GATE Exam 2020 Life Sciences (XL) Question Paper With Answer Key

GATE-2020

XL: Life Sciences

GA-General Aptitude

Q1 – Q5 carry one mark each.

1. Rajiv Gandhi Khel Ratna Award was conferred _____Mary Kom, a six-time world champion in boxing, recently in a ceremony _____ the Rashtrapati Bhawan (the President’s official residence) in New Delhi.

(A)  with, at

(B)  on, in

(C)  on, at

(D)  to, at

Answer: (C)

2. Despite a string of a poor performances, the changes of K. L. Rahul’s selection in the team are ______.

(A)  slim

(B)  bright

(C)  obvious

(D)  uncertain

Answer: (B)

3. Select the word that fits the analogy:

Cover : Uncover :: Associate : _______

(A)  Unassociate

(B)  Inassociate

(C)  Missassociate

(D)  Dissociate

Answer: (D)

4. Hig by floods, he kharif (summer sown) crops in various parts of the county have been affected. Officials believe that the loss in production of the kharif crops can be recovered in the output of the rabi (winter sown) crops so that the country can achieve its food-grain production target of 291 million tons in the crop year 2019-20 (July-June). They are hopeful that good rains in July-August will help the soil retain moisture for a longer period, helping winter sown crops such as wheat and pulses during the November-February period.

Which of the following statements can be inferred from the given passage?

(A)  Officials declared that the food-grain production target will be met due to good rains.

(B)  Officials want the food-grain production target to be met by the November-February period.

(C)  Officials feel that the food-grain production target cannot be met due to floods.

(D)  Officials hope that the food-grain production target will be met due to a good rabi produce.

Answer: (D)

5. The difference between the sum of the first 2n natural numbers and the sum of the first n odd natural numbers is ______.

(A)  n2 – n

(B)  n2 + n

(C)  2n2 – n

(D)  2n2 + n

Answer: (B)

Q6 – Q10 carry two marks each.

6. Repo rate is the at which Reserve Bank of India (RBI) lends commercial banks, and reverse repo rate is the rate at which RBI borrows money from commercial banks.

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

(A)  Decrease in repo rate will increase cost of borrowing and decrease lending by commercial banks.

(B)  Increase in repo rate will decrease cost of borrowing and increase lending by commercial banks.

(C)  Increase in repo rate will decrease cost of borrowing and decrease lending by commercial banks.

(D)  Decrease in repo rate will decrease cost of borrowing and increase lending by commercial banks.

Answer: (D)

7. P, Q, R, S, T, U, V, and W are seated around a circular table.

(I) S is seated opposite to W.

(II) U is seated at the second place to the right of R.

(III) T is seated at the third place to the left of R.

(IV) V is a neighbor of S.

Which of the following must be true?

(A)  P is a neighbor of R.

(B)  Q is a neighbor of R.

(C)  P is not seated opposite to Q.

(D)  R is the left neighbor of S.

Answer: (C)

8. The distance between Delhi and Agra is 233 km. A car P started travelling from Delhi to Agra and another car Q started from Agra to Delhi along the same road 1 hour after the car P started. The two cars crossed each other 75 minutes after the car Q started. Both cars were travelling at constant speed. The speed of car P was 10 km/hr more than the speed of car Q. How many kilometers the car Q had travelled when the cars crossed each other?

(A)  66.6

(B)  75.2

(C)  88.2

(D)  116.5

Answer: (B)

9. For a matrix M = [mij], i. j= 1, 2, 3, 4, the diagonal elements are all zero and mij = −mij. The minimum number of elements required to fully specify the matrix is_______.

(A)  0

(B)  6

(C)  12

(D)  16

Answer: (B)

10. The profit shares of two companies P and Q are shown in the figure. If the two companies have invested a fixed and equal amount every year, then the ratio of the total revenue of company P to the total revenue of company Q, during 2013-2018 is ______.

(A)  15 : 17

(B)  16 : 17

(C)  17 : 15

(D)  17 : 16

Answer: (B)

XL: Life Sciences – P : Chemistry (Compulsory)

Q1 – Q5 carry one mark each.

1. An aqueous solution contains a mixture of 108 M NaCl and 108 M HCl.

Choose the correct statement about this solution.

(A)  The solution is a buffer with pH less than 7.00

(B)  The solution is a buffer with pH greater than 7.00

(C)  The solution is not a buffer but has its pH less than 7.00

(D)  The solution is not a buffer but has its pH greater than 7.00

Answer: (C)

2. The coordination complex which has a distorted octahedral structure is

(Given: Atomic numbers of V: 23; Mn: 25; Ni: 28; Cu: 29)

(A)  [Ni(H2O)6]2+

(B)  [Mn(H2O)6]2+

(C)  [V(H2O)6]2+

(D)  [Cu(H2O)6]2+

Answer: (D)

3. In naphthalene, the value of the integer “n” according to Huckel’s rule of aromaticity is ______.

Answer: (2 to 2)

4. The azimuthal quantum number (l) of an electron in the  orbital of a copper atom (atomic number: 29) is ______.

Answer: (2 to 2)

5. The standard enthalpy of reaction (in kJ mol1) for obtaining three moles of H2(g) from atomic hydrogen in gas phase is ______. (Given: Standard enthalpy of formation of atomic hydrogen is gas phase is 218 kJ mol1)

Answer: (-1308 to -1308)

Q6 – Q15 carry two marks each.

6. The correct order of the first ionization energies of He, B, N and O in their corresponding ground state is

(A)  He > N > O > B

(B)  O > N > B > He

(C)  He > B > N > O

(D)  N > O > B > He

Answer: (A)

7. Based on the molecular orbital theory, which one of the following statements with respect to N2, N2+, O2 and O2+ is correct?

(A)  Bond orders of N2 and O2 are higher than their corresponding cations.

(B)  Bond energy of N2+ is higher than that of N2, whereas bond energy of O2+ is lower than that of O2.

(C)  The unpaired electrons in N2+ and O2+ are present in σ and π* orbitals, respectively.

(D)  The bond in N2+ is shorter than that is N2, whereas bond in O2 is shorter than that in O2+.

Answer: (C)

8. Which one of the following statements is incorrect about the diborane molecule?

(A)  B-Ht bond is 2-centre-2-electron bond (Ht : terminal hydrogen).

(B)  BHbB bond is a 3-centre-2-electron bond (Hb: bridged hydrogen).

(C)  The  bond angle HtBHt is 122° (Ht : terminal hydrogen)

(D)  The B-Ht bond distance is longer than B-Hb bond distance (Ht : terminal hydrogen, Hb: bridged hydrogen).

Answer: (D)

9. Given below are Newman projections of ethylene glycol and 1, 2-difluoroethane about their respective C-C bonds. The most stable conformations (lowest energy) of ethylene glycol and 1, 2-difluoroethane are

(A)  I and III respectively.

(B)  I and IV respectively.

(C)  II and III respectively.

(D)  II and IV respectively.

Answer: (A)

10. In the reaction given below, choose the condition that gives an anti-Markovnikov’s product.

(A)  Peroxide/HCl

(B)  Aqueous mercuric acetate treatment

(C)  Diborane addition

(D)  Sulfuric acid addition

Answer: (C)

11. Which one of the following hexoses will give an osazone that has a different melting point from that of the osazone obtained from D (+) glucose?

Answer: (C)

12. A molecule in solution crystallizes into two different crystal forms with rate constants of 0.02 s1 and 0.13 s1. If the crystallization is assumed to be under kinetic control, then the half-life (in seconds, rounded off to one decimal place) of the molecular is ________.

Answer: (4.5 to 4.7)

13. The standard potential (Eθcell) for a cell reaction given below is +0.7 V. The standard reactions free energy (∆rGθ) for this cell is _____ kJ mol1 (correct up to two decimal places). (Given: Faraday constant, F = 96500 C mol1)

Au3+ (aq) + 3 Ag(s) → Au(s) + 3Ag+ (aq)

Answer: (-202.66 to -202.64)

14. The activation energy (Ea) estimated for a reaction from the Arrhenius equation is 21 kJ mol1. If the frequency factor is assumed to be independent of temperature, then the ratio of the rate constants determined at 298 K and 260 K is ______ (rounded off to two decimal places). (Given: Gas constant, R = 8.315 J K−1 mol−1)

Answer: (3.44 to 3.46)

15. At a given pressure, a substance is heated from 2000 K to 2600 K. If the entropy of the substance is 60 J K1 mol1, and is assumed to be constant over the given temperature range, then the change in the chemical potential (in kJ mol1) of the substance is _________.

Answer: (-36 to -36)

XL: Life Sciences – Q : Biochemistry

Q1 – Q10 carry one mark each.

1. Which one of the following hormones initiates a signaling cascade by directly binding to an intra-cellular receptor?

(A)  Insulin

(B)  Gonadotropin

(C)  Progesterone

(D)  Epinephrine

Answer: (C)

2. Which one of the following bonds is NOT present in ATP ?

(A)  Phosphoester

(B)  Phosphoanhydride

(C)  N-Glycosidic

(D)  α-Glycosidic

Answer: (D)

3. The reaction involved in the direct conversion of L-phenylalanine of L-tyrosine is

(A)  Hydroxylation

(B)  Decarboxylation

(C)  Transamination

(D)  Reduction

Answer: (A)

4. The humn major histocompatibility complex (MHC) is

(A)  Polygenic and monomorphic

(B)  Polygenic and polymorphic

(C)  Monogenic and polymorphic

(D)  Monogenic and monomorphic

Answer: (B)

5. Har Gobind Khorana and Marshall Nirenberg elucidated the genetic code by using a cell-free protein synthesizing system. It was found that poly(U) and poly(C) result in the synthesis of poly(L-Phe) and poly(L-pro), respectively. Based on these observations, which one of the following conclusions is correct?

(A)  Codon GGG specifies L-Phe and codon AAA specifies L-Pro

(B)  Codon CCC specifies L-Phe and codon UUU specifies L-pro

(C)  Codon AAA specifies L-Phe and codon GGG specifies L-Pro

(D)  Codon UUU specifies L-Phe and codon CCC specifies L-Pro

Answer: (D)

6. Binding of an antibody to its cognate antigen does NOT involve

(A)  Covalent bonds

(B)  Electrostatic foces

(C)  Van der Waals forces

(D)  Hydrogen bonds

Answer: (A)

7. A globular protein of molecular weight 50 kDa exists as a mixture of monomers and dimmers in solution. The most appropriate technique for the separation of these two forms of the protein is

(A)  Thin layer chromatography

(B)  Ion exchange chromatography

(C)  Gel filtration chromatography

(D)  Paper chromatography

Answer: (C)

8. Choose the correct order of molecules according to their ability to diffuse across as lipid bilayer.

(A)  CO2 > H2O > Glucose > RNA

(B)  CO2 > Glucose > H2O > RNA

(C)  RNA > Glucose > CO2 > H2O

(D)  H2O > CO2 > RNA > Glucose

Answer: (A)

9. When one glucose unit from glycogen gets converted to lactate in the muscle, the ne number of ATP molecules produced is _______.

Answer: (3 to 3)

10. Considering that the three pKas of histidine are pK1 = 1.8, pK2 = 9.2 and pKR = 6.0, its isoelectric point will be ______ (rounded off to one decimal place).

Answer: (7.5 to 7.7)

Q11-  Q20 carry two marks each.

11. One mole of a native protein upon N-terminal analysis yielded one mole each of Asp and Val. Therefore, the protein in its native state exists as a

(A)  Monomer

(B)  Homo-dimer

(C)  Hetero-dimer

(D)  Tetramer

Answer: (C)

12. The prosthetic groups/cofactors involved in both 1e and 2e transfer in the mitochondrial electron transport chain are

(A)  NAD and NADP

(B)  NAD and FAD

(C)  Heme and FMN

(D)  Coenzyme Q and FMN

Answer: (D)

13. Match the items in Group I with the most appropriate items in Group II and choose the correct option.

(A)  P-2, Q-1, R-3, S-4

(B)  P-4, Q-1, R-3, S-2

(C)  P-1, Q-2, R-3, S-4

(D)  P-4, Q-1, R-2, S-3

Answer: (B)

14. The correct combination of glycosidic linkages present in glycogen is

(A)  α 1 → 4 and α 1 → 6

(B)  α 1 → 4 and β 1 → 6

(C)  α 1 → 6 and β 1 → 4

(D)  α 1 → 6 and β 1 → 6

Answer: (A)

15. Polypeptides are either biosynthesized on the ribosomes using an mRNA template or chemically synthesized by the Merrifield’s solid phase method. The correct directions of peptide synthesis are

(A)  C→ N direction on the ribosomes and N → C direction on the solid phase

(B)  N → C direction on the ribosomes and C → N direction on the solid phase

(C)  N → C direction in both cases

(D)  C → N direction in both cases

Answer: (B)

16. A solution absorbs 20% of the incident light in a cuvette of path length 1.0 cm. The amount of light transmitted by the same solution in a curvette of 3.0 cm path length is _______% (rounded off to one decimal place).

Answer: (51.1 to 51.3)

17. The second pKa of phosphoric acid is 6.8. The ratio of Na2HPO4 to NaH2PO4 required to obtain a buffer of pH 7.0 is _______ (rounded off to two decimal places).

Answer: (1.58 to 1.60)

18. A PCR in a 100 μL reaction volume, containing two primers at a concentration of 0.2 μM each, is set up to amplify a 250 base pair DNA fragment. Consider the average molecular weight of one base pair as 660 Da. If the primers are fully consumed by the end of the reaction, the amount of the final PCR product formed is ________μg (rounded off to one decimal place).

Answer: (3.2 to 3.4)

19. An enzyme obeying Michaelis-Menten kinetics shows as reaction velocity (v) of 10 μmol/min when the substrate concentration [S] equals its KM. The maximal velocity Vmax for this enzyme is _______ μmol/min (correct to integer number). (KM is Michaelis-Menten constant)

Answer: (20 to 20)

20. The enzyme glucose isomerase catalyzes the inter-conversion of glucose and fructose as shown.

The ∆G’0 for this reaction is zero kcal/mol. After adding glucose isomerase  to a 0.12 M glucose solution and allowing the reaction to attain equilibrium, the final concentration of fructose in the reaction mixture will be _____ mM.

Answer: (60 to 60)

XL: Life Sciences – R: Botany

Q1 – Q10 carry one mark each.

1. Indefinite stamen is a characteristic feature of which of the following plant families?

(A)  Malvaceae

(B)  Apocynaceae

(C)  Poaceae

(D)  Brassicaceae

Answer: (A)

2. In natural condition, which of the following plants DOES NOT exhibit anomalous secondary growth?

(A)  Rice

(B)  Aloe

(C)  Yucca

(D)  Dracaena

Answer: (A)

3. In a typical angiosperm under natural condition, primary meristems are usually established during

(A)  Gametogenesis

(B)  Embryogenesis

(C)  Vegetative phase development

(D)  Secondary growth

Answer: (B)

4. 2-Methoxy-3, 6-dichlorobenzoic acid belongs to which class of plant growth regulators?

(A)  Synthetic auxin

(B)  Synthetic cytokinin

(C)  Strigolactone

(D)  Brassinosteroid

Answer: (A)

5. In a typical green plant, the first product of Calvin cycle is

(A)  Oxaloacetic acid

(B)  Succinic acid

(C)  Maleic acid

(D)  3-Phosphoglyceric acid

Answer: (D)

6. Among the following, which best describes an organism that lives at the expense of other organisms, harmful but usually not killing?

(A)  Predator

(B)  Symbiotic

(C)  Prey

(D)  Parasite

Answer: (D)

7. The oleo-gum resin asafoetida (hing) is obtained from the cut surface of

(A)  Stem

(B)  Root

(C)  Leaf

(D)  Fruit

Answer: (B)

8. ‘Bakanae’ disease or ‘foolish seedling’ disease is caused by

(A)  Fungus

(B)  Bacterium

(C)  Virus

(D)  Mycoplasma

Answer: (A)

9. Which of the following chemicals is used for doubling of chromosome numbers during production of ‘doubled haploids’ in crop plants?

(A)  Hygromycin

(B)  Kanamycin

(C)  Colchicine

(D)  Glufosinate

Answer: (C)

10. An mRNA of a nuclear encoded plant gene, DSH20 has an ORF of 1353 nucleotides. Provided that average molecular weight of amino acid is 110 Dalton (Da) calculated molecular weight of DSH20 protein in kDa (round off to 1 decimal place) is ______

Answer: (49.5 to 49.5)

Q11 – Q20 carry two marks each.

11. Group I, Group II and Group III represent enzyme, product of the enzymatic reaction, and metabolic process, respectively.

The CORRECT combination fro Group I, Group II and Group III is

(A)  P-ii-1, Q-iv-3, R-v-2, S-iii-4

(B)  P-ii-1, Q-i-3, R-v-4, S-iii-2

(C)  P-ii-2, Q-v-3, R-i-4, S-iii-1

(D)  P-iii-1, Q-i-3, R-iv-4, S-ii-2

Answer: (B)

12. Match the following in CORRECT combination between Group I and Group II with reference to the agents that interfere with oxidative phosphorylation

(A)  P-iv, Q-i, R-ii, S-iii

(B)  P-v, Q-i, R-iii, S-iv

(C)  P-iv, Q-iii, R-ii, S-v

(D)  P-v, Q-ii, R-iii, S-iv

Answer: (A)

13. In relation to Agrobacterium mediated genetic engineering in plants, match the following in CORRECT combination

(A)  P-iv, Q-iii, R-ii, S-v

(B)  P-ii, Q-i, R-iii, S-v

(C)  P-i, Q-ii, R-iii, S-iv

(D)  P-iii, Q-i, R-ii, S-iv

Answer: (C)

14. Match the plant part (Group I) with the product obtained (Group II) and the representative plant species (Group III) in CORRECT combination

(A)  P-ii-1, Q-i-3, R-iv-2, S-iii-4

(B)  P-ii-1, Q-i-2, R-iv-4, S-iii-3

(C)  P-ii-2, Q-iv-3, R-i-4, S-iii-1

(D)  P-iv-3, Q-i-2, R-ii-4, S-iii-1

Answer: (D)

15. Select the CORRECT combination by matching the disease, causal organism and the affected

(A)  P-iv-1, Q-iii-3, R-i-2, S-ii-4

(B)  P-ii-1, Q-i-6, R-iv-4, S-iii-2

(C)  P-iii-1, Q-iv-3, R-i-5, S-ii-4

(D)  P-iv-1, Q-ii-3, R-iii-2, S-i-5

Answer: (A)

16. Match the following alkaloids with their uses and source plants in CORRECT combination

(A)  P-ii-3, Q-iv-1, R-iii-4, S-i-2

(B)  P-ii-1, Q-i-3, R-iv-4, S-iii-2

(C)  P-ii-2, Q-iv-1, R-i-4, S-iii-3

(D)  P-iii-4, Q-ii-1, R-iv-3, S-i-2

Answer: (A)

17. Match the following ecological terms with their appropriate definitions

(A)  P-i, Q-ii, R-iv, S-iii

(B)  P-ii, Q-iv, R-i, S-iii

(C)  P-iv, Q-iii, R-i, S-ii

(D)  P-iii, Q-i, R-ii, S-iv

Answer: (B)

18. Arrange the following ‘water reservoirs of earth’ in decreasing order of water volume

P-Streams

Q-Groundwater

R-Glaciers

S-Lakes and inland seas

(A)  R-Q-S-P

(B)  P-Q-R-S

(C)  S-P-R-Q

(D)  R-P-Q-S

Answer: (A)

19. Selection markers and the corresponding genes used in plant genetic engineering are given below

Choose the CORRECT combination

(A)  P-ii, Q-i, R-iv, S-iii

(B)  P-iv, Q-ii, R-i, S-iii

(C)  P-iv, Q-i, R-ii, S-iii

(D)  P-iii, Q-iv, R-ii, S-i

Answer: (C)

20. A double homozygous mutant develops green and wrinkled seeds. When it was crossed with true-breeding plant having yellow and round seeds, all the F1 plants developed yellow and round seeds. After self-fertilization of F1, the calculated percentage probability of plants with green and wrinkled seeds in the F2 population (round off to 2 decimal places) is ________

Answer: (6.25 to 6.25)

XL: Life Sciences – S: Microbiology

Q1 – Q10 carry one mark each.

1. The technique of microbial “pure culture” was pioneered by

(A)  Edward Jenner

(B)  Louis Pasteur

(C)  Robert Hooke

(D)  Robert Koch

Answer: (D)

2. The antibacterial trimethoprim is an inhibitor of

(A)  dihydrofolate reductase

(B)  dihydropteroate synthetase

(C)  N5, N10-methenyl tetrahydrofolate synthetase

(D)  serine hydroxymethyl transferase

Answer: (A)

3. Choose the correct taxonomical hierarchy among the following:

(A)  Species, Genus, Family, Order, Class, Phylum, Domain

(B)  Species, Genus, Order, Class, Family, Phylum, Domain

(C)  Species, Genus, Order, Family, Class, Phylum, Domain

(D)  Species, Genus, Family, Class, Order, Phylum, Domain

Answer: (A)

4. Shifting a Sacharomyces cerevisiae culture from fermentative to aerobic respiratory mode will

(A)  decrease carbon dioxide production

(B)  increase alcohol production

(C)  increase glucose consumption

(D)  decrease ATP generation per mole of glucose

Answer: (A)

5. Which one of the following diseases is treated by a neuraminidase inhibitor?

(A)  Chickenpox

(B)  Polio

(C)  Influenza

(D)  Japanese encephalitis

Answer: (C)

6. Which one of the following does NOT provide three-dimensional images?

(A)  Atomic force microscopy

(B)  Confocal scanning laser microscopy

(C)  Differential interference contrast microscopy

(D)  Phase-contrast microscopy

Answer: (D)

7. Which one of the following will increase the resolution of a light microscope ?

(A)  Decreasing the numerical aperture of the objective lens

(B)  Using an objective lens with a longer working distance

(C)  Using a medium of higher refractive index

(D)  Increasing the wavelength of light

Answer: (C)

8. Which one of the following conditions favors maximum expression of lac operon genes in coli?

(A)  Glucose-low, lactose-law, cAMP-high

(B)  Glucose-high, lactose-low, cAMP-high

(C)  Glucose-low, lactose-high, cAMP-high

(D)  Glucose-high, lactose-high, cAMP-low

Answer: (C)

9. Match the cellular organelle in Group I with its function in Group II

(A)  P-3, Q-2, R-1, S-4

(B)  P-3, Q-4, R-1, S-2

(C)  P-1, Q-2, R-4, S-3

(D)  P-3, Q-1, R-4, S-2

Answer: (B)

10. A 250 μl of bacteriophage stock containing 8 × 108 phages/ml is added to 500 μl of coli culture containing 4 × 108 cells/ml. The multiplicity of infection is _______.

Answer: (1 to 1)

Q11 – Q20 carry two marks each.

11. Digestion of an immunoglobulin G (IgG) molecule with pepsin will NOT

(A)  generate a bivalent antigen binding fragment

(B)  generate monovalent antigen binding fragments

(C)  destroy the complement binding site

(D)  cleave the heavy chain of IgG molecule

Answer: (B)

12. Match the process involved in nitrogen or sulfur cycle in Group I with the corresponding microbe in Group II.

(A)  P-2, Q-3, R-4, S-1

(B)  P-2, Q-1, R-3, S-4

(C)  P-3, Q-4, R-1, S-2

(D)  P-3, Q-1, R-2, S-4

Answer: (D)

13. Determine the correctness or otherwise of the following Assertion [a] and the Reason [r].

Assertion [a]: Diphtheria exotoxin is an example of A-B type toxin.

Reason [r]: The A component of the toxin is released from the host cell while the B component inhibits protein synthesis and kills the host cell.

(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: (D)

14. Which one of the following statements about control of microbial growth is NOT correct?

(A)  Nonionizing radiation leads to thymine dimmers formation in DNA

(B)  Spirochetes and mycoplasma can pass through membrane filters (0.22-0.45 μm)

(C)  Use of high concentration of salts and sugars to preserve food is a chemical method of microbial control

(D)  Thermoduric bacteria can survive pasteurization

Answer: (C)

15. An example of a differential and selective medium in which colonies of Gram-negative bacteria produce large amounts of acidic products and appear green with a metallic sheen is

(A)  Blood agar

(B)  EMB agar

(C)  MacConkey agar

(D)  Mannitol salt agar

Answer: (B)

16. Which one of the following is an example of substrate level phosphorylation?

(A)  Glucose to Glucose 6-phosphate

(B)  Fructose 6-phosphate to Fructose 1, 6-biphosphate

(C)  1, 3-bisphosphoglycerate to 3-phosphoglycerate

(D)  2-phosphoglycerate to Phosphoenolpyruvate

Answer: (C)

17. A bacterial culture containing 3 × 105 live cells was exposed to a newly developed sterilizing agent. After 30 minutes of exposure, 3 live cells remained in culture. The decimal reduction time (in minutes) for the new agent is ______.

Answer: (6 to 6)

18. A bacterial culture has a generation time of 34 minutes. The time taken (in minutes, rounded off to two decimal places) for the OD550 of this exponentially growing culture to increase from 0.25 to 0.85 is ______.

Assume that OD550 has a linear relationship with the cell density.

Answer: (58.50 to 61.50)

19. A 100 μl aliquot (104 dilution) of the bacterial culture plated on the nutrient agar gave 4 colonies. The bacterial stock concentration (in million cells/ml, rounded off to one decimal place) is _____.

Answer: (0.4 to 0.4)

20. A continuous bacterial culture carried out in a chemostat is set to a flow rate of 40 ml/hr. The culture volume is equivalent to that of a cubical container having 10 cm sides. The dilution rate (in hr1, rounded off to two decimal places) of this system is ________.

Answer: (0.04 to 0.04)

XL: Life Sciences – T: Zoology

Q1 – Q10 carry one mark each.

1. Which ONE of following leucocytes is phagocytic and has clear cytoplasm?

(A)  Eosinophil

(B)  Monocyte

(C)  TH-lymphocyte

(D)  Basophil

Answer: (B)

2. Which ONE of the following techniques can be used for detecting the subcellular localization of serotonin receptor in intact cells?

(A)  Immunoelectron microscopy

(B)  SDS-PAGE

(C)  Fluorescence in-situ hybridization

(D)  Differential centrifugation

Answer: (A)

3. Which ONE of the following is NOT a site for in situ conservation?

(A)  Biosphere reserve

(B)  Wild life sanctuary

(C)  Zoological garden

(D)  Biodiversity hotspot

Answer: (C)

4. Which ONE of the following is the precursor molecule for corticosteroids?

(A)  Androgen

(B)  Estrogen

(C)  Pregnenolone

(D)  Mineralocorticoids

Answer: (C)

5. Transitional epithelia is found in which ONE of the following organs?

(A)  Liver

(B)  Lung

(C)  Brain

(D)  Urinary bladder

Answer: (D)

6. Visual signal transduction cascade is activated by rhodopsin and involves degradation rather than synthesis of which ONE of the following second messenger molecules?

(A)  cAMP

(B)  IP3

(C)  cGMP

(D)  DAG

Answer: (C)

7. The genomes of both human and Drosophila code for an amylase that acts on the same substrate. However, the sequence of nucleotides in the genes encoding the two is dissimilar. This is an example of which ONE of the following types of evolution?

(A)  Neutral

(B)  Directional

(C)  Convergent

(D)  Divergent

Answer: (C)

8. “Round dance” is performed by forager bees to indicate the distance between a food source and their colony. Which ONE of the following best represents this distance?

(A)  45 meters

(B)  450 meters

(C)  1000 meters

(D)  More than 2000 meters

Answer: (A)

9. Which ONE of the following phyla have choanocytes?

(A)  Ctenophora

(B)  Nematoda

(C)  Cnidaria

(D)  Porifera

Answer: (D)

10. Which ONE of the following glial cells is NOT derived from the ectoderm?

(A)  Astrocytes

(B)  Microglial cells

(C)  Oligodendrocytes

(D)  Ependyma

Answer: (B)

Q11 – Q20 carry two marks each.

11. Tarantulas and mosquitoes both belong to the phylum Arthropoda. Which ONE of the following represents the correct number of legs in them respectively?

(A)  6 and 6

(B)  6 and 8

(C)  8 and 8

(D)  8 and 6

Answer: (D)

12. Match the following subcellular organelles in Column I with associated functions in Column II

(A)  P-(iii), Q-(ii), R-(i), S-(iv)

(B)  P-(i), Q-(ii), R-(iii), S-(iv)

(C)  P-(iv), Q-(ii), R-(i), S-(iii)

(D)  P-(ii), Q-(iii), R-(i), S-(iv)

Answer: (C)

13. Match the following genetic disorders in Column I with associated typical chromosomal changes mentioned in Column II

(A)  P-(iv), Q-(iii), R-(ii), S-(i)

(B)  P-(iv), Q-(ii), R-(i), S-(iii)

(C)  P-(iii), Q-(iv), R-(ii), S-(i)

(D)  P-(iii), Q-(iv), R-(i), S-(ii)

Answer: (D)

14. Match the following components listed in Column I with their respective organs in Column II

(A)  P-(ii), Q-(iv), R-(i), S-(iii)

(B)  P-(ii), Q-(i), R-(iv), S-(iii)

(C)  P-(iii), Q-(iv), R-(i), S-(ii)

(D)  P-(iii), Q-(iv), R-(ii), S-(i)

Answer: (A)

15. Match the following digestive enzymes in Column I with their respective functions in Column II.

(A)  P-(iv), Q-(iii), R-(ii), S-(i)

(B)  P-(iv), Q-(iii), R-(i), S-(ii)

(C)  P-(iii), Q-(iv), R-(i), S-(ii)

(D)  P-(iii), Q-(iv), R-(ii), S-(i)

Answer: (B)

16. Which ONE of the following graphs represents the relationship between ventricular end-diastolic volume and cardiac output in a healthy adult individual at rest (solid line) and upon exercise (dotted line)?

Answer: (A)

17. Match the household insect vectors in Column I with their associated diseases in Column II.

(A)  P-(iv), Q-(iii), R-(ii), S-(i)

(B)  P-(iii), Q-(ii), R-(i), S-(iv)

(C)  P-(i), Q-(iv), R-(iii), S-(ii)

(D)  P-(iii), Q-(iv), R-(ii), S-(i)

Answer: (D)

18. Match the proteins in Column I with the organs in which they are maximally expressed in Column II.

(A)  P-(iv), Q-(i), R-(iii), S-(ii)

(B)  P-(iii), Q-(iv), R-(ii), S-(i)

(C)  P-(iv), Q-(iii), R-(ii), S-(i)

(D)  P-(i), Q-(ii), R-(iii), S-(iv)

Answer: (C)

19. The graph below shows the activity of enzyme pepsin in the presence of inhibitors aliphatic alcohols (P) or N-acetyl-1-phenylalanine (Q). Which ONE of the following represents the nature of inhibition by P and Q, respectively?

(A)  Non-competitive and competitive

(B)  Competitive and non-competitive

(C)  Non-competitive and uncompetitive

(D)  Competitive and uncompetitive

Answer: (B)

20. In Drosophila, the red eye phenotype (W) is dominant over the recessive white eye mutant (w). In a mixed population of red and white eye flies of 10,000 individuals, 3,600 flies were white eyed. The percentage of the heterozygous red eye flies in this population is ________.

Answer: (48 to 48)

XL: Life Sciences – U : Food Technology

Q1 – Q10 carry one mark each.

1. The enzyme majorly involved in postmortem degradation of muscle proteins is

(A)  Trypsin

(B)  Calpin

(C)  Transglutaminase

(D)  Pepsin

Answer: (B)

2. Which of the following is the correct pair of essential fatty acid?

(A)  Oleic acid and Lenoleic acid

(B)  Lenoleic acid and Linolenic acid

(C)  Linolenic acid and Lauric acid

(D)  Linolenic acid and Oleic acid

Answer: (B)

3. Nisin A is produced by

(A)  Aspergillus niger

(B)  Acttobacter aceti

(C)  Lactobacillus lactis

(D)  Clostridium perfringens

Answer: (C)

4. Which of the following bacteria will stain purple color after Gram staining?

(A)  Bacillus subtilis

(B)  Escherichia coli

(C)  Pseudomonas aeruginaosa

(D)  Yersinia pestis

Answer: (A)

5. The enzyme system used for removal of glucose from egg white prior to its drying consists of

(A)  Glucose oxidase and Catalase

(B)  Glucosidase and Glucoisomerase

(C)  Glucoisomerase and Catalase

(D)  Gluccoamylase and Glucose oxidase

Answer: (A)

6. The INCORRECT pair of food borne illness and its causative microorganism is

(A)  Brucellosis-Brucella Sp.

(B)  Peptic ulcers-Bacillus subtilis

(C)  Bubonic plague-Yersinia pestis

(D)  Q fever-Coxiella burnatii

Answer: (B)

7. Which of the following is commonly used as preservative in the tomato sauce?

(A)  Sodium sulphite

(B)  Potassium sorbate

(C)  Potassium sulphite

(D)  Sodium benzoate

Answer: (D)

8. A fluid with flow behvaviour index less than one (n < 1) is

(A)  Dilatant

(B)  Pseudoplastic

(C)  Bingham plastic

(D)  Newtonian

Answer: (B)

9. The velocity of 2.2 μm diameter fat particles inside a cetribfuge, running at 6000 rpm and 20°C, is 0.25 mm s1. The velocity of 1.5 μm diameter fat particles inside the same centrifuge running at 7500 rpm and same temperature (round off to 2 decimal places) will be ____ mm s1.

Answer: (0.15 to 0.21)

10. The initial population of a bacterial strain increases from 1 × 104 cells per mL to 1 × 106 cells per mL in 120 minutes. The generation time for this strain (round off to 2 decimal places) is ______ minutes.

Answer: (17.00 to 19.00)

Q11 – Q20 carry two marks each.

11. Match the protein in Column I with its food source in Column II.

(A)  P-4, Q-1, R-2, S-3

(B)  P-4, Q-3, R-1, S-2

(C)  P-2, Q-3, R-1, S-4

(D)  P-2, Q-4, R-1, S-3

Answer: (D)

12. Match the carbohydrate in Column I with corresponding enzyme used for its hydrolysis in Column II.

(A)  P-3, Q-2, R-1, S-4

(B)  P-2, Q-4, R-1, S-3

(C)  P-1, Q-2, R-3, S-4

(D)  P-4, Q-3, R-1, S-2

Answer: (A)

13. Match the edible oil refining stage in Column I with its purpose in Column II.

(A)  P-3, Q-1, R-2, S-4

(B)  P-1, Q-4, R-2, S-3

(C)  P-4, Q-3, R-1, S-2

(D)  P-3, Q-4, R-2, S-1

Answer: (D)

14. Match the food material in Column I with its related term in Column II.

(A)  P-4, Q-2, R-1, S-3

(B)  P-3, Q-4, R-1, S-2

(C)  P-3, Q-4, R-2, S-1

(D)  P-1, Q-3, R-4, S-2

Answer: (B)

15. Match the components/system in Column I with the peeling method for fruits and vegetables in Column II.

(A)  P-4, Q-3, R-2, S-1

(B)  P-3, Q-4, R-1, S-2

(C)  P-4, Q-3, R-1, S-2

(D)  P-3, Q-4, R-2, S-1

Answer: (C)

16. Which among the given options correctly explains the nature of the microbial culture represented by lines 1, 2 and 3 in the following figure?

Answer: (B)

17. Match the equation/law in Column I with its application in Column II.

(A)  P-1, Q-3, R-4, S-2

(B)  P-2, Q-3, R-1, S-4

(C)  P-2, Q-3, R-4, S-1

(D)  P-4, Q-3, R-1, S-2

Answer: (C)

18. Match the absorber used in modified atmosphere packaging and storage in Column I with the scavenger in Column II.

(A)  P-2, Q-2, R-4, S-1

(B)  P-1, Q-2, R-4, S-3

(C)  P-2, Q-3, R-4, S-1

(D)  P-3, Q-2, R-1, S-4

Answer: (A)

19. During extrusion cooking, food materials are generally subjected to a combination of

(A)  high shear and low pressure

(B)  high temperature and high shear

(C)  low shear and high temperature

(D)  low shear and low pressure

Answer: (B)

20. An orange juice flowing at 0.80 kg s1 enters a counter current double pipe heat exchanger at 20°C and leaves at 72° Inlet and outlet temperatures of the hot water used as heating medium in the exchanger are 81°C and 74°C, respectively. The specific heat of the orange juice is 3.74 kJ kg1 K1 and overall heat transfer coefficient is 492 W m2 K1. The heat transfer surface area (round off to 2 decimal places) will be ______ m2.

Answer: (11.00 to 14.00)

GATE Exam 2020 Engineering Sciences (XE) Question Paper With Answer Key

GATE-2020

XE: Engineering Sciences

GA-General Aptitude

Q1 – Q5 carry one mark each.

1. Rajiv Gandhi Khel Ratna Award was conferred _____Mary Kom, a six-time world champion in boxing, recently in a ceremony _____ the Rashtrapati Bhawan (the President’s official residence) in New Delhi.

(A)  with, at

(B)  on, in

(C)  on, at

(D)  to, at

Answer: (C)

2. Despite a string of a poor performances, the changes of K. L. Rahul’s selection in the team are ______.

(A)  slim

(B)  bright

(C)  obvious

(D)  uncertain

Answer: (B)

3. Select the word that fits the analogy:

Cover : Uncover :: Associate : _______

(A)  Unassociate

(B)  Inassociate

(C)  Missassociate

(D)  Dissociate

Answer: (D)

4. Hig by floods, he kharif (summer sown) crops in various parts of the county have been affected. Officials believe that the loss in production of the kharif crops can be recovered in the output of the rabi (winter sown) crops so that the country can achieve its food-grain production target of 291 million tons in the crop year 2019-20 (July-June). They are hopeful that good rains in July-August will help the soil retain moisture for a longer period, helping winter sown crops such as wheat and pulses during the November-February period.

Which of the following statements can be inferred from the given passage?

(A)  Officials declared that the food-grain production target will be met due to good rains.

(B)  Officials want the food-grain production target to be met by the November-February period.

(C)  Officials feel that the food-grain production target cannot be met due to floods.

(D)  Officials hope that the food-grain production target will be met due to a good rabi produce.

Answer: (D)

5. The difference between the sum of the first 2n natural numbers and the sum of the first n odd natural numbers is ______.

(A)  n2 – n

(B)  n2 + n

(C)  2n2 – n

(D)  2n2 + n

Answer: (B)

Q6 – Q10 carry two marks each.

6. Repo rate is the at which Reserve Bank of India (RBI) lends commercial banks, and reverse repo rate is the rate at which RBI borrows money from commercial banks.

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

(A)  Decrease in repo rate will increase cost of borrowing and decrease lending by commercial banks.

(B)  Increase in repo rate will decrease cost of borrowing and increase lending by commercial banks.

(C)  Increase in repo rate will decrease cost of borrowing and decrease lending by commercial banks.

(D)  Decrease in repo rate will decrease cost of borrowing and increase lending by commercial banks.

Answer: (D)

7. P, Q, R, S, T, U, V, and W are seated around a circular table.

(I) S is seated opposite to W.

(II) U is seated at the second place to the right of R.

(III) T is seated at the third place to the left of R.

(IV) V is a neighbor of S.

Which of the following must be true?

(A)  P is a neighbor of R.

(B)  Q is a neighbor of R.

(C)  P is not seated opposite to Q.

(D)  R is the left neighbor of S.

Answer: (C)

8. The distance between Delhi and Agra is 233 km. A car P started travelling from Delhi to Agra and another car Q started from Agra to Delhi along the same road 1 hour after the car P started. The two cars crossed each other 75 minutes after the car Q started. Both cars were travelling at constant speed. The speed of car P was 10 km/hr more than the speed of car Q. How many kilometers the car Q had travelled when the cars crossed each other?

(A)  66.6

(B)  75.2

(C)  88.2

(D)  116.5

Answer: (B)

9. For a matrix M = [mij], i. j= 1, 2, 3, 4, the diagonal elements are all zero and mij = −mij. The minimum number of elements required to fully specify the matrix is_______.

(A)  0

(B)  6

(C)  12

(D)  16

Answer: (B)

10. The profit shares of two companies P and Q are shown in the figure. If the two companies have invested a fixed and equal amount every year, then the ratio of the total revenue of company P to the total revenue of company Q, during 2013-2018 is ______.

(A)  15 : 17

(B)  16 : 17

(C)  17 : 15

(D)  17 : 16

Answer: (B)

XE: Engineering Sciences – A: Engineering Mathematics (compulsory)

Q1 – Q7 carry one mark.

1. Let A be a 4 × 3 non-zero matrix and let b be a 4 × 1 column vector. Then Ax = b has

(A)  a solution for every b.

(B)  no solution for some b.

(C)  a solution only when b = 0.

(D)  a solution if b and the columns of A form a linearly independent set.

Answer: (B)

2. Let x0, x1, x2, … be the sequence generated by the Newton-Raphson method applied to the function f(x) = x3 – 2x + 2 with x0 = 1 . Then the sequence

(A)  converges to 0.

(B)  becomes unbounded.

(C)  converges to a root of f(x).

(D)  does not converge.

Answer: (D)

3. Let z(t) be the solution of the initial value problem

If the planar curve parameterized by t having x-coordinate z(t) and y-coordinate  is closed, then necessarily

(A)  b > 0.

(B)  b < 0.

(C)  b = 0.

(D)  b is a non-zero rational number.

Answer: (B)

4. Let z be a complex number. Then the series 

(A)  converges for all z.

(B)  converges for |z| ≤ 1 and diverges for |z| > 1.

(C)  converges for z = 0 and diverges for any z ≠ 0.

(D)  converges for |z| < 1 diverges for |z| ≥ 1.

Answer: (A)

5. Let  be a vector field whose curl is zero. Then necessarily

(A)  a = b  c.

(B)  a = −b = c.

(C)  b = c.

(D)  b = −c.

Answer: (D)

6. Let f(x) be a continuous function on the real line such that for any x,  Then f(2) is ______.

Answer: (5 to 5)

7. The number of points at which the function  has local minima is _____.

Answer: (2 to 2)

8. Let f(t) be a real-valued differentiable function on (−1, 1) such that f(0) = 0 and 

Then the series   

(A)  converges but not absolutely.

(B)  is unbounded.

(C)  converges absolutely.

(D)  is bounded but does not converge.

Answer: (C)

9. Let X be a random variable with probability density function 

Let 0 < a < b. Then the probability P(X ≤ b \ X ≥ a) depends only on

(A)  b – a.

(B)  b

(C)  a

(D)  a + b.

Answer: (A)

10. Let A be a 3 × 3 matrix such that A2 = A. Then it is necessary that

(A)  A is the identity matrix or the zero matrix.

(B)  the determinant of A4 is either 0 or 1.

(C)  the rank of A is 3.

(D)  A has one imaginary eigenvalue.

Answer: (B)

11. Players A and B take turns to throw a fair dice with six faces. If A is the first player to throw, then the probability of B being the first one to get a six is _____ (round off to two decimal places).

Answer: (0.43 to 0.47)

XE: Engineering Sciences – B: Fluid Mechanics

Q1 – Q9 carry one mark each.

1. Figures given below show the velocity and shear stress profiles for the flow in a duct. In each option, ‘1’ represents velocity profile and ‘2’ represents shear stress profile.

Choose the correct option that closely represents the turbulent flow condition.

Answer: (A)

2. The variation of shear stress (r) against strain rate (du/dy) is given in the Figure. identify the line/curve among P, Q, R and S, that represents an ideal fluid.

(A)  S

(B)  P

(C)  Q

(D)  R

Answer: (B)

3. A body is under stable equilibrium in a homogeneous fluid, where CG and CB are center of gravity and center of buoyancy, respectively.

Two statements ‘P’ and ‘Q’ are given below:

P: For a fully submerged condition, CG should always be below CB

Q: For a floating body, CG need not be below CB

Choose the option that is valid for the present situation.

(A)  P is false; Q is True when metacentre is below CG

(B)  P is false; Q is True when metacentre is above CG

(C)  P is true; Q is True when metacentre is below CG

(D)  P is True; Q is true when metacentre is above CG

Answer: (D)

4. A laminar hydrodynamics boundary layer over a smooth flat plate is shown in the Figure. The shear stress at the wall is denoted by τw. Which one of the following conditions is correct.

(A)  Pressure is varying along ‘x’ and (τw)x1 > (τw)x2

(B)  Pressure is constant along ‘x’ and (τw)x2 > (τw)x1

(C)  Pressure is constant along ‘x’ and (τw)x1 > ((τw)x2

(D)  Pressure is varying along ‘x’ and (τw)x2 > (τw)x1

Answer: (C)

5. A non-dimensional number known as Weber number is used to characterize which one of the following flows.

(A)  Motion of fluid in open channel

(B)  Motion of fluid droplets

(C)  Motion of fluid at high velocity

(D)  Motion of fluid through a pipe

Answer: (B)

6. A uniform approach flow is subjected to an unsteady and periodic flapping plate as shown in the Figure. Tracer is released to obtain flow visualization lines, which are marked as ‘P’, ‘Q’ and ‘R’.

Choose the correct option that the line ‘R’ represents

(A)  Streakline

(B)  Streamline

(C)  Pathline

(D)  Timeline

Answer: (A)

7. The volume flow between any two points not lying on the same streamline in a flow field is equal to

(A)  Change in strain rate between the points

(B)  Change in vorticity between the points

(C)  Change in potential function between the points

(D)  Change in stream function between the points

Answer: (D)

8. A liquid flow through a horizontal smooth pipe the diameter 5 cm and discharges into a collection tank of dimension 50 cm × 50 cm × 50 cm. Time taken for a 10 cm rise of liquid level in the collection tank is 40 s.

The flow velocity in the pipe is ——– m/s (rounded off to two decimal places).

Answer: (0.30 to 0.33)

9. The potential function for a two dimensional incompressible flow filed is given as:

Magnitude of the velocity vector at point (2, 1) is ______m/s

Answer: (5 to 5)

Q10 – Q22 carry two marks each.

10. Column I represents a list of elementary plane flows and Column II represents flow past geometry obtained by superposition of these elementary plane flows.

The correct match between Columns I and II is,

(A)  P-3; Q-2; R-1; S-4

(B)  P-1; Q-2; R-3; S-4

(C)  P-3; Q-4; R-1; S-2

(D)  P-1; Q-4; R-3; S-2

Answer: (C)

11. The velocity field for a flow is  where t is time. Choose the correct option representing the total acceleration at (x, y, z, t)

Answer: (B)

12. An incompressible viscous fluid is placed between two infinite horizontal parallel plates as shown in the Figure. The plates move in opposite direction with constant velocities U1 and U2. The pressure gradient in the x-direction is zero and the only body force is due to the fluid weight. The flow is steady, laminar and two-dimensional. Assume velocity component in ‘y’ direction to be zero.

The correct expression for the velocity distribution between the plates is:

Answer: (A)

13. The stream function of a flow field is Ψ = k(x2 – y2x) where k is a constant. Which one of the following represents the voriticity?

(A)  -2k

(B)  2k(x + 1)

(C)  2k(x – 1)

(D)  -2k(x + 1)

Answer: (C)

14. Consider a two dimensional, incompressible steady flow of a Newtonian fluid in which the velocity field is u = −2xy, v = y2 – x2. Pressure gradients in the x-and y-directions are

Answer: (A)

15. A hydroelectric power plant takes in 30 m3/s of water through its turbine and discharges it to the atmosphere with V = 2 m/s. The total head loss in the turbine and penstock system is 20 m. (Assume turbulent flow with kinetic energy correction factor as 1.1. Density of water is 1000 kg/m3 and acceleration due to gravity, g is 10 m/s2).

The net  head available to the turbine for power generation is —————- m.

(rounded off to one decimal place).

Answer: (79.60 to 79.90)

16. Water flows at an average velocity, v of 10 m/s through a horizontal smooth tube of diameter, d 5 cm. The friction actor, f is 0.02. Head loss is obtained using Darcy-Weisbach relation The fluid pressure, p measured at various stations are reported in the table below. The length of the pipe, l between station 0 and station 6 is 6 m.

If acceleration due to gravity, g = 10 m/s2 and density of water = 1000 kg/m3, then the fluid pressure at station 6 is ________ kPa (rounded off to one decimal place)

Answer: (183.5 to 184.5)

17. A sphere model of 10 cm diameter is tested in water flowing at 2 m/s. The drag force is measured as 5 N. Prototype of 1.5 m in diameter is tested in air with dynamic similarity conditions. (Density of water is 1000 kg/m3, density of air is 1.2 kg/m3, viscosity of water is 0.001 Ns/m2 and viscosity of air is 1.78 × 105 Ns/m2).

Drag force experienced by the prototype is ______ N (rounded off to two decimal places).

Answer: (1.21 to 1.35)

18. A liquid of viscosity 1.74 × 103 Ns/m2 is flowing through a horizontal capillary tube of diameter 0.5 mm. The flow in the tube is steady, incompressible, and fully developed laminar flow. The pressure drop across two locations spaced 1 m apart in the tube is 1.0 MPa.

The flow rate in the tube _______ mm3/s.

Answer: (857 to 924)

19. A venturimeter with 75 mm diameter throat is placed in a 150 mm diameter pipeline carrying water at 25° The pressure drop between the upstream tap and the venture throat is 40 kPa. (Density of water = 1000 kg/m3).

The flow rate is ______ m3/s (rounded off to three decimal places).

Answer: (0.035 to 0.045)

20. A water jet with velocity  impinges normal to a moving flat plat with velocity  such that the jet splits equally into two halves as shown in Figure. The jet cross-sectional area is 2 cm2,  is 20 m/s and  is 10 m/s and density of water is 1000 kg/m3. Consider steady flow and neglect weight of the jet, weight of the plate and frictional losses.

The absolute value of the force required to keep the plate moving at constant velocity  is ____ N.

Answer: (20 to 20)

21. In an inverted manometer (as shown in the Figure), the pressure difference, pB – pA is 100 kPa.

Use specific gravity of oil as 08, density of water as 1000 kg/m3, density of mercury as 13600 kg/m3 and acceleration due to gravity as 10 m/s2.

The height of the water column, H is _____ cm. (rounded off to one decimal place).

Answer: (30.5 to 34.5)

22. An incompressible, steady flow with uniform velocity condition at the inlet between parallel plates is shown in Figure. The flow develops into a parabolic laminar profile with u = ay(y0 – y) at the downstream end, where ‘a’ is a constant. Assume unit depth of the plate. For U0 = 7.5 cm/s, y0 = 3 cm and the fluid with density, ρ = 800 kg/m3

The value of ‘a’ is _____.

Answer: (5 to 5 OR 500 to 500)

XE: Engineering Sciences – C: Materials Science

Q1 – Q9 carry one mark each.

1. A Pb-Sn sample of eutectic composition, containing α-and β-phases, is examined in a scanning electron microscope. The α-phase contains ~97% Pb (atomic number 82) while β-phase contains ~99 wt% Sn (atomic number 50). The ratio of number of backscattered electrons from α-phase to that from β-phase would be:

(A)  Less than 1

(B)  Equal to 1

(C)  Greater than 1

(D)  Equal to 0

Answer: (C)

2. Smallest or minimum feature size that can be theoretically resolved in an optical microscope does NOT depend on:

(A)  Refractive index of the medium between the lens and the focal point

(B)  Intensity of radiation

(C)  Wavelength of radiation

(D)  Numerical aperture of the objective lens

Answer: (B)

3. Following diagram shows a square 2-D lattice with a hexagonal motif(dark colored). The rotational symmetry element that must be present in the system is:

(A)  Six-fold rotation

(B)  Two-fold rotation

(C)  Three-fold rotation

(D)  Four-fold rotation

Answer: (B)

4. Density of states, D(E), in a three dimenstional solid varies with energy (E) as

(A)  E1/2

(B)  E0

(C)  E1/2

(D)  E3/2

Answer: (A)

5. The variation of molar volume (Vm) of a liquid showing glass transition temperature (Tg) while cooling from its melting temperature ™ is depicted by:

(A)  I

(B)  II

(C)  III

(D)  IV

Answer: (A)

6. Find the correct match between polymer name in Column I and the monomer type in Column II.

(A)  I-P, II-S, III-R, IV-Q

(B)  I-R, II-Q, III-S, IV-P

(C)  I-S, II-P, III-Q, IV-R

(D)  I-S, II-R, III-Q, IV-P

Answer: (C)

7. A ceramic has a fracture toughness (KIc) of 1 MPa.m1/2. If this ceramic is to be exposed to a maximum stress (σ) of 200 MPa, the maximum value of half crack length ‘a’ (in micrometer, μm), below which the material does not fail, is _____ μm (round off to one decimal place). Loading condition for the sample is shown in the schematic. Assume geometrical factor f = 1.2.

Answer: (5.3 to 5.7)

8. A ceramic material is periodically heated and cooled between 25°C and a higher temperature, Tf. During thermal cycling, the material remains dimensionally constrained. The material can withstand a maximum compressive stress of 200 MPa without failure. Material’s coefficient of thermal expansion is 7.5 × 106 °C1 and modulus of elasticity (E) is 200 GPa. The lowest value of T­f(in °C) at which material will fails is _______ °C (round-off to the nearest integer). Assume that there is no plastic deformation during thermal cycling.

Answer: (157 to 159)

9. During homogeneous solidification of a liquid metal, the radius of critical nucleus (in nanometer, nm) at a temperature TS which is below the melting point (Tm), is ______ nm (round-off to one decimal place). Given that γsl (solid liquid interfacial energy) is 0.18 J.m2 and ∆Gv (change in volume free energy upon transformation from liquid to solid) at TS is 0.18 × 109m3.

Answer: (1.29 to 2.1)

Q10 – Q22 carry two marks each.

10. Read the two statements related to sintering and select the correct option.

Statement-1: Sintering in vacuum leads to improved densification as compared to sintering under ambient (at atmospheric pressure) condition.

Statement-2: Closed pores formed during sintering inhibit full densification.

(A)  Both Statement-1 and Statement-2 are FALSE

(B)  Both Statement-1 and Statement-2 are TRUE

(C)  Statement-1 is TRUE but Statement-2 is FALSE

(D)  Statement-1 is FALSE but Statement-2 is TRUE

Answer: (B)

11. Select the correct option that appropriately matches the process to the material/product that can be fabricated using them.

(A)  I-S, II-P, III-R, IV-Q

(B)  I-S, II-R, III-Q, IV-P

(C)  I-S, II-P, III-Q, IV-R

(D)  I-P, II-R, III-Q, IV-S

Answer: (C)

12. Consider a FCC structured metal with lattice parameter a = 3.5 Å. If the material is irradiated using X-rays of wavelength λ = 1.54056 Å, the Bragg angle (2θ) corresponding to the fourth reflection will be:

(A)  88.21°

(B)  76.99°

(C)  99.35°

(D)  93.80°

Answer: (D)

13. The number of Schottky defects per mole of KCl at 300°C under equilibrium condition will be:

Given:

Activation energy for the formation of Schottky defect = 250 kJ.mol1

Avogadro number = 6.023 × 1023 mol1

Universal Gas Constant = 8.314 J.K1.mol1

(A)  1.21 × 1018

(B)  1.52 × 1016

(C)  9.75

(D)  2.42 × 1012

Answer: (D)

14. In an industry, the probability of an accident occurring in a given month is 1/100. Let P(n) denote the probability that there will be no accident over a period of ‘n’ months. Assume that the events of individual months are independent of each other. The smallest integer value of ‘n’ such that P(n) ≤ 1/2 is _____ (round off to the nearest integer).

Answer: (69 to 69)

15. For a FCC metal, the ratio of surface energy of {111} surface to {100} surface is _____ (round-off to two decimal places). Assume that only the nearest neighbor broken bonds contribute to the surface energy.

Answer: (0.84 to 0.90)

16. Pure silicon (Si) has a band gap (Eg) of 1.1 eV. This Si is doped with 1 ppm (part per million) of phosphorus atoms. Si contains 5 × 1028 atoms per m3 in pure form. At temperature T = 300 K, the shift in Fermi energy upon doping with respect to intrinsic Fermi level of pure Si will be ______ eV (with appropriate sign and round-off to two decimal places).

Intrinsic carrier concentration of Si, ni, is given as:

Given:

Mass of an electron, m = 9.1 × 1031 kg

Charge of an electron, e = 1.6 × 1019 C

Boltzmann constant, kB = 1.38 × 1023 J.K1

Planck’s constant, h = 6.6 × 1034 J.s1

Answer: (0.33 to 0.45)

17. The schematic diagram shows the light of intensity I0 incident on a material (shaded grey) of thickness, x, which has an absorption coefficient, α and reflectance, R. The intensity of transmitted light is I. The reflection of light (of a particular wavelength) occurs at both the surfaces (surfaces indicated in the diagram). The transmittance is estimated to be _______ (round-off to three decimal places).

Given that for the wavelength used, α = 103 m1 and R = 0.05.

Answer: (0.330 to 0.334)

18. Fe3O4 (also represented as FeO.Fe2O3) is a FCC structured inverse spinel (AB2O4) material where 1/8 of tetrahedral sites are occupied by half of B cations and 1/2 of the octahedral sites are occupied by remaining B and A cations. The magnetic moments of cations on octahedral sites are antiparalel with respect to those on tetrahedral sites. Atomic number of Fe is 26 and that of O is 8. The saturation magnetic moment of Fe3O4 per formula unit in terms of Bohr magnetons (μB) will be _____ μB. Ignore contribution from orbital magnetic moments.

Answer: (4 to 4)

19. A piezoelectric ceramic with piezoelectric coefficient (d­zz) value of 100 × 1012N1 is subjected to force Fz, of 10 N, applied normal to its x-y face, as shown in the figure. If relative dielectric constant (εr) of the material is 1100, the voltage developed along the z-direction of the sample will be _______ Volts (round-off to two decimal places). Ignore any nonlinear effects.

Given: Permittivity of free space (ε0) is 8.85 × 1012 F.m1.

Answer: (0.97 to 1.09)

20. Silicon carbide (SiC) particles are added to Aluminum (Al) matrix to fabricate particle reinforced Al-SiC composite. The resulting composite is required to possess specific modulus (E/ρ; E: elastic modulus, ρ: density) three times that of pure Al. Assuming iso-strain condition, the volume fraction of SiC particles in the composite will be _______ (round-off to two decimal places).

Answer: (0.36 to 0.45)

21. Isothermal weight gain per unit area (∆W/A, where ∆W is the weight gain (in mg) and A is the area (in cm2)) during oxidation of a metal at 600°C follows parabolic rate law, where, ∆W/A = 1.0 mg.cm2 after 100 min of oxidation. The ∆W/A after 500 min at 600°C will be _______ mg.cm2 (round-off to two decimal places).

Answer: (2.20 to 2.28)

22. A plain carbon steel sample containing 0.1 wt% carbon is undergoing carburization at 1100°C in a carbon rich surroundings with fixed carbon content of 1.0 wt% all the time. The carburization time necessary to achieve a carbon concentration of 0.46 wt% at a depth of 5 mm at 1100°C is ______ hour (round off to the nearest integer).

Given: Diffusivity of carbon in iron at 1100°C is 6.0 × 1011 m2.s1 and

Answer: (77 to 83)

XE: Engineering Sciences – D: Solid Mechanics

Q1 – Q9 carry one mark each.

1. Which among the following statements is true for a body moving on a dry surface under the action of applied forces?

(A)  Kinetic-friction force is zero.

(B)  Kinetic-friction force is equal to the static-friction force.

(C)  Kinetic-friction force is greater than the static-friction force.

(D)  Kinetic-friction force is lower than the static-friction force.

Answer: (D)

2. Consider an isotropic material with Young’s modulus E and Poisson’s ratio v. The bulk modulus of this material is given by_____.

Answer: (C)

3. A body subjected to ______ does not undergo change in volume.

(A)  uniform tension

(B)  pure shear

(C)  pure bending

(D)  hydrostatic pressure

Answer: (B)

4. The angular momentum of a particle moving under a central force is

(A)  zero

(B)  constant in both magnitude and direction.

(C)  constant in magnitude but not direction.

(D)  constant in direction but not magnitude.

Answer: (B)

5. According to Euler-Bernoulli beam theory, which one of the following statements best describes the state of a beam subjected to pure bending?

(A)  Transverse shear stress and transverse shear strain are zero.

(B)  Transverse shear stress is not zero but transverse shear strain is zero.

(C)  Transverse shear stress is zero but transverse shear strain is not zero.

(D)  Transverse shear stress and transverse shear strain are not zero.

Answer: (A)

6. A rigid square ABCD is subjected to planar forces at the corners as shown.

For this planar force system, the equivalent force couple system at corner A can be represented as

(A)  System I

(B)  System II

(C)  System III

(D)  System IV

Answer: (B)

7. A particle of mass 0.1 kg, which is released from rest, falls vertically downward under gravity in a fluid. The fluid offers a resistive force, which is linearly proportional to the particle velocity with 0.1 N.s/m as the constant of proportionality. The uniform gravitational acceleration is 10 m/s2 throughout the trajectory of the particle. The magnitude of the particle velocity (in m/s) at time 1 s after release (rounded off to two decimal places) is _______.

Answer: (6.25 to 6.40)

8. The state of two-dimensional plane stress at a point in a body is shown on the triangular element ABC, where cos θ = 3/5 and sin θ = 4/5. The normal stress (in MPa) on the plane AC is ________.

Answer: (90 to 90)

9. Consider two point masses m = 10 kg and M = 30 kg connected by a massless inextensible string passing over a massless and frictionless pulley with radius a = 100 mm as shown. The masses are released from rest and move vertically under the action of gravity. Let acceleration due to gravity, g = 10 m/s2. The tension (in N) in the string is_______.

Answer: (150 to 150)

Q10 – Q22 carry two marks each.

10. The cantilever beam AC is composed of two segments AB and BC that are rigidly connected at B. The flexural rigidity of the segment AB is EI, whereas, the flexural rigidity of the segment BC is assumed to be infinite. Determine the magnitude of slope at B due to a force P applied at C.

Answer: (D)

11. Determine the correctness or otherwise of the following Assertion [a] and Reason [r].

Assertion [a]: Efficient columns are designed so that most of the column’s cross-sectional area is located as far away as possible from the principal centroidal axes of the section.

Reason [r]: Load carrying capacity of columns will increase as the moment of inertia of the cross-section increases.

(A)  Both [a] and [r] are true and [r] is the correct reason for [a].

(B)  Both [a] and [r] are 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)

12. Consider the structure consisting of two massless elastic bars AB and BC, each of length L, cross-sectional area A, and Young’s modulus E. Connections at A, B, C are all pinned. A horizontal force P acts on the joint B as shown. Calculate the horizontal deflection of the joint B.

Answer: (B)

13. A rigid bar ABC of mass m and length L is hinged at A and has a point mass M attached at C. An elastic spring with linear stiffness k is attached at B as shown. Ignore the effect of gravity and damping. The natural frequency of small oscillations of this system is _______.

Answer: (D)

14. A beam of flexural rigidity EI is fixed at A and supported by a linear spring of stiffness k = EI/L3 at B. Determine the compressive force developed in the spring, when the beam is subjected to a uniformly distributed load of w per unit length.

Answer: (A)

15. The bar AB is fixed at A and is separated by a gap of 0.005 mm from wall at C as shown. The temperature of the bar is increased by 10° If the Young’s modulus of the bar is E = 200 GPa and the coefficient of thermal expansion is α = 10 × 106/°C, then the magnitude of the compressive stress (in MPa) developed in the bar is _________.

Answer: (9.99 to 10.00)

16. A thin walled spherical pressure vessel has mean radius 1000 mm and wall thickness 10 mm. The material has Young’s modulus 200 GPa and Poisson’s ratio 0.25. If the internal pressure is 100 MPa, the radial displacement (in mm) of the spherical pressure vessel ( rounded off to two decimal places) is _____.

Answer: (18.60 to 18.90)

17. A particles of mass m = 100 kg is released from rest and falls under gravity through a height of H = 1 mm directly onto an upright massless elastic bar of length L = 200 mm, Young’s modulus 200 GPa, and cross-sectional area 100 mm2. Assume the following during impact : (a) particle mass sticks to the bar, (b) the bar does not buckle, and (c) no energy is lost. Use gravitational acceleration g = 10 m/s2. The maximum axial compression (in mm) of the bar due to the impact (rounded off to three decimal places) is _______.

Answer: (4.477 to 4.487)

18. A pin-jointed truss has a pin support at A and a roller support at C. All the members are made of same material and have the same cross-section. Neglect the self-weight of the members. Due to the applied loading shown, the total number of zero force members is _______.

Answer: (7 to 7)

19. Two beams AB and BC having diameter of 100 mm are connected by an internal hinge at B. The structure is fixed at A and roller supported at C. Load of P = 1 kN is applied at B. Ignoring the effect of any transverse shear stress, the tensile stress (in MPa) developed at A due to bending (rounded off to three decimal places) is _______.

Answer: (10.160 to 10.340)

20. The shear force diagram for a beam AD, which is simply supported at A and D, is shown. The magnitude of the maximum bending moment (in kN.m) is ______ (rounded off to three decimal places).

Answer: (5.600 to 5.650)

21. A rectangular thin plate with Young’s modulus 200 GPa and Poisson’s ratio 0.30 is subjected to uniform stress distribution at its edges as shown. However, it is stated the dimension b of the plate does not change under the action of the stress components σxx and σyy. Considering micro-strains (in 106), the change in the length of dimension a (in mm) is ______ (rounded off to three decimal places).

Answer: (0.175 to 0.190)

22. A solid transmission shaft has length 10 m and diameter 100 mm. The shaft is supported by frictionless bearings at ends that act as simple supports. In addition to its self-weight acting as a uniformly distributed load per unit length, an operational torque of 5πm is applied. The density and yield strength of the material are 8000 kg/m3 and  350 MPa, respectively. Use gravitational acceleration as 10 m/s2 and ignore the effect of transverse shear stress. The factor of safety of the shaft as per maximum shear stress failure theory (Tresca criterion) is _________(rounded off to two decimal places).

Answer: (1.90 to 2.05)

XE: Engineering Sciences – E: Thermodynamics

Q1 – Q9 carry one mark each.

1. If x and y are two independent intensive properties of a thermodynamic system, then which relation among the followings fails to identify z as another thermodynamics property?

(A)  dz = x dy + y dx

(B)  dz = x dy – y dx

(C)  dz = 2 dy + dx

(D)   

Answer: (B)

2. Internal energy of a thermodynamic system is defined by the

(A)  zeroth law of thermodynamics

(B)  first law of thermodynamics

(C)  second law of thermodynamics

(D)  third law of thermodynamics

Answer: (B)

3. In a polytropic process described by PVn = constant, if n = 0, the process is called as

(A)  isobaric

(B)  isochoric

(C)  isothermal

(D)  isentropic

Answer: (A)

4. The relation between the coefficient of performance of a refrigerator (COP)R and the coefficient of performance of a heat pump (COP)HP is

(A)  (COP)HP = (COP)R + 1

(B)  (COP)HP = (COP)R − 1

(C)  (COP)HP = 1 − (COP)R

(D)  (COP)HP × (COP)R = 1

Answer: (A)

5. If L1, L2 and L3 are the latent heats of vaporization at the critical temperature of nitrogen, water and ammonia, respectively, then which one of the following is true?

(A)  L1 > L2 > L3

(B)  L1 > L2 and L­2 = L3

(C)  L1 < L2 < L3

(D)  L1 = L2 = L3

Answer: (D)

6. A new temperature scale (°N) has been proposed where the normal freezing and normal boiling points of water are marked as 500 °N and 100 °N, respectively. If the temperature of a system is measured to be 0 °N, its temperature according to the Celsius scale (in °C) is ________.

Answer: (125 to 125)

7. Let Z1 represents the compressibility factor of air at 2 bar and 600 K, and Z2 represents the compressibility factor of air at 1 bar and 300 K. If air is assumed to be an ideal gas having gas constant of 0.287 kJ/kg.K, then Z1/Z2 is _______.

Answer: (1 to 1)

8. The rate of heat received by a heat engine from a source at 900 K is600 kJ/s. The engine rejects heat to the sink of 300 K. The heat engine produces a power of 200 kW. The irreversibility rate (in kW) of the process is _______.

Answer: (198 to 202)

9. A engine working on the air standard Diesel cycle has compression ratio of 18. The cycle has a cut-off of 1.7. If the ratio of specific heats of air is 1.4, then the thermal efficiency (in %) of the cycle (rounded off to 1 decimal place) is ________.

Answer: (63.5 to 65.5)

Q10 – Q22 carry two marks each.

10. A system with rigid wall is initially at a temperature of T1. It is used as the heat source for a heat engine, which rejects heat to a reservoir maintained at T0 (T0 < T1). The specific heats of the system are constant. If the temperature of the system finally reduces to T0, then the maximum work recoverable from the heat engine per unit mass of the system is

Answer: (A)

11. A reversible heat engine is operating between two reservoirs maintained at T1 and T2, where T1 > T2. Which one of the following is the most effective option for increasing its thermal efficiency ?

(A)  increasing T1, while keeping T2 constant

(B)  decreasing T1, while keeping T­2 constant

(C)  increasing T2, while keeping T1 constant

(D)  decreasing T2, while keeping T1 constant

Answer: (D)

12. A 4-m3 reservoir contains 10 kg of a real gas at 200 K. If this gas follows the van der Waal’s equation of state with a = 0.0687 m6.kPa/kg2, b = 0.00657 m3/kg and R = 0.187 kJ/kg.K, then the reservoir pressure (in kPa) is

(A)  93.5

(B)  94.6

(C)  95.7

(D)  101.3

Answer: (B)

13. Air at a pressure of 86 kPa and specific volume of 1 m3/kg is heated at constant pressure till it reaches 627 ° Air is assumed to be an ideal gas with constant specific heats. It has the gas constant of 0.287 kJ/kg.K and ratio of specific heats of 1.4. The change in specific entropy of air (in kJ/kg.K) during this process will be

(A)  1.104

(B)  0.740

(C)  0.788

(D)  0.529

Answer: (A)

14. An air standard Otto cycle has compression ratio of 4. The compression ratio of this cycle is changed to 6. If the ratio of specific heats is 1.4, the percentage increase in its thermal efficiency will be

(A)  20.2

(B)  27.2

(C)  42.6

(D)  51.2

Answer: (A)

15. In a mixture of gas there are 0.1 kmol of oxygen (O2), 0.1 kmol of nitrogen (N­2) and 0.8 kmol of methane (CH4). If the molar mass of O2, N2 and CH4 are 32 kg/mol, 28 kg/mol and 16 kg/mol, respectively, then the mass fraction of N2 in the gas mixture is

(A)  0.100

(B)  0.170

(C)  0.148

(D)  0.680

Answer: (C)

16. A particular gas sample is initially maintained at 6000 cm3 and 100 kPa. It is compressed during a quasistatic process following the relation PV2 = constant. The compression continues till the volume becomes 2000 cm3. The magnitude of the corresponding work transfer (in kJ) (rounded off to 20 decimal places) is

Answer: (1.15 to 1.25)

17. Carbon dioxide (CO2) enters an adiabatic rigid nozzle steadily at 1 MPa and 500 °C with a mass flow rate of 1.5 kg/s. The inlet area of the nozzle is 40 cm2 and the exit velocity is 10 times of that at the inlet. If CO2 can be considered as an ideal gas with gas constant of 0.19 kJ/kg.K and the ratio of specific heats of 1.29, the exit temperature (in K) (rounded off to 1 decimal place) is ________.

Answer: (590 to 600)

18. A closed system containing 8 kg of gas undergoes an expansion process following the relation PV2 = constant. The initial and final pressures are 1 MPa and 5 kPa, respectively, while the initial volume is 1 m3. If the specific internal energy of the gas decreases by 40 kJ/kg during the process, the heat transfer (in kJ) associated with the process (rounded off to 1 decimal place) is _____.

Answer: (2610 to 2614)

19. Saturation pressure of water at 5 °C is 0.8725 kPa. If the latent heat of vaporization is 2489.1 kJ/kg and gas constant is 0.4615 kJ/kg.K, then the saturation pressure at 10 °C (in kPa) (rounded off to 2 decimal places) is ________.

Answer: (1.20 to 1.26)

20. The turbine inlet conditions of a Rankine cycle are 10 MPa and 500 °C, while the condenser pressure is 10 kPa. The enthalpy and entropy of saturated liquid at 10 kPa are 191.8 kJ/kg and 0.6492 kJ/kg.K, respectively, while the enthalpy and entropy of vapourization at 10 kPa are 2392.1 kJ/kg and 7.4996 kJ/kg.K, respectively. The enthalpy and entropy at the inlet to the turbine are 3375.1 kJ/kg and 6.5995 kJ/kg.K, respectively. The condenser outlet has saturated liquid. Neglecting the pump work, the thermal efficiency (in %) of the cycle (rounded off to 1 decimal place) is _______.

Answer: (39 to 42)

21. The minimum and maximum temperatures of an air standard Brayton cycle are 300 K and 1100 K, respectively. The pressure ratio of this cycle is 6. The ratio of specific heats is 1.4 and the specific heats are constant. For this cycle, the ratio of network output to the turbine work (rounded off to 2 decimal places) is _______.

Answer: (0.52 to 0.57)

22. The specific humidity of air at 100 kPa is 0.015 kg of vapour per kg of dry air. The partial pressure of vapour (in kPa) in the existing state (rounded off to 2 decimal places) is ________.

Answer: (2.30 to 2.40)

XE: Engineering Sciences – F: Polymer Science and Engineering

Q1 – Q9 carry one mark each.

1. The solvent in which chain transfer is maximum in a radical polymerization is

(A)  Benzene

(B)  Chloroform

(C)  Carbon tetrachloride

(D)  Toluene

Answer: (C)

2. The monomer that can NOT be polymerized by anionic polymerization is

(A)  Styrene

(B)  Ethyl vinyl ether

(C)  Butadiene

(D)  Methyl methacrylate

Answer: (B)

3. The elastomer retaining flexibility at the lowest temperature is

(A)  Styrene butadiene rubber

(B)  Nitrile rubber

(C)  Silicone rubber

(D)  Butyl rubber

Answer: (C)

4. The polymer with minimum number of branches is

(A)  LDPE

(B)  LLDPE

(C)  HDPE

(D)  VLDPE

Answer: (C)

5. The nearest value of conductivity of Nylon 6 is

(A)  106 S/m

(B)  100 S/m

(C)  1013 S/m

(D)  1021 S/m

Answer: (C)

6. Aramid is a

(A)  Polyamide

(B)  Polyether

(C)  Polyester

(D)  Polyimide

Answer: (A)

7. A miscible blend in 1 : 1 (by weight) composition is formed with

(A)  Polystyrene and polybutadiene

(B)  Polystyrene and poly(phenylene oxide)

(C)  Polystyrene and poly(methyl methacrylate)

(D)  Polystyrene and poly(dimethyl siloxane)

Answer: (B)

8. Dicumyl peroxide is

(A)  Plasticizer

(B)  Cross-linking agent

(C)  Mold release agent

(D)  Peptizer

Answer: (B)

9. The change in stress of a polymer as a function of time at a fixed strain is known as

(A)  Fatigue

(B)  Creep

(C)  Stress relaxation

(D)  Fracture toughness

Answer: (C)

Q10 – Q22 carry two marks each.

10. Match the polymers in Column A with their corresponding polymerization methods of Column B

(A)  P-3, Q-2, R-4, S-1

(B)  P-4, Q-3, R-2, S-1

(C)  P-2, Q-3, R-4, S-1

(D)  P-1, Q-3, R-4, S-2

Answer: (C)

11. Match the appropriate processing technique in Column A to fabricate the product in Column B

(A)  P-2, Q-3, R-4, S-1

(B)  P-3, Q-4, R-2, S-1

(C)  P-4, Q-2, R-1, S-3

(D)  P-4, Q-3, R-1, S-2

Answer: (D)

12. Match the appropriate characterization technique in Column A used to determine the polymer attributes in Column B

(A)  P-2, Q-3, R-4, S-1

(B)  P-3, Q-4, R-1, S-2

(C)  P-2, Q-4, R-1, S-3

(D)  P-4, Q-1, R-3, S-2

Answer: (D)

13. Match each additive in Column A with its function given in Column B

(A)  P-2, Q-3, R-1, S-2

(B)  P-3, Q-4, R-1, S-2

(C)  P-4, Q-3, R-2, S-1

(D)  P-1, Q-3, R-4, S-2

Answer: (B)

14. Plot of shear stress against rate for various types of fluids is given below. The appropriate assignment for P, Q, R and S is

(A)  P-Dilatant, Q-Bingham plastic, R-Pseudoplastic, S-Newtonian

(B)  P-Bingham plastic, Q-Pseudoplastic, R-Dilatant, S-Newtonian

(C)  P-Pseudoplastic, Q-Bingham  plastic, R-Newtonian, S-Dilatant

(D)  P-Newtonian, Q-Diltant, R-Pseudoplastic, S-Bingham plastic

Answer: (B)

15. The number average molecular weight of a polyester formed from equimolar mixture of adipic acid and ethylene glycol at a conversion of 99.5% will be _____ (round off to nearest integer).

Answer: (17150 to 17250)

16. For a freely jointed linear polyethylene chain with molar mass of 1.4 × 105 g mol1, the value of root mean square end-to-end distance in nanometer is _________(round off to 1 decimal place). [Given: C-C bond length = 0.154 nanometer]

Answer: (15.3 to 15.5)

17. Viscosity measurements were performed for a set of PMMA solutions of different concentrations in toluene at 25° The plot of reduced viscosity against concentration (c) of the PMMA solutions produced an intercept of 21.0 cm3 g1 on the ordinate at c = 0. The value of viscosity average molecular weight of PMMA in toluene at 25 °C is ________ (round off to nearest integer). [Given: Mark-Houwink constants K = 7.5 × 103 cm3 g1 and a = 0.72 for PMMA is toluene at 25°C]

Answer: (60000 to 62000)

18. Glass fibre reinforced PP composite is to be prepared with 20 volume % of glass fibre. The densities of glass fibre and PP are 2540 kg m3 and 900 kg m3, respectively. The mass of glass fibre required to produce 1 kg of the composite in kg is ______ (round off to 2 decimal places).

Answer: (0.40 to 0.42)

19. A polymer solution flows through a cylindrical tube with a diameter of 4 mm at a volumetric flow rate of 109 m3 s1. Under laminar flow condition and assuming the polymer solution to be a Newtonian fluid with viscosity 102 N s m2, the value of pressure drop per unit length of the tube in N m3 is _______ (round off the nearest integer). [Consider the value of π as 3.14]

Answer: (15800 to 16000)

20. A molten polymer with a bulk modulus of 1 GPa is pressurized to 200 MPa during injection molding.. The fractional decrease in volume of the molten polymer at this pressurized condition is ________ (round off to 1 decimal place).

Answer: (0.2 to 0.2)

21. Assume that each cross-link produced by vulcanization of polyisoprene contains an average of two sulphur atoms and that the sulphur is present only in the cross-links. If 40% of the isoprene units are cross-linked, the sulphur content in weight percentage is _______ (round off to 2 decimal places)/.

Answer: (15.75 to 15.95)

22. A tensile force of 160 N is applied to a piece of vulcanized rubber of dimension 30 mm × 4 mm × 4 mm. Assuming the vulcanized rubber to be incompressible, if the sample is elongated to 150% of its original length under the same applied force, the true stress in N mm−2 will be ________ (round off to 1 decimal place).

Answer: (14.9 to 15.1)

XE: Engineering Sciences – G: Food Technology

Q1 – Q9 carry one mark each.

1. The enzyme majorly involved in postmortem degradation of muscle proteins is

(A)  Trypsin

(B)  Calpin

(C)  Transglutaminase

(D)  Pepsin

Answer: (B)

2. Which of the following is the correct pair of essential fatty acids?

(A)  Oleic acid and Lenoleic acid

(B)  Lenoleic acid and Linolenic acid

(C)  Linolenic acid and Lauric acid

(D)  Linolenic aci and Oleic acid

Answer: (B)

3. Nisin A is produced by

(A)  Aspergillus niger

(B)  Acteobacter acetis

(C)  Lactobacillus lactis

(D)  Clostridium perfringers

Answer: (C)

4. Which of the following bacteria will stain purple color after Gram staining?

(A)  Bacillus subtilis

(B)  Escherichia coli

(C)  Pseudomonas aeruginaosa

(D)  Yersinia pestis

Answer: (A)

5. The enzyme system used for removal of glucose form egg white prior to its drying consists of

(A)  Glucose oxidase and Catalase

(B)  Glucosidase and Glucoisomerase

(C)  Glucoisomerase and Catalase

(D)  Glucoamylase and Glucose oxidase

Answer: (A)

6. The INCORRECT pair of food borne illness and its causative microorganism is

(A)  Brucellosis-Brucella Sp.

(B)  Peptic ulcers-Bacillus subtilis

(C)  Bubonic plague-Yersinia pestis

(D)  Q fever-Coxiella burnatii

Answer: (B)

7. Which of the following is commonly used as a preservative in the tomato sauce?

(A)  Sodium sulphite

(B)  Potassium sorbate

(C)  Potassium sulphite

(D)  Sodium benzoate

Answer: (D)

8. The velocity of 2.2 μm diameter fat particles inside a centrifuge, running at 6000 rpm and 20 °C, is 0.25 mm s1. The velocity of 1.5 μm diameter fat particles inside the same centrifuge running at 7500 rpm and same temperature (round of to 2 decimal places) will be ______ mm s1.

Answer: (0.15 to 0.21)

9. The initial population of a bacterial strain increases from 1 × 104 cells per mL to 1 × 106 cells per mL in 120 minutes. The generation time for this strain (round off to 2 decimal places) is _______ minutes.

Answer: (17.00 to 19.00)

Q10 – Q22 carry two marks each.

10. Match the protein in Column I with its food source in Column II.

(A)  P-4, Q-1, R-2, S-3

(B)  P-4, Q-3, R-1, S-2

(C)  P-2, Q-3, R-1, S-4

(D)  P-2, Q-4, R-1, S-3

Answer: (D)

11. Match the carbohydrate in Column I with corresponding enzyme used for its hydrolysis in Column II.

(A)  P-3, Q-2, R-1, S-4

(B)  P-2, Q-4, R-1, S-3

(C)  P-1, Q-2, R-3, S-4

(D)  P-4, Q-3, R-1, S-2

Answer: (A)

12. Match the edible oil refining stage in Column I with its purpose in Column II.

(A)  P-3, Q-1, R-2, S-4

(B)  P-1, Q-4, R-2, S-3

(C)  P-4, Q-3, R-1, S-2

(D)  P-3, Q-4, R-2, S-1

Answer: (D)

13. Match the food material in Column I with its related term in Column II.

(A)  P-4, Q-2, R-1, S-3

(B)  P-3, Q-4, R-1, S-2

(C)  P-3, Q-4, R-2, S-1

(D)  P-1, Q-3, R-4, S-2

Answer: (B)

14. Match the component/system in Column I with the peeling method for fruits and vegetables in Column II.

(A)  P-4, Q-3, R-2, S-1

(B)  P-3, Q-4, R-1, S-2

(C)  P-4, Q-3, R-1, S-2

(D)  P-3, Q-4, R-2, S-1

Answer: (C)

15. Which among the given options correctly explains the nature of the microbial culture represented by curves 1, 2 and 3 in the following figure?

Answer: (B)

16. Match the equation/law in Column I with its application in Column II.

(A)  P-1, Q-3, R-4, S-2

(B)  P-2, Q-3, R-1, S-4

(C)  P-2, Q-3, R-4, S-1

(D)  P-4, Q-3, R-1, S-2

Answer: (C)

17. Match the absorber used in modified atmosphere packaging and storage in Column I with the scavenger in Column II.

(A)  P-3, Q-2, R-4, S-1

(B)  P-1, Q-2, R-4, S-3

(C)  P-2, Q-3, R-4, S-1

(D)  P-3, Q-2, R-1, S-4

Answer: (A)

18. During extrusion cooking, food materials are generally subjected to a combination of

(A)  high shear and low pressure

(B)  high temperature and high shear

(C)  low shear and high temperature

(D)  low shear and low pressure

Answer: (B)

19. The whole milk at 22°C is pumped through a stainless steel pipe at a flow rate of 3 L s1. The length and inner diameter of the pipe are 40 m and 4 cm, respectively. If viscosity and density of the milk at the pumping temperature of 0.2 Pa s and 1032 kg m3, respectively, the Revnolds number (rounded off to nearest integer) will be ______.

Answer: (491.00 to 495.00)

20. A hammer mill, operating at a feed rate of 108 ton h1, consumes 10 kW power for reducing size of wheat gain from 3.92 mm to 1.25 mm. If Bond’s law holds good, the feed rate (round off to 2 decimal places) for reducing the size of the wheat grain to 0.75 mm at the same power consumption level is _______ ton h1.

Answer: (63.00 to 67.00)

21. During spray drying of a milk sample, inlet and outlet temperatures are maintained at 132°C and 80°C, respectively. If the ambient temperature is 29°C, the thermal efficiency (round of to 2 decimal places) of the dryer will be _______ %.

Answer: (49.00 to 52.00)

22. An orange juice flowing at 0.80 kg s1 enters a counter current double pipe heat exchanger at 20°C and leaves at 72° Inlet and outlet temperatures of the hot water used as heating medium in the exchanger are 81°C and 74°C, respectively. The specific heat of the orange juice is 3.74 kJ kg1 K1 and overall heat transfer coefficient is 492 W m2 K1. The heat transfer surface are (round off to 2 decimal places) will be ______m3.

Answer: (11.00 to 14.00)

XE: Engineering Sciences – H: Atmospheric and Oceanic Sciences

Q1 – Q9 carry one mark each.

1. In the northern hemisphere, the flow in the middle depths of the ocean is geostrophic. As we go down from that level and start approaching the bottom of the ocean, the flow deflects to the left of the geostrophic current because

(A)  friction decreases and Coriolis force increases

(B)  friction decreases and Coriolis force decreases

(C)  friction increases and Coriolis force increases

(D)  friction increases and Coriolis force decreases

Answer: (D)

2. Which one of the following is the definition of a monsoon?

(A)  Seasonal reversal of wind direction

(B)  High rainfall

(C)  Occurs in the summer

(D)  Occurs in the tropics

Answer: (A)

3. Anthropogenic emission of ______ is the main contributor to the ongoing ocean acidification.

(A)  Methane

(B)  Carbon dioxide

(C)  Nitrous oxide

(D)  Sulpuric acid

Answer: (B)

4. What are phytoplankton?

(A)  Microscopic animal life floating on surface of water bodies

(B)  Pollen floating freely on surface of water bodies

(C)  Microscopic plant life floating on surface of water bodies

(D)  Microscopic plant life living on the floor of water bodies

Answer: (C)

5. Consider the two atmospheric virtual temperature profiles observed in Delhi given in Figures (i) and (ii) blow.

At what times of the day are you most likely to see such profiles?

(A)  (i) Midnight and (ii) noon

(B)  (i) 3 pm and (ii) 3 am

(C)  (i) Sunrise and (ii) sunset

(D)  (i) 3 am and (ii) 3 pm

Answer: (B)

6. A south-easterly wind is blowing towards which direction?

(A)  135°

(B)  157.5°

(C)  315°

(D)  225°

Answer: (C)

7. Consider a dry parcel at 30°C in an isothermal environment at 25° The parcel rises adiabatically by 1 km. Assuming g = 10 ms2 and air density = 1 kgm3, the buoyancy force at the new location (rounded off to 2 decimal places) is _______ ms2.

Answer: (-0.17 to -0.16)

8. The emissivity of polluted air that reflects and transmits 20% and 60% of the incoming solar radiation, respectively, at a given wavelength (correct up to 1 decimal place) is ______.

Answer: (0.2  to 0.2)

9. Given that the angular velocity of rotation of the Earth = 7.3 × 105 s1, the period of inertial oscillations generated in the oceans by surface winds at 30° N latitude (rounded off to the nearest integer) is ______ hours.

Answer: (24 to 24)

Q10 – Q22 carry two marks each.

10. Consider a high pressure centre in the northern hemisphere with tangential winds of 10 ms1 at a distance of 500 km from the centre. Assuming solid body rotation principles, what is the relative vorticity of the flow?

(A)  2 × 105 s1

(B)  −2 × 105 s1

(C)  4 × 105 s1

(D)  −4 × 105 s1

Answer: (D)

11. Which one of the following statements is true for atmospheric and oceanic general circulation models?

(A)  Vertical velocity is ignored in oceanic models but not in atmospheric models.

(B)  Boussinesq approximation is adequate in oceanic models but not in atmospheric models.

(C)  Atmospheric models need a longer spin-up and integration time than oceanic models.

(D)  Atmospheric models need parameterizations for subgrid scale processes but oceanic models do not.

Answer: (B)

12. Consider a scenario where air temperature increases by 2 ° We know that saturation vapour pressure for water is increases with temperature. As a result of this effect, the water vapour content of the atmosphere will _____ and the net warming will be ______ than 2°C. The correct pair of words to fill in the blanks (in the right order) is

(A)  increase, more

(B)  increase, less

(C)  decrease, more

(D)  decrease, less

Answer: (A)

13. The prevailing Trade winds over the Equator in the Pacific Ocean result in piling up of water in the ______ part of the ocean. As a result, the gradients of the thermocline and the ocean surface have ______ signs. The correct pair of words to fill in the blanks (in the right order) is

(A)  western, opposite

(B)  western, same

(C)  eastern, opposite

(D)  eastern, same

Answer: (A)

14. Consider two different cases, shown in the Figures (i) and (ii) below, with two layers of water of same density on top of each other.

Which one of the following statements is true about convective plumes across the interface of the two layers?

(A)  Upward convective plumes in (i) and downward convective plumes in (ii)

(B)  Downward convective plumes in (i) and upward convective plumes in (ii)

(C)  No convective plume in (i) and (ii)

(D)  No convective plume in (i) but upward convective plumes in (ii)

Answer: (B)

15. During the Indian summer monsoon, surface outgoing longwave radiation (OLR) over the Arabian Sea is often observed to be low because

(A)  of enhanced convection

(B)  monsoon winds advect the OLR away into the Indian subcontinent

(C)  monsoon clouds limit incoming solar radiation

(D)  surface Bowen ratio is low

Answer: (C)

16. A tsunami wave in the ocean is approaching the coast. Assuming g = 10 ms2, the correct group speed of the wave at a depth of 1 km is

(A)  1 ms1

(B)  10 ms1

(C)  100 ms1

(D)  1000 ms1

Answer: (C)

17. A tornado is in cyclostrophic balance where the horizontal pressure gradient and centrifugal forces balance each other. Consider a tornado with 100 m radius and a tangential velocity of 100 ms1 at the edge. Assuming air density = 1 kgm3, the magnitude of the pressure-drop between the centre and the edge of the tornado is ______ kgm1 s2.

Answer: (10000 to 10000)

18. While driving south a distance of 1000 km, the temperature outside your car increases from 10 °C to 20 ° Assuming the air is completely dry, g = 10 ms2 and Coriolis parameter = 104 s1, the vertical gradient of the geostrophic wind (rounded off to 2 decimal places) is _______ ms1km1.

Answer: (3.40 to 3.50)

19. A westerly wind of 10 ms1 is blowing at a location in the Pacific Ocean in the northern hemisphere. Assuming density of sea water = 1000 kgm3, Coriolis parameter = 104 s1 and drag coefficient for sea water = 106, the Ekman transport due to the wind at that location is ______ kgm1 s1.

Answer: (-1000 to -1000)

20. Mx and My represent the ocean mass transport in the x and y directions, respectively. Lx and Ly are the corresponding east-west and north-south length scales. For a typical equatorial ocean gyre, if the ratio of zonal to meridional mass transport ≈ 10, then Lx ≈ _______ Ly.

Answer: (10 to 10)

21. Assume the pressure varies exponentially with height: p(z) = p0ez/H, where p(z) is the pressure at a height z above the surface, p0 is the surface pressure, and the scale height H= 7.5 km. Under these conditions, one-fourth of the total mass of the atmosphere lies above a height (rounded off to 1 decimal place) of km above the surface.

Answer: (10.3 to 10.5)

22. Consider an atmospheric column of depth 300 m at the Earth’s surface with an average temperature of 300 K. If the temperature of the layer rises by ∆T = 10 °C, the layer depth h will increase by ∆ Assuming ∆T/T ≈ ∆h/h, air density remains unchanged at 1 kgm3 and g = 10 ms2, the change in surface pressure is _______ kgm1s2.

Answer: (-100 to -100 or 100 to 100)

GATE Exam 2020 Textile Engineering and Fibre Science (TF) Question Paper With Answer Key

GATE-2020

TF: Textile Engineering and Fibre Science

GA- General Aptitude

Q1 – Q5 carry one mark each.

1. This book, including all its chapters, ______ interesting. The students as well as the instructor ______ in agreement about it.

(A)  is, was

(B)  are, are

(C)  is, are

(D)  were, was

Answer: (C)

2. People were prohibited ______ their vehicles near the entrance of the main administrative building.

(A)  to park

(B)  from parking

(C)  parking

(D)  to have parked

Answer: (B)

3. Select the word that fits the analogy:

Do : Undo :: Trust : ________

(A)  Entrust

(B)  Intrust

(C)  Distrust

(D)  Untrust

Answer: (C)

4. Stock markets ________ at the news of the coup.

(A)  poised

(B)  plunged

(C)  plugged

(D)  probed

Answer: (B)

5. If P, Q, R, S are four individuals, how many teams of size exceeding one can be formed, with Q as a member ?

(A)  5

(B)  6

(C)  7

(D)  8

Answer: (C)

Q6 – Q10 carry two marks each.

6. Non-performing Assets (NPAs) of a bank in India is defined as an asset, which remains unpaid by a borrower for a certain period of time in terms of interest, principal, or both. Reserve Bank of India (RBI) has changed the definition of NPA thrice during 1993-2004, in terms of the holding period of loans. The holding period was reduced by one quarter each time. In 1993, the holding period was four quarters (360 days).

Based on the above paragraph, the holding period of loans in 2004 after the third revision was ______ days.

(A)  45

(B)  90

(C)  135

(D)  180

Answer: (B)

7. Select the next element of the series: Z, WV, RQP, ______

(A)  LKJI

(B)  JIHG

(C)  KJIH

(D)  NMLK

Answer: (C)

8. In four-digit integer numbers from 1001 to 9999, the digit group “37” (in the same sequence) appears ______ times.

(A)  270

(B)  279

(C)  280

(D)  299

Answer: (C)

9. Given a semicircle with O as the centre, as shown in the figure, the ratio  is ______. where  are chords.

(A)  √2

(B)  √3

(C)  2

(D)  3

Answer: (A)

10. The revenue and expenditure of four different companies P, Q, R and S in 2015 are shown in the figure. If the revenue of company Q in 2015 was 20% more than that in 2014, and company Q had earned a profit of 10% on expenditure in 2014, then its expenditure (in million rupees) in 2014 was _______.

(A)  32.7

(B)  33.7

(C)  34.1

(D)  35.1

Answer: (C)

TF: Textile Engineering and Fibre Science

Q1 – Q25 carry one mark each.

1. For the matrix  the eigenvalues of matrix A2 are

(A)  1, 0, 1

(B)  1, 0, 0

(C)  1, 1, 0

(D)  1, 1, 1

Answer: (D)

2. The integrating factor of the differential equation  is

(A)  ex

(B)  ex

(C)  xex

(D)  xex

Answer: (A)

3. Laplace transform of cosh(t) is

Answer: (C)

4. In wool, the sulfur containing amino acid is

(A)  Alanine

(B)  Cystine

(C)  Glycine

(D)  Serine

Answer: (B)

5. Viscose rayon is soluble in

(A)  Acetone

(B)  Chloroform

(C)  Formic acid 85% (v/v)

(D)  Sulfuric acid 59% (w/w)

Answer: (D)

6. In carding, the highest draft is kept between

(A)  Lap roller and feed roller

(B)  Feed roller and licker-in

(C)  Licker-in and cylinder

(D)  Cylinder and doffer

Answer: (B)

7. The spinning system in which one revolution of twisting element imparts several turns to the fibre strand is

(A)  Ring

(B)  Rotor

(C)  Friction

(D)  Wrap

Answer: (C)

8. The technology that does NOT produce a nonwoven fabric is

(A)  Spunbonding

(B)  Hydroentangling

(C)  Meltblowing

(D)  Braiding

Answer: (D)

9. For the same, yarn and fabric sett, the weave that gives the maximum tearing strength is

(A)  Plain

(B)  2 × 2 matt

(C)  5-end satin

(D)  2/1 twill

Answer: (C)

10. Two yarns have variance of strength as V1 and V2. If V1 < V2, the variance ratio ‘F’ would be

(A)  V2/V1

(B)  V1/V2

(C)  V12/V22

(D)  V22/V12

Answer: (A)

11. Cotton fibre length parameter that CANNOT be obtained from Baer Sorter diagram is

(A)  Mean length

(B)  Dispersion

(C)  Uniformity ratio

(D)  Modal length

Answer: (C)

12. The purpose of cabonization of wool fibres is to remove

(A)  Waxy matter

(B)  Surface scales

(C)  Vegetable matter

(D)  Ortho-cortex

Answer: (C)

13. Bio-polishing of cotton fabrics is done using

(A)  Cellulase

(B)  Amylase

(C)  Proteinase

(D)  Esterase

Answer: (A)

14. For the given system of linear equations, 2x – z = 1; 5x + y = 7; y + 3z = 5, the sum of x, y and z is_______.

Answer: (4 to 4)

15. If F = xi + yj + zk, then the magnitude of ∇ × F is ______.

Answer: (0 to 0)

16. A polypropylene filament is drawn in two stages with draw ratios of 1.5 and 2 respectively. The overall draw ratio is _______.

Answer: (3 to 3)

17. The refractive indices of a filament in axial and radial directions are 1.58 and 1.52 respectively. The birefringence of the filament (correct up to 2 decimal places) is ______.

Answer: (0.06 to 0.06)

18. A twin-delivery drawframe, running at a delivery speed of 800 m/min with an efficiency of 95%, is producing 5.39 ktex sliver. The rate of production of the drawframe in kg/h (rounded off to 2 decimal places) is _____.

Answer: (537.00 to 539.00)

19. The diameter (mm) of a yarn having twist of 700 turns per meter and surface-twist angle of 20° (rounded off to 2 decimal places) is ______.

Answer: (0.16 to 0.18)

20. A magazine creel has 800 package holders. The effective creel capacity (number) is ______.

Answer: (400 to 400)

21. A shuttle loom is running at 180 picks per minute. The angular velocity of crank shaft (degree/second) is ______.

Answer: (1080 to 1080)

22. The length (km) of 5 kg of 30 Ne yarn (rounded off to the nearest integer) is _____.

Answer: (253 to 255)

23. The limit irregularity and measured irregularity of a yarn are 8.4% and 9.6%, respectively. The index of Irregularity (rounded off to 2 decimal places) is _____.

Answer: (1.10 to 1.15)

24. A padding mangle is processing a fabric at 1320 m/h. The bottom bowl of the mangle is rotating at 25 rpm. Assuming zero slippage at the nip, the diameter (cm) of this bowl is ______.

Answer: (28.00 to 29.00)

25. A Procion H (monochlorotriazine based) reactive dye used for printing of cotton has a molecular weight of 471. Taking the atomic weight of H = 1, C = 12, N = 14, O = 16, Cl = 35.5, the molecular weight of the fully hydrolyzed dye (correct up to 1 decimal place) would be _______.

Answer: (452.5 to 452.5)

Q26 – Q55 carry two marks each.

26. Let  The value o L is

(A)  0

(B)  1

(C)  2

(D)  ∞

Answer: (B)

27. The solution of the differential equation  which satisfies the conditions, y(0) = 0, y’(0) = 3 is

(A)  ex

(B)  ex

(C)  ex + e2x

(D)  ex – e2x

Answer: (D)

28. In melt spinning of poly(ethylene terephthalate), pre-drying of polymer chips is essential to avoid

(A)  Hydrolytic degradation

(B)  Oxidative degradation

(C)  Microbial degradation

(D)  Photo-induced degradation

Answer: (A)

29. Determine the correctness or otherwise of the following Assertion [a] and Reason [r]

[a]: Caprolactam is polymerized in the presence of small amount of water of produce fibre grade nylon 6.

[r]: Water reacts as a catalyst and converts caprolactam to aminocaproic acid.

(A)  Both [a] and [r] and 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)

30. Determine the correctness or otherwise of the following Assertion [a] and Reason [r]

[a]: Melting point of nylon 66 fibre is much higher that of polyethylene fibre.

[r]: The molecular weight of nylon 66 fibre is significantly higher than that of polyethylene fibre.

(A)  Both [a] and [r] and 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: (D)

31. Carding of polyester fibres requires that the values of wire-point density (points/inch2) of

(P) Licker-in       (Q) Cylinder    (R) Flat

follow the order

(A)  P < Q < R

(B)  P < R < Q

(C)  Q < R < P

(D)  Q < P < R

Answer: (B)

32. For combing with forward feed, the given parameters are:

Detachment setting = 15 mm, length of feed per combing cycle = 6 mm, Longest fiber length = 30 mm. According to Gegauff’s theory, the noil (%) would be

(A)  9

(B)  16

(C)  30

(D)  49

Answer: (B)

33. Determine the correctness or otherwise of the following Assertion [a] and Reason [r]

[a]: Open-loop autolevelling system needs a signal storage device with time delay function.

[r]: The signal must be stored until the material reaches the adjusting point.

(A)  Both [a] and [r] and 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)

34. If both the concentration (%, w/w) of size paste and target add-on are 12%, the total wet pick-up (kg) by 12 kg bone-dry warp sheet is

(A)  6

(B)  12

(C)  18

(D)  24

Answer: (B)

35. At front centre (0°) and a back centre (180°) of a shuttle loom.

(A)  The sley velocities are the same but accelerations are different

(B)  The sley velocities are different but accelerations are the same

(C)  The sley velocities are the same and also accelerations are the same

(D)  The sley velocities are different and also accelerations are different

Answer: (A)

36. Match the looms listed in Group with the corresponding components given in Group II. The correct option is

(A)  P-1, Q-4, R-2, S-3

(B)  P-1, Q-2, R-4, S-3

(C)  P-4, Q-1, R-2, S-3

(D)  P-3, Q-1, R-2, S-4

Answer: (C)

37. Consider two yarns, one 100% wool and the other 100% cotton, each containing 100 fibres in the yarn cross-section. The respective limit irregularities (%) of wool and cotton yarns will approximately be

(A)  11.2 and 10.6

(B)  10.6 and 11.2

(C)  11.8 and 11.2

(D)  11.8 and 10.6

Answer: (A)

38. If the numerical value X of yarn linear density, expressed in denier is the same as that expressed in English (Ne) system, then X approximately is

(A)  24.3

(B)  48.6

(C)  72.9

(D)  97.2

Answer: (C)

39. Determine the correctness or otherwise of the following Assertion [a] and Reason [r]

[a]: Sodium chlorite is a bleaching agent for cotton.

[r]: Sodium chlorite is an effective reducing agent.

(A)  Both [a] and [r] and 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: (D)

40. Determine the correctness or otherwise of the following Assertion [a] and Reason [r]

[a]: Acrylic fibres are dyed with basic dyes in acidic medium.

[r]: In acidic medium the acrylic fibre acquires positive charge.

(A)  Both [a] and [r] and 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: (D)

41. Determine the correctness or otherwise of the following Assertion [a] and Reason [r]

[a]: Foam finishing significantly reduces the energy consumed in drying.

[r]: The specific heat of air is significantly lower than that of water.

(A)  Both [a] and [r] and 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: (B)

42. If the probability density function of a continuous random variable X is given by f(x) = ex, 0 ≤ x < ∞, the mean of random variable X is _______.

Answer: (1 to 1)

43. Assuming the step size h = 1, the numerical value of the definite integral  obtained using Trapezoidal rule (rounded off to 2 decimal places) is ______.

Answer: (0.70 to 0.75)

44. In the production of PET, diglycol terephthalate (DGT) is an intermediate. Taking the atomic weights of H = 1, C = 12, O = 16, the molecular weight of DGT is______.

Answer: (254 to 254)

45. In wet spinning of acrylic filament yarn, the volumetric flow rate of the spinning dope per spinneret hole is 0.1 cm3/min. If the surface speed at the first take up roller is 1.5 m/min and the diameter of spinneret hole is 0.02 cm, then the jet stretch (rounded off to 2 decimal places) is _______.

Answer: (0.46 to 0.48)

46. Two types of polyester staple fibers of fineness 3 and 6 denier and having the same length are mixed in a ratio of 2 : 3 by weight. The mean fibre fineness (denier) of the mix (rounded off to 2 decimal places) is _____.

Answer: (4.25 to 4.35)

47. Two rovings, each with mass CV of 10%, are fed to a ring spinning machine that adds a mass CV of 20%. The mass CV (%) of the yearn (rounded off to 2 decimal places) is _____.

Answer: (21.00 to 22.00)

48. In a drum-driven winder, the grooved drum having a width of 20 cm is rotating at 1000 rpm. If the drum makes 5 revolutions per double traverse, the traverse speed (m/min) is ______.

Answer: (80 to 80)

49. The wale constant and course constant are 4.2 and 5.04 respectively. If the loop length is 4.2 mm, then stitch density (number/cm2) is _______.

Answer: (120 to 120)

50. A cotton fibre has degree of cell wall thickening (θ) of 0.9 and perimeter of 40 μ The actual cross-sectional area of the wall (μm2) of the fibre (rounded off two 1 decimal place) is _______.

Answer: (112.0 to 117.0)

51. A fabric with mass per unit area of 250 g/m2 has flexural rigidity of 275 μN-m. The bending length (mm) of the fabric (rounded off to 2 decimal places) is______.

Answer: (46.00 to 50.00)

52. The ‘standard machine rate of loading’ of a tensile tester, working on pendulum lever principle, is 440 N/cm. As the pendulum lever swings from 30° to 45°, the ‘machine rate of loading’ (N/cm), reduces by (rounded off to 2 decimal places) ________.

Answer: (69.00 to 71.00)

53. Under a load of 500 cN, the extension of a yarn of 300 mm length is 10%. If the elastic recovery is 90%, then the length (mm) of the yarn after removal of load is _______.

Answer: (303 to 303)

54. Given that one gram mole of a gas occupies 22.4 L of volume at STP, the atomic weights of H = 1, and that of O = 16, the concentration (g/L) of hydrogen peroxide solution of 25 volume strength (rounded off to 2 decimal places) is _______.

Answer: (75.00 to 77.00)

55. The work of adhesion (WSL) depends on the surface tension (γLV) of the liquid and the contact angle (θ) formed on a surface and is expressed as γLV(1 + cos θ). The WSL for a given fabric and a liquid is reduced to 1/3rd of the original value after oil repellent treatment. If the measured contact angle of untreated fabric is 60°, the percent change in the contact angle after the treatment is ______.

Answer: (100 to 100)

GATE Exam 2020 Stastics (ST) Question Paper With Answer Key

GATE-2020

ST: Statistics

GA-General Aptitude

Q1 – Q5 carry one mark each.

1. Rajiv Gandhi Khel Ratna Award was conferred _____Mary Kom, a six-time world champion in boxing, recently in a ceremony _____ the Rashtrapati Bhawan (the President’s official residence) in New Delhi.

(A)  with, at

(B)  on, in

(C)  on, at

(D)  to, at

Answer: (C)

2. Despite a string of a poor performances, the changes of K. L. Rahul’s selection in the team are ______.

(A)  slim

(B)  bright

(C)  obvious

(D)  uncertain

Answer: (B)

3. Select the word that fits the analogy:

Cover : Uncover :: Associate : _______

(A)  Unassociate

(B)  Inassociate

(C)  Missassociate

(D)  Dissociate

Answer: (D)

4. Hig by floods, he kharif (summer sown) crops in various parts of the county have been affected. Officials believe that the loss in production of the kharif crops can be recovered in the output of the rabi (winter sown) crops so that the country can achieve its food-grain production target of 291 million tons in the crop year 2019-20 (July-June). They are hopeful that good rains in July-August will help the soil retain moisture for a longer period, helping winter sown crops such as wheat and pulses during the November-February period.

Which of the following statements can be inferred from the given passage?

(A)  Officials declared that the food-grain production target will be met due to good rains.

(B)  Officials want the food-grain production target to be met by the November-February period.

(C)  Officials feel that the food-grain production target cannot be met due to floods.

(D)  Officials hope that the food-grain production target will be met due to a good rabi produce.

Answer: (D)

5. The difference between the sum of the first 2n natural numbers and the sum of the first n odd natural numbers is ______.

(A)  n2 – n

(B)  n2 + n

(C)  2n2 – n

(D)  2n2 + n

Answer: (B)

Q6 – Q10 carry two marks each.

6. Repo rate is the at which Reserve Bank of India (RBI) lends commercial banks, and reverse repo rate is the rate at which RBI borrows money from commercial banks.

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

(A)  Decrease in repo rate will increase cost of borrowing and decrease lending by commercial banks.

(B)  Increase in repo rate will decrease cost of borrowing and increase lending by commercial banks.

(C)  Increase in repo rate will decrease cost of borrowing and decrease lending by commercial banks.

(D)  Decrease in repo rate will decrease cost of borrowing and increase lending by commercial banks.

Answer: (D)

7. P, Q, R, S, T, U, V, and W are seated around a circular table.

(I) S is seated opposite to W.

(II) U is seated at the second place to the right of R.

(III) T is seated at the third place to the left of R.

(IV) V is a neighbor of S.

Which of the following must be true?

(A)  P is a neighbor of R.

(B)  Q is a neighbor of R.

(C)  P is not seated opposite to Q.

(D)  R is the left neighbor of S.

Answer: (C)

8. The distance between Delhi and Agra is 233 km. A car P started travelling from Delhi to Agra and another car Q started from Agra to Delhi along the same road 1 hour after the car P started. The two cars crossed each other 75 minutes after the car Q started. Both cars were travelling at constant speed. The speed of car P was 10 km/hr more than the speed of car Q. How many kilometers the car Q had travelled when the cars crossed each other?

(A)  66.6

(B)  75.2

(C)  88.2

(D)  116.5

Answer: (B)

9. For a matrix M = [mij], i. j= 1, 2, 3, 4, the diagonal elements are all zero and mij = −mij. The minimum number of elements required to fully specify the matrix is_______.

(A)  0

(B)  6

(C)  12

(D)  16

Answer: (B)

10. The profit shares of two companies P and Q are shown in the figure. If the two companies have invested a fixed and equal amount every year, then the ratio of the total revenue of company P to the total revenue of company Q, during 2013-2018 is ______.

(A)  15 : 17

(B)  16 : 17

(C)  17 : 15

(D)  17 : 16

Answer: (B)

ST: Statistics

Q1 – Q25 carry one mark each.

1. Let M be a 3 × 3 non-zero idempotent matrix and let I3 denote the 3 × 3 identity matrix. Then which of the following statements is FLASE?

(A)  The eigenvalues of M are 0 and 1

(B)  Rank(M) = Trace(M)

(C)  I3 – M is idempotent

(D)  (I3 + M)1 = I3 – 2M

Answer: (D)

2. Let ℂ denote the set of all complex numbers. Consider the vector space

over the field of real numbers, where for any complex number z,  denotes its complex conjugate. If i = √−1, then a basis of V is

(A)  {(1, −1, 1), (i, i, i)}

(B)  {(1, −1, 1), (i, −i, i)}

(C)  {(1, −i, 1), (i, 1, i)}

(D)  {(1, −i, 1), (i, 1, −i)

Answer: (A)

3. Let S = {(x, y) ∈ ℝ × ℝ: x2 – y2 = 4} and f : S → ℝ be defined by f(x, y) = 6x + y2, where ℝ denotes the set of all real numbers. Then

(A)  f is bounded of S

(B)  the maximum value of f on S is 13

(C)  the minimum value of f on S is −14

(D)  the minimum value of f on S is −13

Answer: (D)

4. Let f : ℝ × ℝ → ℝ be defined by

        

where ℝ denotes the set of all real numbers and c ∈ ℝ is fixed constant. Then, which of the following statements is TRUE?

(A)  There does NOT exists a value of c for which f is continuous at (0, 0)

(B)  f is continuous at (0, 0) if c = 0

(C)  f is continuous at (0, 0) if c = 10

(D)  f is continuous at (0 0) if c = 16

Answer: (D)

5. The moment generating function of a random variable X is given by

Then P(X ≤ 2) equals

(A)  1/3

(B)  1/6

(C)  1/2

(D)  5/6

Answer: (D)

6. Consider the following two-way fixed effects analysis of variance model

Yijk = μ + αi + βj + ϵijk, i = 1, 2; j = 1, 2, 3; k = 1, 2, 3;

where ϵijk’s are independently and identically distributed N(0, σ2) random variables, σ ∈ (0, ∞), α1 + α2 = 0 and β1  + β2 + β3 = 0. Let SSE denote the sum of squares due to error. For any positive integer v and any α ∈ (0, 1), let χ2v,α denote the (1 – α)-th quantile of the central chi-square distribution with v degrees of freedom. Then a 95% confidence interval for σ2 is given by

Answer: (D)

7. Let X1, …, X20 be independent and identically distributed random variables with the common probability density function 

Then the distribution of the random variableis

(A)  central chi-square with 10 degrees of freedom

(B)  central chi-square with 20 degrees of freedom

(C)  central chi-square with 30 degrees of freedom

(D)  central chi-square with 40 degrees of freedom

Answer: (D)

8. Let X1, …, X10 be a random sample from a Weibull distribution with the probability density function 

where θ ∈ (0, ∞). For any positive integer v and any α ∈ (0, 1), let χ2v,α denote the (1 – α)-th quantile of the central chi-square distribution with v degrees of freedom. Then, a 90% confidence interval for θ is

Answer: (A)

9. Let X1, …, Xn be a random sample of size n (≥2) from a uniform distribution on the interval [−θ, θ], where θ ∈ (0, ∞). A minimal sufficient for θ is

Answer: (C)

10. Let X1 …, Xn be a random sample of size n(≥2) from N(θ, 2θ2) distribution, where θ ∈ (0, ∞). Which of the following statements is TRUE?

(A)  is the unique unbiased estimator of θ2 that is a function of minimal sufficient statistic

(B)  is an unbiased estimator of θ2

(C)  There exist infinite number of unbiased estimators of θ2 which are functions of minimal sufficient statistic

(D)  There does NOT exist any unbiased estimator of θ(θ + 1) that is a function of minimal sufficient statistic

Answer: (C)

11. Let {N(t), t ≥ 0} be a Poisson process with rate λ = 2. Given that N(3) = 1, the expected arrival time of the first event of the process is

(A)  1

(B)  3/2

(C)  2/3

(D)  3

Answer: (B)

12. Consider the regression model

Yi = β0 + β1xi2 + ϵi, i = 1, 2, …, n(n ≥ 2);

where β0 and β1 are unknown parameters and ϵis are random errors. Let y­i be the observed value of Yi, i = 1, …, n. Using the method of ordinary least squares, the estimate of β1 is

Answer: (B)

13. Let  be a random sample of size n (≥2) from  distribution, where 1 ≤ p ≤ n – 1 and ∑ is a positive definite matrix. Define

where for any column vector  denotes its transpose. Then the distribution of the statistic  is

(A)  χ2p, the central chi-square distribution with p degrees of freedom

(B)  Fp,np, the central F distribution with p and n – p degrees of freedom

(C)   where Fp,np, is the central F distribution with p and n – p degrees of freedom

(D)   where Fp,np, is the central F distribution with n – p and p degrees of freedom

Answer: (C)

14. Consider a two-way fixed effects analysis of variance model without interaction effect and one observation per cell. If there are 5 factors and 4 columns, then the degrees of freedom for the error sum of squares is

(A)  20

(B)  19

(C)  12

(D)  11

Answer: (C)

15. Let X1, …, Xn be a random sample of size n (≥ 2) from an exponential distribution with the probability density function

where θ ∈ {1, 2}. Consider the problem of testing H0­ : θ = 1 against H1 : θ = 2, based on X1, …, Xn. Which of the following statements is TRUE?

(A)  Likelihood ratio test at level α (0 < α < 1) leads to the same critical region as the corresponding most powerful test at the same level.

(B)  Critical region of level α (0 < α < 1) likelihood ratio test is  is the α-th quantile of the central chi-square distribution with 2n degrees of freedom

(C)  Likelihood ratio test for testing H0 against H1 does not exist

(D)  At any fixed level α (0 < α < 1), the power of the likelihood ratio test is lower than that of the most powerful test

Answer: (A)

16. Te characteristic function of a random variable X is given by

Then P(|X| ≤ 3/2) = _____ (correct up to two decimal places).

Answer: (0.75 to 0.75)

17. Let the random  follow  distribution, where

Then P(X1 + X2 + X3 + X4 > 0) = _______ (correct up to one decimal  place).

Answer: (0.5 to 0.5)

18. Let {Xn}n0 be a homogeneous Markov chain with state space {0, 1} and one-step transition probability matrix   If P(X0 = 0) = 1/3, then 27 × E(X2) = ______ (correct  up to two decimal places).

Answer: (16.25 to 16.25)

19. Let E, F and G be mutually independent events with P(E) = 1/2, P(F) = 1/3 and P(G) = 1/4. Let p be the probability that at least two of the events among E, F and G occur. Then 12 × p = _______ (correct up to one decimal place).

Answer: (3.5 to 3.5)

20. Let the joint probability mass function of (X, Y, Z) be

where k = 10 – x – y – z; x, y, z = 0, 1, … , 10; x + y + z ≤ 10. Then the variance of the random Y + Z equals ______ (correct up to one decimal place).

Answer: (2.1 to 2.1)

21. The total number of standard 4 × 4 Latin squares is _______

Answer: (4 to 4)

22. Let  be a 4 × 1 random vector with  and variance-covariance matrix

Let  be the 4 × 1 random vector of principal components derived from ∑. The proportion of total variation explained by the first two principal components equals ______ (correct up to two decimal places).

Answer: (0.75 to 0.75 OR 75 to 75)

23. Let X1, …, Xn be a random sample of size n (≥ 2) from an exponential distribution with the probability density function

where θ ∈ (0, ∞). If X(1) = min{X1, …, Xn} then the conditional expectation

Answer: (2 to 2)

24. Let Yi = α + βxi + ϵi, i = 1, 2, …, 7, where xi’s are fixed covariates and ϵi’s are independent and identically distributed random variables with mean zero and finite variance. Suppose that  are the least squares estimators of α and β, respectively. Given the following data:

where yi is the observed value of Yi, i = 1, …, 7. Then the correlation coefficient between equals_____

Answer: (0 to 0)

25. Let {0, 1, 2, 3} be an observed sample of size from N(θ, 5) distribution, where θ ∈ [2, ∞). Then the maximum likelihood estimate of θ based on the observed sample is ________.

Answer: (2 to 2)

Q26 – Q55 carry two marks each.

26. Let f : ℝ × ℝ → ℝ be defined by

f(x, y) = x4 – 2x3y + 16y + 17,

where ℝ denotes the set of all real numbers. Then

(A)  f has a local minimum at (2, 4/3)

(B)  f has a local maximum at (2, 4/3)

(C)  f has a saddle point at (2, 4/3)

(D)  f is bounded

Answer: (C)

27. Consider the linear transformation T : ℂ3 = ℂ × ℂ × ℂ. Which of the following statements is TRUE?

(A)  There exists a non-zero vector X such that T(X) = −X

(B)  There exist a non-zero vector Y and a real number λ ≠ 1 such that T(Y) = λY

(C)  T is diagonalizable

(D)  T2 = I3, where I3 is the 3 × 3 identity matrix

Answer: (C)

28. For real numbers a, b and c, let 

Then, which of the following statements is TRUE?

(A)  Rank (M) = 3 for every, a, b, c ∈ ℝ

(B)  If a + c = 0 then M is diagonalizable for every b ∈ ℝ

(C)  M has a pair of orthogonal eigenvectors for every a, b, c ∈ ℝ

(D)  If b= 0 and a + c = 1 then M is NOT idempotent

Answer: (C)

29. Let M be a 4 × 4 matrix with (x – 1)2 (x – 3)2 as its minimal polynomial. Then, which of the following statements is FALSE?

(A)  The eigenvalues of M are 1 and 3

(B)  The algebraic multiplicity of the eigenvalue 1 is 3

(C)  M is NOT diagonalizable

(D)  Trace(M) = 8

Answer: (B)

30. Let f : ℝ × ℝ → ℝ be defined by 

where ℝ denotes the set of all real numbers. Then which of the following statements is TRUE?

(A)  f is differentiable at (1, 2)

(B)  f is continuous at (1, 2) but NOT differentiable at (1, 2)

(C)  The partial derivative of f, with respect to x, at (1, 2) does NOT exist

(D)  The directional derivative of f at (1, 2) along  equals 1

Answer: (A)

31. Which of the following functions is uniformly continuous on the specified domain?

Answer: (C)

32. Let the random vector  have the joint probability density function

Which of the following statements is TRUE?

(A)  X1, X­2 and X3 are mutually independent

(B)  X1, X2 and X3 are pairwise independent

(C)  (X1, X2) and X3 are independently distributed

(D)  Variance of X1 + X2 is π2

Answer: (B)

33. Suppose that P1 and P2 are two populations having bivariate normal distributions with mean vectors  respectively, and the same variance-covariance matrix  two new observations. If the prior probabilities for P1 and P2 are assumed to be equal and the misclassification costs are also assumed to be equal then, according to linear discriminant rule,

(A)  Z1 is assigned to P1 and Z2 is assigned to P2

(B)  Z1 is assigned to P2 and Z2 is assigned to P1

(C)  both Z1 and Z2 are assigned to P1

(D)  both Z1 and Z2 are assigned to P2

Answer: (B)

34. Let X1, …, Xn be a random sample of size n (≥2) from an exponential distribution with the probability density function

where θ ∈ (0, ∞). Which of the following statements is TRUE?

Answer: (D)

35. Let the joint distribution of (X, Y) be bivariate normal with mean vector  and variance-covariance matrix   where −1 < ρ < 1. Then E[max(X, Y)] equals

(A)   

(B)   

(C)  0

(D)  1/2

Answer: (B)

36. Let  be independent and identically distributed  random vectors, where I3 is the 3 × 3 identity matrix. Let

where J3 is the 3 × 3 matrix with each entry 1 and for any column vector  denotes its transpose. Then the distribution of T is

(A)  central chi-square with 5 degrees of freedom

(B)  central chi-square with 10 degrees of freedom

(C)  central chi-square with 20 degrees of freedom

(D)  central chi-square with 30 degrees of freedom

Answer: (C)

37. Let  be independent and identically distributed  random vectors, where ∑ is a positive definite matrix. Further, let  be a 3 × 4 matrix, where for any matrix M, Mt denotes its transpose. If Wm (n, ∑) denotes a Wishart distribution of order m with n degrees of freedom and variance-covariance matrix ∑, then which of the following statements is TRUE?

(A)  ∑1/2 XtX∑1/2 follows W4(3, I4) distribution

(B)  ∑1/2XtX∑1/2 follows W3(4, I3) distribution

(C)  Trace(X∑1Xt) follows χ24 distribution

(D)  XtX follows W3(4, ∑) distribution

Answer: (A)

38. Let the joint distribution of the random variables X1, X2 and X3 be  where

Then which of the following statements is TRUE?

(A)  X1 – X2 + X3 and X1 are independent

(B)  X1 + X2 and X3 – X1 are independent

(C)  X1 – X2 + X3 and X1 + X2 are independent

(D)  X1 – 2X2 and 2X1 + X2 are independent

Answer: (C)

39. Consider the following one-way fixed effects analysis of variance model

Yij = μ + τi + ϵij, i = 1, 2, 3; j = 1, 2, 3, 4;

where ϵij’s are independent and identically distributed N(0, σ2) random variables, σ ∈ (0, ∞) and τ1 + τ2 + τ3 = 0. Let MST and MSE denote the mean sum of squares due to treatment and the mean sum of squares due to error, respectively. For testing H0 : τ1 = τ2 =  τ3 = 0 against H1 : τi ≠ 0, for some i = 1, 2, 3, consider the test based on the statistic  For positive integers v1 and v2, let Fv1,v2 be a random variable having the central F-distribution with v1 and v2 degrees of freedom. If the observed value of  is given to be 104.45, then the p-value of this test equals

(A)  P(F2, 9 > 104.45)

(B)  P(F9, 2 < 104.45)

(C)  P(F3, 11 < 104.45)

(D)  P(F2, 6 > 104.45)

Answer: (A)

40. Let X1, …, Xn be a random sample of size n (≥ 2) from N(θ, 1) distribution, where θ ∈ (−∞, ∞). Consider the problem of testing H0 : θ ∈ [1, 2] against H1 : θ < 1 or θ > 2, based on X1, …, Xn. Which of the following statements is TRUE?

(A)  Critical region, of level α (0 < α < 1) of uniformly most powerful test for H0 against H1 is of the form  where c1 and c2 are such that test is of level α

(B)  Critical region, of level α(0 < α < 1) of uniformly most powerful test for H0 against H1 is of the form {(x1, …, xn) :   where c and d are such that the test is level α

(C)  At any level α ∈ (0, 1), uniformly most powerful test for H0 against H1 does NOT exist

(D)  At any level α ∈ (0, 1), the power of uniformly most powerful test for H0 against H1 is less than α

Answer: (C)

41. In a pure birth process with birth rates λn = 2n, n ≥ 0, let the random variable T denote the time taken for the population size to grow from 0 to 5. If Var(T) denotes the variance of the random variable T, then 256 × Var(T) = _______

Answer: (341 to 341)

42. Let {Xn}n0 be a homogenous Markov chain whose state space is {0, 1, 2} and whose one-step transition probability matrix is  Then   _____ (correct up to one decimal place).

Answer: (0.7 to 0.7)

43. Let (X, Y) be a random vector such that, for any y > 0, t he conditional probability density function of X given by Y = y is fx|Y=y (x) = yeyx, x > 0.

If the marginal  probability density function of Y is g(y) = yey, y > 0 then E(Y|X = 1) = ______ (correct up to one decimal place).

Answer: (1.5 to 1.5)

44. Let (X, Y) be a random vector with the joint moment generating function

Let Φ(∙) denote the distribution function of the standard normal distribution and p = P(X + 2Y < 1). If Φ(0) = 0.5, Φ(0.5) = 0.6915, Φ(1) = 0.8413 and Φ(1.5) = 0.9332 then the value of 2p + 1 (round off to two decimal places) equals______

Answer: (1.61 to 1.63)

45. Consider a homogeneous Markov chain {Xn}n0 with state space {0, 1, 2, 3} and one-step transition probability matrix

Assume that P(X0 = 1) = 1. Let p be the probability that state 0 will be visited before state 3. Then 6 × p = ______

Answer: (4 to 4)

46. Let (X, Y) be a random vector with joint probability mass function

where  Then the variance of Y equals ______

Answer: (1 to 1)

47. Let X be a discrete random variable with probability mass function f ∈ {f0, f1}, where

The power of the most powerful level α = 0.1 test for testing H0 : X ~ f0 against H1:X ~ f1, based on X, equals _______ (correct up to two decimal places).

Answer: (0.12 to 0.12)

48. Let   be a random vector following  distribution, where  Then the partial correlation coefficient between X2 and X3, with fixed X1, equals _______ (correct up to two decimal places).

Answer: (0.25 to 0.25)

49. Let X1, X2, X3 and X4 be a random sample from a population having probability density function fθ(x) = f(x – θ), −∞ < x < ∞, where θ ∈ (−∞, ∞) and f(−x) = f(x), for all x ∈ (−∞, ∞). For testing H0: θ = 0 against H1: θ < 0, let T+ denote the Wilcoxon Signed-rank statistic. Then under H0, 32 × P(T+ ≤ 5) ______

Answer: (18 to 18)

50. A simple linear regression model with unknown intercept and unknown slope is fitted to the following data

using the method of ordinary least squares. Then the predicted value of y corresponding to x = 5 is _______

Answer: (16 to 16)

51. Let D = {(x, y, z) ∈ ℝ × ℝ × ℝ : 0 ≤ x, y, z ≤ 1, x + y + z ≤ 12}, where ℝ denotes the set of all real numbers. If  then 84 × I = _____

Answer: (7 to 7)

52. Let the random vector (X, Y) have the joint distribution function 

Let Var(X) and Var(Y) denote the variances of random variables X and Y, respectively. Then 16 Var(X) + 32 Var(Y) = _______

Answer: (22 to 22)

53. Let {Xn}n1 be a sequence of independent and identically distributed random variables with E(X1) = 0, E(X12) = 1 and E(X14) = 3. Further, let 

If 

where Φ(∙) denotes the cumulative distribution function of the standard normal distribution, then c2 = ______(correct up to one decimal place.

Answer: (1.5 to 1.5)

54. Let the random vector  have the joint probability density function

Then the variance of the random variable X1 +  X2 + X3 equals ______ (correct up to one decimal place).

Answer: (1.8 to 1.8)

55. Let X1, …, X5 be a random sample from a distribution with the probability density function

where θ (−∞, ∞). For testing H0 : θ = 0 against H1 : θ, let  be the sign test statistic, where

Then the size of the test, which rejects H0 if and only if  equals ______ (correct up to one decimal place).

Answer: (0.5 to 0.5)

GATE Exam 2020 Production and Industrial Engineering (PI) Question Paper With Answer Key

GATE-2020

PI: Production and Industrial Engineering

GA-General Aptitude

Q1 – Q5 carry one mark each.

1. While I agree _____ his proposal this time, I do not often agree _____ him.

(A)  to, with

(B)  with, to

(C)  with, with

(D)  to, to

Answer: (A)

2. The recent measures to improve the output would _______ the level of production to our satisfaction.

(A)  increase

(B)  decrease

(C)  speed

(D)  qualize

Answer: (A)

3. Select the word that fits the analogy:

White : Whitening : Light: ______

(A)  Lightning

(B)  Lightening

(C)  Lighting

(D)  Enlightening

Answer: (B)

4. In one of the greatest innings ever seen in 142 years of Test history, Ben Stokes upped the tempo in a five-and-a-half hour long stay of 219 balls including 11 fours and 8 sixes that saw him finish on a 135 not out as England squared the five-match series.

Based on their connotations in the given passage, which one of the following meanings DOES NOT match?

(A)  upped = increased

(B)  squared = lost

(C)  tempo = enthusiasm

(D)  saw = resulted in

Answer: (B)

5. There are five levels {P, Q, R, S, T} in a linear supply chain before a product reaches customers, as shown in the figure.

At each of the five levels, the price of the product is increased by 25%. If the product is produced at level P at the cost of Rs. 120 per unit, what is the price paid (in rupees) by the customers?

(A)  187.50

(B)  234.38

(C)  292.26

(D)  366.21

Answer: (D)

Q6 – Q10 carry two marks each.

6. Climate change and resilience deal with two aspects – reduction of sources of non-renewable energy resources and reducing vulnerability of climate change aspects. The terms ‘mitigation’ and ‘adaptation’ are used to refer to these aspects, respectively.

Which of the following assertions is best supported by the above in information?

(A)  Mitigation deals with consequences of climate change.

(B)  Adaptation deals with causes of climate change.

(C)  Mitigation deals with actions taken to reduce the use of fossil fuels.

(D)  Adaptation deals with actions taken to combat gree-house gas emissions.

Answer: (C)

7. Find the missing element in the following figure.

(A)  d

(B)  e

(C)  w

(D)  y

Answer: (A)

8. It was estimated that 52 men can complete a strip in a newly constructed highway connecting cities P and Q in 10 days. Due to an emergency, 12 men were sent to another project. How many number of days, more than the original estimate, will be required to complete the strip?

(A)  3 days

(B)  5 days

(C)  10 days

(D)  13 days

Answer: (A)

9. An engineer measures THREE quantities X, Y and Z in an experiment. She finds that they follow a relationship that is represented in the figure below : (the product of X and Y linearly varies with Z)

Then, which of the following statements is FALSE?

(A)  For fixed Z; X is proportional to Y

(B)  For fixed Y; X is proportional to Z

(C)  For fixed X; Z is proportional to Y

(D)  XY/Z is constant

Answer: (A)

10. The two pie-charts given below show the data of total students and only girls registered in different streams in a university. If the total number of students registered in the university is 5000, and the total number of the registered girls is 1500; then, the ratio of boys enrolled in Arts to the girls enrolled in Management is ______.

(A)  2:1

(B)  9:22

(C)  11:9

(D)  22:9

Answer: (D)

PI: Production and Industrial Engineering

Q1 – Q25 carry one mark each.

1. The divergence of the vector  is

(A)  2x

(B)  2y

(C)  2z

(D)  0

Answer: (D)

2. An integrating factor for the differential equation  is

(A)  em

(B)  em

(C)  emx

(D)  emx

Answer: (D)

3. For the complex numbers z1 = 2 + 3i and z2 = 4 – 5i, the value of (z1 + z2)2 is

(A)  32 – 24i

(B)  −32 – 24i

(C)  32 + 24i

(D)  −32 + 24i

Answer: (A)

4. To solve x2 – 2 = 0, the Newton-Raphson method has been employed. If the initial guess x0 = 1.0, the next estimate of the root, x1, will be

(A)  0.5

(B)  1.0

(C)  1.5

(D)  2.0

Answer: (C)

5. If x is a random variable with the expected value of 5 and the variance of 1, then the expected value of x2 is

(A)  24

(B)  25

(C)  26

(D)  36

Answer: (C)

6. Group I lists phases of steel and Group II lists crystal structures in the table below.

Match the phase with the corresponding crystal structure.

(A)  P-2, Q-4, R-3

(B)  P-4, Q-2, R-3

(C)  P-2, Q-4, R-1

(D)  P-4, Q-2, R-1

Answer: (A)

7. The figure shows two bodies P and Q. The body Q is placed on the ground and the body P is placed on top of it. The weights of P and Q are WP and WQ, respectively. The bodies are at rest and all the surfaces are assumed to be frictionless. R represents reaction force, if any, between the bodies.

The correct free body diagram of the body P is

Answer: (B)

8. The figure shows as mechanism with 3 revolute pairs (between the links 1 and 2, 2 and 3, and 3 and 4) and a prismatic pair (between the links 1 and 4). Which one of the four links should be fixed to obtain the mechanism that forms the basis of the quick-return mechanism widely used in a shaper?

(A)  Link 1

(B)  Link 2

(C)  Link 3

(D)  Link 4

Answer: (B)

9. The state of stress at a point in the body under plane stress condition is shown in the figure. The positive directions of x and y axes are also shown. The material of the body is homogeneous and isotropic, with modulus of elasticity E and Poisson’s ratio v. The longitudinal strain in the x-direction is

Answer: (C)

10. The figure shows two bodies connected through a riveted joint with one rivet. The diameter of the rivet is d (in m). The joint transmits a load of F(in N) whose line of action is perpendicular to and intersects the vertical axis of the rivet. Neglect any effect of bending of the rivet. If the allowable shear stress for the material of the rivet is τ N/m2, the diameter of the rivet required to prevent failure in shear is

Answer: (B)

11. Consider flow of an oil with Reynolds number 1500 in a pipe of diameter 5 cm. The kinematic viscosity of the oil, v = 0.75 cm2/s. The value of average velocity in m/s is

(A)  0.75

(B)  1.50

(C)  2.25

(D)  4.50

Answer: (C)

12. A Carnot heat engine receives 600 kJ of heat per cycle from a source at 627°C and rejects heat to a sink at 27° The amount of heat rejected to the sink per cycle (rounded off to the nearest integer) in kJ is

(A)  26

(B)  200

(C)  400

(D)  574

Answer: (B)

13. The process used for producing long bars of fiber reinforced plastics (FRP) with uniform cross-section is

(A)  Extrusion

(B)  Pultrusion

(C)  Injection Molding

(D)  Thermoforming

Answer: (B)

14. The purpose of the ratchet in a micrometer is to

(A)  impart smooth movement to the spindle

(B)  compensate for the wear of the screw thread

(C)  prevent rotation of the spindle while reading the scale

(D)  maintain sufficient and uniform measuring pressure

Answer: (D)

15. End mill cutters are mounted on the spindle of a vertical milling machine using

(A)  vice

(B)  collet

(C)  fact plate

(D)  driver plate

Answer: (B)

16. Self-sharpening tendency of a conventional grinding wheel depends upon

(A)  wheel structure

(B)  wheel grade

(C)  grit hardness

(D)  grit size

Answer: (B)

17. A non-traditional machining process which utilizes mechanical energy as the principal energy source for removing the material is

(A)  Electric discharge machining

(B)  Laser beam machining

(C)  Ultrasonic machining

(D)  Plasma arc machining

Answer: (C)

18. In a manufacturing of self-lubricating bearings by powder metallurgy, an important secondary operation that is carried out after sintering is

(A)  Cold isostatic pressing

(B)  Hot isostatic pressing

(C)  Impregnation

(D)  Infiltration

Answer: (C)

19. Which of the following is a causal forecasting method?

(A)  Naïve approach

(B)  Moving average

(C)  Exponential smoothing

(D)  Linear regression

Answer: (D)

20. An approach used in the product development which combines the efforts of design, manufacturing, and other functions to reduce the total time in introducing a new product in the market is

(A)  Concurrent engineering

(B)  Lean manufacturing

(C)  Value engineering

(D)  Break-even anlaysis

Answer: (A)

21. The Bellman’s principle of optimality is related to

(A)  Linear programming problem

(B)  Transportation problem

(C)  Dynamic programming problem

(D)  Assignment problem

Answer: (C)

22. The process capability ratio Cp is given by

Answer: (A)

23. In a uniaxial tensile test on a specimen of a ductile material, the ultimate tensile strength is found to be 400 MPa and the elongation up to the maximum load is 25%. The true stress at the maximum load in MPa is ______.

Answer: (500 to 500)

24. Suppose the control system of a fighter jet consists of three unrelated components in series, and it is desired to have 98% reliability of the system. If the reliability level of all the components is the same, then the reliability of each component (rounded off to three decimal places) is ________.

Answer: (0.993 to 0.994 OR 99.300 to 99.400)

25. The product structure tree in the figure below shows the components needed to assemble one unit of product P.

The number of units of component D needed to assemble 10 units of product P is ___________.

Answer: (220 to 220)

Q26 – Q55 carry two marks each.

26. General solution of  is

Answer: (C)

27. For the matrix  the eigenvectors are

Answer: (B)

28. A truss with two bars PR and QR, making angles α and β, respectively, with the vertical, is shown in the figure below. The connections at P, Q and R are hinged connections. The truss supports body of weight W (in N) at R as shown. The tension in the bar QR(in N) is

Answer: (D)

29. The figure shows a beam of length L (in m) with a uniformly distributed transverse load of W (in N/m) acting over it. The width and depth of the beam cross section are b (in m) and t (in m), respectively. The magnitude of the maximum bending stress in the beam in N/m2 is

Answer: (A)

30. The vertices of rectangle PQRS are as follows in a 2-D CAD system.

P(-4, -2); Q(-2, -3); R(-3, -5); S(-5, -4)

The coordinates of the corresponding new vertices, P’, Q’, R’, S’ after translation of the rectangle along x-axis in the positive direction by 6 units and along y-axis in the positive direction by 3 units are

(A)  P’(-10, -5); Q’(-8, -6); R’(-9, -8); S’(-11, -7)

(B)  P’(2, 1); Q’(4, 0); R’(3, -2); S’ (1, -1)

(C)  P’(2, -5); Q’(4, -6); R’(3, -8); S’(1, -7)

(D)  P’(-10, 1); Q’(-8, 0); R’(-9, -2); S’(-11, -1)

Answer: (B)

31. The statement that best describes the function of a GO gauge in the context of Taylor’s principle of gauging is

(A)  GO gauge checks the Maximum Material Condition and is designed to check as many dimensions as possible

(B)  GO gauge checks the Least Material Condition and is designed to check as many dimensions as possible

(C)  Go gauge checks the maximum Material Condition and is designed to check only one dimension

(D)  GO gauge checks the Least Material Condition and is designed to check only one dimension

Answer: (A)

32. The figures shows revenue generated over different product life cycle stages marked as P, Q, R and S. Group I lists these product life cycle stages. Group II lists typical efforts leading to revenue maximizing during a stage.

Match the stage with the efforts.

(A)  P-3; Q-4; R-2; S-1

(B)  P-1; Q-4; R-2; S-3

(C)  P-1; Q-3; R-4; S-2

(D)  P-3; Q-1; R-2; S-4

Answer: (D)

33. A company manufactures products P and Q in quantities x1 and x2, respectively, using two resources. The following Linear Programming Problem (LPP) is Maximize Z = 3x1 + 2x2

subject to x1 + 2x2 ≤ 2 (for Resource 1)

               2x1 + x2 ≤ 2 (for Resource 2)

   and x1, x2 ≥ 0.

The shadow price for Resource 2 is

(A)  0

(B)  2/3

(C)  1/

(D)  4/3

Answer: (D)

34. A rectifying inspection is performed on a lot of size W = 1000 using a Single-Sampling Plant with the sample size n = 60 and the acceptance number c = 1. If t he Acceptable Quality Level is 1.0%, the producer’s risk associated with the sampling plan (rounded off to the nearest integer) in % is

(A)  12

(B)  33

(C)  67

(D)  88

Answer: (A)

35. For y = −x2 + 9x – 2, the value of  using Simpson’s 1/3 rule with two intervals (rounded off to two decimal places) is ______.

Answer: (58.00 to 59.00)

36. If the probability density function of a random variable x is given by

                                         

the value of k is ______.

Answer: (3 to 3)

37. A solid shaft has to transmit 50 kW of power at a speed of 1910 RPM. Ignore any possible bending of the shaft. The maximum allowable shear stress for the material of the shaft is 80 MPa. The minimum diameter of the shaft required to prevent failure due to shear (rounded off to one decimal place) in cm is _______.

Answer: (2.0 to 3.0)

38. A flywheel is to be used in an IC engine to limit fluctuation of angular speed. The average of the maximum and the minimum angular speed is 500 RPM, and the maximum fluctuation of energy is 10,000 N-m. Neglecting rotary inertia of any other components, the moment of inertia of the flywheel about its axis of rotation required to limit the maximum fluctuation of speed of 30 RPM (rounded off to one decimal place) in kg-m2 is ________.

Answer: (59.0 to 62.0)

39. A tank of large cross-sectional area contains water up to a height of 5 m as shown in the figure. The top water surface is under a pressure of p1 = 0.2 MPa. A small, smooth and round tap at the bottom of the tank is opened to the atmosphere (p2 = 0.1 MPa).

Use the acceleration due to gravity, g = 9.81 m/s2 and the density of water, ρ = 1000 kg/m3. The velocity with which the water will exit from the tap under the conditions shown in the figure (rounded off to one decimal place) is m/s is _______.

Answer: (17.2 to 17.4)

40. A steel ball of 12 mm diameter is heated to 1225 K. It is then slowly cooled in air to a temperature of 475 K. During the cooling process, the ambient temperature is 325 K and the heat transfer coefficient is 30 W/m2-k. Assume the density of steel is 7800 kg/m3 and the specific heat is 600 J/kg-K. Using the lumped capacitance method of analysis, the calculated time for the required cooling (rounded off to one decimal place) in second is _______.

Answer: (557.0 to 561.0)

41. A mass of 3 kg of Argon gas at 3 bar, 27°C is contained in a rigid, insulated vessel. Paddle wheel work is done on the gas for 30 minutes at the rate of 0.015 kW. Specific heat at constant volume, Cv, for Argon is 0.3122 kJ/kg-K. The final temperature of the gas (rounded off to one decimal place) in Kelvin is ________.

Answer: (327.0 to 331.0)

42. The figure shows drawing of a part with dimensions and tolerances, both in mm. The permissible tolerance for slot A (rounded off to one decimal place) in mm is ±_______.

Answer: (0.6 to 0.6)

43. To manufacture a product by casting, molten metal is poured in a cavity of rectangular cross section in a sand mold with a side blind riser as shown in the figure. The dimensions of the mold cavity are 60 cm × 40 cm × 20 cm.

The riser is cylindrical in shape with diameter equal to height. It is required that the solidification time of the riser should be 25% greater than that of the mold. Using Chvorinov’s rule, the diameter of the riser (rounded off to one decimal place) in cm should be ______.

Answer: (36.0 to 37.0)

44. A cylindrical billet of 90 mm diameter is extruded to produce an I-section as shown in the figure (all dimensions in mm).

The total extrusion pressure (p­e) in MPa required for the above process is given by

                                           

where, σm is the mean flow stress of the material, and A0 and Af are the initial and the final cross-sectional areas, respectively. If the mean flow stress of the extruded material is 80 MPa, the force required for the above extrusion (rounded off to one decimal place) in kN is _________.

Answer: (1672.0 to 1675.0)

45. The heat generated in resistance spot welding operation for joining two metal sheets with a certain set of process parameters is 2000 J. For a second spot welding operation on the same sheets without any change in the overall resistance of the system, the current is increased by 25% and the time for which the current is applied is reduced to half. The heat generated in the second operation (rounded off to one decimal place) in J is _______.

Answer: (1560.0 to 1563.0)

46. A vertical boring operation is performed in a cast iron plate to enlarge a blind hole to a diameter of 25 mm up to a depth of 100 mm in a single pass. The cutting speed and the feed used in the process are 100 m/min and 0.1 mm/rev, respectively. Considering the allowance for tool approach as 2 mm, the actual machining time (rounded off to two decimal places) in minutes is ________.

Answer: (0.78 to 0.82)

47. For a particular tool-workpiece combination, the value of exponent n in Taylor’s tool life equation is 0.5. If the cutting speed is reduced by 50% keeping all the other machining conditions same, the increase in tool life in % is _______.

Answer: (300 to 300)

48. In a waterjet machining process, the water pressure used is 500 MPa. The diameter of orifice of the nozzle through which the waterjet comes out is 0.25 mm. Neglecting frictional and other losses, and using the density of water as 1000 kg/m3, the mass flow rate of the waterjet (rounded off to two decimal places) in kg/min is _________.

Answer: (2.85 to 3.00)

49. The movement along the z-axis of a CNC drilling machine is controlled by using a servo motor, a lead screw and an incremental encoder. The lead screw has 2 threads/cm and it is directly coupled to the servo motor. The incremental encoder attached to the lead screw emits 100 pulses/revolution. The control resolution in microns is _______.

Answer: (50 to 50)

50. A project consists of seven activities as listed in the table. The time required for each activity and its immediate predecessor(s) are also given.

The project completion time using Critical Path Method (CPM) in weeks is  _______.

Answer: (20 to 20)

51. A company is planning to procure a machine to produce a component. There are two alternatives available – machine A and machine B. The cost of producing x units of the component (in Rs.) using machine A is given as C(x) = 10000 + 170x + x2. The cost of producing x units of the component (in Rs.) using machine B is given as CB(x) = 15000 + 400x. If machine B is to be preferred, then the minimum number of units to be produced should be ________.

Answer: (250 to 250)

52. The availability of an old photocopier was 90% and the Mean Time between Failure (MTBF) was 200 days. It has been replaced with a new photocopier having an availability of 95%. Now, the Mean Time to Repair (the time during which the photocopier is unavailable for service) has increased by 5 days. The MTBF of the new photocopier (rounded off to the nearest integer) in days is _______.

Answer: (500 to 523)

53. A car company manufactures 200 units of a component per day. The component is installed in different car models at a rate of 15000 units per year. The company operates its production facility 300 days per year to manufacture the component. The setup cost for each production run is Rs. 200 and the inventory holding cost per year is Rs. 2 per The Economic Production Quantity (EPQ) is ________.

Answer: (2000 to 2000)

54. A company has to perform five tasks (P, Q, R, S and T) to make an assembly. Task times and immediate predecessors of the tasks are listed below. If an assembly line is designed to obtain the maximum output rate, the efficiency of the line in % is ______.

Answer: (95 to 95)

55. In a work study experiment, it is observed that a worker completes a job in an average time of 15 minutes with a performance rating of 120%. The time required for another worker having a performance rating of 80% to complete the same job (rounded off to one decimal place) in minutes is ______.

Answer: (22.5 to 22.5)

GATE Exam 2020 Physics (PH) Question Paper With Answer Key

GATE-2020

PH: Physics

GA – General Aptitude

Q1 – Q5 carry one mark each.

1. He is known for his unscrupulous ways. He always sheds______ tears to deceive people.

(A)  fox’s

(B)  crocodile’s

(C)  crocodile

(D)  fox

Answer: (C)

2. Jofra Archer, the England fast bowler, is ____ than accurate.

(A)  more fast

(B)  faster

(C)  less fast

(D)  more faster

Answer: (A)

3. Select the word that fits the analogy:

Build : Building :: Grow : ______

(A)  Grown

(B)  Grew

(C)  Growth

(D)  Growed

Answer: (C)

4. I do not think you know the case well enough to have opinions. Having said that, I agree with your other point.

What does the phrase “having said that” mean in the given text?

(A)  as opposed to what I have said

(B)  despite what I have said

(C)  in addition to what I have said

(D)  contrary to what I have said

Answer: (B)

5. Define [x] as the greatest integer less than or equal to x, for each x ∈ (−∞, ∞). If y = [x], then area under y for x ∈ [1, 4] is _______.

(A)  1

(B)  3

(C)  4

(D)  6

Answer: (D)

Q6 – Q10 carry two marks each.

6. Crowd funding deals with mobilization of funds for a project from a large number of people, who would be willing to invest smaller amounts through web-based platforms in the project.

Based on the above paragraph, which of the following is correct about crowd funding?

(A)  Funds raised through unwilling contributions on web-based platforms.

(B)  Funds raised through large contributions on web-based platforms.

(C)  Funds raised through coerced contributions on web-based platforms.

(D)  Funds raised through voluntary contributions on web-based platforms.

Answer: (D)

7. P, Q, R and S are to be uniquely coded using α and β. If P is coded as αα and Q as αβ, then R and S, respectively, can be coded as ______.

(A)  βα and αβ

(B)  ββ and αα

(C)  αβ and ββ

(D)  βα and ββ

Answer: (D)

8. The sum of the first n terms in the sequence 8, 88, 888, 8888, … is ______.

(A)   

(B)   

(C)   

(D)   

Answer: (D)

9. Select the graph that schematically represents BOTH y = xm and y = x1/m properly in the interval 0 ≤ x ≤ 1, for integer values of m, where m > 1.

Answer: (A)

10. The bar graph shows the data of the students who appeared and passed in an examination for four schools P, Q, R and S. The average of success rates (in percentage) of these four schools is ________.

(A)  58.5%

(B)  58.8%

(C)  59.0%

(D)  59.3%

Answer: (C)

PH: Physics

Q1 – Q25 carry one mark each.

1. Which one of the following is a solution of  for k real?

(A)  ekx

(B)  sin kx

(C)  cos kx

(D)  sin hx

Answer: (A)

2. A real, invertible 3 × 3 matrix M has eigenvalues λi, (i = 1, 2, 3) and the corresponding eigenvectors are  Which one of the following is correct?

Answer: (B)

3. A quantum particle is subjected to the potential

The ground state wave function of the particle is proportional to

Answer: (D)

4. Let  respectively denote the lowering and raising operators of a one-dimensional simple harmonic oscillator. Let  be the energy eigenstate of the simple harmonic oscillator. Given that is also an eigenstate of   the corresponding eigenvalue is

(A)  n(n – 1)

(B)  n(n + 1)

(C)  (n + 1)2

(D)  n2

Answer: (A)

5. Which one of the following is a universal logic gate?

(A)  AND

(B)  NOT

(C)  OR

(D)  NAND

Answer: (D)

6. Which one of the following is the correct binary equivalent of the hexadecimal F6C?

(A)  0110 1111 1100

(B)  1111 0110 1100

(C)  1100 0110 1111

(D)  0110 1100 0111

Answer: (B)

7. The total angular momentum j of the ground state of the  nucleus is

(A)  1/2

(B)  1

(C)  3/2

(D)  5/2

Answer: (D)

8. A particle X is produced in the process π+ + p → K+ + X via the strong interaction. If the quark content of the K+ is , the quark content of X is

(A)   

(B)  u u d

(C)  u u s

(D)   

Answer: (C)

9. A medium (εr > 1, μr = 1, σ > 0) is semi-transparent to an electromagnetic wave when

(A)  Conduction current >> Displacement current

(B)  Conduction current << Displacement current

(C)  Conduction current = Displacement current

(D)  Both Conduction current and Displacement current are zero

Answer: (B)

10. A particle is moving in a central force field given by  is the unit vector pointing away from the center of the field. The potential energy of the particle is given by

(A)  k/r2

(B)  k/2r2

(C)  −k/r2

(D)  −k/2r2

Answer: (D)

11. Choose the correct statement related to the Fermi energy (EF) and the chemical potential (μ) of a metal.

(A)  μ = EF only at 0 K

(B)  μ = EF at finite temperature

(C)  μ < EF at 0 K

(D)  μ > EF at finite temperature

Answer: (A)

12. Consider a diatomic molecule formed by identical atoms. If EV and Ee represent the energy of the vibrational nuclear motion and electronic motion respectively, then in terms of the electronic mass m and nuclear mass M, EV/Ee is proportional to

(A)  (m/M)1/2

(B)  m/M

(C)  (m/M)3/2

(D)  (m/M)2

Answer: (A)

13. Which one of the following relations determines the manner in which the electric field lines are refracted across the interface between two dielectric media having dielectric constants ε1 and ε2 (see figure) ?

(A)  ε1 sinθ1 = ε2 sinθ2

(B)  ε1 cosθ1 = ε2 cosθ2

(C)  ε1 tanθ1 = ε2 tanθ2

(D)  ε1 cotθ1 = ε2 cotθ2

Answer: (D)

14. If  are the electric and magnetic fields respectively, then  is

(A)  odd under parity and even under time reversal

(B)  even under parity and odd under time reversal

(C)  odd under parity and odd under time reversal

(D)  even under parity and even under time reversal

Answer: (C)

15. A small disc is suspended by a fiber such that it is free to rotate about the fiber axis (see figure). For small angular deflections, the Hamiltonian for the disc is given by

                                                             

where I is the moment of inertia and α is the restoring torque per unit deflection. The disc is subjected to angular deflections (θ) due to thermal collisions from the surrounding gas at temperature T and p0 is the momentum conjugate to θ. The average and t he root-mean-square angular deflection, θavg and θrms, respectively are

Answer: (B)

16. As shown in the figure, an ideal gas is confined to chamber A of an insulated container, with vacuum in chamber B. When the plug in the wall separating the chambers A and B is removed, the gas fills both the chambers. Which one of the following statements is true?

(A)  The temperature of the gas remains unchanged

(B)  Internal energy of the gas decreases

(C)  Temperature of the gas decreases as it expands to fill the space in chamber B

(D)  Internal energy of the gas increases as its atoms have more space to move around

Answer: (A)

17. Particle A with angular momentum j = 3/2 decays into two particles B and C with angular momenta j1 and j2, respectively. If  the value of α is ______.

Answer: (1 to 1)

18. Far from the Earth, the Earth’s magnetic field can be approximated as due to bar magnet of magnetic pole strength 4 × 1014 Assume this magnetic field is generated by a current carrying loop encircling the magnetic equator. The current required to do so is about 4 × 10n A, where n is an integer. The value of n is _____.

(Earth’s circumference: 4 × 107 m)

Answer: (7 to 7)

19. The number of distinct ways the primitive unit cell can be constructed for the two dimensional lattice as shown in the figure is_____.

Answer: (5 to 5)

20. A hydrogenic atom is subjected to a strong magnetic field. In the absence of spin-orbit coupling, the number of doubly degenerated states created out of the d-level is _______.

Answer: (3 to 3)

21. A particle Y undergoes strong decay Y → π + π. The isospin of Y is ______.

Answer: (2 to 2)

22. For a complex variable z and the contour c: |z| = 1 taken in the counter clockwise direction, _______.

Answer: (-2 to -2)

23. Let p be the momentum conjugate to the generalized coordinate q. If the transformation

Q = √2qm cos p

P = √2qm sin p

is canonical, then m = ______.

Answer: (0.5 to 0.5)

24. A conducting sphere of radius 1 m is placed in air. The maximum number of electrons that can be put on the sphere to avoid electrical breakdown is about 7 × 10n, where n is integer. The value of n is ______.

Assume:

Breakdown electric field strength in air is   

Permittivity of free space ε0 = 8.85 × 1012 F/m

Electron charge e = 1.60 × 1019 C

Answer: (14 to 15)

25. If a particle is moving along a sinusoidal curve, the number of degrees of freedom of the particle is ______.

Answer: (1 to 1)

Q26 – Q55 carry two marks each.

26. The product of eigenvalues of  is

(A)  −1

(B)  1

(C)  0

(D)  2

Answer: (A)

27. Let  Let ℝ3 denote the three-dimensional real vector space. Which one of the following is correct?

(A)  S is an orthonormal set

(B)  S is a linearly dependent set

(C)  S is a basis for ℝ3

(D)

Answer: (C)

28. denotes the spin operator defined as  Which one of the following is correct?

(A)  The eigenstates of spin operator  

(B)  The eigenstates of spin operator  

(C)  In the spin state upon the measurement of , the probability for obtaining  

(D)  In the spin state  upon the measurement of , the probability for obtaining  

Answer: (D)

29. The input voltage (Vin) to the circuit shown in the figure is 2cos(100t) V. The output voltage (Vout) is  If R = 1 kΩ, the value of C (in μF) is

(A)  0.1

(B)  1

(C)  10

(D)  100

Answer: (C)

30. Consider a 4-bit counter constructed out of four flip-flops. It is formed by connecting the J and K inputs to logic high and feeding the Q output to the clock input of the following flip-flop (see the figure). The input signal to the counter is series of square pulses and the change of state is triggered by the falling edge. At time t = t0 the outputs are in logic low state (Q0 = Q1 = Q2 = Q3 = 0). Then at t = t1, the logic state of the outputs is

(A)  Q0 = 1, Q1 = 0, Q2 = 0 and Q3 = 0

(B)  Q0 = 0, Q1 = 0, Q2 = 0 and Q3 = 1

(C)  Q0 = 1, Q1 = 0, Q2 = 1 and Q3 = 0

(D)  Q0 = 0, Q1 = 1, Q2 = 1 and Q3 = 1

Answer: (B)

31. Consider the Lagrangian  where a, b and c are constants. If px and py are the momenta conjugate to the coordinates x and y respectively, then the Hamiltonian is

Answer: (A)

32. Which one of the following matrices does NOT represent a proper rotation in a plane?

Answer: (D)

33. A uniform magnetic field  exists in an inertial frame K. A perfect conducting sphere moves with a constant velocity  with respect to this inertial frame. The rest frame of the sphere is K’ (see figure). The electric and magnetic fields in K and K’ are related as

The induced surface charge density on the sphere (to the lowest order in v/c) in the frame K’ is

(A)  maximum along z’

(B)  maximum along y’

(C)  maximum along x’

(D)  uniform over the sphere

Answer: (A)

34. A charge q moving with uniform speed enters a cylindrical region in free space at t = 0 and exits the region at t = τ (see figure). Which one of the following options best describes the time dependence of the total electric flux φ(t), through the entire surface of the cylinder?

Answer: (D)

35. Consider a one-dimensional non-magnetic crystal with one atom per unit cell. Assume that the valence electrons (i) dot not interact with each other and (ii) interact weakly with the ions. If n is the number of valence electrons per unit cell, then at 0 K,

(A)  the crystal is metallic for any value of n

(B)  the crystal is non-metallic for any value of n

(C)  the crystal is metallic for even values of n

(D)  the crystal is metallic for odd values of n

Answer: (D)

36. According to the Fermi gas model of the nucleus, the nucleons move in a spherical volume of radius R(=R0A1/3, where A is the mass number and R0 is an empirical constant with the dimensions of length). The Fermi energy of the nucleus EF is proportional to

(A)  R02

(B)  1/R0

(C)  1/R02

(D)  1/R03

Answer: (C)

37. Consider a two dimensional crystal with 3 atoms in the basis. The number of allowed optical branches (n) and acoustic branches (m) due to the lattice vibrations are

(A)  (n, m) = (2, 4)

(B)  (n, m) = (3, 3)

(C)  (n, m) = (4, 2)

(D)  (n, m) = (1, 5)

Answer: (C)

38. The internal energy U of a system is given by U(S, V) = λV2/3S2, where λ is a constant of appropriate dimensions; V and S denote the volume and entropy, respectively. Which one of the following gives the correct equation of state of the system?

Answer: (A)

39. The potential energy of a particle of mass m is given by U(x) = a sin(k2x – π/2), a > 0, k2 > 0. The angular frequency of small oscillations of the particle about x = 0 is

Answer: (B)

40. The radial wave function of a particle in a central potential is given by  where A is the normalization constant and a is positive constant of suitable dimensions. If γa is the most probable distance of the particle from the force center, the value of γ is _________.

Answer: (4 to 4)

41. A free particle of mass M is located in a three-dimensional cubic potential well with impenetrable walls. The degeneracy of the fifth excited state of the particle is __________.

Answer: (6 to 6)

42. Consider the circuit given in the figure. Let the forward voltage drop across each diode be 0.7 V. The current I (in mA) through the resistor is ____________.

Answer: (8 to 8)

43. Let uu denote the 4-velocity of a relativistic particle whose squre uuuμ = 1. If εμvρσ is the Levi-Civita tensor then the value of εμvρσuμuvuρuσ is ______.

Answer: (0 to 0)

44. Consider a simple cubic monoatomic Bravias lattice which has a basis with vectors  a is the lattice parameter. The Bragg reflection is observed due to t he change in the wave vector between the incident and the scattered beam as given by  where  are primitive reciprocal lattice vectors. For n1 = 3, n2 = 3 and n3 = 2, the geometrical structure factor is _______.

Answer: (2 to 2)

45. A plane electromagnetic wave of wavelength λ is incident on a circular loop of conducting wire. The loop radius is a(a << λ). The angle (in degrees), made by the Poynting vector with t he normal to the plane of the loop to generate a maximum induced electrical signal, is _______.

Answer: (-270 to -270 or -90 to -90 or 90 to 90 or 270 to 270)

46. An electron in a hydrogen atom is in the state n = 3, l = 2, m = − Let  denote the y-component of the orbital angular momentum operator. If  the value of α is ________.

Answer: (1 to 1)

47. A sinusoidal voltage of the form V(t) = V0 cos(ωt) is applied across a parallel plate capacitor placed in vacuum. Ignoring the edge effects, the induced emf within the region between the capacitor plates can be expressed as a power series in ω. The lowest non-vanishing exponent in ω is ________.

Answer: (2 to 2)

48. If  for –π ≤ x ≤ π, the value of a2 is ______.

Answer: (-1 to -1)

49. Let  

The value of  is _______.

Answer: (0 to 0)

50. Consider the Hamiltonian  where

 is the time independent penturbation given by

  where k > 0. If the maximum energy eigenvalue of  is 3 eV corresponding to E = 2 eV, the value of k (rounded off to three decimal places) in eV is ______.

Answer: (0.706 to 0.708)

51. A hydrogen atom is in an orbital angular momentum state  lies on a cone which makes a half angle 30° with respect to the z-axis, the value of l is _______.

Answer: (3 to 3)

52. In the center of mass frame, two protons each having energy 7000 GeV, collide to produce protons and anti-protons. The maximum number of anti-protons produced is_______.

(Assume the proton mass to be 1 GeV/c2)

Answer: (6999 to 6999)

53. Consider a gas of hydrogen atoms in the atmosphere of the Sun where the temperature is 5800 K. If a sample from this atmosphere contains 6.023 × 1023 of hydrogen atoms in the ground state, the number of hydrogen atoms in the first excited state is approximately 8 × 10n, where n is an integer. The value of n is ______.

(Boltzmann constant: 8.617 × 10−5 eV/K)

Answer: (14 to 15)

54. For a gas of non-interacting particles, the probability that a particle has a speed v in the interval v to v + dv is given by

             

If E is the energy of a particle, then the maximum in the corresponding energy distribution in units of E/kBT occurs at _______ (rounded off to one decimal place).

Answer: (0.5 to 0.5)

55. The Planck’s energy density distribution is given by  At long wavelengths, the energy density of photons in thermal equilibrium with a cavity at temperature T varies as Tα, where α is _______.

Answer: (1 to 1)

GATE Exam 2020 Petroleum Engineering (PE) Question Paper With Answer Key

GATE-2020

PE-Petroleum Engineering

GA – General Aptitude

Q1 – Q5 carry one mark each.

1. He is known for his unscrupulous ways. He always sheds______ tears to deceive people.

(A)  fox’s

(B)  crocodile’s

(C)  crocodile

(D)  fox

Answer: (C)

2. Jofra Archer, the England fast bowler, is ____ than accurate.

(A)  more fast

(B)  faster

(C)  less fast

(D)  more faster

Answer: (A)

3. Select the word that fits the analogy:

Build : Building :: Grow : ______

(A)  Grown

(B)  Grew

(C)  Growth

(D)  Growed

Answer: (C)

4. I do not think you know the case well enough to have opinions. Having said that, I agree with your other point.

What does the phrase “having said that” mean in the given text?

(A)  as opposed to what I have said

(B)  despite what I have said

(C)  in addition to what I have said

(D)  contrary to what I have said

Answer: (B)

5. Define [x] as the greatest integer less than or equal to x, for each x ∈ (−∞, ∞). If y = [x], then area under y for x ∈ [1, 4] is _______.

(A)  1

(B)  3

(C)  4

(D)  6

Answer: (D)

Q6 – Q10 carry two marks each.

6. Crowd funding deals with mobilization of funds for a project from a large number of people, who would be willing to invest smaller amounts through web-based platforms in the project.

Based on the above paragraph, which of the following is correct about crowd funding?

(A)  Funds raised through unwilling contributions on web-based platforms.

(B)  Funds raised through large contributions on web-based platforms.

(C)  Funds raised through coerced contributions on web-based platforms.

(D)  Funds raised through voluntary contributions on web-based platforms.

Answer: (D)

7. P, Q, R and S are to be uniquely coded using α and β. If P is coded as αα and Q as αβ, then R and S, respectively, can be coded as ______.

(A)  βα and αβ

(B)  ββ and αα

(C)  αβ and ββ

(D)  βα and ββ

Answer: (D)

8. The sum of the first n terms in the sequence 8, 88, 888, 8888, … is ______.

(A)   

(B)   

(C)   

(D)   

Answer: (D)

9. Select the graph that schematically represents BOTH y = xm and y = x1/m properly in the interval 0 ≤ x ≤ 1, for integer values of m, where m > 1.

Answer: (A)

10. The bar graph shows the data of the students who appeared and passed in an examination for four schools P, Q, R and S. The average of success rates (in percentage) of these four schools is ________.

(A)  58.5%

(B)  58.8%

(C)  59.0%

(D)  59.3%

Answer: (C)

PE: Petroleum Engineering

Q1 – Q25 carry one mark each.

1. Consider a vector field,    are the unit vectors along the x,  y, and z directions, respectively. The divergence of A at the point (1, 1, 1) is equal to

(A)  0

(B)  2

(C)  3

(D)  4

Answer: (D)

2. Inverse Laplace transform of the function,  is given by

(A)  1 – et

(B)  1 + et

(C)  1 – et

(D)  1 + et

Answer: (C)

3. The solution of the differential equation,  with the condition y = 1 at x = 1, is given by

Answer: (D)

4. Two complex numbers are given as,  where, I = √−1, and θ1 and θ2 are the principal arguments, Given, θ1 ≠ θ2 and |θ1 – θ2| ≠ π. If  which one of the following conditions is correct?

(A)  2 < m < 3

(B)  0 < m < 2

(C)  m = 2

(D)  m = 0

Answer: (B)

5. Match the following

(A)  P-I, Q-II, R-III

(B)  P-II, Q-I, R-III

(C)  P-I, Q-III, R-II

(D)  P-III, Q-I, R-II

Answer: (D)

6. Shear stress versus shear rate plots for four different fluids are given in the Figure. Which curve represents a pseudoplastic fluid?

(A)  I

(B)  II

(C)  III

(D)  IV

Answer: (C)

7. Which one of the following is NOT a desired function of a hydraulic fracturing fluid additive?

(A)  Oxygen scavenging to prevent attack on polymers.

(B)  Increasing viscosity of fracturing fluid during flow back.

(C)  Work as bactericide.

(D)  Work as surfactant to facilitate post treatment clean-up.

Answer: (B)

8. Formation damage could be a result of

(i) scale formation near the wellbore

(ii) coke formation due to in-situ combustion

(iii) precipitation of asphaltene

(iv) condensate banking

Which one of the following options is correct?

(A)  (i) and (iv) only

(B)  (i) and (iii) only

(C)  (i), (ii), and (iii) only

(D)  (i), (ii), (iii) and (iv)

Answer: (D)

9. Which of the following statement(s) about gas and water coning in the reservoir is/are correct?

(i) Gas and water coning is characterized by downward movement of water and  upward movement of gas near the producing wellbore.

(ii) Gas and water coning is characterized by downward movement of gas and upward movement of water near the producing wellbore.

(iv) Gas and water coning is caused when gravitational forces dominate over viscous forces.

(A)  (i) and (iv) only

(B)  (ii) only

(C)  (ii), (iii), and (iv) only

(D)  (iv) only

Answer: (B)

10. Given the figure

Which one of the following options represents the correct combination of the trajectory number and the corresponding drilling type?

(A)  i → Build and Hold, ii → S-Type, iii → Modified S-Type, iv → Continuous Build

(B)  i → Continuous Build, ii → Build and Hold, iii → Modified S-Type, iv → S-Type

(C)  i → Continuous Build, ii → S-Type, iii → Modified S-Type, iv → Build and Hold

(D)  i → Build and Hold, ii → Modified S-Type, iii → S-Type, iv → Continuous Build

Answer: (B)

11. A stable geothermal gradient (approx. 25°C/km) in the earth’s crust will suddenly increase to a higher gradient value, when

(A)  there is excessive erosion or upliftment

(B)  there is excessive subsidence or deposition

(C)  there is excessive subsidence and  upliftment simultaneously

(D)  there is excessive subsidence and erosion simultaneously

Answer: (A)

12. A drawdown test is conducted at a constant flow rate in an oil well for a reservoir with constant compressibility. Which one of the following is valid for semi steady state condition?

(A)  Rate of pressure change at the wellbore is less than that at the boundary.

(B)  The effect of the outer boundary of the reservoir is felt at the wellbore.

(C)  Reservoir permeability does not affect the wellbore pressure.

(D)  Pressure in the reservoir does not change with time.

Answer: (B)

13. Formation volume factor (B0) versus Pressure (P) plot for an oil is given in the Figure.

Match the following with the corresponding pressure given in the Figure.

(I) Bubble point

(II) Saturated oil

(III) Under-saturated oil

(A)  I-P1, II-P2, III-P3

(B)  I-P1, II-P3, III-P2

(C)  I-P2, II-P1, III-P3

(D)  I-P2, II-P3, III-P1

Answer: (C)

14. Which one of the following statements is NOT correct?

(A)  Flash point of gasoline is lower than that of diesel.

(B)  Pour point is the temperature at which oil creases to flow.

(C)  Higher the Diesel Index of a fuel, higher is its cetane number.

(D)  Higher the aromatic content of diesel, higher is its aniline point.

Answer: (D)

15. Which one of the following additives is commonly added to drilling fluids to remove hydrogen sulfide?

(A)  Sodium chloride

(B)  Calcium chloride

(C)  Zinc carbonate

(D)  Bentonite

Answer: (C)

16. Two rigid spherical particles of the same density, with a diameter ratio D1 : D2 = 1:2, settle freely through a pool of liquid. The terminal settling velocity is given by the Stoke’s law. What is the ratio of their terminal settling velocities, V1 : V2 ?

(A)  1:2

(B)  2:1

(C)  1:4

(D)  4:1

Answer: (C)

17. Which one of the following options best represents the correct order of increasing thermal conductivity of the subsurface formations?

(A)  Coal < Shale < Dolomite < Evaporite

(B)  Evaporite < Shale < Coal < Dolomite

(C)  Coal < Shale < Evaporite < Dolomite

(D)  Shale < Coal < Evaporite < Dolomite

Answer: (A)

18. Which one of the following options is the correct combination of kerogen Type and the source from which it is derived?

(A)  Type I-Lacustrine, Type II-Terrestrial, Type III-Marine, Type IV-Varied

(B)  Type I-Lacustrine, Type II- Marine, Type III- Terrestrial, Type IV-Varied

(C)  Type I-Lacustrine, Type II- Varied, Type III- Marine, Type IV- Terrestrial

(D)  Type I- Marine, Type II- Terrestrial, Type III- Varied, Type IV- Lacustrine

Answer: (B)

19. The number of power outages in a city in a given time interval is a Poisson random variable with a mean of 2 power outages per month. The Poisson distribution is given by, 

The probability of exactly 2 power outages in 2 months (rounded off to two decimal places) is _______.

Answer: (0.12 to 0.18)

20. Anhydrous sodium hydroxide is added to 10 litre of water to raise its pH from 7.0 to 9.0. The molar mass of sodium hydroxide is 40 g/mol. Assuming complete dissociation of sodium hydroxide and zero volume change of mixing, the amount of sodium hydroxide added (rounded off to two decimal places) is ______ mg.

Answer: (3.85 to 4.10)

21. Consider unidirectional, laminar flow of water through a homogeneous porous media as shown in the Figure. Here, H = 100 m, W = 500 m, L = 500 m, permeability of the porous media is 1012 m2, and the driving pressure drop (across length L) is 106 Use the viscosity of water as 103 Pa.s.