.0

Answer: (D)

9. 

The number of students passing or failing in an exam for a particular subject are presented in the bar chart above. Students who pass the exam cannot appear for the exam again. Students who fail the exam in the first attempt must appear for the exam in the following year. Students always pass the

exam in their second attempt.

The number of students who took the exam for the first time in the year 2 and the year 3 respectively, are __________.

(A)  65 and 53

(B)  60 and 50

(C)  55 and 53

(D)  55 and 48

Answer: (D)

10. Seven cars P, Q, R, S, T, U and V are parked in a row not necessarily in that order. The cars T and U should be parked next to each other. The cars S and V also should be parked next to each other, whereas P and Q cannot be parked next to each other. Q and S must be parked next to each other. R is parked to the immediate right of V. T is parked to the left of U.

Based on the above statements, the only INCORRECT option given below is:

(A)  There are two cars parked in between Q and V.

(B)  Q and R are not parked together.

(C)  V is the only car parked in between S and R.

(D)  Car P is parked at the extreme end.

Answer: (A)

Electrical Engineering (EE)

Q.1 – Q.12 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Let p and q be real numbers such that p2 + q2 = 1. The eigenvalues of the matrix  are

(A)  1 and 1

(B)  1 and -1

(C)  j and − j

(D)  pq and −pq

Answer: (B)

2. Let p(z) = z3 + (1 + j)z2 + (2 + j)z + 3, where z is a complex number. Which one of the following is true?

(A)  conjugate {p(z)} = p(conjugate{z}) for all z

(B)  The sum of the roots of p(z) = 0 is a real number

(C)  The complex roots of the equation p(z) = 0 come in conjugate pairs

(D)  All the roots cannot be real

Answer: (D)

3. Let f(x) be a real-valued function such that f'(x0) = 0 for some x0 ∈ (0, 1), and f”(x) > 0 for all x ∈ (0, 1). Then f(x) has

(A)  no local minimum in (0, 1)

(B)  one local maximum in (0, 1)

(C)  exactly one local minimum in (0, 1)

(D)  two distinct local minima in (0, 1)

Answer: (C)

4. For the network shown, the equivalent Thevenin voltage and Thevenin impedance as seen across terminals ‘ab’ is

(A)  10 V in series with 12 Ω

(B)  65 V in series with 15 Ω

(C)  50 V in series with 2 Ω

(D)  35 V in series with 2 Ω

Answer: (B)

5. Which one of the following vector functions represents a magnetic field  are unit vectors along x-axis, y-axis, and z-axis, respectively)

Answer: (A)

6. If the input x(t) and output y(t) of a system are related as y(t) = 0 max(0, x(t)), then the system is

(A)  linear and time-variant

(B)  linear and time-invariant

(C)  non-linear and time-variant

(D)  non-linear and time-invariant

Answer: (D)

7. Two discrete-time linear time-invariant systems with impulse responses h1­[n] = δ[n – 1] + δ[n+ 1] and h2[n] = δ[n] + δ[n – 1] are connected in cascade, where δ[n] is the Kronecker delta. The impulse response of the cascaded system is

(A)  δ[n – 2] + δ[n + 1]

(B)  δ[n – 1] δ[n] + δ[n + 1] δ[n – 1]

(C)  δ[n – 2] + δ[n – 1] + δ[n] + δ[n + 1]

(D)  δ[n] δ[n – 1] + δ[n – 2] δ[n + 1]

Answer: (C)

8. Consider the table given:

The correct combination that relates the constructional feature, machine type and mitigation is

(A)  P-V-X, Q-U-Z, R-T-Y

(B)  P-U-X, Q-S-Y, R-V-Z

(C)  P-T-Y, Q-V-Z, R-S-X

(D)  P-U-X, Q-V-Y, R-T-Z

Answer: (B)

9. Consider a power system consisting of N number of buses. Buses in this power system are categorized into slack bus, PV buses and PQ buses for load flow study. The number of PQ buses is NL. The balanced Newton-Raphson method is used to carry out load flow study in polar form. H, S, M, and R are sub-matrices of the Jacobian matrix J as shown below:

The dimension of the sub-matrix M is

(A)  NL × (N – 1)

(B)  (N – 1) × (N – 1 – NL)

(C)  NL × (N – 1 + NL)

(D)  (N – 1) × (N – 1 + NL)

Answer: (A)

10. Two generators have cost functions F1 and F2. Their incremental-cost characteristics are

They need to deliver a combined load of 260 MW. Ignoring the network losses, for economic operation, the generations P1 and P2 (in MW) are

(A)  P1 = P2 = 130

(B)  P1 = 160, P2 = 100

(C)  P1 = 140, P2 = 120

(D)  P1 = 120, P2 = 140

Answer: (B)

11. For the closed-loop system shown, the transfer function  is

Answer: (C)

12. Inductance is measured by

(A)  Schering bridge

(B)  Maxwell bridge

(C)  Kelvin bridge

(D)  Wien bridge

Answer: (B)

Q.13 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

13. Suppose the circles x2 + y2 = 1 and (x – 1)2 + (y – 1)2 = r2 intersect each other orthogonally at the point (u, v). Then u + v = ______.

Answer: (1 to 1)

14. In the given circuit, the value of capacitor C that makes current I=0 is________ μF.

Answer: (20.00 to 20.00)

15. Two single-core power cables have total conductor resistances of 0.7 Ω and 0.5 Ω, respectively, and their insulation resistances (between core and sheath) are 600 MΩ and 900 MΩ, respectively. When the two cables are joined in series, the ratio of insulation resistance to conductor resistance is _____×106.

Answer: (300 to 300)

16. In the given circuit, for voltage Vy to be zero, the value of β should be _____. (Round off to 2 decimal places).

Answer: (-3.30 to -3.20)

17. A 1 μC point charge is held at the origin of a cartesian coordinate system. If a second point charge of 10 μC is moved from (0, 10, 0) to (5, 5, 5) and subsequently to (5, 0, 0), then the total work done is ____ mJ. (Round off to 2 decimal places).

Take  in SI units. All coordinates are in meters.

Answer: (8.90 to 9.10)

18. The power input to a 500 V, 50 Hz, 6-pole, 3-phase induction motor running at 975 RPM is 40 kW. The total stator losses are 1 kW. If the total friction and windage losses are 2.025 kW, then the efficiency is __________%.

Answer: (89.50 to 90.50)

19. An alternator with internal voltage of 1 ∠δ1u and synchronous reactance of 0.4 p.u is connected by a transmission line of reactance 0.1 p.u to a synchronous motor having synchronous reactance 0.35 p.u and internal voltage of 0.85 ∠δ2 p.u. If the real power supplied by the alternator is 0.866 p.u, then (δ1 – δ2) is ____ degrees. (Round off to 2 decimal places.)

(Machines are of non-salient type. Neglect resistances.)

Answer: (59.00 to 61.00)

20. The Bode magnitude plot for the transfer function  of the circuit is as shown. The value of R is _______ Ω. (Round off to 2 decimal places.)

Answer: (0.09 to 0.11)

21. A signal generator having a source resistance of 50 Ω is set to generate a 1 kHz sinewave. Open circuit terminal voltage is 10 V peak-to-peak. Connecting a capacitor across the terminals reduces the voltage to 8 V peak-to-peak. The value of this capacitor is ______ μ (Round off to 2 decimal places.)

Answer: (2.30 to 2.50)

22. A 16-bit synchronous binary up-counter is clocked with a frequency fCLK. The two most significant bits are OR-ed together to form an output Y. Measurements show that Y is periodic, and the duration for which Y remains high in each period is 24 ms. The clock frequency fCLK is __________ MHz. (Round off to 2 decimal places.)

Answer: (2.00 to 2.10)

23. In the BJT circuit shown, beta of the PNP transistor is 100. Assume VBE = −7 V. The voltage across RC will be 5 V when R2 is ____ kΩ. (Round off to 2 decimal places.)

Answer: (16.70 to 17.70)

24. In the circuit shown, the input Vi is a sinusoidal AC voltage having an RMS value of 230 V ±20%. The worst-case peak-inverse voltage seen across any diode is ________ V. (Round off to 2 decimal places.).

Answer: (389 to 391)

25. In the circuit shown, a 5 V Zener diode is used to regulate the voltage across load R0. The input is an unregulated DC voltage with a minimum value of 6 V and a maximum value of 8 V. The value of RS is 6 Ω. The Zener diode has a maximum rated power dissipation of 2.5 W. Assuming the Zener diode to be ideal, the minimum value of R0 is _______ Ω.

Answer: (29.00 to 31.00)

Q.26 – Q.37 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

26. In the open interval (0, 1) , the polynomial p(x) = x4 – 4x3 + 2 has

(A)  two real roots

(B)  one real root

(C)  three real roots

(D)  no real roots

Answer: (B)

27. Suppose the probability that a coin toss shows “head” is p, where 0 < p < 1. The coin is tossed repeatedly until the first “head” appears. The expected number of tosses required is

(A)  p/(1 – p)

(B)  (1 – p)/p

(C)  1/p

(D)  1/p2

Answer: (C)

28. Let (−1 – j), (3 – j), (3 + j) and (−1 + j) be the vertices of a rectangle C in the complex plane. Assuming that C is traversed in counter-clockwise direction, the value of the contour integral  is

(A)  jπ/2

(B)  0

(C)  −jπ/8

(D)  jπ/16

Answer: (C)

29. In the circuit, switch ‘S’ is in the closed position for a very long time. If the switch is opened at time t = 0, then iL (t) in amperes, for t ≥ 0 is

(A)  8e10t

(B)  10

(C)  8 + 2e10t

(D)  10(1 − e2t)

Answer: (C)

30. The input impedance, Zin(s), for the network shown is

(A) 

(B)  6s + 4

(C)  7s + 4

(D) 

Answer: (A)

31. The causal signal with z-transform z2(z – a)2 is (u[n] is the unit step signal)

(A)  a2nu[n]

(B)  (n+1)anu[n]

(C)  n1anu[n]

(D)  n2anu[n]

Answer: (B)

32. Let f(t) be an even function, i.e. f(−t) = f(t) for all t. Let the Fourier transform of f(t) be defined as  Suppose  for all ω, and F(0) = 1. Then

(A)  f(0) < 1

(B)  f(0) > 1

(C)  f(0) = 1

(D)  f(0) = 0

Answer: (A)

33. In a single-phase transformer, the total iron loss is 2500 W at nominal voltage of 440 V and frequency 50 Hz. The total iron loss is 850 W at 220 V and 25 Hz. Then, at nominal voltage and frequency, the hysteresis loss and eddy current loss respectively are

(A)  1600 W and 900 W

(B)  900 W and 1600 W

(C)  250 W and 600 W

(D)  600 W and 250 W

Answer: (B)

34. In the figure shown, self-impedances of the two transmission lines are 1.5j p.u each, and Zm = 0.5j p.u is the mutual impedance. Bus voltages shown in the figure are in p.u. Given that δ > 0, the maximum steady-state real power that can be transferred in p.u from Bus-1 to Bus-2 is

(A)  |E||V|

(B)  |E||V|/2

(C)  2|E||V|

(D)  3|E||V|/2

Answer: (A)

35. A 3-Bus network is shown. Consider generators as ideal voltage sources. If rows 1, 2 and 3 of the YBus matrix correspond to Bus 1, 2 and 3, respectively, then YBus of the network is

Answer: (C)

36. Suppose IA, IB and IC are a set of unbalanced current phasors in a three- phase system. The phase-B zero-sequence current IB0 = 0.1∠0°u. If phase-A current IA = 1.1∠0° p.u and phase-C current IC = (1∠120° + 0.1)p.u, then IB in p.u is

(A)  1∠240° − 0.1∠0°

(B)  1.1∠240° − 0.1∠0°

(C)  1.1∠−120° + 0.1∠0°

(D)  1∠−120° + 0.1∠0°

Answer: (D)

37. A counter is constructed with three D flip-flops. The input-output pairs are named (D0, Q0), (D1, Q1), and (D2, Q2), where the subscript 0 denotes the least significant bit. The output sequence is desired to be the Gray-code sequence 000, 001, 011, 010, 110, 111, 101, and 100, repeating periodically. Note that the bits are listed in the Q2 Q1 Q0 The combinational logic expression for D1 is

Answer: (C)

Q.38 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

38. Let A be a 10 × 10 matrix such that A5 is a null matrix, and let I be the 10 × 10 identity matrix. The determinant of A + I is _______.

Answer: (1 to 1)

39. A three-phase balanced voltage is applied to the load shown. The phase sequence is RYB. The ratio  is ________.

Answer: (1 to 1)

40. In the given circuit, for maximum power to be delivered to RL, its value should be _________ Ω. (Round off to 2 decimal places.)

Answer: (1.40 to 1.42)

41. One coulomb of point charge moving with a uniform velocity  m/s enters the region x ≥ 0 having a magnetic flux density  The magnitude of force on the charge at x = 0+ is _______ N.

( are unit vectors along x-axis, y-axis, and z-axis, respectively.)

Answer: (100 to 100)

42. Consider a large parallel plate capacitor. The gap d between the two plates is filled entirely with a dielectric slab of relative permittivity 5. The plates are initially charged to a potential difference of V volts and then disconnected from the source. If the dielectric slab is pulled out completely, then the ratio of the new electric field E2 in the gap to the original electric field E1 is __________.

Answer: (5 to 5)

43. Consider a continuous-time signal x(t) defined by x(t) = 0 for |t| > 1, and x(t) = 1 – |t| for |t| ≤ Let the Fourier transform of x(t) be defined as The maximum magnitude of X(ω) is______.

Answer: (1 to 1)

44. A belt-driven DC shunt generator running at 300 RPM delivers 100 kW to a 200 V DC grid. It continues to run as a motor when the belt breaks, taking 10 kW from the DC grid. The armature resistance is 0.025 Ω, field resistance is 50 Ω, and brush drop is 2 V. Ignoring armature reaction, the speed of the motor is _____________ RPM. (Round off to 2 decimal places.)

Answer: (273.00 to 277.00)

45. An 8-pole, 50 Hz, three-phase, slip-ring induction motor has an effective rotor resistance of 0.08 Ω per phase. Its speed at maximum torque is 650 RPM. The additional resistance per phase that must be inserted in the rotor to achieve maximum torque at start is __________ Ω. (Round off to 2 decimal places.) Neglect magnetizing current and stator leakage impedance. Consider equivalent circuit parameters referred to stator.

Answer: (0.50 to 0.54)

46. Consider a closed-loop system as shown . is the plant transfer function and Gc(s) = 1 is the compensator. For a unit-step input, the output response has damped oscillations. The damped natural frequency is ________________ rad/s. (Round off to 2 decimal places.)

Answer: (10.80 to 11.00)

47. In the given figure, plant  and compensator  The external disturbance input is D(s). It is desired that when the disturbance is a unit step, the steady-state error should not exceed 0.1 unit. The minimum value of K is ________. (Round off to 2 decimal places.)

Answer: (9.50 to 9.60)

48. The waveform shown in solid line is obtained by clipping a full-wave rectified sinusoid (shown dashed). The ratio of the RMS value of the full- wave rectified waveform to the RMS value of the clipped waveform is _____. (Round off to 2 decimal places.)

Answer: (1.20 to 1.23)

49. The state space representation of a first-order system is given as

where, x is the state variable, u is the control input and y is the controlled output. Let u x =−K be the control law, where K is the controller gain. To place a closed-loop pole at −2, the value of K is ___________.

Answer: (1 to 1)

50. An air-core radio-frequency transformer as shown has a primary winding and a secondary winding. The mutual inductance M between the windings of the transformer is ______ μ (Round off to 2 decimal places.)

Answer: (50.00 to 52.00)

51. A 100 Hz square wave, switching between 0 V and 5 V, is applied to a CR high-pass filter circuit as shown. The output voltage waveform across the resistor is 6.2 V peak-to-peak. If the resistance R is 820 Ω, then the value C is _____ μ (Round off to 2 decimal places.)

Answer: (12.30 to 12.60)

52. A CMOS Schmitt-trigger inverter has a low output level of 0 V and a high output level of 5 V. It has input thresholds of 1.6 V and 2.4 V. The input capacitance and output resistance of the Schmitt-trigger are negligible. The frequency of the oscillator shown is _______ Hz. (Round off to 2 decimal places.)

Answer: (3150.00 to 3170.00)

53. Consider the boost converter shown. Switch Q is operating at 25 kHz with a duty cycle of 0.6. Assume the diode and switch to be ideal. Under steady-state condition, the average resistance Rin as seen by the source is ______ Ω. (Round off to 2 decimal places.)

Answer: (1.55 to 1.65)

54. Consider the buck-boost converter shown. Switch Q is operating at 25 kHz and 0.75 duty-cycle. Assume diode and switch to be ideal. Under steady- state condition, the average current flowing through the inductor is_______ A.

Answer: (24 to 24)

55. A single-phase full-bridge inverter fed by a 325 V DC produces a symmetric quasi-square waveform across ‘ab’ as shown. To achieve a modulation index of 0.8, the angle θ expressed in degrees should be ________. (Round off to 2 decimal places.)

(Modulation index is defined as the ratio of the peak of the fundamental component of vab to the applied DC value.)

Answer: (50.00 to 52.00)

GATE Exam 2021 Electronics and Communication Engineering (EC) Question Paper With Answer Key

GATE-2021

EC: Electronics and Communication Engineering

GA: General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. The current population of a city is 11,02,500. If it has been increasing at the rate of 5% per annum, what was its population 2 years ago?

(A)    9,92,500

(B)    9,95,006

(C)    10,00,000

(D)    12,51,506

Answer: (C)

2. p and q are positive integers and 

(A)    3

(B)    7

(C)    9

(D)    11

Answer: (B)

3. 

The least number of squares that must be added so that the line P-Q becomes the line of symmetry is ________

(A)    4

(B)    3

(C)    6

(D)    7

Answer: (C)

4. Nostalgia is to anticipation as _______ is to ________

Which one of the following options maintains a similar logical relation in the above sentence?

(A)    Present, past

(B)    Future, past

(C)    Past, future

(D)    Future, present

Answer: (C)

5. Consider the following sentences:

(i) I woke up from sleep.

(ii) I woked up from sleep.

(iii) I was woken up from sleep.

(iv) I was wokened up from sleep.

Which of the above sentences are grammatically CORRECT?

(A)    (i) and (ii)

(B)    (i) and (iii)

(C)    (ii) and (iii)

(D)    (i) and (iv)

Answer: (B)

Q. 6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

6. Given below are two statements and two conclusions.

Statement 1: All purple are green.

Statement 2: All black are green.

Conclusion I: Some black are purple.

Conclusion II: No black is purple.

Based on the above statements and conclusions, which one of the following options is logically CORRECT?

(A)    Only conclusion I is correct.

(B)    Only conclusion II is correct.

(C)    Either conclusion I or II is correct.

(D)    Both conclusion I and II are correct.

Answer: (C)

7. Computers are ubiquitous. They are used to improve efficiency in almost all fields from agriculture to space exploration. Artificial intelligence (AI) is currently a hot topic. AI enables computers to learn, given enough training data. For humans, sitting in front of a computer for long hours can lead to health issues.

Which of the following can be deduced from the above passage?

(i) Nowadays, computers are present in almost all places.

(ii) Computers cannot be used for solving problems in engineering.

(iii) For humans, there are both positive and negative effects of using computers.

(iv) Artificial intelligence can be done without data.

(A)    (ii) and (iii)

(B)    (ii) and (iv)

(C)    (i), (iii) and (iv)

(D)    (i) and (iii)

Answer: (D)

8. Consider a square sheet of side 1 unit. In the first step, it is cut along the main diagonal to get two triangles. In the next step, one of the cut triangles is revolved about its short edge to form a solid cone. The volume of the resulting cone, in cubic units, is ________

(A)    π/3

(B)    2π/3

(C)    3π/2

(D)    3π

Answer: (A)

9. 

The number of minutes spent by two students, X and Y, exercising every day in a given week are shown in the bar chart above.

The number of days in the given week in which one of the students spent a minimum of 10% more than the other student, on a given day, is

(A)    4

(B)    5

(C)    6

(D)    7

Answer: (C)

10. 

Corners are cut from an equilateral triangle to produce a regular convex hexagon as shown in the figure above.

The ratio of the area of the regular convex hexagon to the area of the original equilateral triangle is

(A)    2 : 3

(B)    3 : 4

(C)    4 : 5

(D)    5 : 6

Answer: (A)

Electronics and Communication Engineering (EC)

Q.1 – Q.15 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. The vector function  is defined over a circular arc C shown in the figure.

The line integral of ∫C F(r).dr is

(A)    1/2

(B)    1/4

(C)    1/6

(D)    1/3

Answer: (A)

2. Consider the differential equation given below.

The integrating factor of the differential equation is

(A)    (1 – x2)3/4

(B)    (1 – x2)1/4

(C)    (1 – x2)3/2

(D)    (1 – x2)1/2

Answer: (B)

3. Two continuous random variables X and Y are related as

Y = 2X + 3

Let  denote the variances of X and Y, respectively. The variances are related as

Answer: (B)

4. Consider a real-valued base-band signal x(t), band limited to 10 kHz. The Nyquist rate for the signal  is

(A)    15 kHz

(B)    30 kHz

(C)    60 kHz

(D)    20 kHz

Answer: (B)

5. Consider two 16-point sequences x[n] and h[n]. Let the linear convolution of x[n] and h[n] be denoted by y[n], while z[n] denotes the 16-point inverse discrete Fourier transform (IDFT) of the product of the 16-point DFTs of x[n] and h[n]. The value(s) of k for which z[k] = y[k] is/are

(A)    k = 0, 1, 2, … , 15

(B)    k = 0

(C)    k = 15

(D)    k = 0 and k = 15

Answer: (C)

6. A bar of silicon is doped with boron concentration of 1016 cm−3 and assumed to be fully ionized. It is exposed to light such that electron-hole pairs are generated throughout the volume of the bar at the rate of 1020 cm−3s−1. If the recombination lifetime is 100 μs, intrinsic carrier concentration of silicon is 1010 cm3 and assuming 100% ionization of boron, then the approximate product of steady-state electron and hole concentrations due to this light exposure is

(A)    1020 cm6

(B)    2 × 1020 cm6

(C)    1032 cm6

(D)    2 × 1032 cm6

Answer: (D)

7. The energy band diagram of a p-type semiconductor bar of length L under equilibrium condition (i.e., the Fermi energy level EF is constant) is shown in the figure. The valance band EV is sloped since doping is non-uniform along the bar. The difference between the energy levels of the valence band at the two edges of the bar is ∆.

If the charge of an electron is q, then the magnitude of the electric field developed inside this semiconductor bar is

(A)    ∆/qL

(B)    2∆/qL

(C)    ∆/2qL

(D)    3∆/2qL

Answer: (A)

8. In the circuit shown in the figure, the transistors M1 and M2 are operating in saturation. The channel length modulation coefficients of both the transistors are non-zero. The trans conductance of the MOSFETs M1 and M2 are gm1 and gm2, respectively, and the internal resistance of the MOSFETs M1 and M2 are r01 and r02, respectively.

Ignoring the body effect, the ac small signal voltage gain (∂Vout⁄∂Vin) of the circuit is

Answer: (D)

9. For the circuit with an ideal OPAMP shown in the figure, VREF is fixed.

If VOUT = 1 volt for VIN = 0. 1 volt and VOUT = 6 volt for VIN = 1 volt, where VOUT is measured across RL connected at the output of this OPAMP, the value of RF⁄RIN is

(A)    3.285

(B)    2.860

(C)    3.825

(D)    5.555

Answer: (MTA)

10. Consider the circuit with an ideal OPAMP shown in the figure.

Assuming |VIN| ≪ |VCC| and |VREF| ≪ |VCC|, the condition at which VOUT equals to zero is

(A)    VIN = VREF

(B)    VIN = 0.5 VREF

(C)    VIN = 2 VREF

(D)    VIN = 2 + VREF

Answer: (A)

11. If (1235)x = (3033)y, where x and y indicate the bases of the corresponding numbers, then

(A)    x = 7 and y = 5

(B)    x = 8 and y = 6

(C)    x = 6 and y = 4

(D)    x = 9 and y = 7

Answer: (B)

12. Addressing of a 32K × 16 memory is realized using a single decoder. The minimum number of AND gates required for the decoder is

(A)    28

(B)    232

(C)    215

(D)    219

Answer: (C)

13. The block diagram of a feedback control system is shown in the figure.

The transfer function  of the system is

Answer: (C)

14. The complete Nyquist plot of the open-loop transfer function G(s)H(s) of a feedback control system is shown in the figure.

If G(s)H(s) has one zero in the right-half of the s-plane, the number of poles that the closed-loop system will have in the right-half of the s-plane is

(A)    0

(B)    1

(C)    4

(D)    3

Answer: (D)

15. Consider a rectangular coordinate system (x, y, z) with unit vectors ax, ay, and az. A plane wave traveling in the region z ≥ 0 with electric field vector E = 10 cos(2 × 108t + βz)ay is incident normally on the plane at z = 0, where β is the phase constant. The region z ≥ 0 is in free space and the region z < 0 is filled with a lossless medium (permittivity ε = ε0, permeability μ = 4μ0, where ε0 = 8. 85 × 10−12 F/m and μ0 = 4π × 10−7 H/m). The value of the reflection coefficient is

(A)    1/3

(B)    3/5

(C)    2/5

(D)    2/3

Answer: (A)

Q.16 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

16. If the vectors (1. 0, −1. 0, 2. 0), (7. 0, 3. 0, x) and (2. 0, 3. 0, 1. 0) in ℝ3 are linearly dependent, the value of x is __________

Answer: (8.0 to 8.0)

17. Consider the vector field F = ax(4y − c1z) + ay (4x + 2z) + az(2y + z) in a rectangular coordinate system (x, y, z) with unit vectors ax, ay, and az. If the field F is irrotational (conservative), then the constant c1 (in integer) is __________

Answer: (0 to 0)

18. Consider the circuit shown in the figure.

The current I flowing through the 7 Ω resistor between P and Q (rounded off to one decimal place) is __________ A.

Answer: (0.5 to 0.5)

19. Consider the circuit shown in the figure.

The value of v0 (rounded off to one decimal place) is __________ V.

Answer: (1.0 to 1.0)

20. An 8-bit unipolar (all analog output values are positive) digital-to-analog converter (DAC) has a full-scale voltage range from 0 V to 7. 68 V. If the digital input code is 10010110 (the leftmost bit is MSB), then the analog output voltage of the DAC (rounded off to one decimal place) is __________ V.

Answer: (4.5 to 4.5)

21. The autocorrelation function RX(τ) of a wide-sense stationary random process X(t) is shown in the figure.

The average power of X(t) is __________

Answer: (2.0 to 2.0)

22. Consider a carrier signal which is amplitude modulated by a single-tone sinusoidal message signal with a modulation index of 50%. If the carrier and one of the sidebands are suppressed in the modulated signal, the percentage of power saved (rounded off to one decimal place) is __________

Answer: (94.2 to 94.6)

23. A speech signal, band limited to 4 kHz, is sampled at 1. 25 times the Nyquist rate. The speech samples, assumed to be statistically independent and uniformly distributed in the range −5 V to +5 V, are subsequently quantized in an 8-bit uniform quantizer and then transmitted over a voice-grade AWGN telephone channel. If the ratio of transmitted signal power to channel noise power is 26 dB, the minimum channel bandwidth required to ensure reliable transmission of the signal with arbitrarily small probability of transmission error (rounded off to two decimal places) is __________ kHz.

Answer: (9.24 to 9.28)

24. A 4 kHz sinusoidal message signal having amplitude 4 V is fed to a delta modulator (DM) operating at a sampling rate of 32 kHz. The minimum step size required to avoid slope overload noise in the DM (rounded off to two decimal places) is __________ V.

Answer: (2.80 to 3.20)

25. The refractive indices of the core and cladding of an optical fiber are 1. 50 and 1. 48, respectively. The critical propagation angle, which is defined as the maximum angle that the light beam makes with the axis of the optical fiber to achieve the total internal reflection, (rounded off to two decimal places) is __________ degree.

Answer: (9.30 to 9.44)

Q.26 – Q. 35 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

26. Consider the integral

where C is a counter-clockwise oriented circle defined as |x − i| = 2. The value of the integral is

Answer: (MTA)

27. A box contains the following three coins.

(I) A fair coin with head on one face and tail on the other face.

(II) A coin with heads on both the faces.

(III) A coin with tails on both the faces.

A coin is picked randomly from the box and tossed. Out of the two remaining coins in the box, one coin is then picked randomly and tossed. If the first toss results in a head, the probability of getting a head in the second toss is

(A)    2/5   

(B)    1/3

(C)    1/2

(D)    2/3

Answer: (B)

28. The switch in the circuit in the figure is in position P for a long time and then moved to position Q at time t = 0.

The value of  at t = 0+ is

(A)    0 V/s

(B)    3 V/s

(C)    −3 V/s

(D)    −5 V/s

Answer: (C)

29. Consider the two-port network shown in the figure.

The admittance parameters, in siemens, are

(A)    y11 = 2, y12 = −4, y21 = −4, y22 = 2

(B)    y11 = 1, y12 = −2, y21 = −1, y22 = 3

(C)    y11 = 2, y12 = −4, y21 = −1, y22 = 2

(D)    y11 = 2, y12 = −4, y21 = −4, y22 = 3

Answer: (C)

30. For an n-channel silicon MOSFET with 10 nm gate oxide thickness, the substrate sensitivity (∂VT/∂|VBS|) is found to be 50 mV/V at a substrate voltage |VBS| = 2 V, where VT is the threshold voltage of the MOSFET. Assume that, |VBS| ≫ 2ΦB, where qΦB is the separation between the Fermi energy level EF and the intrinsic level Ei in the bulk. Parameters given are

Electron charge (q) = 1. 6 × 10−19 C

Vacuum permittivity (ε0) = 8. 85 × 10−12 F/m

Relative permittivity of silicon (εSi) = 12

Relative permittivity of oxide (εox) = 4

The doping concentration of the substrate is

(A)    7.37 × 1015 cm−3

(B)    4.37 × 1015 cm−3

(C)    2.37 × 1015 cm−3

(D)    9.37 × 1015 cm−3

Answer: (A)

31. The propagation delays of the XOR gate, AND gate and multiplexer (MUX) in the circuit shown in the figure are 4 ns, 2 ns and 1 ns, respectively.

If all the inputs P, Q, R, S and T are applied simultaneously and held constant, the maximum propagation delay of the circuit is

(A)    3 ns

(B)    5 ns

(C)    6 ns

(D)    7 ns

Answer: (C)

32. The content of the registers are R1 = 25H, R2 = 30H and R3 = 40H. The following machine instructions are executed.

PUSH{R1}

PUSH{R2}

PUSH{R3}

POP{R1}

POP{R2}

POP{R3}

After execution, the content of registers R1, R2, R3 are

(A)    R1 = 40H, R2 = 30H, R3 = 25H

(B)    R1 = 25H, R2 = 30H, R3 = 40H

(C)    R1 = 30H, R2 = 40H, R3 = 25H

(D)    R1 = 40H, R2 = 25H, R3 = 30H

Answer: (A)

33. The electrical system shown in the figure converts input source current is(t) to output voltage vo(t).

Current iL(t) in the inductor and voltage vC(t) across the capacitor are taken as the state variables, both assumed to be initially equal to zero, i.e., iL(0) = and vC (0) = 0 The system is

(A)    completely state controllable as well as completely observable

(B)    completely state controllable but not observable

(C)    completely observable but not state controllable

(D)    neither state controllable nor observable

Answer: (D)

34. A digital transmission system uses a (7, 4) systematic linear Hamming code for transmitting data over a noisy channel. If three of the message-codeword pairs in this code (mi; ci) where ci is the codeword corresponding to the ith message mi, are known to be ( 1 1 0 0 ; 0 1 0 1 1 0 0 ), ( 1 1 1 0 ; 0 0 1 1 1 1 0 ) and (0 1 1 0 ; 1 0 0 0 1 1 0 ), then which of the following is a valid codeword in this code?

(A)    1 1 0 1 0 0 1

(B)    1 0 1 1 0 1 0

(C)    0 0 0 1 0 1 1

(D)    0 1 1 0 1 0 0

Answer: (C)

35. The impedance matching network shown in the figure is to match a lossless line having characteristic impedance Z0 = 50 Ω with a load impedance ZL. A quarter-wave line having a characteristic impedance Z1 = 75 Ω is connected to ZL. Two stubs having characteristic impedance of 75 Ω each are connected to this quarter-wave line. One is a short-circuited (S.C.) stub of length 0. 25λ connected across PQ and the other one is an open-circuited (O.C.) stub of length 0. 5λ connected across RS.

The impedance matching is achieved when the real part of ZL is

(A)    112.5 Ω

(B)    75.0 Ω

(C)    50.0 Ω

(D)    33.3 Ω

Answer: (A)

Q.36 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

36. A real 2 × 2 non-singular matrix A with repeated eigenvalue is given as

where x is a real positive number. The value of x (rounded off to one decimal place) is __________

Answer: (10.0 to 10.0)

37. For a vector field D = ρ cos2 φ aρ + z2 sin2 φ aφ in a cylindrical coordinate system (ρ, φ, z) with unit vectors aρ, aφ and az, the net flux of D leaving the closed surface of the cylinder (ρ = 3, 0 ≤ z ≤ 2) (rounded off to two decimal places) is __________

Answer: (56.50 to 56.60)

38. In the circuit shown in the figure, the switch is closed at time t = 0, while the capacitor is initially charged to −5 V (i.e., vc(0) = −5 V).

The time after which the voltage across the capacitor becomes zero (rounded off to three decimal places) is __________ ms.

Answer: (0.132 to 0.146)

39. The exponential Fourier series representation of a continuous-time periodic signal x(t) is defined as

where ω0 is the fundamental angular frequency of x(t) and the coefficients of the series are ak. The following information is given about x(t) and ak.

(I) x(t) is real and even, having a fundamental period of 6

(II) The average value of x(t) is 2

The average power of the signal x(t) (rounded off to one decimal place) is __________

Answer: (31.9 to 32.1)

40. For a unit step input u[n], a discrete-time LTI system produces an output signal ( 2δ[n + 1] + δ[n] + δ[n − 1] ). Let y[n] be the output of the system for an input  The value of y[0] is __________

Answer: (0.0 to 0.0)

41. Consider the signals x[n] = 2n−1 u[−n + 2] and y[n] = 2−n+2 u[n + 1], where u[n] is the unit step sequence. Let X(e) and Y(e) be the discrete- time Fourier transform of x[n] and y[n], respectively. The value of the integral  (rounded off to one decimal place) is _________

Answer: (7.9 to 8.1)

42. A silicon P-N junction is shown in the figure. The doping in the P region is 5 × 1016 cm−3 and doping in the N region is 10 × 1016 cm−3. The parameters given are

The magnitude of reverse bias voltage that would completely deplete one of the two regions (P or N) prior to the other (rounded off to one decimal place)

is ________V.

Answer: (8.1 to 8.4)

43. An asymmetrical periodic pulse train vin of 10 V amplitude with on-time TON = 1 ms and off-time TOFF = 1 μs is applied to the circuit shown in the figure. The diode D1 is ideal.

The difference between the maximum voltage and minimum voltage of the output waveform vo (in integer) is __________ V.

Answer: (10 to 10)

44. For the transistor M1 in the circuit shown in the figure, μnCox = 100 μA/V2 and (W⁄L) = 10, where μn is the mobility of electron, Cox is the oxide capacitance per unit area, W is the width and L is the length.

The channel length modulation coefficient is ignored. If the gate-to-source voltage VGS is 1 V to keep the transistor at the edge of saturation, then the threshold voltage of the transistor (rounded off to one decimal place) is __________ V.

Answer: (0.5 to 0.5)

45. A circuit with an ideal OPAMP is shown in the figure. A pulse VIN of 20 ms duration is applied to the input. The capacitors are initially uncharged.

The output voltage VOUT of this circuit at t = 0+ (in integer) is __________V.

Answer: (-12 to -12)

46. The propagation delay of the exclusive-OR (XOR) gate in the circuit in the figure is 3 ns. The propagation delay of all the flip-flops is assumed to be zero. The clock (Clk) frequency provided to the circuit is 500 MHz.

Starting from the initial value of the flip-flop outputs Q2Q1Q0 = 1 1 1 with

D2 = 1, the minimum number of triggering clock edges after which the flip-flop outputs Q2Q1Q0 becomes 1 0 0 (in integer) is __________

Answer: (5 to 5)

47. The circuit in the figure contains a current source driving a load having an inductor and a resistor in series, with a shunt capacitor across the load. The ammeter is assumed to have zero resistance. The switch is closed at time t = 0.

Initially, when the switch is open, the capacitor is discharged and the ammeter reads zero ampere. After the switch is closed, the ammeter reading keeps fluctuating for some time till it settles to a final steady value. The maximum ammeter reading that one will observe after the switch is closed (rounded off to two decimal places) is __________ A.

Answer: (1.40 to 1.50)

48. A unity feedback system that uses proportional-integral (PI) control is shown in the figure.

The stability of the overall system is controlled by tuning the PI control parameters KP and KI. The maximum value of KI that can be chosen so as to keep the overall system stable or, in the worst case, marginally stable (rounded off to three decimal places) is _________.

Answer: (3.125 to 3.125)

49. A sinusoidal message signal having root mean square value of 4 V and frequency of 1 kHz is fed to a phase modulator with phase deviation constant 2 rad/volt. If the carrier signal is c(t) = 2 cos(2π106t), the maximum instantaneous frequency of the phase modulated signal (rounded off to one decimal place) is __________ Hz.

Answer: (1011310.0 to 1011320.0)

50. Consider a super heterodyne receiver tuned to 600 kHz. If the local oscillator feeds a 1000 kHz signal to the mixer, the image frequency (in integer) is __________ kHz.

Answer: (1400 to 1400)

51. In a high school having equal number of boy students and girl students, 75% of the students study Science and the remaining 25% students study Commerce. Commerce students are two times more likely to be a boy than are Science students. The amount of information gained in knowing that a randomly selected girl student studies Commerce (rounded off to three decimal places) is _______ bits.

Answer: (3.320 to 3.325)

52. A message signal having peak-to-peak value of 2 V, root mean square value of 0.1 V and bandwidth of 5 kHz is sampled and fed to a pulse code modulation (PCM) system that uses a uniform quantizer. The PCM output is transmitted over a channel that can support a maximum transmission rate of 50 kbps. Assuming that the quantization error is uniformly distributed, the maximum signal to quantization noise ratio that can be obtained by the PCM system (rounded off to two decimal places) is __________

Answer: (30.00 to 34.00)

53. Consider a polar non-return to zero (NRZ) waveform, using +2 V and −2 V for representing binary ‘1’ and ‘0’ respectively, is transmitted in the presence of additive zero-mean white Gaussian noise with variance 0. 4 V2. If the a priori probability of transmission of a binary ‘1’ is 0. 4, the optimum threshold voltage for a maximum a posteriori (MAP) receiver (rounded off to two decimal places) is __________ V.

Answer: (0.03 to 0.05)

54. A standard air-filled rectangular waveguide with dimensions a = 8 cm, b = 4 cm, operates at 3. 4 GHz. For the dominant mode of wave propagation, the phase velocity of the signal is vp. The value (rounded off to two decimal places) of vp⁄c, where c denotes the velocity of light, is __________

Answer: (1.15 to 1.25)

55. An antenna with a directive gain of 6 dB is radiating a total power of 16 kW. The amplitude of the electric field in free space at a distance of 8 km from the antenna in the direction of 6 dB gain (rounded off to three decimal places) is __________ V/m.

Answer: (0.224 to 0.264)

GATE Exam 2021 Chemistry (CY) Question Paper With Answer Key

GATE-2021

CY: Chemistry

GA-General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Getting to the top is ___________than staying on top.

(A)  more easy

(B)  much easy

(C)  easiest

(D)  easier

Answer: (D)

2. The mirror image of the above text about the x-axis is

Answer: (B)

3. In a company, 35% of the employees drink coffee, 40% of the employees drink tea and 10% of the employees drink both tea and coffee. What % of employees drink neither tea nor coffee?

(A)  15

(B)  25

(C)  35

(D)  40

Answer: (C)

4. ⊕ and ⨀ are two operators on numbers p and q such that

If x ⊕ y = 2 ⊙ 2, then x =

(A)  y/2

(B)  y

(C)  3y/2

(D)  2y

Answer: (B)

5. Four persons P, Q, R and S are to be seated in a row, all facing the same direction, but not necessarily in the same order. P and R cannot sit adjacent to each other. S should be seated to the right of Q. The number of distinct seating arrangements possible is:

(A)  2

(B)  4

(C)  6

(D)  8

Answer: (C)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

6. Statement: Either P marries Q or X marries Y

Among the options below, the logical NEGATION of the above statement is:

(A)  P does not marry Q and X marries Y.

(B)  Neither P marries Q nor X marries Y.

(C)  X does not marry Y and P marries Q.

(D)  P marries Q and X marries Y.

Answer: (B)

7. Consider two rectangular sheets, Sheet M and Sheet N of dimensions 6 cm x 4 cm each.

Folding operation 1: The sheet is folded into half by joining the short edges of the current shape.

Folding operation 2: The sheet is folded into half by joining the long edges of the current shape.

Folding operation 1 is carried out on Sheet M three times.

Folding operation 2 is carried out on Sheet N three times.

The ratio of perimeters of the final folded shape of Sheet N to the final folded shape of Sheet M is ______.

(A)  13 : 7

(B)  3 : 2

(C)  7 : 5

(D)  5 : 13

Answer: (A)

8. Five line segments of equal lengths, PR, PS, QS, QT and RT are used to form a star as shown in the figure above.

The value of θ, in degrees, is ______

(A)  36

(B)  45

(C)  72

(D)  108

Answer: (A)

9. A function, λ, is defined by

The value of the expression  is:

(A)  −1

(B)  0

(C)  16/3

(D)  16

Answer: (B)

10. Humans have the ability to construct worlds entirely in their minds, which don’t exist in the physical world. So far as we know, no other species possesses this ability. This skill is so important that we have different words to refer to its different flavors, such as imagination, invention and innovation.

Based on the above passage, which one of the following is TRUE?

(A)  No species possess the ability to construct worlds in their minds.

(B)  The terms imagination, invention and innovation refer to unrelated skills.

(C)  We do not know of any species other than humans who possess the ability to construct mental worlds.

(D)  Imagination, invention and innovation are unrelated to the ability to construct mental worlds.

Answer: (C)

Chemistry (CY)

Q.1 – Q.14 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. The rates of alkaline hydrolysis of the compounds shown below

follow the order:

(A)  I > II > III

(B)  II > I > III

(C)  II > III > I

(D)  III > I > II

Answer: (C)

2. The major product formed in the following reaction

is

Answer: (A)

3. The major product formed in the following reaction

is

Answer: (C)

4. The least acidic among the following compounds

is

(A)  M

(B)  N

(C)  O

(D)  P

Answer: (A)

5. The major product formed in the following reaction

is

Answer: (A)

6. The reagent(s) required for the conversion of hex-3-yne to (E)-hex-3-ene is/are:

(A)  H2, Pd/BaSO4

(B)  Bu3SnH

(C)  Li / liquid NH3

(D)  LiAlH0

Answer: (C)

7. An organic compound exhibits the [M]+, [M+2]+ and [M+4]+ peaks in the intensity ratio 1:2:1 in the mass spectrum, and shows a singlet at δ49 in the 1H NMR spectrum in CDCl3. The compound is:

(A)  1,4-dichlorobenzene

(B)  1,4-dibromobenzene

(C)  1,2-dibromobenzene

(D)  1,2-dichlorobenzene

Answer: (B)

8. Reaction of LiAlH4 with one equivalent of Me3N∙HCl gives a tetrahedral compound, which reacts with another equivalent of Me3N∙HCl to give compound N. The compound N and its geometry, respectively, are:

(A)  LiAlH4NMe3 and trigonal bipyramidal

(B)  Li2AlH4Cl and square pyramidal

(C)  AlH3(NMe3)2 and trigonal bipyramidal

(D)  AlH3(NMe3)2 and pentagonal

Answer: (C)

9. Which one of the following is a non-heme protein?

(A)  hemoglobin

(B)  hemocyanin

(C)  myoglobin

(D)  cytochrome P-450

Answer: (B)

10. A correct example of a nucleotide is:

(A)  adenosine monophosphate (AMP)

(B)  RNA

(C)  uridine

(D)  DNA

Answer: (A)

11. The equilibrium constant for the reaction

3 NO (g) ⇌ N2O (g) + NO2 (g)

at 25 °C is closest to:

[ΔG° = −104.18 kJ; R = 8.314 J mol−1 K−1]

(A)  1.043

(B)  1.8 × 108

(C)  1.651

(D)  5.7 × 1019

Answer: (B)

12. The reaction of NiBr2 with two equivalents of PPh3 in CS2 at –78 °C gives a red-colored diamagnetic complex, [NiBr2(PPh3)2]. This transforms to a green-colored paramagnetic complex with the same molecular formula at 25 °C. The geometry and the number of unpaired electrons in the green-colored complex, respectively, are:

(A)  tetrahedral and 1

(B)  tetrahedral and 2

(C)  square planar and 2

(D)  square planar and 4

Answer: (B)

13. The rate of the substitution reaction of [Co(CN)5Cl]3– with OH to give [Co(CN)5(OH)]3–

(A)  depends on the concentrations of both [Co(CN)5Cl]3– and OH

(B)  depends on the concentration of [Co(CN)5Cl]3– only

(C)  is directly proportional to the concentration of OH only

(D)  is inversely proportional to the concentration of OH

Answer: (B)

14. The ∆o of [Cr(H2O)6]3+, [CrF6]3– and [Cr(CN)6]3– follows the order:

(A)  [Cr(H2O)6]3+ > [CrF6]3– > Cr(CN)6]3–

(B)  [CrF6]3– > [Cr(H2O)6]3+ > [Cr(CN)6]3–

(C)  [Cr(CN)6]3– > [Cr(H2O)6]3+ > [CrF6]3–

(D)  [CrF6]3– > [Cr(CN)6]3– > [Cr(H2O)6]3+

Answer: (C)

Q.15 – Q.18 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).

15. The phase diagram of CO2 is shown below:

The correct statement(s) about CO2 is/are:

(A)  Below Tc, it does not exist in liquid state.

(B)  Above Tc, it does not exist in liquid state.

(C)  At Tc, it can exist in all three phases.

(D)  Above T1, it does not exist in solid state.

Answer: (A; C)

16. Acceptable wavefunctions for a quantum particle must be:

(A)  odd

(B)  even

(C)  single-valued

(D)  continuous

Answer: (C; D)

17. The characters of E, C2, σv, and σ’v symmetry operations, in this order, for valid irreducible representation(s) of the C2v point group is/are:

(A)  1, 1, 1, 1

(B)  −1, 1, 1, −1

(C)  1, −1, 1, −1

(D)  1, −1, −1, −1

Answer: (A; C)

18. The normal mode(s) of vibration of H2O is/are:

Answer: (A; B; C)

Q.19 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

19. A reversible heat engine absorbs 20 kJ of heat from a source at 500 K and dissipates it to the reservoir at 400 K. The efficiency of the heat engine is _______%.

Answer: (20 to 20)

20. Among the following eight compounds,

the number of compound(s) which can exhibit stereoisomerism is _______.

Answer: (6 to 6)

21. The Mo−Mo bond order in [(η5-C5H5)Mo(CO)2]2 which obeys the 18-electron rule is _______.

Answer: (3 to 3)

22. The change in enthalpy (ΔH) for the reaction

2 P (s) + 3 Br2 (l) → 2 PBr3 (l)

is −243 kJ. In this reaction, if the amount of phosphorus consumed is 3.1 g, the change in enthalpy (rounded off to two decimal places) is ______ kJ.

[Atomic Wt. of P = 31]

Answer: (-12.16 to -12.14)

23. The number of signal(s) in the 1H NMR spectrum of the following compound

recorded at 25 °C in CDCl3 is __________.

Answer: (3 to 3)

24. A 5 V battery delivers a steady current of 1.5 A for a period of 2 h. The total charge that has passed through the circuit is ______ Coulombs.

Answer: (10800 to 10800)

25. The spin-only magnetic moment of [Co(H2O)6]2+ (rounded off to one decimal place) is _______ BM.

Answer: (3.8 to 4.0)

Q.26 – Q.42 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

26. The geometry and the number of unpaired electrons in tetrakis(1-norbornyl)Co

respectively, are:

(A)  tetrahedral and one

(B)  tetrahedral and five

(C)  square planar and one

(D)  square planar and three

Answer: (A)

27. The yellow color of an aqueous solution of K2CrO4 changes to red-orange upon the addition of a few drops of HCl. The red-orange complex, the oxidation state of its central element(s), and the origin of its color, respectively, are:

(A)  chromium chloride, +3, d-d transition

(B)  dichromate ion, +6 and +6, charge transfer

(C)  perchlorate ion, +7, charge transfer

(D)  chromic acid, +6, charge transfer

Answer: (B)

28. The shapes of the compounds

ClF3, XeOF2, N3and XeO3F2

respectively, are:

(A)  T-shape, T-shape, linear and trigonal bipyramidal

(B)  trigonal planar, T-shape, V-shape and square pyramidal

(C)  T-shape, trigonal planar, linear and square pyramidal

(D)  trigonal planar, trigonal planar, V-shape and trigonal bipyramidal

Answer: (A)

29. The metal borides that contain isolated boron atoms are:

(A)  Tc7B3 and Re7B3

(B)  Cr5B3 and V3B2

(C)  Ti4B4 and V3B4

(D)  TiB and HfB

Answer: (A)

30. The major product formed in the following reaction

is

(A)  non-6-yn-2-one

(B)  non-3-yn-8-one

(C)  non-2-yn-6-one

(D)  non-3-en-8-one

Answer: (A)

31. The major product formed in the following reaction

is:

Answer: (B)

32. The major product formed in the following reaction

is:

Answer: (D)

33. In the following reaction sequence

the major products P and Q, respectively, are:

Answer: (B)

34. In an electrochemical cell, Ag+ ions in AgNO3 are reduced to Ag metal at the cathode and Cu is oxidized to Cu2+ at the anode. A current of 0.7 A is passed through the cell for 10 min. The mass (in grams) of silver deposited and copper dissolved, respectively, are:

[Faraday Constant = 96,485 C mol−1, Atomic Weight of Ag = 107.9, Atomic Weight of Cu = 63.55]

(A)  0.469 and 0.138

(B)  0.235 and 0.138

(C)  0.469 and 0.069

(D)  0.235 and 0.069

Answer: (A)

35. Among the following

the compounds which can be prepared by nucleophilic substitution reaction are:

(A)  III, IV, and V

(B)  I, II, and VI

(C)  II, IV, and VI

(D)  I, III, and V

Answer: (C)

36. In the following reaction

the major products X and Y, respectively, are:

Answer: (C)

37. The major products P and Q formed in the following reactions

respectively, are:

Answer: (B)

38. The major product formed in the reaction of (2R,3R)-2-bromo-3-methylpentane with NaOMe is:

(A)  (Z)-3-methylpent-2-ene

(B)  (E)-3-methylpent-2-ene

(C)  (2R,3R)-2-methoxy-3-methylpentane

(D)  (2S,3R)-2-methoxy-3-methylpentane

Answer: (B)

39. The major product formed in the following reaction

is:

Answer: (A)

40. Hexane and heptane are completely miscible. At 25 °C, the vapor pressures of hexane and heptane are 0.198 atm and 0.06 atm, respectively. The mole fractions of hexane and heptane in the vapor phase for a solution containing 4 M hexane and 6 M heptane, respectively, are:

(A)  0.688 and 0.312

(B)  0.400 and 0.600

(C)  0.312 and 0.688

(D)  0.600 and 0.400

Answer: (A)

41. The correct order of Lewis acid strengths of BF2Cl, BFClBr, BF2Br and BFBr2 is:

(A)  BF2Cl > BFClBr > BF2Br > BFBr2

(B)  BFBr2 > BFClBr > BF2Br > BF2Cl

(C)  BF2Cl > BF2Br > BFClBr > BFBr2

(D)  BFClBr > BFBr2 > BF2Cl > BF2Br

Answer: (B)

42. The correct order of increasing intensity (molar absorptivity) of the UV-visible absorption bands for the ions [Ti(H2O)6]3+, [Mn(H2O)6]2+, [CrO4]2–, and [NiCl4]2– is:

(A)  [Ti(H2O)6]3+ < [Mn(H2O)6]2+ < [CrO4]2– < [NiCl4]2–

(B)  [Mn(H2O)6]2+ < [Ti(H2O)6]3+ < [NiCl4]2– < [CrO4]2–

(C)  [NiCl4]2– < [Ti(H2O)6]3+ < [Mn(H2O)6]2+ < [CrO4]2–

(D)  [Ti(H2O)6]3+ < [NiCl4]2– < [CrO4]2– < [Mn(H2O)6]2+

Answer: (B)

Q.43 – Q.44 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).

43. The correct statement(s) about the concentration of Na+ and K+ ions in animal cells is/are:

(A)  [K+] inside the cell > [K+] outside the cell

(B)  [Na+] inside the cell > [Na+] outside the cell

(C)  [Na+] inside the cell < [Na+] outside the cell

(D)  [K+] inside the cell < [K+] outside the cell

Answer: (A; C)

44. The correct statement(s) about actinides is/are:

(A)  The 5f electrons of actinides are bound less tightly than the 4f electrons.

(B)  The trans uranium elements are prepared artificially.

(C)  All the actinides are radioactive.

(D)  Actinides do not exhibit actinide contraction.

Answer: (A; B; C)

Q.45 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

45. The number of photons emitted per nanosecond by a deuterium lamp (400 nm) having a power of 1 microwatt (rounded off to the nearest integer) is ______.

[h = 6.626 × 10−34 kg m2s−1; c = 3.0 108 m s−1]

Answer: (2000 to 2020)

46. Given the initial weight of 1 mg of radioactive  (half-life = 5.27 years), the amount disintegrated in 1 year (rounded off to two decimal places) is _______mg.

Answer: (0.11 to 0.13)

47. The de Broglie wavelength of an argon atom (mass = 40 amu) traveling at a speed of 250 ms−1 (rounded off to one decimal place) is __________ picometers.

[N = 6.022 × 1023; h = 6.626 × 10−34 kg m2s−1]

Answer: (39.5 to 40.5)

48. The molar absorption coefficient of a substance dissolved in cyclohexane is 1710 L mol−1 cm−1 at 500 nm. The reduction in intensity of light of the same wavelength that passes through a cell of 1 mm path length containing a 2 m mol L−1solution (rounded off to one decimal place) is ___________%.

Answer: (54.0 to 55.0)

49. The fundamental vibrational frequency of 1H127I is 2309 cm−1. The force constant for this molecule (rounded off to the nearest integer) is _____N m−1.

[N = 6.022 × 1023, c = 3.0 × 108 m s−1]

Answer: (309 to 315)

50. A laser Raman spectrometer operating at 532 nm is used to record the vibrational spectrum of Cl2 having its fundamental vibration at 560 cm−1. The Stokes line corresponding to this vibration will be observed at _______ cm−1. (Rounded off to the nearest integer)

Answer: (18225 to 18245)

51. The vapor pressure of toluene (Mol. Wt. = 92) is 0.13 atm at 25°C. If 6 g of a hydrocarbon is dissolved in 92 g of toluene, the vapor pressure drops to 0.12 atm. The molar mass of the hydrocarbon (rounded off to the nearest integer) is _______.

Answer: (71 to 73)

52. The reaction

CO (g) + Cl2 (g) ⇌ COCl2 (g)

at 500°C, with initial pressures of 0.7 bar of CO and 1.0 bar of Cl2, is allowed to reach equilibrium. The partial pressure of COCl2 (g) at equilibrium is 0.15 bar. The equilibrium constant for this reaction at 500°C (rounded off to two decimal places) is ________.

Answer: (0.30 to 0.34)

53. The rate constants for the decomposition of a molecule in the presence of oxygen are 0.237 × 10−4 L mol−1 s−1 at 0 °C and 2.64 × 10−4 L mol−1 s−1 at 25 °C (R = 8.314 J mol−1 K−1).

The activation energy for this reaction (rounded off to one decimal place) is ___________ kJ mol−1.

Answer: (151 to 153)

54. 2 L of a gas at 1 atm pressure is reversibly heated to reach a final volume of 3.5 L. The absolute value of the work done on the gas (rounded off to the nearest integer) is _______ Joules.

Answer: (151 to 153)

55. The quantity of the cobalt ore [Co3(AsO4)2∙H2O] required to obtain 1 kg of cobalt (rounded off to two decimal places) is _________ kg.

[Atomic Wt. of Co = 59, As = 75, O = 16, H = 1]

Answer: (2.50 to 2.80)

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