Gate 2017 Life Sciences Question Paper 12th Feb 2017 PDF Download

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Life Sciences 12th Feb 2017

Subject Name: Life Sciences

Duration : 180

Total Marks: 100

 

Chemistry (XL-P)

1. CO reacts readily with

(A)  Fe

(B)  Fe2+

(C)  Fe4+

(D)  Fe3+

Ans: (A)

2. Molecules that are NOT isoelectronic to  ion are

(A)   

(B)   

(C)   

(D)   

Ans: (D)

3. The extensive quantity among the following is

(A)  Pressure

(B)  Temperature

(C)  Chemical potential

(D)  Volume

Ans: (D)

4. The compound that gives characteristic foul smell upon heating with potassium hydroxide and chloroform is

(A) 

(B) 

(C) 

(D) 

Ans: (B)

5. The correct order of stability in water is

(A) 

(B) 

(C) 

(D) 

 Ans: (A)

6. The pair o f molecules having non-linear structures is

(A) 

(B) 

(C) 

(D) 

Ans: (C)

7. The decreasing order of bond lengths for O2, B2, N2 and C2 is

(A)  B2 > C2 > N2 > O2

(B)  B2 > C2 > O2 > N­2

(C)  N2 > C2 > O2 > B2

(D)  B2 > O2 > N2 > C2

Ans: (B)

8. The octahedral metal oxide with the highest CFSE value is

(A)  ZnO

(B)  MnO

(C)  VO

(D)  TiO

Ans: (C)

9. Assuming independent non-interacting electrons, the first ionization energy of Helium atom is

(A)  13.6 eV

(B)  27.2 eV

(C)  54.4 eV

(D)  108.8 eV

Ans: (C)

10. For a reaction A + B → products, the following data was obtained.

A0 and B0 are initial concentrations of A and B, respectively. The overall order of the reaction is

(A)  2

(B)  3

(C)  4

(D)  6

Ans: (B)

11. The EMF for the following cell at 298.15 K is

Ag(s) | Ag+ (aq., 0.01 M)|| Ag+(aq., 1.0 M)|Ag(s)

(Standard reduction potential for Ag+ + e → Ag is −0.80 V)

(A)  0.12 V

(B)  0.68 V

(C)  0.80 V

(D)  0.92 V

Ans: (A)

12. One gram of a protein is dissolved in one liter of water. The resulting solution exerts an osmotic pressure of 1.4 Torr at 298 K. Assuming that the protein does not ionize in solution, the molecular weight of the protein is ______ g mol1. (R = 0.082 L atm mol1 K1)

Ans: (13260 to 13285)

13. The type of nucelophilic substitution and the possible products for each of the reactions P and Q are

(A) 

(B) 

(C) 

(D) 

Ans: (A)

14. If mono-chlorination occurs at every carbon in the following reaction, the number of isomers (stereo isomers + constitutional isomers) that one can have is

(A)  4

(B)  5

(C)  6

(D)  8

Ans: (C)

15. The major product in the following reaction is 

(A) 

(B) 

(C) 

(D) 

Ans: (A)

Biochemistry (XL-Q)

16. The molecular weights of a protein as determined by native PAGE is 400 kDa. This protein when run on a non-reducing SDS-PAGE gave band of 200 kDa and on a reducing SDS-PAGE, gave a band of 100 kDa. The protein is

(A)  four subunits of which two sets are linked by two disulfide bridges

(B)  four subunits of which are linked by four disulfide bridges

(C)  two subunits only and none are linked by disulfide bridges

(D)  two subunits which are linked by disulfide bridges

Ans: (A)

17. Which one of the following techniques CANNOT be used to determine the sequence of a novel protein?

(A)  Deo novo sequencing by ESI-MS/MS

(B)  Edman degradation

(C)  Sanger sequencing

(D)  Peptide mass fingerprinting

Ans: (D)

18. Which type of polyacrylamide gel can be used for analyzing the four different proteins listed below?

Protein P: 60 kDa, pI 4

Protein Q: 45 kDa, pI 8

Protein R: 60 kDa, pI 6

Protein S: 45 kDa, pI 7.5

(A)  20% gel, pH 4-7

(B)  20% gel, pH 3-10

(C)  12% gel, pH 3-10

(D)  12% gel, pH 4-7

Ans: (C)

19. The number of fragments generated when the peptide ‘ANDCQEGKFMLKPDTWRYVSFMRPA’ is subjected to complete digestion with trypsin are ….

Ans: (3.0)

20. Puromycin is a structural analog of

(A)  alanyl-tRNA

(B)  tyrosyl-tRNA

(C)  methionyl-tRNA

(D)  glycyl-tRNA

Ans: (B)

21. Which one of the enzymes is responsible for arsenic toxicity?

(A)  Pyruvate kinase

(B)  Aldolase

(C)  Phosphofructokinase

(D)  Pyruvate dehydrogenase

Ans: (D)

22. Which one is TRUE for Calvin cycle?

(A)  Glycerol 3-phosphate is generated in this cycle

(B)  CO2 is not consumed in this cycle

(C)  This is a reductive pentose phosphate cycle

(D)  Ribose 5-phospate is a carboxylation substrate in this cycle

Ans: (C)

23. Administration of primaquine causes severe hemolytic anemia because it

(A)  increases the demand for NADPH to a level that cells can’t meet

(B)  decreases the demand for NADPH

(C)  inactivates glutathione peroxidase of erythrocytes

(D)  increases reduced glutathione level of erythrocytes

Ans: (A)

24. Which one of the following will NOT from lipid bilayer?

(A)  Cholesterol

(B)  Phosphatidyl ethanolamine

(C)  Triacylglycerol

(D)  Phosphatidyl serine

Ans: (C)

25. Which one of the following features is NOT appropriate for Fab fragment of IgG?

(A)  Contains antigen binding site

(B)  Contains an intact L chain

(C)  Two fragments are formed from one IgG molecule

(D)  Mediates complement fixation in the intact IgG molecule

Ans: (D)

26. The duration of DNA synthesis (S phase) in plant cells is 11 h and the DNA is replicated at rate of 100 bp/s fork. A plant species has about 3.0 × 1010 bp DNA/genome. The number of bidirectional forks per genome required for replication will be …………..

Ans: (7575 to 7576)

27. In a PCR reaction, with one double stranded DNA of 600 bp, nano gram of DNA produced after 40 cycles of amplification will be ………

Ans: (722 to 725)

28. A solution containing GTP has molar extinction coefficient of 1.55 × 104 mol1 dm3 cm1 at a given wavelength. The concentration of GTP solution is 1.290 × 105 mol dm3. The absorbance of GTP solution in 1 cm cuvette at the same wavelength will be ….

Ans: (0.19 to 0.20)

29. Which one of the following is NOT TRUE for class I MHC protein?

(A)  MHC class I protein are polymorphic

(B)  T-cell receptors recognizes MHC class I  protein

(C)  MHC class I protein are displayed on the surface of nucleated vertebrate cells

(D)  β2-microglobulin is covalently associated with MHC class I protein

Ans: (D)

30. In an enzyme catalyzed reaction, the initial reaction velocity is only one fourth of its maximum velocity. If the substrate concentration is 3.0 × 103 mM, the value of Km in micro molar (μM) will be ….

Ans: (9.0 to 9.0)

31. Match the following enzymes in column I with their cofactors in column II

Column I

(P) Pyruvate decarboxylase

(Q) Glyceraldehyde 3-phosphate dehydrogenase

(R) Pyruvate carboxylase

(S) Glucose-6-phosphate dehydrogenase

Column II

i. Biocytin

ii, NADP+

iii. NAD+

iv. Thiamine pyrophosphate

(A)  P-ii; Q-i; R-iv; S-iii

(B)  P-iv; Q-iii; R-i; S-ii

(C)  P-i; Q-ii; R-iii; S-iv

(D)  P-iii; Q-i; R-iv; S-ii

Ans: (B)

32. Match the molecule in column I with its function in column II

Column I

(P) Cholera toxin

(Q) Pertussis toxin

(R) IP3

(S) Caffeine

Column II

(i) modifies Gαi

(ii) inhibits c-AMP phosphodiesterase

(iii) modifies GαS

(iv) increases interacellular Ca2+ level

(A)  P-iii; Q-i; R-iv; S-ii

(B)  P-iv; Q-i; R-iii; S-ii

(C)  P-ii; Q-iv; R-i; S-iii

(D)  P-iii; Q-i; R-ii; S-iv

Ans: (A)

33. In an in vitro dehydrogenatin reaction of succinate catalyzed by succinate dehydrogenase, malonate is added. Which one of the following curves represents the effect of malonate on the catalysis of succinate dehydrogenase?

(A) 

(B) 

(C) 

(D) 

Ans: (A)

34. Cardiotonic steroids have ability to strengthen heart muscle contraction due to the fact that these steroids

(A)  inhibit K+-dependent dephosphorylation of Na+-K+ ATPase

(B)  activate Na+-K+ ATPase

(C)  increase uptake of Na+ by activation of Na+-Ca2+ exchanger

(D)  increase uptake of Ca2+ by activation of Na+-Ca2+ exchanger

Ans: (A)

35. A newly isolated circular plasmid gave two bands of 3.2 and 3 kb on digestion with EcoRI and two bands of 5.0 kb and 1.2 kb on digestion with BamHI. Double digestion with EcoRI and BamHI, yielded four bands of 2.6 kb, 2.4 kb, 0.8 kb and 0.4 kb. Digestion with SalI led to disruption of ampicillin resistance gene cassette. The correct restriction map is

(A) 

(B) 

(C) 

(D) 

Ans: (B)

Botany (XL-R)

36. As per the Angiosperm Phylogeny Group (APG II, 2003) classification, which of the following plant families comprises of only single genus with single species?

(A)  Lauraceae

(B)  Aristolochiaceae

(C)  Amborellaceae

(D)  Typhaceae

Ans: (C)

37. A cavity, lysigenous in origin and possessing volatile oil is found in the pericarp of one of the following plants. Identify the CORRECT answer.

(A)  Litchi

(B)  Citrus

(C)  Mango

(D)  Coconut

Ans: (B)

38. Among the following, which genetic material is naturally inherited through maternal inheritance in higher plants?

(A)  Nuclear DNA 

(B)  Plasmid DNA

(C)  Chloroplast DNA

(D)  T-DNA

Ans: (C)

39. A typical floral meristem differs from shoot apical meristem on the basis of

(A)  Determinate growth

(B)  Presence of auxin

(C)  Presence of stem cells

(D)  Negative geotropism

Ans: (A)

40. Which of the following plant hormones is a carotenoid-cleavage product?

(A)  Phytosulfokine

(B)  Brassinosteroid

(C)  Methyl jasmonate

(D)  Strigolactone

Ans: (D)

41. Two of the vir operons of Ti plasmid in Agrobacterium tumefaciens are constitutively expressed. Identify the CORRECT pair.

(A)  virA and virG

(B)  virF and virH

(C)  virC and virD

(D)  virB and virE

Ans: (A)

42. Which of the following fungi is an example of obligate biotrophic plant pathogen?

(A)  Alternaria brassicicola

(B)  Botrytis cinerea

(C)  Puccinia triticina

(D)  Sclerotinia sclerotiorum

Ans: (C)

43. The phenomenon where an organism lives at the expense of another organism by harming it but not killing, is called

(A)  Commensalism

(B)  Predation

(C)  Symbiosis

(D)  Parasitism

Ans: (D)

44. Which of the following is TRUE for K-strategist species?

(A)  Produce relatively large number of offspring

(B)  Population often grow exponentially

(C)  Provide relatively little or no parental care to offspring

(D)  Occur in stable and predictable habitats

Ans: (D)

45. Identify the INCORRECT statement with relation to plant secondary metabolites.

(A)  Atropine is a member of indole alkaloids

(B)  Limonene is a cyclic terpene found in citrus plants

(C)  Green tea is rich in polyphenols

(D)  Cyanidin contributes to the red colour in rose petals

Ans: (A)

46. Choose the CORRECT set of matches between group I and group II in relation to nitrogen fixation and assimilation

Group I                           Group II

(P) Nitrobacter                 1. NO3 → NO2

(Q) Nitrite reductase        2. N2 → 2NH3

(R) Nitrogenase               3. NO2 → NH4+

(S) Nitrate reductase       4. NO2 → NO3

(A)  P-4, Q-3, R-2, S-1

(B)  P-4, Q-3, R-1, S-2

(C)  P-1, Q-2, R-4, S-3

(D)  P-3, Q-4, R-2, S-1

Ans: (A)

47. Two plant cells M and N are lying side by side making direct contact. “M” has osmotic potential (Ψs) of -10 bar and pressure potential (Ψp) of 4 bar. On the other hand, “N” has osmotic potential (Ψs) of -12 bar and pressure potential (Ψp) of 5 bar.

Based on these data, what would be the direction of movement of water between M and N?

(A)  M to N

(B)  N to M

(C)  There will be no movement

(D)  In both directions

Ans: (A)

48. Two independent non-segregating recessive mutants (m1 and m2) display similar defects in petal formation. When they were crossed with each other (m1 x m2), all the F1 plants developed normal petals. In view of this observation, which of the following conclusions is CORRECT?

(A)  Mutations in both m1 and m2 are in the same gene

(B)  Mutations in both m1 and m2 are in two separate genes

(C)  Inheritance is non-Mendelian

(D)  None of the above

Ans: (B)

49. In a hypothetical trihybrid cross of three loci (viz. A, B, C), all were inherited in a complete dominant manner over their recessive alleles a, b, c, respectively. When a test cross between F1 and parent ‘aabbcc’ was performed, following genotypes of eight phenotypically distinct classes were observed with respective numbers

The genetic distance (up to one decimal) between A and C loci will be _____cM.

Ans: (18.3 to 18.5)

50. In a typical sexually reproducing angiospermic plant, if an endosperm cell contains 4.8 × 108 nucleotide pairs of DNA, then microsporocyte of this plants will have ________× 108 nucleotide pairs of DNA.

Ans: (3.2)

51. Identify the CORRECT matching between group I and group II in relation to ecology

Group I

(P) The physical environment of an organism

(Q) The totality of the needs of a population for survival and its resource utilization

(R) The position of a species in a food chain

(S) Basic functional unit comprising living community and its physical environment

Group II

1. Trophic level

2. Habitat

3. Ecosystem

4. Niche

5. Ecological pyramid

(A)  P-2, Q-5, R-4, S-1

(B)  P-2, Q-4, R-1, S-3

(C)  P-5, Q-2, R-3, S-1

(D)  P-1, Q-3, R-4, S-2

Ans: (B)

52. Choose the CORRECT set of matches between group I and group II in relation to plant genetic transformation methods.

Group I                           Group II

(P) Helium                        1. Agrobacterium tumefaciens

(Q) Acetosyringone          2. Microinjection

(R) Polyethylene glycol    3. Particle bombardment

(S) Agarose embedding   4. Protoplast

(A)  P-4, Q-3, R-2, S-1

(B)  P-2, Q-1, R-4, S-3

(C)  P-3, Q-4, R-1, S-2

(D)  P-3, Q-1, R-4, S-2

Ans: (D)

53. Match the pathogen, disease caused and the affected plant in the CORRECT combination.

Pathogen Disease Plant
(P) Blumeria graminis i. Blast disease 1. Groundnut
(Q) Magnaparthe grisea ii. Powdery mildew 2. Apple
(R) Venturia inaequalis iii. Tikka disease 3. Barley
(S) Cercospora personata iv. Scab disease 4. Rice

(A)  P-i-1, Q-ii-2, R-iii-3, S-iv-4

(B)  P-i-2, Q-ii-1, R-iii-4, S-iv-3

(C)  P-ii-3, Q-i-4, R-iv-2, S-iii-1

(D)  P-ii-3, Q-i-4, R-iii-2, S-iv-1

Ans: (C)

54. Choose the plant part, its use and the source species in CORRECT combination.

Plant Part Use Species
P. Bark i. Insecticide 1. Crocus sativus
Q. Leaf ii. Food colorant 2. Papaver somniferum
R. Capsule iii. Flavoring agent 3. Azadirachta indica
S. Stigma iv. Analgesic 4. Cinnamomum zeylanicum

(A)  P-i-1, Q-ii-2, R-iii-3, S-iv-4

(B)  P-iii-4, Q-ii-1, R-iv-2, S-i-3

(C)  P-ii-1, Q-i-3, R-iv-2, S-iii-4

(D)  P-iii-4, Q-i-3, R-iv-2, S-ii-1

Ans: (D)

55. Which two of the following reactions are INCORRECT in relation to C2 oxidative photosynthetic carbon cycle in land plants?

P. 2(Ribulose-1, 5-biphosphate) + 2(CO2) → 2(phosphoglycolate) + 2(3-phosphoglycerate) + 4H+

Q. Serine + α-ketoglutarate → hydroxypyruvate + glutamine

R. 2(Phosphoglycolate) + 2(H2O) → 2(glycolate) + 2Pi

S. Hydroxypyruvate + NADH + H+ → glycerate + NAD+

(A)  P and Q

(B)  Q and R

(C)  R and S

(D)  S and P

Ans: (A)

Microbiology (XL-S)

56. Which one of the following is the end product of dissimilatory sulfate reduction by sulfate reducing bacteria?

(A)  Hydrogen sulfide

(B)  Sulfur dioxide

(C)  Sulfur

(D)  Thiosulfate

Ans: (A)

57. Which one of the following is the terminal electron acceptor in the given metabolic reaction catalyzed by methanogens?

4H2 + CO2 → CH4 + 2H2O

(A)  H2

(B)  CO2

(C)  CH4

(D)  H2O

Ans: (A)

58. Microbes that have their optimal growth rate near 15℃ but can still grow at 0℃ to 20℃ are known as

(A)  mesophiles

(B)  psychrotrophs

(C)  psychrotolerant

(D)  psychrophiles

Ans: (D)

59. Which one of the following is NOT a contribution by Robert Koch?

(A)  Identification of causative agent of anthrax.

(B)  Discovery of causative agent of tuberculosis.

(C)  Discovery of causative agent of leprosy.

(D)  Identification of causative agent of cholera.

Ans: (C)

60. Unicellular eukaryotic organisms belong to which one of the following kingdoms of classification?

(A)  Monera

(B)  Plantae

(C)  Protista

(D)  Animalia

Ans: (C)

61. Which one of the following is a contagious disease?

(A)  Chickenpox

(B)  Tetanus

(C)  Malaria

(D)  Filariasis

Ans: (A)

62. The inner mitochondrial membrane comprises of a series of folds known as

(A)  cristae

(B)  thylakoids

(C)  cisterns

(D)  cilia

Ans: (A)

63. Which one of the following antibiotics is NOT produced by Streptomyces?

(A)  Amphotericin B

(B)  Neomycin

(C)  Vancomycin

(D)  Gentamicin

Ans: (D)

64. Which one of the following statements is TRUE about MacConkey (MAC) agar medium?

(A)  MAC agar medium is a selective and differential medium for Gram-positive bacteria.

(B)  MAC agar medium is a selective and differential medium for Gram-negative bacteria.

(C)  MAC agar medium is an enriched medium for Gram-positive bacteria.

(D)  MAC agar medium is a synthetic medium for Gram-positive and Gram-negative bacteria.

Ans: (B)

65. As an antiseptic, alcohol is effective against

(A)  bacteria and non-enveloped viruses

(B)  bacterial endospores and fungi

(C)  bacteria and fungi

(D)  fungi and non-enveloped viruses

Ans: (C)

66. An antigen X was injected into a rabbit for the first time at time P. Then the rabbit was given a booster dose of X at time Q. Which one of the following figures accurately depicts the adaptive immune response by the rabbit against X?

(A)  i

(B)  ii

(C)  iii

(D)  iv

Ans: (A)

67. A bactericidal agent X is added after 3 hours of growth of a bacterial culture. Following the addition of X, the bacterial growth was measured using the standard plate count method till 24 hours. Which one of the following figures is the most accurate representation of the action of X?

(A)  i

(B)  ii

(C)  iii

(D)  iv

Ans: (B)

68. Match the diseases given in Group I with their causative agents from Group II.

Group I                           Group II

(P) Plague               (I) Coxiella burnetii

(Q) Rabies              (II) Plasmodium spp.

(R) Q fever              (III) Yersinia pestis

(S) Malaria              (IV) Lyssavirus

(A)  P-III, Q-IV, R-I, S-II

(B)  P-III, Q-I, R-II, S-IV

(C)  P-IV, Q-III, R-I, S-II

(D)  P-III, Q-I, R-IV, S-II

Ans: (A)

69. Match the enzymes given in Group I with the events from Group II.

Group I

(P) UvrABC endonulcease

(Q) Reverse transcriptase

(R) AP endonuclease

(S) ATP sulfurylase

Group II

(I) Retrovirus replication

(II) Base excision repair

(III) Nucleotide excision repair

(IV) Pyrosequencing

(A)  P-II, Q-I, R-IV, S-III

(B)  P-III, Q-I, R-II, S-IV

(C)  P-IV, Q-III, R-I, S-II

(D)  P-II, Q-I, R-III, S-IV

Ans: (B)

70. Match the terms given in Group I with the descriptions from Group II.

Group I

(P) Photoautotrophs

(Q)Chemoautotrophs

(R) Photoheterotrophs

(S) Chemoheterotrophs

Group II

(I) Use inorganic chemical reactions for energy production

(II) Use organic compounds for energy production

(III) Use sunlight as energy source and carbon dioxide as carbon source

(IV) Use sunlight as energy source and organic compounds as carbon source

(A)  P-II, Q-I, R-IV, S-III

(B)  P-III, Q-I, R-IV, S-II

(C)  P-IV, Q-III, R-I, S-II

(D)  P-II, Q-IV, R-III, S-I

Ans: (B)

71. One-ml sample of a bacterial culture was serially diluted to 105 times, and 46 colonies were obtained after plating this diluted sample on an agar medium. The number of cells present per ml in the undiluted original sample were_______

Ans: (4550000 to 4650000)

72. The transformation efficiency of competent cells prepared in a laboratory is 104 CFU/μg of plasmid DNA. If 0.01 μg of this plasmid is used to transform these competent cells, the number of transformed bacteria in CFU after plating will be ________

Ans: (99 to 101)

73. Assume that the average DNA content of a single microbial cell is 4 femtogram. A soil sample analyzed for its microbial community DNA is found to contain 0.32μg DNA per gram of the soil. The number of microbial cells per milligram of the soil are _______

Ans: (78000 to 82000)

74. Assume that a bacterial culture has mean generation time of 2 hours. If the number of bacteria present after 24 hours of culture are 4.1 × 107, the initial number of bacteria present were ________

Ans: (78000 to 82000)

75. The minimal inhibitory concentration (MIC) of an antibiotic X against Clostribdium tetaniStaphylococcus Shigella sp., and Streptococcus sp. is 25, 15, 2 and 1 μg/ml, respectively. Assuming that the bioavailable concentration of X in an animal model is 20 μg/ml, which one of these bacteria may develop resistance against X in the animal model?

(A)  Clostridium tetani

(B)  Staphylococcus sp.

(C)  Shigella sp.

(D)  Streptococcus sp.

Ans: (A)

Zoology (XL-T)

76. The characteristic feature of deuterostomes is depicted by

(A)  coelom formed  by the hollowing out of a previously solid cord of mesodermal cells

(B)  spiral and determinate cleavage

(C)  formation of mouth from blastopore

(D)  formation of anus from blastopore

Ans: (D)

77. One of the most remarkable features of evolution is the formation of amnion and allantoin. This appeared for the “first time” in evolutionary time scale in

(A)  reptiles

(B)  birds

(C)  fishes

(D)  humans

Ans: (A)

78. A woman with blood group A gave birth to a baby with blood group AB. The blood group of the father would be

(A)  only AB

(B)  only B

(C)  either AB or B

(D)  blood group O

Ans: (C)

79. The enzyme amylase can break alpha glycosidic linkages between glucose monomers. Hence amylase can digest which one of the following carbohydrates?

(A)  Cellulose

(B)  Starch

(C)  Chitin

(D)  Xylans

Ans: (B)

80. The metabolic pathway which is common to both fermentation and cellular respiration is

(A)  the TCA cycle

(B)  the electron transport chain

(C)  glycolysis

(D)  synthesis of acetyl CoA from pyruvate

Ans: (C)

81. A female “Spotted sand piper” courts males repeatedly. This behavior can be explained by the term

(A)  polyandry

(B)  polygyny

(C)  monogamy

(D)  sexual cannibalism

Ans: (A)

82. Malaria is caused by Plasmodium species, which is a parasite having a complex life cycle. The fusion between male and female gametocytes of Plasmodium happens inside

(A)  human liver

(B)  human RBCs

(C)  mosquito midgut

(D)  mosquito salivary glands

Ans: (C)

83. Aromatase inhibitors are often prescribed for post-menopausal women to treat estrogen receptor positive breast cancer patients, because these class of drugs

(A)  reduce prostaglandin biosynthesis

(B)  reduce the level of estradiol biosynthesis

(C)  inhibit conversion of testosterone to dihydrotestosterone

(D)  are non-toxic in post-menopausal women

Ans: (B)

84. The covalent modification performed by kinases which regulate proteins in signaling pathways is

(A)  glycosylation

(B)  methylation

(C)  ubiquitination

(D)  phosphorylation

Ans: (D)

85. Which one of the following statements is NOT correct?

(A)  During metaphase, the 2 copies of chromosomal DNA are  held together at the centromere

(B)  The short arm of chromosomes is referred to as p and the long arm is referred to as q

(C)  The terminal structures at the end of the chromatids are referred to as telomeres.

(D)  The terms heterochromatin and euchromatin refer to the active and repressed regions of the chromosome respectively.

Ans: (D)

86. A particular species is found to have 2n = 16 chromosomes. The n umber of linkage groups in this species will be ______

Ans: (8.0 to 8.0)

87. In the Meselson and Stahl experiment. coli was grown in a medium containing 15NH4Cl. After 24 hours. E. coli were transferred to medium containing 14NH4Cl. After the fourth generation in medium containing 14NH4Cl, the ratio between hybrids (15N/14N) and light (14/14N)labeled DNA will be 1 : n, where the value of n is ______

Ans: (7.0 to 7.0)

88. The population data present in an island is as follows

Genotype               Number

AA                          300

Aa                           500

aa                            200

Total                        1000

The allele frequency of A(upto two decimals) will be ______

Ans: (0.55 to 0.55)

89. A cell in G1 phase has 16 chromosomes. The total number of chromatids that would be found per cell during Metaphase II of meiosis are _____

Ans: (16 to 16)

90. Upon activation of phospholipase C by ligand binding to G-protein coupled receptor, the Ca+2 concentration in cytosol will

(A)  decrease due to blockage of InsP3 gated channel on endoplasmic reticulum

(B)  decrease due to blockage of InsP3 gated channel on plasma membrane

(C)  increase due to efflux of Ca+2 from InsP3 gated channel on mitochondria

(D)  increase due to efflux of Ca+2 from InsP3 gated channel on endoplasmic reticulum as well as influx of Ca+2 from InsP3 gated channel on plasma membrane

Ans: (D)

91. Match the following molecules in Group I with their function in Group II

Group I                             Group II

P. Transferrin                  (i) Uptake of glucose

Q. Insulin                        (ii) Binds iron

R. α-macroglobulin        (iii) Substratum for cell attachment

S. Fibronectin                (iv) Proteinase inhibitor

                                       (v) Binds to oxygen in RBC

(A)  P-ii; Q-i; R-iv; S-iii

(B)  P-ii; Q-i; R-v; S-iii

(C)  P-ii; Q-i; R-iv; S-ii

(D)  P-i; Q-iii; R-ii; S-iv

Ans: (A)

92. If a heavy chain of an antibody molecule weighs 65,000 Daltons (Da) and a light chain weighs 25,000 Da, the approximate calculated weight of an IgM antibody in Da will be

(A)  90,000

(B)  180,000

(C)  360,000

(D)  900,000

Ans: (D)

93. MATCH the signaling pathways in Group I with their functions in Group II, during the process of development

Group I

P. Hedgehog signaling

Q. Hox proteins

R. Wnt signaling

S. Notch signaling

Group II

(i) Involved in signaling at 4-cell embryo stage in C. elegans through glp 1 expression

(ii) Involves frizzled receptor on target cell membrane and establish polarity in insects

(iii) Plays critical role in facial morphogenesis in vertebrates and its mutation causes cyclopia

(iv) Required for T-bx transcription factor expression for vertebrate limb development

(A)  P-iii; Q-ii; R-iv; S-i

(B)  P-iii; Q-iv; R-ii; S-i

(C)  P-iv; Q-iii; R-ii; S-i

(D)  P-iii; Q-iv; R-i; S-ii

Ans: (B)

94. In a population which is Hardy-Weinberg equilibrium the frequency of the recessive genotype of a certain trait is 0.09. The percentage of individuals with heterozygous genotype is ______%

Ans: (42.0 to 42.0)

95. An enzyme preparation has activity of 2 Units per 20 μl, and protein concentration 0.4 mg/ml. The specific activity (Units/mg) of this enzyme will be_____

Ans: (250 to 250)

Food Technology (XL-U)

96. Indicate the correct group that contains a monosaccharide, a disaccharide and a trisaccharide.

(A)  Glucose, sucrose, mannose

(B)  Ribose, lactose, raffinose

(C)  Mannose, maltose, lactose

(D)  Raffinose, stachyose, glucose

Ans: (B)

97. In which of the following products, ‘must’ is used as the substrate for fermentation?

(A)  Beer

(B)  Wine

(C)  Idli

(D)  Tempeh

Ans: (B)

98. Identify the foodborne illness which is not caused by bacteria.

(A)  Botulism

(B)  Listeriosis

(C)  Vibriosis

(D)  Cysticercosis

Ans: (D)

99. Nutrient composition of wheat flour changes with extent of extraction from whole wheat grain. Which of the following statements is true if the extraction rate increased from 50% to 90%?

(A)  Starch increases, protein increases, fat increases, mineral increases

(B)  Starch decreases, protein increases, fat increases, mineral increases

(C)  Starch decreases, protein decreases, fat increases, mineral decreases

(D)  Starch decreases, protein increases, fat decreases, mineral decreases

Ans: (B)

100. You have two samples of milk, one (X) with 3.8% fat and another (Y) with 0.5% fat. In order to produce a milk with 3.5% fat, 100 ml of Y should be mixed with ______ml of X.

Ans: (1000 to 1000)

101. Match the items in column I with the items in column II in relation to food safety and standards.

Column I               Column II

P. HACCP             1. International food standards

Q. FSSAI               2. Quality control protocol

R. CIP                    3. Food plant sanitation and hygiene protocol

S. CODEX              4. Indian food standards

(A)  P-2, Q-4, R-3, S-1

(B)  P-4, Q-3, R-2, S-1

(C)  P-1, Q-4, R-2, S-3

(D)  P-4, Q-2, R-3, S-1

Ans: (A)

102. A 50% sucrose solution at 20℃ is flowing at a rate of 3.5 m3/h through a pipe with an inside diameter of 0.0475 m and length of 12 m. The viscosity and the density of the solution are 15.43 cp and 1232 kg/m3, respectively. The Reynolds number of the flow is ______.

Ans: (2078 to 2086)

103. In a pineapple juice, fibre particles having mean diameter of 160 μm and density of 1075 kg/m3 are settling by gravity. If the density and viscosity of the juice are 1015 kg/m3 and 0.98 cp, respectively, terminal velocity of the fibre particles is _____mm/s.

Ans: (0.80 to 0.90)

104. Power consumption in liquid mixing is proportional to ______.

(A)  Powder number × liquid density × (rotational speed)3 ×(impeller diameter)5

(B)  Powder number × liquid density × (rotational speed)2 × (impeller diameter)3

(C)  Liquid density × viscosity of the liquid × (rotational speed)2 × (impeller diameter)3

(D)  Acceleration due to gravity × liquid density × (rotational speed)3 × (impeller diameter)5

Ans: (A)

105. A dye-reduction test for estimation of viable microorganisms, the most commonly used dyes are methylene blue, triphenyltetrazolium-chloride and _________

(A)  Malachite green

(B)  Amaranth

(C)  Tartrazine

(D)  Resazurin

Ans: (D)

106. Match the following items of group I with the items of group II in relatin to the quality of fat.

Group I

P. Saponification number

Q. Iodine number

R. Reichert Meissl number

S. Acetyl value

Group II

1. Unsaturation of fatty acid

2. Volatile water soluble fatty acid

3. Hydroxy fatty acid

4. Molecular weight of fatty acid

(A)  P-1, Q-2, R-3, S-1

(B)  P-1, Q-3, R-4, S-2

(C)  P-4, Q-1, R-2, S-3

(D)  P-2, Q-1, R-3, S-4

Ans: (C)

107. Match the following metabolic product (Column I) that indicates the quality of food (Column II)

Column I                         Column II

P. Ethanol                         1. Canned vegetable

Q. Lactic acid                   2. Fish

R. Trimehylamine             3. Butter

S. Volatile fatty acid         4. Apple juice

(A)  P-3, Q-2, R-4, S-1

(B)  P-4, Q-1, R-2, S-3

(C)  P-4, Q-3, R-2, S-1

(D)  P-3, Q-4, R-2, S-1

Ans: (B)

108. Correlate the vitamins in column I with their role in promoting reaction/process in column II.

Column I                         Column II

P. Riboflavin                      1. Visual cycle

Q. Vitamin D                      2. Acyl group transfer

R. Pantothenic acid           3. Regulation of Ca2+ metabolism

S. Vitamin A                       4. Oxidation-reduction reaction

(A)  P-1, Q-2, R-4, S-3

(B)  P-2, Q-1, R-3, S-4

(C)  P-3, Q-4, R-1, S-2

(D)  P-4, Q-3, R-2, S-1

Ans: (D)

109. A pure strain with generation time of 60 min is used in a fermentation process. Following inoculation (0 h), the stain takes 2 h for adaptation, 10 h to achieve maximum growth and 12 h to arrive at the point where the death rate is higher than the growth rate. If the inoculation load is 100 cells, the total populatin at the end of 10 h will be ______.

Ans: (25550 to 25650)

110. Refer to the shear stress – shear rate plot shown in the figure below. Match the lines (Column I) with appropriate rheological behavior (Column II)

Column I               Column II

P. Line 1                    1. Dilatant

Q. Line 2                   2. Newtonian

R. Line 3                   3. Pseudoplastic

S. Line 4                   4. Bingham plastic

(A)  P-2, Q-3, R-4, S-1

(B)  P-1, Q-3, R-4, S-2

(C)  P-2, Q-4, R-3, S-1

(D)  P-4, Q-3, R-2, S-1

Ans: (D)

111. Water flowing at a rate of 1 kg/mi is heated from 12 to 80℃ with flue gas supplied at a rate of 3 kg/min. The temperature and specific heat of the flue gas are 180℃ and 1.05 kJ/kg.K, respectively. If specific heat of water is 4.2 kJ/kg.K and the flow is parallel, then the logarithmic mean temperature difference will be _______℃.

Ans: (53.30 to 55.25)

112. The Lineweaver-Burk plot of an enzymatic reaction shows Vmax of 160 μmol/l.min and km of 60 μmol/l. For a substrate concentration of 40 μmol/l the velocity of the reaction is estimated to be ______μmol/l.min.

Ans: (64.0 to 64.0)

113. A suspension containing 2 × 104 spores of organism A having a D1 value of 1.5 min and 8 × 105 spores of organism B having a D121.1 value of 0.8 min is heated at a constant temperature of 121.1℃. The heating time needed to obtain a probability of spoilage ‘1 in 1000’ is _____min.

Ans: (10.80 to 11.20)

114. In a evaporation process, a compressor picks up 0.05 m3 air in each revolution and compresses 500 kg of air per minute. If the specific volume of air is 0.9 m3/kg, then the compressor speed is _____rpm.

Ans: (9000 to 9000)

115. For a soybean oil extraction system, solvent: soy ratio is maintained at 0.5:1 (w/w). Original seed contains 18% oil (w/w). If the meal (soy solid) after final desolventization has 0.01 kg oil per kg oil free meal, then the effectiveness of the solvent (kg oil/kg solvent) in the extraction process is ______

Ans: (0.30 to 0.40)

General Aptitude

116. The event would have been successful if you ______ able to come.

(A)  are

(B)  had been

(C)  have been

(D)  would have been

Ans: (B)

117. There was no doubt that their work was thorough.

Which of the words below is closest in meaning to the underlined word above?

(A)  Pretty

(B)  Complete

(C)  Sloppy

(D)  Haphazard

Ans: (B)

118. Four cards lie on a table. Each card has a number printed on one side and a colour on the other. The faces visible on the cards are 2, 3, red, and blue.

Proposition: If a card has an even value on one side, then its opposite face is red.

The cards which MUST be turned over to verify the above proposition are

(A)  2, Red

(B)  2, 3, Red

(C)  2, blue

(D)  2, red, blue

Ans: (C)

119. What is the value of x when vertical-align: middle; margin-bottom: 1px;

(A)  1

(B)  −1

(C)  −2

(D)  Cannot be determined

Ans: (B)

120. Two dice are thrown simultaneously. The probability that the product of the numbers appearing on the top faces of the dice is a perfect square is

(A)  1/9

(B)  2/9

(C)  1/3

(D)  4/9

Ans: (B)

121. Bhaichung was observing the pattern of people entering and leaving a car service centre. There was a single window where customers were being served. He saw that people inevitably came out of the centre in the order that they went in. However, the time they spent inside seemed to vary a lot: some people came out in a matter of minutes while for others it took much longer.

From this, what can one conclude?

(A) The centre operates on a first-come-first-served basis but with variable service times, depending on specific customer needs.

(B) Customers were served in an arbitrary order since they took varying amounts of time for service completion in the centre.

(C) Since some people came out within a few minutes of entering the centre. The system is likely to operate on a last-come-first-served basis.

(D) Entering the centre early ensured that one would have shorter service times and most people attempted to do this.

Ans: (A)

122. A map shows the elevations of Darjeeling, Gangtok, Kalimpong, pelling, and Siliguri, Kalimpong is at a lower elevation than Gangtok. Pelling is at a lower elevation than Gangtok. Pelling is at a higher elevation that siliguri. Darjeeling is at a higher elevation than Gangtok.

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

i. Pelling is at a higher elevation than Kalimpong

ii. Kalimpong is at a lower elevation than Darjeeling

iii. Kalimpong is at a higher elevation than siliguri

iv. Siliguri is at a lower elevation than Gangtok

(A)  Only ii

(B)  Only ii and iii

(C)  Only ii and iv

(D)  Only iii and iv

Ans: (C)

123. P,Q,R,S,T and U are seated around a circular table. R is seated two places to the right of Q.P is seated three places to the left of R. S is seated opposite U. If P and U now switch seats.

Which of the following must necessarily be true?

(A) P is immediately to the right of R

(B) T is immediately to the left of P

(C) T is immediately to the left of P or P is immediately to the right of Q

(D) U is immediately to the right of R or P is immediately to the left of T

Ans: (C)

124. Budhan covers a distance of f19 km in 2 hours by cycling one fourth of the time and walking the rest. The next day he cycles (at the same speed as before) for half the time and walks the rest (at the same speed as before) and covers 26 km in 2 hours. The speed in km/h at which Budhan walks is

(A)  1

(B)  4

(C)  5

(D)  6

Ans: (D)

125. The points in the graph below represent the halts of a lift for duration of 1 minute, over a period of 1 hour.

Which of the following statements are correct?

i. The elevator never moves directly from any non-ground floor to another non-ground floor over the one hour period

ii. The elevator stays on the fourth floor for the longest duration over the one hour period

(A)  Only i

(B)  Only ii

(C)  Both i and ii

(D)  Neither i nor ii

Ans: (D)

Gate 207 Engineering Sciences Question Paper 12th Feb 2017 PDF Download

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Engineering Sciences 12th Feb 2017

Subject Name: Engineering Sciences

Duration : 180

Total Marks: 100

Engineering Mathematics (XE-A) (Compulsory)

1. If  for some α ≥ 1, then the value of α is ______.

Ans: (2.98 to 3.02)

2. Three fair dice are rolled simultaneously. The probability of getting a sum of 5 is

(A)  

(B)   

(C)   

(D)   

Ans: (D)

3. Suppose α, β, γ and δ are constants such that

p(x) = δ + γ(x + 1) + βx(x + 1) + αx(x + 1) (x – 1)

is the interpolating polynomial for the data (−1, −3), (0, 1), (1, −1), and (2, −3). Then the value of γ – β is _______.

Ans: (6.98 to 7.02)

4. Consider the ordinary differential equation

yʹʹ + αyʹ + βy = 0,

where α and β are constants. If y(x) = xex is a solution of the above equation, then the value of β – α is ________.

Ans: (2.98 to 3.02)

5. Consider the system of linear equations

2x + x3 = 0

−2x1 – x3 = 0

−x1 + x2 = 1.

The above system has

(A)  a unique solution

(B)  infinite number of solutions

(C)  no solution

(D)  only two distinct solutions

Ans: (C)

6. Let C be a simple smooth closed curve enclosing the region R in the xy-plane. Let C be oriented counterclockwise. If the value of the integral  is 16, then the area of R is ________.

Ans: (7.98 to 8.02)

7. Consider the ordinary differential equation

x2yʹʹ + xyʹ – y = x, x > 0.

In terms of arbitrary constants c1 and c2, the general solution of the above equation is

(A)    y(x) = c1­x + c2x−1 + x3

(B) 

(C) 

(D)  y(x) = c1x + c2 + x1

Ans: (C)

8. Let f : ℝ → ℝ and g : ℝ → ℝ be defined by

 and 

where ℝ denotes the set of real numbers. Then, at x = 0,

(A)  f is differentiable but g is NOT differentiable

(B)  f is NOT differentiable but g is differentiable

(C)  both f and g are differentiable

(D)  neither f nor g is differentiable

Ans: (A)

9. If u(x, t) = g(t) sin x is the solution of the wave equation utt = uxx, t > 0, 0 < x < π, with the initial conditions u(x, 0) = 2 sin x, ut(x, 0) = 0, 0 ≤ x ≤ π, and the boundary conditions u(0, t), = u(π, t) = 0, t ≥ 0, then the value of g(π/3) is _______.

Ans: (0.98 to 1.02)

10. Let  where t is a real variable and i = √−1. The value of I is ______.

Ans: (-0.02 to 0.02)

11. Let ak = 2−kk4 sin k and  for k = 1, 2, …. Then

(A)   converges but  does NOT converge

(B)   does NOT converge but  converges

(C)     both   and  converge

(D)    neither  nor  converges

Ans: (C)

Fluid Mechanics (XE-B)

12. In a given flow field, the velocity vector in Cartesian coordinate system is given as:

What is the volume dilation rate of the fluid at a point where x = 1, y = 2 and z = 3?

(A)  6

(B)  5

(C)  10

(D)  0

Ans: (B)

13. A steady, incompressible, two-dimensional velocity field in Cartesian coordinate system is represented by the following expression.

The coordinate of the point (x, y) in the flow filed having “zero” velocity is,

(A)  (1.75, −3)

(B)  (−1.75, 3)

(C)  (1.75, 3)

(D)  (−1.75, −3)

Ans: (B)

14. During an experiment, the position of a fluid particle is monitored by an instrument over a time period of 10 s. The trace of the particle given by the following figure represents a

(A)  streamline

(B)  streakline

(C)  pathline

(D)  timeline

Ans: (C)

15. In a Cartesian two-dimensional coordinate system, u and v represent the velocities in x and y directions, respectively. For a certain flow, the velocity filed is represented by the following expression:

where, the coefficients a, b, c and d are constants. For an incompressible flow, which one of the following relations is TRUE?

(A)  a + d = 0

(B)  a + c = 0

(C)  b + d = 0

(D)  b + c = 0

Ans: (A)

16. Which one of the following figures represents potential flow past a circular cylinder with clockwise rotation of the cylinder?

(A) 

(B) 

(C) 

(D) 

Ans: (D)

17. The stream function (Ψ) of a velocity field at any location(x, y) is given as, Ψ = xy2 – 2x2y2. What is the rate of rotation of a fluid element located at (x = 2, y = 2)?

(A)  8

(B)  10

(C)  12

(D)  14

Ans: (D)

18. The nature of velocity profile within the laminar viscous sublayer in a turbulent pipe flow is

(A)  linear

(B)  parabolic

(C)  logarithmic

(D)  exponential

Ans: (A)

19. In a 5 m deep vertical cylindrical tank, water is filled up to a level of 3 m from the bottom and the remaining space is filled with oil of specific gravity 0.88. Assume density of water as 1000 kg/m3 and acceleration due to gravity to be 10 m/s2. The gauge pressure (in kN/m2, rounded off to the first decimal place) at a depth of 2.5 m from the top of the tank will be______

Ans: (22.6)

20. In a two-dimensional potential flow, a point source is located at the origin (x = 0, y = 0) as shown in the figure. The strength of the point source is 2 cm2/s. A uniform flow with velocity 1 cm/s is approaching towards the point source at an angle of 30° from the horizontal axis. What is the distance (cm) of the stagnation point in the flow field from the point source?

(A)   

(B)   

(C)   

(D)   

Ans: (A)

21. Two infinite parallel horizontal plates are separated by a small gap(d = 20 mm) as shown in figure. The bottom plate is fixed and the gap between the plates is filled with oil having density of 890 kg/m3 and kinematic viscosity of 0.00033 m2/s. A shear flow is induced by moving the upper plate with a velocity of 5 m/s. Assume, linear velocity profile between the plates and the oil to be Newtonian fluid. The shear stress(N/m2) at the upper plate is _______

Ans: (72.5 to 75)

22. A spherical balloon of diameter 15 m is supposed to lift a load of 3000 N. The lifting of load is achieved by heating the air inside the balloon. Assume, air to be an ideal and atmospheric pressure either outside or inside the balloon. The value of acceleration due to gravity is 9.81 m/s2 and the values of temperature and density of atmospheric air are 15℃ and 1.2 kg/m3, respectively. In order to lift the specified load, the air inside the balloon should be heated to a temperature (℃) of _______

Ans: (62 to 66)

23. The velocity field in Cartesian coordinate system for a two-dimensional steady flow is given as :

where, V0 and L are constants. Which one of the following expressions represents the acceleration field  for this flow?

(A)   

(B)   

(C)   

(D)   

Ans: (D)

24. A cylindrical tank of 0.8 m diameter is completely filled with water and its top surface is open to atmosphere as shown in the figure. Water is being discharged to the atmosphere from a circular hole of 15 mm diameter located at the bottom of the tank. The value of acceleration due to gravity is 9.81 m/s2. How much time (in seconds) would be required for water level to drop from a height of 1 m to 0.5m?

(A)  188

(B)  266

(C)  376

(D)  642

Ans: (C)

25. Consider steady laminar flow of a incompressible Newtonian fluid between two infinite parallel plates, separated by a distance of 1 m, as shown in the figure. The bottom plate is stationary but the top one is moving in positive x-direction with a velocity of 3 m/s. The fluid pressure gradient in the flow direction is: If the viscosity of the fluid is 1 kg m−1 s−1 then the distance of the point of maximum velocity (in meters, rounded off to the second decimal place) from the bottom plate would be _______

Ans: (0.66 to 0.67)

26. An inviscid incompressible fluid of density 1000 kg/m3 is flowing in a horizontal pipe of tapered cross-section with a flow rate of 4000 cm3/s. The area of cross-section at two different locations ‘A’ and ‘B’ are 10 cm2 and 20 cm2, respectively. The velocity of fluid at the location ‘A’ is 4 m/s and pressure is 5 N/m2. The pressure (N/m2) at location ‘B’ would be ______

Ans: (6005 to 6005)

27. A viscous, incompressible and Newtonian fluid flowing through the main branch of a circular pipe bifurcates into two daughter branches whose radii are 4 cm and 2 cm, respectively. The flow in both the daughter branches are laminar and fully developed. If the pressure gradients in both the daughter branches are same, then fraction of total volumetric flow rate (rounded off to the second decimal place) coming out from the branch with 4 cm diameter is _______

Ans: (0.05 to 0.06)

28. The volumetric flow rate (Q) of a triangular notch is a function of the upstream liquid surface elevation (H) measured from the bottom of the notch, acceleration due to gravity (g), notch angle (ϕ) and the approach velocity (V). Which one of the following is the correct expression for Q?

(A)  

(B)   

(C)   

(D)   

Ans: (D)

29. Model tests are to be carried out to study the flow through a large prototype value of 0.6 m diameter at a flow rate of 10 m3/s. The same working fluid is used for both the model and the prototype. A complete geometric similarity is maintained between the model and the prototype. If the valve diameter of the model is 80 mm, its required flow rate (in m3/s, rounded off to the first decimal place) would be ________

Ans: (1.3 to 1.4)

30. Water is flowing at a rate of 0.5 m3/s in a horizontal pipeline of inside diameter 0.5 m. The density and kinemat4ic viscosity of water is 1000 kg/m3 and 106 m2/s, respectively. Assume Darcy-Weisbach friction factor value to be 0.0093 and acceleration due to gravity as 9.81 m/s2. To maintain constant flow rate, the required power per unit length of the pipeline (in W/m, rounded off to the first decimal place) would be ______

Ans: (28.9 to 31.4)

31. Air flows over a smooth flat plate at a velocity of 4.39 m/s. The density of air is 1.031 kg/m3 and the kinematic viscosity is 1.34 × 10−5 m2/s. The plate length is 12.2 m in the direction of the flow. The boundary layer thickness (δ) is given as  where X is the distance from the leading edge and ReX is the Reynlods number. The boundary layer thickness (in meters, rounded off to the second decimal place) at 12.2 m from the leading edge will be ______

Ans: (0.21 to 0.22)

32. A venturimeter of diameter 0.2 m at the entrance and 0.1 m at the throat is inclined upwards. The vertical elevation difference between the entrance and the throat is 0.5 m. The density of water is 1000 kg/m3 and the coefficient of velocity is 0.97. The differential U-tube manometer connected to the entrance and throat shows a pressure difference of 30 kN/m2. Assume acceleration due to gravity as 9.81 m/s2. The velocity of the water (in m/s, rounded off to the first decimal place) at the throat would be ______

Ans: (7.0 to 7.2)

33. A spherical bubble of radius r is rising upward with a constant velocity U, in quiescent water of dynamic viscosity μ. The density of air and water are denoted by ρa and ρw, respectively, and g is acceleration due to gravity. The bubble motion is such that, the Reynolds number, Re <<1. The density of air can be neglected in comparison to the water density (ρa << pw). Which one of the following expressions is TRUE for the density of water?

(A)   

(B)   

(C)   

(D)   

Ans: (B)

Material Science (XE-C)

34. Which of the following is a Frenkel defect?

(A)  One Cl vacancy and one Na vacancy in NaCl

(B)  One Zn vacancy and one Zn interstitial in ZnO

(C)  K at the Na site in NaCl

(D)  None of the above

Ans: (B)

35. Which processing technique is best suited for manufacturing decorative PVC floor tiles?

(A)  Blow molding

(B)  Filament winding

(C)  Rotational molding

(D)  Calendering

Ans: (D)

36. During deformation of a semi-crystalline polymer, with spherulitic morphology, stressed in tension, what happens to the amorphous and the crystalline regions at the later stages?

(A)  Amorphous regions remain intact and only crystallites experience bending and stretching of chains

(B)  Only amorphous regions elongate in the stress direction and crystallites remain intact

(C)  Amorphous regions elongate in the stress direction and crystallites experience bending and stretching of chains

(D)  None of the above

Ans: (C)

37. Which of the following statement(s) is/are true regarding the structure-property correlation in polymers?

(i) Polymer that are less coiled are more crystalline than those that are more coiled

(ii) Branched polymers are more crystalline than the linear ones

(iii) Polymers with inter-chain interactions have higher glass transition than those without inter-chain interactions

(iv) Polymers with inter-chain interactions are more crystalline than those without interchain interactions

(A)  (i) and (ii)

(B)  (i) and (iii)

(C)  (ii) and (iv)

(D)  (ii) and (iii)

Ans: (B)

38. The contrast obtained in scanning electron microscope using back scattered electrons depends on

(A)  Atomic number of the specimen material

(B)  Accelerating voltage of the microscope

(C)  Working distance in the microscope

(D)  Type of the electron emitter in the microscope

Ans: (A)

39. Ceramic material fail at stresses much lower than their theoretical strength due to

(A)  Presence of dislocations

(B)  High elastic modulus

(C)  Presence of voids

(D)  Anisotropy in crystal structure

Ans: (C)

40. The Miller indices of the first three Bragg peaks in the X-ray diffraction pattern obtained from a polycrystalline iron sample at room temperature are

(A)  (111), (200), (220)

(B)  (100), (110), (111)

(C)  (1000), (110), (200)

(D)  (110), (200), (220)

Ans: (D)

41. The number of close packed planes in the lattice of an FCC metal is

(A)  2

(B)  4

(C)  6

(D)  12

Ans: (B)

42. Which of the following treatment(s) can increase the electrical conductivity of silicon

(i) Heating

(ii) Doping with arsenic

(iii) Doping with aluminium

(iv) Exposure to light

(A)  Only (i)

(B)  Only (i) and (ii)

(C)  Only (i), (ii) and (iv)

(D)  All (i), (ii), (iii) and (iv)

Ans: (D)

43. The unit cell volume of polyethylene (PE) is 0.0933 nm3. Assuming two ethylene repeat units are contained within each unit cell, the density of a totally crystalline PE will be …….g/cm3 (Take the atomic weights for carbon and hydrogen as 12.01 g/mol and 1.008 g/mol, respectively and the Avogadro’s number as 6.023 × 1023 repeat units/mol)

Ans: (0.990 to 1.010)

44. A continuous, aligned carbon fibre (CF) reinforced polymer composite with 30 vol% of CF and rest resin was designed for a specific application. The modulus of elasticity of CF is 170 GPa and that of the resin is 3.0 GPa. The modulus of elasticity for this composite in the direction of fibre alignment is ……GPa.

Ans: (53.0 to 53.2)

45. Match the composites in Column I with the most suitable application in Column II

Column I

(P) Exfoliated silicates filled butyl rubber

(Q) Fiber reinforced aluminium alloy

(R) Silicon carbide whiskers reinforced alumina

(S) Carbon particles reinforced plastic composites

Column II

(1) Automobile pistons

(2) Contact lenses

(3) Ski boards

(4) Tennis balls

(5) Cutting tool inserts for machining

(A)  P-4; Q-1; R-5; S-3

(B)  P-2; Q-3; R-4; S-5

(C)  P-3; Q-5; R-5; S-3

(D)  P-2; Q-1; R-3; S-5

Ans: (A)

46. Match the processes in Column I with products in Column II

Column I                                   Column II

(P) Slip casting                 (1) Metal powders

(Q) Zone refining              (2) Thin films

(R) Sputtering                   (3) Ceramic part

(S) Atomization                 (4) Single crystal

                                          (5) Metal sheets

(A)  P-3; Q-4; R-2; S-1

(B)  P-2; Q-1; R-2; S-1

(C)  P-3; Q-4; R-5; S-1

(D)  P-3; Q-4; R-1; S-5

Ans: (A)

47. The value of diffusivity (D) for the diffusion of carbon (C) in γ-iron at 727℃ is …….×103 m2/s (Given Do = 2 × 105 m2/s; activation energy, Q = 142 kJ/mol; R = 8.314 J/mol.K)

Ans: (7.5 to 7.7)

48. Refer to the figure below:

If the alloy contains 47 wt. % of A and 53 wt. % of B at 1300℃, the wt. % of liquid present in the alloy at this temperature will be ……

Ans: (37.5 to 38.5)

49. Which of the following statement(s) is/are true

(i) All piezoelectric material are necessarily ferroelectric

(ii) All ferroelectric materials are necessarily piezoelectric

(iii) All pyroelectric materials are necessarily piezoelectric

(iv) All pyroelectric materials are necessarily ferroelectric

(A)  (i) and (ii)

(B)  (ii) and (iii)

(C)  (i) and (iv)

(D)  (ii) and (iv)

Ans: (B)

50. If the energy of formation of vacancies in pure copper is 0.9 eV, the fraction of vacancies in pure copper at 27℃ will be …..×106 (Boltzmann’s constant is 8.62 × 105 eV/K)

Ans: (7.50 to 7.80)

51. A ceramic material with a critical flaw size of 30 μm has fracture stress of 300 MPa For the same material the fracture stress for a critical flaw size of 90 μm will be ……..MPa.

Ans: (172 to 174)

52. An inorganic material that is transparent under solar light appears coloured when doped with transition metal ions. The possible reason(s) for the colour is/are

(i) The electronic energy levels of the host material changes significantly by doping

(ii) The doped element selectively absorbs certain wavelength of light other than the perceived colour

(iii) The doped element emits radiation of specific wavelength

Which of the above statement(s) is/are true?

(A)  Only (i)

(B)  Both (i) and (ii)

(C)  Both (i) and (iii)

(D)  Both (ii) and (iii)

Ans: (D)

53. Copper in an FCC metal with lattice parameter of 3.62 Å. Hall effect measurement shows electron mobility to be 3.2 × 103 m2V1s1. Electrical resistivity of copper is 1.7 × 108 Ω The average number of free electrons per atom in copper is ……..(Charge of an electron : 1.6 × 1019 C)

Ans: (1.35 to 1.37)

54. In an ionic solid the cation and the anion have ionic radii as 0.8 Å and 1.6 Å respectively. The maximum coordination number of the cation in the structure will be

(A)  3

(B)  4

(C)  6

(D)  8

Ans: (C)

55. Which of the following statement(s) is/are true regarding susceptibility of a material

(i) Magnetic susceptibility is positive for a diamagnetic material

(ii) Magnetic susceptibility is negative for a diamagnetic material

(iii) Magnetic susceptibility is negative for an antiferromagnetic material

(iv) Magnetic susceptibility is positive for a paramagnetic material

(A)  (ii) and (iv)

(B)  (i) and (iii)

(C)  (ii) and (iii)

(D)  (i) and (iv)

Ans: (A)

Solid Mechanics (XE-D)

56. In the truss shown, a mass = 10 kg is hung from the node J. .The magnitude of net force (in Newtons) transferred by the truss EFGHIJ onto the trus JKLMNO at the node J is _______.

Assume acceleration due to gravity, g = 10 m/s2

Ans: (69 to 73)

57. A ball moves along a planar frictionless slot as shown. Which one of the paths shown closely matches the path taken by the ball after it exits the slot at E?

(A)  path m

(B)  path n

(C)  path p

(D)  path q

Ans: (B)

58. A rod EF moving in a plane has velocity Vat E and VF at F that are parallel to each other. Which of the following CANNOT be true?

(A)  Both VE and VF are perpendicular to EF.

(B)  Magnitude of VE is equal to the magnitude of VF and the angular velocity of EF is zero.

(C)  The velocity VE is not perpendicular to EF and the angular velocity of EF is nonzero.

(D)  Magnitude of VE is not equal to the magnitude of VF and the angular velocity of EF is nonzero.

Ans: (C)

59. The beam shown below carries two external moments. A counterclockwise moment of magnitude 2M acts at point B and a clockwise moment of magnitude M acts at the free end, C. The beam is fixed at A. The shear force at a section close to the fixed end is equal to

(A)  

(B)   

(C)   

(D)   

Ans: (C)

60. Two pendulum are shown below. Pendulum-A carries a bob of mass m, hung using a hinged massless rigid rod of length L whereas Pendulum-B carries a bob of mass 4m and length L/4. The ratio of the natural frequencies of Pendulum-A and Pendulum-B is given by

(A)  1 : 2

(B)  1 : 1

(C)  √2 : 1

(D)  2 : 1

Ans: (A)

61. A closed thin-walled cylindrical steel pressure vessel of wall thickness t = 1mm is subjected to internal pressure. The maximum value of pressure p(in kPa) that the wall can withstand based on the maximum shear stress failure theory is given by

(Yield strength of steel is 200MPa and mean radius of the cylinder r = 1m).

(A)  100

(B)  200

(C)  300

(D)  400

Ans: (B)

62. The state of stress at a point in a body is represented using components of stresses along X and Y directions as shown. Which one of the following represents the state of stress along X’ and Y’ axes? (X’ – axis is at 45° clockwise with respect to X-axis)

(A) 

(B)

(C) 

(D) 

Ans: (A)

63. An aluminum specimen with an initial gauge diameter d0 = 10mm and a gauge length l0 = 100mm is subjected to tension test. A tensile force P = 50kN is applied at the ends of the specimen as shown resulting in an elongation of 1mm in the gauge length. The Poisson’s ratio (v) of the specimen is _____.

Shear modulus of the material G = 25GPa. Consider engineering stress-strain conditions.

Ans: (0.26 to 0.28)

64. A rectangular sheet ABCD of dimensions a and b along X and Y directions, respectively, is stretched to a rectangle AB’C’D, as shown. The maximum principal strain (ε1) and minimum principal strain (ε2) due to the stretch are given by

(A)  ε­1 = 0.001 and ε­2 = 0.001

(B)  ε­1 = −0.001 and ε­2 = 0.001

(C)  ε­1 = 0.001 and ε­2 = −0.001

(D)  ε­1 = −0.001 and ε­2 = −0.001

Ans: (A)

65. A solid bar of uniform square cross-section of side b and length L is rigidly fixed to the supports at the two ends. When the temperature in the rod is increased uniformly by Tc, the bar undergoes elastic buckling. Assume Young’s modulus E and coefficient of thermal expansion α to be independent of temperature. The coefficient of thermal expansion α is given by

(A)   

(B)   

(C)   

(D)   

Ans: (D)

66. Two rigid blocks, of masses 10 kg and 15 kg, are arranged one on top of the other and placed on a horizontal rough surface as shown. The blocks are connected to each other through an inextensible cable passing over a frictionless pulley. The coefficients of static friction between the blocks and also between the bottom block and the surface are all equal to 0.3. The force P(in Newtons) needed to set the blocks in motion towards right is ______

(Assume acceleration due to gravity g = 10m/s2)

Ans: (134 to 136)

67. A truss system EFGH shown below is built using members EF, GH and FH of the same cross-sectional area 10 mm2 and member FG of cross-sectional area (20 mm2). The total strain energy stored (in Nm) in the system due to a force P = 1kN acting at F is _______.

Assume elastic deformations and members are made of steel with elastic modulus of 200GPa.

Ans: (0.55 to 0.65)

68. A rigid frame grips on to a steel wall as shown using a powerful magnet at the top support G and with a roller support at E. EF is horizontal. A man stands on the platform attached to the frame 1m away from the wall as shown. Assume the frame and magnet assembly to be of negligible weight and the mass of the man to be 80kg. The magnitude of the reaction (in Newtons) exerted by the frame onto the steel wall due to the weight of the man is ______.

The magnetic force of attraction of the magnet at no load condition is 1kN. Magnet can be assumed to be small enough that it offers negligible moment resistance. Assume accelerations due to gravity. g = 10 m/s2

Ans: (1785 to 1792)

69. A manually operated band  brake has a control lever EFG as shown has a coefficient of kinetic friction equal to 0.2. The cylinder initially rotates clockwise at a constant frequency of 10revolutions per second. A force P = 300 N is applied at G. The pin support at O is frictionless. The radius of the cylinder is r = 0.15m and the radius of gyration is 0.1m. The mass of the cylinder  is 50 kg. Assume acceleration due to gravity g = 10 m/s2. The time required (in second) to reduce the rotational frequency to 5 revolutions per second is ______.

Ans: (0.45 to 0.50)

70. In a pin-connected mechanism shown, load P applied at F is 50N. Neglect the weight of the links and assume k = 1kN/m for the spring. The bars EH and FG are pinned at O at their centre such that the lengths of EO, GO, HO and FO are all to ℓ = 0.2 m. The spring between G and H is unstretched when θ = 45°.

The angle θ(in degrees) under equilibrium is ______

Ans: (32 to 35)

71. The frame shown below carries a vertical load P = 10kN at its free end D. The frame is fixed at A and has a roller support at B. Magnitude of the reaction force at B(in kN) is ________

Assume that the effect of the axial force on bending is negligible.

Ans: (10 to 10)

72. Consider the system shown below. Mass M is fixed to the rod AC at a distance x from the hinge point at B. Two springs of stiffness 3K and K are attached at the rod at points A and C, respectively. The natural frequency of angular oscillation of the system about B is 20 rad/s. Assume the rod to be rigid and massless. Magnitude of x(in metres) is _______.

(M = 30 kg, and K = 1kN/m).

Ans: (02 to 02)

73. The simply supported beam shown below is subjected to a clockwise moment M at point A and two counterclockwise moments 2M and M at points B and C, respectively. Which one of the following is the correct bending moment diagram (tensile at bottom is positive moment) for the  beam?

(A) 

(B) 

(C) 

(D) 

Ans: (A)

74. The structure shown below is of rectangular cross section and carries a load of 10kN at its free end E. Maximum bending stress (in MPa) developed in the beam due to the external load is ______.

The depth of the beam is 300 mm and the width is 150mm.

Ans: (17 to 18)

75. Two circular rods shown below carry the same axial load P. The rod-A has uniform cross-section and the Rod-B has non-uniform cross-section as shown. The ratio of elongation of Rod-A to Rod-B is given by

(A)  1 : 1

(B)  1 : 2

(C)  2 : 1

(D)  3 : 1

Ans: (C)

76. A composite shaft is made of a steel tube with an inner brass core perfectly bonded together as shown. The shaft is fixed at one end and subjected to be torque of 2T at the other end. Shear modulus  of steel is G and that of brass is G/2. The outer radius of the steel tube is R =2r and radius of the inner brass core is r. The magnitude of shear stress at the interface (point X) and in the steel tube is closest to

(A)   

(B)   

(C)   

(D)   

Ans: (B)

77. A massless rod of rectangular cross-section is subjected to a force P at origin O as shown. The expression for the stress σzz at point Q is given by

(A)   

(B)   

(C)   

(D) 

Ans: (B)

Thermodynamics (XE-E)

78. Given dϕ = f(T)dT + (T/V)dV and dΨ = Tdp + (T/p2)dV, then

(A)  both ϕ and Ψ are properties

(B)  neither ϕ nor Ψ is a property

(C)  ϕ is a property but Ψ is not a property

(D)  Ψ is a property but ϕ is not a property

Ans: (B)

79. A paddle wheel is installed in a rigid insulated tank containing 10 kg air (Cv = 0.718 kJ/kg.K). A torque of 100 N.m is applied on the paddle wheel to rotate it at 60 revolutions per minute for 2 minutes. At the end of the process, the increase in temperature of air in ℃ is

(A)  0

(B)  5.25

(C)  10.50

(D)  21.50

Ans: (C)

80. Consider two systems each containing 20 kg of air at the same temperature and pressure. It is desired to increase the temperature of the air in both systems by 10℃. One system undergoes a constant pressure heat addition process and the other undergoes a constant volume heat addition. The difference in the values of heat transferred to the two systems in kJ is

(A)  30.5

(B)  44.2

(C)  57.5

(D)  73.2

Ans: (C)

81. A refrigerator is used to maintain certain space at 10℃. It pumps 18000 kJ/hour of heat from the space to the atmosphere at 30℃. If the power input to the refrigerator is 2 kW, the ratio of COP of this refrigerator to the of a Carnot refrigerator (up to 2 decimal places) is _______.

Ans: (0.17 to 0.18)

82. A thermal cycle receives 2000 kJ of heat from a heat source at 1000 K. It rejects 300 kJ of heat to a heat sink at 300 K and also rejects 250 kJ of heat to another heat sink at 200 K during the cycle. The cycle is

(A)  reversible

(B)  irreversible

(C)  impossible

(D)  work absorbing

Ans: (B)

83. Saturated liquid water is slowly heated at a constant pressure of 200 kPa toa final state where its quality reaches 0.65. For water at 200 kPa: Tsat = 120.23℃, hf = 504.68 kJ/kg, hg = 2706.60 kJ/kg. The change in the specific entropy in kJ/kg.K is

(A)  3.04

(B)  3.24

(C)  3.44

(D)  3.64

Ans: (D)

84. Given the thermodynamic functional relations: p = p(v, T) and T = T(p, v), the term  is equal to

(A)   

(B)   

(C)   

(D)   

Ans: (A)

85. Two closed cycle gas turbine engines, A and B, operate on air standard Brayton cycle with efficiencies of nA and nB, respectively. If they operate between the same maximum and minimum temperatures, but with different pressure ratios of rpA and rpB, (rpA > rpB), then,

(A)  nA = nB

(B)  nA > nB

(C)  nA < nB

(D)  cannot be determined as the efficiencies are maximum only at optimal rp values.

Ans: (B)

86. The values of density and isentropic compressibility of water at certain pressure and temperature are given as 1000 kg/m3 and 40 × 1010 Pa1, respectively. The speed at which sound travels in water under these conditions in m/s is equal to ________.

Ans: (499 to 501)

87. Length of a certain metal rod at 0℃ is 10 c. The coefficient of linear expansion of that metal varies with temperature as 104 + 105 × T (cm/cm)/℃. When the length of the metal rod is 10.2 cm, the rise in temperature in ℃ is ______.

Ans: (53 to 55)

88. In a polytropic compression process, one kg of an ideal gas having a molecule weight of 40 kg/kmol is compressed from 100 kPa, 300 K to 400 kPa, 360 K. The magnitude of the work in kJ for the process is

(A)  52.3

(B)  62.3

(C)  72.3

(D)  82.3

Ans: (D)

89. Two streams of air (Cp = 1005 J/kg.K) flow through insulated pipes 1 and 2 with the conditions as shown in figure. They mix in an insulated pipe-3 and the mixture steadily exits with a velocity of 100 m/s at 150 kPa. Neglecting the change in potential energy in all the pipes, the exit area of the pipe-3 in m2(up to 3 decimal places) is ______.

Ans: (0.026 to 0.030)

90. A 1 m3 rigid vessel contains air at 200 kPa. A vacuum pump is connected to the vessel in order to control the pressure inside. The volume flow rate of air through the pump is maintained at a constant value of 0.1 m3/s. If the pump operates for 10 seconds and the temperature of the air is maintained constant during operations, the pressure in the tank in kPa after 10 seconds (up to 2 decimal places) is ________.

Ans: (73.5 to 73.8)

91. A heat engine receives Q1 kJ of heat from a hot reservoir and rejects Q2kJ of heat to a cold reservoir. The work delivered by the heat engine is entirely supplied to a heat pump, which receives Q3kJ of heat from another reservoir and rejects Q4kJ of heat to the same cold reservoir. If the efficiency of the heat engine is 0.4 and COP of heat pump is 4.0, the value of (Q2 + Q4/Q1 (up to 1 decimal place) is ______.

Ans: (2.2 to 2.2)

92. A block of ice of mass 2 kg at 0℃ is dropped into an insulated vessel containing 10 kg of liquid water at 25℃. The latent heat of melting of ice is 330 kJ/kg and specific heat of water is 4.2 kJ/kg.K. The change in the entropy of the universe in kJ/K (up to 3 decimal places) is ______

Ans: (0.140 to 0.150)

93. A pure substance (Cv = 0.733 kJ/kg.K) undergoes a reversible process in which its temperature increases linearly from 40℃ to 85℃ and its specific entropy increases by 600 J/kg.K. The work done by the system in kJ/kg is

(A)  160.2

(B)  164.3

(C)  168.3

(D)  172.3

Ans: (C)

94. An ideal gas having a mass of 0.5 kg is initially at 300 kPa, 80℃ and occupies a volume of 0.14 m3. The gas undergoes an adiabatic process, where 50 kJ of work is transferred to the gas. The pressure and volume at the final state are 300 kPa and 0.20 m3. The change in the entropy of the gas in J/K is

(A)  160.3

(B)  175.3

(C)  190.3

(D)  195.3

Ans: (A)

95. The van der Waals equation of state is given as,

 where p in bar, v in m3/kmol and T is in K.

For air, the constants, a and b, are 1.368 bar.(m3/kmol)2 and 0.0367 m3/kmol, respectively. Air is contained in a system at 160 K and 0.08 m3/kmol. If p1 is the pressure calculated using ideal gas equation of state and p2 is pressure calculated using van der Walls equation of state, then p1/p2 is equal to

(A)  1.78

(B)  1.52

(C)  1.28

(D)  1.0

Ans: (A)

96. The values of specific volume of H2O at 100℃ for saturated liquid and saturated vapor states are 0.001044 m3/kg and 1.673 m3/kg, respectively. The slope of saturation pressure versus temperature curve, i.e., (dp/dT)sat­ is 3570 Pa/K. The change in enthalpy in kJ/kg between the two saturation states is ______.

Ans: (2225 to 2230)

97. In a steam power plant, stem is first expanded isentropically in a turbine from an initial condition of 100 bar and 500℃ to a pressure of 40 bar. Then the steam is reheated up to 500℃ at constant pressure. The steam is then expanded isentropically in another turbine up to a condenser pressure 0.01 bar. For steam, at 100 bar, 500℃: h = 3373.7 kJ/kg, s = 6.5966 kJ/kg.K; at 40 bar, 500℃: h = 3445.3 kJ/kg, s = 7.0901 kJ/kg.K and at 0.01 bar: hf = 29.3 kJ/kg, hg = 2514.2 kJ/kg, sf = 0.1059 kJ/kg.K, sg = 8.9756 kJ/kg.K. The dryness fraction at the condenser inlet (up to 2 decimal places) is _________.

Ans: (0.76 to 0.82)

98. Air contains by volume 79% N2(molecular weight = 28 kg/kmol) and 21% O2(molecular weight = 32 kg/kmol)). A stream of air flows at 32℃, 1 bar, at a rate of 2 m3/s and is mixed with another stream of O2 flowing at 0.4 kg/s. The molecular weight of the mixture (up to 2 decimal places) is _____.

Ans: (29.0 to 30.0)

99. Moist air enters a duct at a rate of 3 kg/s at 10℃, 80% relative humidity. The air is heated as it flows through the duct and exits at 30℃. No moisture is added or removed and the pressure of air in the duct is constant at 1 bar. The saturation vapor pressure (pg) of H2O at 10℃ is 0.01228 bar. Specific enthalpy values of dry air at inlet and outlet of the duct are respectively 283.1 kJ/kg and 303.2 kJ/kg. The corresponding specific enthalpy values for water vapor are 2519.8 kJ/kg and 2556.3 kJ/kg. For steady state operation the amount of heat added to the moist air in kW (up to 2 decimal places) is ______.

Ans: (60.5 to 61.5)

Polymer Science and Engineering (XE-F)

100. Poly(ethylene terephthalate) is synthesized from

(A)  Ethylene + dimethyl terephthalate

(B)  Ethylene + terephthalic acid

(C)  Glycerol + terephthalic acid

(D)  Ehylene  Glycol + terephthalic acid

Ans: (D)

101. Poly(vinyl chloride) has a higher Tg than polypropylene due to the presence of

(A)  Bulky side groups

(B)  Polar interactions

(C)  Restriction of bond rotation

(D)  Non-polar interactions

Ans: (B)

102. The filler which would impart electrical conductivity to a polymer is

(A)  Carbon black

(B)  Talc

(C)  Glass beads

(D)  Calcium carbonate

Ans: (A)

103. Which one of the following catalysts is used to prepare ‘isotactic’ polypropylene?

(A)  Alkyl lithium

(B)  BF3

(C)  Ziegler-Natta

(D)  AIBN

Ans: (C)

104. Novolac and resole are A-stage low molecular weight phenolic resin products that are

(A)  Soluble and fusible

(B)  Insoluble but fusible

(C)  Insoluble and infusible

(D)  Soluble and infusible

Ans: (A)

105. Which of the following reagents can act as an initiator at room temperature?

(A)  AIBN

(B)  Dicumyl peroxide

(C)  Dibenzoyl peroxide

(D)  Fe2+ + H2O2

Ans: (D)

106. The impact strength of polystyrene can be enhanced by blending/mixing with

(A)  Carbon black

(B)  PMMA

(C)  Polybutadiene

(D)  Glass fibre

Ans: (C)

107. The melt processing temperatures of a semicrystalline thermoplastic polymer is

(A)  Between Tg and Tm

(B)  Equal to Tm

(C)  Lower than Tm

(D)  Higher than Tm

Ans: (D)

108. The unit of viscosity of a polymer is expressed as

(A)  Pa.s

(B)  Pa.s1

(C)  Pa.s2

(D)  Pa.s3

Ans: (A)

109. Based on the graph 1-5, which option best describes the stress-strain behavior of materials listed as P, Q, R, S and T

P-Hard and brittle

Q-Hard and tough

R-Soft and weak

S-Hard and strong

T-Soft and tough

(A)  P-2; Q-1; R-5; S-4; T-3

(B)  P-1; Q-3; R-4; S-2; T-5

(C)  P-1; Q-2; R-5; S-3; T-4

(D)  P-2; Q-3; R-1; S-4; T-5

Ans: (B)

110. The two characterization techniques which can be used to determine degree of crystallinity of a polymer are

P. Scanning Electron Microscopy

Q. Thermogravimetric Analysis

R. Wide Angle X-ray Diffraction

S. Differential Scanning Calorimetry

(A)  P & R

(B)  Q & R

(C)  R & S

(D)  Q & S

Ans: (C)

111. The density of polyethylene crystals is 998 kg/m3 and that of totally amorphous polyethylene is 886 kg/m3. If the density of a polyethylene sample is 949 kg/m3, the crystallinity in volume fraction is ______% (round off final answer to two digits after decimal place).

Ans: (55.95 to 56.55)

112. The polydispersity index of a polymer sample containing 200 molecules each of molecular weight 10,000 gmol1, 300 molecules each of molecular weight 30,000 gmol1 and 500 molecules each of molecular weight 50,000 gmol1 is _______(round off final answer to two digits after decimal place).

Ans: (1.14 to 1.24)

113. Match the following rubber additives to their function:

Additive                                     Function

P. Dicumyl peroxide                   1. Ultrafast accelerator

Q. Pentachlorothiophenol          2. Activator

R. ZnO with stearic acid             3. Curing agent

S. Zinc diethyldithiocarbamate   4. Peptizer

(A)  P-3; Q-1; R-2; S-4

(B)  P-3; Q-1; R-4; S-2

(C)  P-3; Q-4; R-2; S-1

(D)  P-3; Q-4; R-1; S-2

Ans: (C)

114. A composite of polypropylene reinforced with 20% by volume of glass fibre is to be prepared. If the density of glass fibre is 2540 kg/m3 and polypropylene is 900 kg/m3, then the mass of glass fibre required per kg composite is ______g(round off answer to the nearest whole number).

Ans: (410 to 418)

115. Match the following terminology to the appropriate polymer processing technique:

Terminology                    Processing Technique

P. Die-swell                         1. Two roll mill mixing

Q. Breathing                        2. Thermoforming

R. Plug-assisted                  3. Extrusion

S. Mastication                      4. Compression moulding

(A)  P-1; Q-2; R-3; S-4

(B)  P-3; Q-4; R-2; S-1

(C)  P-2; Q-3; R-4; S-1

(D)  P-2; Q-1; R-4; S-3

Ans: (B)

116. Match the polymer in Column A to its application in Column B:

Column A                                                Column B

P. Nylon                                                  1. Television cabinet

Q. Polyethylene                                      2. Tyre

R. Cis-1, 4-polyisoprene                         3. Mechanical gear

S. Acrylonitrile-butadiene-styrene           4. Packaging

(A)  P-3; Q-4; R-2; S-1

(B)  P-4; Q-3; R-2; S-1

(C)  P-4; Q-2; R-3; S-1

(D)  P-3; Q-4; R-1; S-2

Ans: (A)

117. For the polycondensation of equimolar amounts of adipic acid with hexamethylene diamine, if the number average degree of polymerization is 100, then the extent of reaction is ______%.

Ans: (98.5 to 99.5)

118. The relaxation time for a rubber band at 23℃ is 60 days. If it is stressed to 2 MPa initially, then the time required before the stress relaxes to 1 MPa is ______days (round of final answer to two digit after decimal point).

Ans: (41.00 to 42.20)

119. Match the processing technique in Column A to the corresponding shear rate (s1) in Column B:

Column A                                 Column B

P. Injection Moulding                  1. 1-10

Q. Extrusion                                2. 10-100

R. Calendering                            3. 100-1000

S. Compression Moulding           4. 1000-10000

(A)  P-1; Q-3; R-2; S-4

(B)  P-4; Q-2; R-3; S-1

(C)  P-4; Q-3; R-1; S-2

(D)  P-4; Q-3; R-2; S-1

Ans: (D)

120. Given Tg of polymer A is 100℃ and that of polymer B is −100℃ , then the Tg of a miscible blend of A and B containing 30 wt% of A is _____℃(round off final answer to angle digit after decimal point).

Ans: (-67.3 to -66.3)

121. Match plots 1-4 given in the figure below with the correct flow behavior of polymeric fluid listed as P, Q, R & S:

P. Newtonian

Q. Shear thickening

R. Pseudoplastic

S. Bingham plastic

(A)  P-4; Q-2; R-3; S-1

(B)  P-4; Q-3; R-2; S-1

(C)  P-4; Q-3; R-1; S-2

(D)  P-1; Q-3; R-2; S-4

Ans: (B)

Food Technology (XE-G)

122. Indicate the correct group that contains a monosaccharide, a disaccharide and a trisaccharide.

(A)  Glucose, sucrose mannose

(B)  Ribose, lactose, raffinose

(C)  Mannose, maltose, lactose

(D)  Raffinose, stachyose, glucose

Ans: (B)

123. In which of the following products, ‘must’ is used as the substrate for fermentation?

(A)  Beer

(B)  Wine

(C)  Idli

(D)  Tempeh

Ans: (B)

124. Identify the foodborne illness which is not caused by bacteria.

(A)  Botulism

(B)  Listeriosis

(C)  Vibriosis

(D)  Cysticercosis

Ans: (D)

125. Nutrient composition of wheat flour changes with extent of extraction from whole wheat grain. Which of the following statements is true if the extraction rate increased from 50% to 90%?

(A)  Starch increases, protein increases, fat increases, mineral increases

(B)  Starch decreases, protein increases, fat increases, mineral increases

(C)  Starch decreases, protein decreases, fat increases, mineral decreases

(D)  Starch decreases, protein increases, fat decreases, mineral decreases

Ans: (B)

126. You have two samples of milk, one (X) with 3.8% fat and another (Y) with 0.5% fat. In order to produce a milk with 3.5% fat, 100 ml of Y should be mixed with ____ ml of X.

Ans: (1000 to 1000)

127. Match the items in column I with the items in column II in relation to food safety and standards.

Column I               Column II

P. HACCP                1.International food standards

Q. FSSAI                  2. Quality control protocol

R. CIP                       3. Food plant sanitation and hygiene protocol

S. CODEX                 4. Indian food standards

(A)  P-2, Q-4, R-3, S-1

(B)  P-2, Q-3, R-2, S-1

(C)  P-1, Q-4, R-2, S-3

(D)  P-4, Q-2, R-3, S-1

Ans: (A)

128. A 50% sucrose solution at 20℃ is flowing at a rate of 3.5 m3/h through a pipe with an inside diameter of 0.0475 m and length of 12 m. The viscosity and the density of the solution are 15.43 cp and 1232 kg/m3, respectively. The Reynolds number of the flow is ______.

Ans: (2078 to 2086)

129. In a pineapple juice, fibre particles having mean diameter of 160 μm and density of 1075 kg/m3 are settling by gravity. If the density and viscosity of the juice are 1015 kg/m3 and 0.98 cp, respectively, terminal velocity of the fibre particles is ______mm/s.

Ans: (0.80 to 0.90)

130. Power consumption in liquid mixing is proportional to ______.

(A)  Power number × liquid density × (rotational speed)3 × (impeller diameter)3

(B)  Power number × liquid density × (rotational speed)2 × (impeller diameter)3

(C)  Liquid density × viscosity of the liquid × (rotational speed)2 × (impeller diameter)3

(D)  Acceleration due to gravity × liquid density × (rotational speed)3 × (impeller diameter)5

Ans: (A)

131. Match the following items of group I with items group II in relation to the quality of fat.

Group I                                     Group II

P. Saponification number          1. Unsaturation of fatty acid

Q. Iodine number                       2. Volatile water soluble fatty acid

R. Reichert Meissel number       3. Hydroxy fatty acid

S. Acetyl value                            4. Molecular weight of fatty acid

(A)  P-1, Q-2, R-3, S-4

(B)  P-1, Q-3, R-4, S-2

(C)  P-4, Q-1, R-2, S-3

(D)  P-2, Q-1, R-3, S-4

Ans: (C)

132. Match the following metabolic product (Column I) that indicates the quality of food (Column II).

Column I                         Column II

P. Ethanol                        1. Canned vegetable

Q. Lactic acid                   2. Fish

R. Trimehylamine             3. Butter

S. Volatile fatty acid          4. Apple juice

(A)  P-3, Q-2, R-34, S-1

(B)  P-4, Q-1, R-2, S-3

(C)  P-4, Q-3, R-2, S-1

(D)  P-3, Q-4, R-2, S-1

Ans: (B)

133. Correlate the vitamins in column I with their role in promoting reaction/process in column II.

Column I                        Column II

P. Ribofalvin                   1. Visual cycle

Q. Vitamin D                   2. Acyl group transfer

R. Pantothenic acid        3. Regulation of Ca2+ metabolism

S. Vitamin A                    4. Oxidation-reduction reaction

(A)  P-1, Q-2, R-4, S-3

(B)  P-2, Q-1, R-3, S-4

(C)  P-3, Q-4, R-1, S-2

(D)  P-4, Q-3, R-2, S-1

Ans: (D)

134. A pure strain with generation time of 60 min is used in a fermentation process. Following inoculation (0 h), the strain takes 2 h for adaptation, 10 h to achieve maximum growth and 12 h to arrive at the point where the death rate is higher than the growth rate. If the inoculation load is 100 cells, the total population at the end of 10 h will be ______

Ans: (25550 to 25650)

135. Refer the shear stress – shear rate plot shown in the figure below. Match the lines (Column I) with appropriate rheological behavior (Column II).

Column I                      Column II

P. Line 1                      1. Dilatant

Q. Line 2                      2. Newtonian

R. Line 3                      3. Pseudoplastic

S. Line 4                      4. Bingham plastic

(A)  P-2, Q-3, R-4, S-1

(B)  P-1, Q-3, R-4, S-2

(C)  P-2, Q-4, R-3, S-1

(D)  P-4, Q-3, R-2, S-1

Ans: (D)

136. Water flowing at a rate of 1 kg/min is heated from 12 to 80℃ with flue g as supplied at a rate of 3 kg/min. The temperature and specific heat of the flue gas are 180℃ and 1.05 kJ/kg.K, respectively. If specific heat of water is 4.2 kJ/kg.K and the flow is parallel, then the logarithmic mean temperature difference will be ______℃

Ans: (53.30 to 55.25)

137. The Lineweaver-Burk plot of an enzymatic reaction shows Vmax of 160 μmol/l.min and km of 60 μmol/l. For a substrate concentration of 40 μmol/l, the velocity of the reaction is estimated to be ______μmol/l.min.

Ans: (64.0 to 64.0)

138. Bread is wrapped in 0.1 mm thick cellophane film having water vapour permeability of 1.82 × 1010 m3 water (STP)/s.m2.atm/m at 38℃. If the surface area of pack, vapour pressure of water inside and outside of the pack is 0.20 m2, 10 mm Hg and 5 mm Hg, respectively, the loss of water vapour at 38℃ in g/day is ______.

Ans: (0.14 to 0.18)

139. Match the following methods/system (column I) with the appropriate operations (column II)

Column I                         Column II

P. Parboiling               1. Sugarcane juice extraction

Q. Pearling                 2. Hydrothermal treatment

R. Wet milling             3. Corn milling

S. Degerming             4. Wheat milling

T. Break rolls              5. Barley processing

U. Crushing rolls         6. Pulse milling

(A)  P-4, Q-1, R-3, S-6, T-2, U-5

(B)  P-4, Q-5, R-2, S-6, T-1, U-3

(C)  P-3, Q-5, R-2, S-1, T-3, U-4

(D)  P-2, Q-5, R-6, S-3, T-4, U-1

Ans: (D)

140. A 12 mm thick fish filler having 80% moisture content (wet basis) is to be frozen using a plate freezer. The plates maintained at −35℃. Assume the heat transfer coefficient, initial freezing temperature and latent heat of fusion are 2.0 W/m2 K, −2℃ and 330 kJ/kg, respectively. If the density and thermal conductivity of frozen fish filler are 1050 kg/m3 and 1.48 W/m-K, respectively, the time required to freeze the fillet from the initial freezing temperature is ______h.

Ans: (6.80 to 7.20)

141. A suspension containing 2 × 104 spores of organism A having a D1 value of 1.5 min and 8 × 105 spores organism B having a D121.1 value of 0.8 min is heated at a constant temperature of 121.1℃. The heating time needed to obtain a probability of spoilage ‘1 in 1000’ is ____min.

Ans: (10.80 to 11.20)

142. In an evaporation process, a compressor picks up 0.05 m3 air in each revolution and compresses 500 kg of air per minute. If the specific volume of air is 0.9 m3/kg, then the compressor speed is _____ rpm.

Ans: (9000 to 9000)

143. For a soybean oil extraction system, solvent : soy ratio is maintained at 0.5 : 1 (w/w). Original seed contains 18% oil (w/w). If the meal (soy solid) after final desolventization has 0.01 kg oil per kg oil free meal then, the effectiveness of the solvent (kg oil/kg solvent) in the extraction process is _____

Ans: (0.30 to 0.40)

Atmospheric and Oceanic Sciences (XE-H)

144. Rossby Number is the ratio of

(A)  Coriolis Force to Inertial Force

(B)  Inertial Force to Coriolis Force

(C)  Gravitational Force to Coriolis Force

(D)  Viscous Force to inertial Force

Ans: (B)

145. Kuroshio Current and Gulf Stream are

[WBC : Western Boundary Current, EBC : Eastern Boundary Current]

(A)  EBC, WBC

(B)  EBC, EBC

(C)  WBC, WBC

(D)  WBC, EBC

Ans: (C)

146. The velocity of a tsunami wave in an ocean basin of depth 1 km is _____ ms1

[Density of seawater : 1025 kg m3, g: 10 ms2]

Ans: (98.9 to 100.5)

147. A thin iceberg is observed to move southeastward in the Arctic Ocean. If the surface current is wind driven, the prevailing wind is

(A)  Easterly

(B)  Northerly

(C)  Southerly

(D)  Westerly

Ans: (D)

148. Equatorial Kelvin and Rossby waves respectively propagate

(A)  Westward and Eastward

(B)  Eastward and Westward

(C)  Westward and Westward

(D)  Eastward and Eastward    

Ans: (B)

149. The largest contributor to the atmospheric greenhouse effect is

(A)  CO2

(B)  N2

(C)  CH4

(D)  H2O

Ans: (D)

150. If Tv, T, Tw and Td denote virtual, dry bulb, wet bulb and dew point temperatures of a moist air parcel, then the correct order of their values is

(A)  Tv > T > Tw > Td

(B)  Tv ≥ T ≥ Tw ≥ Td

(C)  Tv > T ≥ Tw ≥ Td

(D)  T > Tv > Tw > Td

Ans: (C)

151. Burning of fossil fuel is increasing the concentration of CO­2 in the atmosphere. A consequence of this is

(A)  Ocean water which is presently basic will drift toward pH neutral

(B)  Ocean water which is presently acidic will become more acidic

(C)  No effect on ocean pH

(D)  Ocean water which is presently slightly basic will become more basic

Ans: (A)

152. Mixed layer depths measured in the Pacific Ocean in two different years are schematically shown in the figure below.

Years P and Q belong to

(A)  P: El-Nino, Q: La-Nina

(B)  P: La-Nina, Q:El-Nino

(C)  P: El-Nino, Q:QBO

(D)  P: QBO, Q: La-Nina

Ans: (B)

153. Average surface temperatures of the Sun and the Earth are 6300 K and 285 K, respectively. The ratio of the wavelength of peak radiation of the Earth to that of the Sun is _______.

Ans: (22.05 to 22.15)

154. In the month of April, the mixed layer in the Arabian Sea received a net heat flux of 50 W m2. If the mixed layer depth is 50 m, the increase in temperature at the end of April is ______℃

[Density of seawater: 1025 kg m3, Density of freshwater : 1000 kg m3, Specific heat of seawater: 4200 J kg1 K1, Latent heat of evaporation: 2.45 × 106 J kg1]

Ans: (0.59 to 0.61)

155. The thickness of an atmospheric layer between 600 hPa and 500 hPa is 1.5 km. If the layer is isothermal, then its temperature is _____K.

[Gas constant of air: 287 J kg1 K1, g : 10 ms2]

Ans: (286.55 to 287.55)

156. At 17°N, a mass of fluid moving under geostrophic balance at 0.3 ms1 towards east. Suddenly the pressure gradient force becomes zero. Then the fluid will

(A)  continue to move towards the east at 0.3 ms1

(B)  undergo circular motion with radius of about 17 km

(C)  undergo circular motion with radius of about 7 km

(D)  move southward

[Angular velocity of the Earth: 7.27 × 105 rad s1]

Ans: (C)

157. At 45°N, wind is blowing northward and its magnitude decreases eastward from 10 ms1 to 1 ms1 over a distance of 18 km. The absolute vorticity of the flow is ________× 104 s1

(Angular velocity of the Earth: 7.27 × 105 rad s1]

Ans: (-4.10 to -3.90)

158. Sea surface height anomalies at the locations A, B, C and D are −10, −15, 5 and 0 cm respectively.

The magnitude of geostrophic velocity at P is _____ms1.

[Take 1° = 100 km, g = 10 ms2, Angular velocity of the Earth: 7.27 × 105 rad s1]

Ans: (0.42 to 0.46)

159. In a severe tropical cyclone, 250 m of rainfall occurs in an area having a radius of 200 km. If the energy supplied to the system from this rainfall is N times the energy of one atomic bomb (=1.5 × 1015 kJ), then the value of N is _______.

[Density of freshwater: 1000 kg m3, Specific heat of seawater: 4200 J kg1 K1, Latent heat of evaporation: 2.45 × 106 J kg1]

Ans: (51 to 52)

160. A student wants to numerically solve the linear 1-D advection equation  where c = 300 ms−1. The value of the maximum time-step the student can consider according to CFL criterion for a spatial resolution of 3 km is

(A)  15 s

(B)  10 s

(C)  25 s

(D)  20 s

Ans: (B)

161. Planets in the solar system are in radiative equilibrium. Let S0, α, T0 and R denote solar constant, albedo, average temperature and radius of a planet, respectively, and σ is Stefan’s constant. Then the energy balance of this planet is given by the expression

(A)   

(B)   

(C)   

(D)   

Ans: (A)

162. A cumulonimbus cloud forms by an air parcel rising from the sea level with an initial temperature and specific humidity of 27℃ and 20 gm kg1, respectively. Assume that moist static energy is conserved in this cloud. Then the cloud temperature at an altitude of 15 km is ______K.

[Specific heat of dry air at constant pressure: 1005 J kg1 K1, Specific heat of water vapour at constant pressure: 1850 J kg1 K1, g = 10 ms2, Latent heat of evaporation 2.45 × 106 J kg1]

Ans: (199 to 205)

163. If ug and vg are respectively zonal and meridional components of a flow field in geostrophic balance, then the divergence of this flow is

(A)   

(B)   

(C)   

(D)   

Ans: (D)

164. During the Indian summer monsoon season, depressions do not intensify to tropical cyclones because

P: Indian sub-continent is very hot and large land-sea temperature difference pulls depressions quickly to land before they can intensify into cyclones.

Q: southwesterly winds at low level are not conductive for the formation of tropical cyclones.

R: SST cooling due to strong monsoonal winds prevents cyclone formation.

S: strong zonal wind shear during the monsoon season does not allow warm core formation.

Which of the above statement(s) is(are) correct

(A)  P & Q

(B)  only R

(C)  Only S

(D)  R & S

Ans: (C)

165. Which among the following statement(s) is (are) correct,

P: ENSO and El-Nino are the same refer to the warming of Equatorial Eastern Pacific SST.

Q: ENSO is an atmosphere-ocean coupled phenomenon and El-Nino is its oceanic part.

R: ENSO is an atmospheric phenomenon and El-Nino is an oceanic phenomenon

S: ENSO is the oscialltory component of El-Nino having a period of 4.7 years.

(A)  P & R

(B)  Only Q

(C)  P, Q and S

(D)  R & S

Ans: (B)

General Aptitude

166. The event would have been successful if you ______ able to come.

(A)  are

(B)  had been

(C)  have been

(D)  would have been

Ans: (B)

167. There was no doubt that their work was thorough.

Which of the words below is closest in meaning to the underlined word above?

(A)  Pretty

(B)  Complete

(C)  Sloppy

(D)  Haphazard

Ans: (B)

168. Four cards lie on a table. Each card has a number printed on one side and a colour on the other. The faces visible on the cards are 2, 3, red, and blue.

Proposition: If a card has an even value on one side, then its opposite face is red.

The cards which MUST be turned over to verify the above proposition are

(A)  2, Red

(B)  2, 3, Red

(C)  2, blue

(D)  2, red, blue

Ans: (C)

169. What is the value of x when 

(A)  1

(B)  −1

(C)  −2

(D)  Cannot be determined

Ans: (B)

170. Two dice are thrown simultaneously. The probability that the product of the numbers appearing on the top faces of the dice is a perfect square is

(A)  1/9

(B)  2/9

(C)  1/3

(D)  4/9

Ans: (B)

171. Bhaichung was observing the pattern of people entering and leaving a car service centre. There was a single window where customers were being served. He saw that people inevitably came out of the centre in the order that they went in. However, the time they spent inside seemed to vary a lot: some people came out in a matter of minutes while for others it took much longer.

From this, what can one conclude?

(A) The centre operates on a first-come-first-served basis but with variable service times, depending on specific customer needs.

(B) Customers were served in an arbitrary order since they took varying amounts of time for service completion in the centre.

(C) Since some people came out within a few minutes of entering the centre. The system is likely to operate on a last-come-first-served basis.

(D) Entering the centre early ensured that one would have shorter service times and most people attempted to do this.

Ans: (A)

172. A map shows the elevations of Darjeeling, Gangtok, Kalimpong, pelling, and Siliguri, Kalimpong is at a lower elevation than Gangtok. Pelling is at a lower elevation than Gangtok. Pelling is at a higher elevation that siliguri. Darjeeling is at a higher elevation than Gangtok.

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

i. Pelling is at a higher elevation than Kalimpong

ii. Kalimpong is at a lower elevation than Darjeeling

iii. Kalimpong is at a higher elevation than siliguri

iv. Siliguri is at a lower elevation than Gangtok

(A)  Only ii

(B)  Only ii and iii

(C)  Only ii and iv

(D)  Only iii and iv

Ans: (C)

173. P,Q,R,S,T and U are seated around a circular table. R is seated two places to the right of Q.P is seated three places to the left of R. S is seated opposite U. If P and U now switch seats.

Which of the following must necessarily be true?

(A) P is immediately to the right of R

(B) T is immediately to the left of P

(C) T is immediately to the left of P or P is immediately to the right of Q

(D) U is immediately to the right of R or P is immediately to the left of T

Ans: (C)

174. Budhan covers a distance of f19 km in 2 hours by cycling one fourth of the time and walking the rest. The next day he cycles (at the same speed as before) for half the time and walks the rest (at the same speed as before) and covers 26 km in 2 hours. The speed in km/h at which Budhan walks is

(A)  1

(B)  4

(C)  5

(D)  6

Ans: (D)

175. The points in the graph below represent the halts of a lift for duration of 1 minute, over a period of 1 hour.

Which of the following statements are correct?

i. The elevator never moves directly from any non-ground floor to another non-ground floor over the one hour period

ii. The elevator stays on the fourth floor for the longest duration over the one hour period

(A)  Only i

(B)  Only ii

(C)  Both i and ii

(D)  Neither i nor ii

Ans: (D)

Gate 2017 Textile Engineering and Fibre Science Question Paper 4th Feb 2017 PDF Download

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Textile Engineering and Fibre Science 4th Feb 2017

Subject Name: Textile Engineering and Fibre Science

Duration : 180

Total Marks: 100

1. If the scalar projection of the vector  on the vector  is 5, then a value of β is equal to

(A)  21

(B)  9

(C)  −1

(D)  −6

Ans: (B)

2. The Laplace transform of et cos(2t) is

(A)   

(B)   

(C)   

(D)   

Ans: (D)

3. If z(x, y) = x2 – y2, x(t) = t – t2 and y(t) = t2 + t−3 then  at t = 1 is equal to ________

Ans: (3.99 to 4.01)

4. The characteristic observation in burning test of cotton fibre is

(A)  Burns readily with whitish ash as residue

(B)  Burns with dripping

(C)  Burns with burning hair smell

(D)  Melts and forms a hard bead

Ans: (A)

5. The given structure is a repeat unit of

(A)  Cellulose acetate

(B)  Cellulose

(C)  Polyamide

(D)  Polyester

Ans: (B)

6. Which of the following is(are) bast fibre(s)

P. Cotton

Q. Flax

R. Silk

S. Jute

(A)  P only

(B)  Q and R only

(C)  Q and S only

(D)  S only

Ans: (C)

7. During crystallization of polyester

(A)  Heat is evolved

(B)  Heat is absorbed

(C)  No exchange of heat takes place

(D)  Small molecule such as water is eliminated

Ans: (A)

8. Which of the following fibre(s) is(are) manufactured by melt spinning process

P. Viscose

Q. Cellulose acetate

R. Nylon-6

S. Aramid

(A)  P only

(B)  Q and R only

(C)  R only

(D)  R and S only

Ans: (C)

9. Keeping card production same, the quality of carding will improve by setting

(A)  Higher doffer rpm and coarser sliver hank

(B)  Higher doffer rpm and finer silver hank

(C)  Lower doffer rpm and coarser sliver hank

(D)  Lower doffer rpm and finer sliver hank

Ans: (B)

10. The tenacity of

P. Carded sliver

Q. First drawn sliver

R. Second drawn sliver

S. Combed sliver

follows the order

(A)  P > Q > R > S

(B)  S > R > Q > P

(C)  R > S > P > Q

(D)  Q > R > S > P

Ans: (A)

11. For a given yarn fineness, use of ring traveler of too small a mass gives

(A)  Small balloon size but more yarn content on the bobbin

(B)  Small balloon size but less yarn content on the bobbin

(C)  Big balloon size but more yearn content on the bobbin

(D)  Big balloon size  but less yarn content on the bobbin

Ans: (D)

12. In cotton combing process, the counter-feed system gives

(A)  Low removal of noil and low elimination of impurities

(B)  Low removal of noil and high elimination of impurities

(C)  High removal of noil and l ow elimination of impurities

(D)  High removal of noil and high elimination of impurities

Ans: (D)

13. Probability of warp breakage during weaving increases, when

(A)  Warp extensibility is decreased

(B)  Warp unevenness is decreased

(C)  End density is decreased

(D)  Warp hairiness is decreased

Ans: (A)

14. In terms of weft insertion rate, which of the following is correct?

(A)  Airjet > Waterjet > Multiphase > Projectile

(B)  Multiphase > Airjet > Waterjet > Projectile

(C)  Projectile > Waterjet > Airjet > Multiphase

(D)  Waterjet > Projectile > Multiphase > Airjet

Ans: (B)

15. A tuck stitch in knitting makes the fabric

(A)  Narrower

(B)  Thinner

(C)  More rigid in course direction

(D)  Wider and porous

Ans: (D)

16. A perpendicular-laid nonwoven

(A)  Should not contain thermoplastic fibre

(B)  Does not form a 3-D structure

(C)  Cannot be used as a replacement of foam

(D)  Exhibits high recovery from compression

Ans: (D)

17. The cut squaring technique of sampling of fibres is NOT applicable to

(A)  Bale

(B)  Sliver

(C)  Roving

(D)  Yarn

Ans: (A)

18. The ratio of wet-strength ot dry-strength of viscose fibre is

(A)  Equal to one

(B)  Always less than one

(C)  Always greater than one

(D)  Sometimes greater and sometimes less than one

Ans: (B)

19. Theoretical limit for mass irregularity (CVlim) of a cotton yarn does NOT depend on

(A)  Mean fibre length

(B)  Mean  firbe fitness

(C)  Mean yarn count

(D)  Coefficient of variation of fibre fineness

Ans: (A)

20. Diamond bars appear in woven fabric due to

(A)  Faulty loom parts

(B)  Excessive warp irregularity

(C)  Periodic fault in warp yarn

(D)  Periodic fault in weft yarn

Ans: (D)

21. In a three-sigma control chart, the probability that a point falls outside the control limits, when a process is under control, is

(A)  0

(B)  0.0027

(C)  0.01

(D)  0.05

Ans: (B)

22. Shrinkage of cotton fabric during wetting is caused by

(A)  Extension of fibre

(B)  Crimpling of fibre

(C)  Swelling of fibre

(D)  Compression of fibre

Ans: (C)

23. Vapour-phase flame retardant agents are based on compound containing

(A)  Nitrogen

(B)  Phosphorus

(C)  Halogens

(D)  Aluminium

Ans: (C)

24. White specks observed in dyed cotton fabric are attributed to

(A)  Poor wash fastness of dyes

(B)  Non-uniform agitation of dye bath

(C)  Low temperature of dyeing

(D)  Presence of immature cotton fibres

Ans: (D)

25. Number of moles, accurate to one decimal place, required in 200 cm3 to make 0.5 mol l1 sodium hydroxide solution is _____

Ans: (0.09 to 0.11)

26. The median, accurate to two decimal places, of a random variable X with the  probability density function  is _______

Ans: (1.25 to 1.27)

27. Using Simpson’s 1/3 rule, the value of the integral  accurate to two decimal places, is _____

Ans: (1.65 to 1.68)

28. If a solution curve of the differential equation  passes through the point (1, 0), then this curve also passes through the point

(A)  (−1, 0)

(B)  (0, −1)

(C)  (2, 10)

(D)  (−2, 6)

Ans: (A)

29. The system of linear equations  has

(A)  No solution for α = 1, β = −8

(B)  Unique solution for α = −1, β = 8

(C)  Infinitely many solutions for α = −1, β = −8

(D)  Infinitely many solutions for α = 1, β = 8

Ans: (C)

30. The function f(x) = x3 – 3x2 – 9x + 10 is

(A)  Increasing in the interval (1, ∞)

(B)  Increasing in the interval (−∞, 1)

(C)  Decreasing in the interval (−1, 3)

(D)  Decreasing in the interval (−3, 1)

Ans: (C)

31. Group I contains techniques of fibre manufacturing. Group II gives the physical phenomena associated with these techniques. Match the technique with the phenomenon

Group I

P. Melt spinning

Q. Wet spinning

R. Dry spinning

Group II

1. Diffusion of only solvent

2. Diffusion of both solvent and non-solvent

3. No solvent diffusion

(A)  P-1, Q-2, R-3

(B)  P-3, Q-1, R-2

(C)  P-3, Q-2, R-1

(D)  P-1, Q-3, R-2

Ans: (C)

32. The average molecular mass, in g/mol, of nylon-6 polymer, having average degree of polymerization of 100, is ______

(given S = 32 amu, N = 14 amu, O = 16 amu, C = 12 amu, H = 1 amu)

Ans: (11299 to 11370)

33. Group I consists of names of fibres. Group II gives characteristic structural features of these fibres. Match the fibre from Group I to its respective feature from Group II

Group I        Group II

P. Cotton        1. Para- and ortho-cortex

Q. Jute           2. Primary and secondary wall

R. Wool          3. Fibroin β-sheets

S. Silk             4. Multicellular

(A)  P-4, Q-1, R-2, S-3

(B)  P-2, Q-4, R-1, S-3

(C)  P-2, Q-3, R-4, S-1

(D)  P-2, Q-4, R-3, S-1

Ans: (B)

34. Wool gives warmth because it has

P. A helical structure which can entrap air

Q. High heat of sorption

R. Low crystallinity

S. High extensibility

(A)  P and Q only

(B)  Q and R only

(C)  P and S only

(D)  P and R only

Ans: (A)

35. To obtain high molecular weight nylon-66, if 11.6 g of hexamethylene diamine (molecular weight 116 g/mol) is used, then the required amount of adipic acid (molecular weight 146 weight 146 g/mol), in gram, accurate to one decimal place, is _______

Ans: (14.5 to 14.7)

36. If the distance between two adjacent fibres of circular cross-section in a hexagonally packed yarn is equal to the radius of the fibre, then the packing density of yarn, accurate to three decimal places, is _______

Ans: (0.380 to 0.420)

37. A 30 tex open-end rotor yarn having 650 twist per meter is produced using 33 mm rotor diameter and 1,20,000 rotor rpm. The rotational speed of the peel-off point is ______× 103 rpm

Ans: (121 to 123)

38. A bobbin lead roving frame is running at 25 m/min delivery speed and 1250 rpm spindle speed. The rotational speed of the bobbin, at the instant of 0.10 m bobbin diameter, accurate to two decimal places, is _____ rpm

Ans: (1327 to 1331)

39. A T-shirt is produced from cotton fibre of 1520 kg m3 density, 1.4 dtex fineness and 30 mm length. The total number of fibres in the T-shirt of 0.15 kg is ______× 106

Ans: (34 to 37)

40. Pilling resistance of

(A)  Ring yarn is higher than open-end rotor yarn but lesser than air vortex yarn

(B)  Air vortex yarn is higher than ring yarn but lesser than open-end rotor yarn

(C)  Open-end rotor yarn is higher than ring yarn but lesser than air vortex yarn

(D)  Ring yarn is higher than air vortex yarn but lesser than open-end rotor yarn

Ans: (C)

41. A needle loom, having a needle board with 2000 needles/m, is operating at a stroke frequency of 2000 strokes/min and producing a needle-punched nonwoven fabric at 5m/min. The punch density, in number of punches per cm2 is _______

Ans: (79 to 81)

42. Compared to conventional sizing, the wet sizing process reduces

(A)  Size consumption substantially

(B)  Consumption of drying energy

(C)  Weavability of warp yarn

(D)  Tensile strength of yarn

Ans: (A)

43. In a fabric, warp count is 25 tex, weft count is 32 tex, ends per cm is 25, picks per cm is 15, warp crimp is 6% and weft crimp is 8%. The areal density of the fabric, in g/m2 accurate to two decimal places, is ______

Ans: (117.00 to 119.00)

44. Let a cheese of 160 mm traverse length be wound on a rotary traverse machine having a drum of 75 mm diameter and 2.5 crossings. If the drum rotates at 3250 rpm, then the coil angle, in degrees, accurate to one decimal place, is _______

Ans: (73.5 to 76.0)

45. Group I consists of weave designs. Group II lists end-use/property. Match the weave design from Group I with the corresponding end-use/property from Group II

Group I                  Group II

P. Leno                     1. Furnishing

Q. Honeycomb         2. Broken and irregular surface

R. Jacquard              3. Mosquito net

S. Crepe                    4. Towel

(A)  P-3, Q-4, R-1, S-2

(B)  P-4, Q-1, R-3, S-2

(C)  P-1, Q-2, R-4, S-3

(D)  P-3, Q-4, R-2, S-1

Ans: (A)

46. At 65% relative humidity and 20℃ temperature, the moisture regain of the fibres

(P) Wool       (Q) Nylon 6                   (R) Cotton  (S) Polyester

follows the order

(A)  P > Q > R > S

(B)  P > R > Q > S

(C)  R > P > Q > S

(D)  R > P > S > Q

Ans: (B)

47. While measuring tensile properties using Stelometer at 3.2 mm gauge length, a cotton fibre bundle of 15 mm length and 4.5 mg weight registers a breaking load of 6 kg. The bundle tenacity (g/tex) is _____

Ans: (19.9 to 20.1)

48. The tenacity of a two-fold yarn is 1.1 times the tenacity of its component single yarn. The breaking load of the two-fold yarn is X times the breaking load of its single component yarn. Neglecting length contraction due to twist, the value of X, accurate to one decimal place, is ______

Ans: (2.1 to 2.3)

49. The compressive pressure applied onto a fabric is inversely proportional to the cube of thickness of the fabric. If the thickness is halved during compression, then the pressure increase by _______ times.

Ans: (7.9 to 8.1)

50. The coefficient of correlation between packing density and porosity of a set of yarns is _______

Ans: (1.01 to 0.99)

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

Assertion : Jet dyeing machines yield level dyeing in short dyeing time

Reason : Jet dyeing machines use pressure jets to force dye into the fibre

(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

Ans: (D)

52. Group I lists chemical processes. Group II lists chemicals used in these processes. Match the process with the corresponding chemical

Group I                  Group II

P. Carbonising          1. Na2CO3

Q. Scouring              2. H2SO4

R. Bleaching             3. NaOH

S. Mercerising          4. H2O2

(A)  P-2, Q-3, R-4, S-1

(B)  P-2, Q-1, R-4, S-3

(C)  P-3, Q-1, R-2, S-3

(D)  P-2, Q-1, R-3, S-4

Ans: (B)

53. Determine the correctness or otherwise of the following statements

[p] The contact angle θ is indicated of the wetability of a textile surface by a liquid

[q] Values of θ > 90° indicate poor wetting surfaces

(A)  Both [p] and [q] are true

(B)  Both [p] and [q] are false

(C)  [p] is true but [q] is false

(D)  [p] is false but [q] is true

Ans: (A)

54. The add-on of a chemical finish required on a fabric is 3% on-weight-of-fabric (owf). If the wet pick up is 80%, then the concentration of finish required in the padding bath, in % (wt/wt), accurate to two decimal places, is ______

Ans: (3.50 to 4.00)

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

Assertion : Burnt out effect on polyester/cotton blend fabric can be obtained by printing

Reason : Printing paste contains a reagent that releases an acid during steaming

(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

Ans: (A)

56. He was one of my best __________ and I felt his loss _________.

(A) friend, keenly

(B) friends, keen

(C) friend, keener

(D) friends, keenly

Ans: (D)

57. As the two speakers became increasingly agitated, the debate became __________.

(A)  lukewarm

(B)  poetic

(C)  forgiving

(D)  heated

Ans: (D)

58. A right – angled cone (with base radius 5cm and height 12cm), as shown in the figure below, is rolled on the ground keeping the point P fixed until the point Q (at the base of the cone, as shown) touches the ground again.

(A)   

(B)   

(C)   

(D)   

Ans: (D)

59. In a company with 100 employees, 45 earn Rs. 20,000 per month, 25 earn Rs. 30,000, 20 earn Rs. 40,000 8 earn Rs. 60,000, and 2 earn Rs. 150,000. The median of the salaries is

(A)  Rs. 20,000

(B)  Rs. 30,000

(C)  Rs. 32,300

(D)  Rs. 40,000

Ans: (B)

60. P,Q, and R talk about S’s car collection. P states that S has at least 3 cars. Q believes that S has less than 3 cars. R indicates that to his knowledge, S has at least one Car. Only one of P, Q and R is right the number cars owned by S is.

(A)  0

(B)  1

(C)  3

(D)  Cannot be determined

Ans: (A)

61. “Here, throughout the early 1820s, Stuart continued to fight his losing battle to allow his sepoys to wear their caste-marks and their own choice of facial hair on parade, being again reprimanded by the commander-in-chief. His retort that ‘A stronger instance than this of European prejudice with relation to this country has never come under my observations’ had no effect on his superiors.”

According to this paragraph, which of the statements below is most accurate?

(A)  Stuart’s commander – in chief was moved by this demonstration of his prejudice.

(B)  The Europeans were accommodating of the sepoys’ desire to weak their caste – marks.

(C)  Stuart’s losing battle’ refers to his inability to succeed in enabling sepoys to wear caste-marks.

(D)  The commander– in – Chief was exempt from the European preiudice that dictated how the sepoys were to dress.

Ans: (C)

62. What is the sum of the missing digits in the subtraction problem below?

(A)  8

(B)  10

(C)  11

(D)  Cannot be determined

Ans: (D)

63. Let S1 be the plane figure consisting of the points (x,y) given by the inequalities |x – 1| ≤ 2 and |y + 2| ≤ Let S2 be the plane figure given by the inequalities x – y ≥ −2, y ≥ 1, and x ≤ 3 Let S be the union of S1 and S2. The area of S is

(A)  26

(B)  28

(C)  32

(D)  34

Ans: (C)

64. Two very famous sportsmen Mark and Steve happened to be brothers, and played for country K. Mark teased James, an opponent from country E, “There is no way you are good enough to play for your country.’’ James replied, “Maybe not, but at least I am the best player in my own family.”

Which one of the following can be inferred from this conversation?

(A) Mark was known to play better than James

(B) Steve was known to play better than Mark

(C) James and Steve were good friends

(D) James played better than Steve

Ans: (B)

65. The growth of bacteria (lactobacillus) in milk leads to curd formation. A minimum bacterial population density of 0.8(in suitable units) is needed to form curd. In the graph below, the population density of lactobacillus in 1 litre of milk is plotted as a function of time, at two different temperatures, 25°C and 37°C.

Consider the following statements based on the data shown above:

(i) The growth in bacterial population stops earlier at 37°C as compared to 25°C

(ii) The time taken for curd formation at 25°C is twice the time taken at 37°C

Which one of the following options is correct?

(A)  Only i

(B)  only ii

(C)  Both i and ii

(D)  Neither i nor ii

Ans: (A)

Gate 2017 Production and Industrial Engineering Question Paper 5th Feb 2017 PDF Download

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Production and Industrial Engineering 5th Feb 2017

Subject Name: Production and Industrial Engineering

Duration : 180

Total Marks: 100

1. Divergence of the curl of a twice differentiable continuous vector function is

(A)  unity

(B)  infinity

(C)  zero

(D)  a unit vector

Ans: (C)

2. For two non-zero vectors  is perpendicular to  then

(A)  the magnitude of  is twice the magnitude of 

(B)  the magnitude of  is half the magnitude of 

(C)   and  cannot be orthogonal

(D)  the magnitudes of  and  are equal

Ans: (D)

3. For an orthogonal matrix Q, the valid equality is

(A)  QT = Q1

(B)  Q = Q1

(C)  QT = Q

(D)  det(Q) = 0

Ans: (A)

4. The product of a complex number z = x + iy and its complex conjugate is

(A)  x2

(B)  y2

(C)  x2 – y2

(D)  x2 + y2

Ans: (D)

5. Using Simpson’s 1/3 rule for numerical integration, the consecutive points are joined by a

(A)  line

(B)  parabola

(C)  polynomial with power 3

(D)  polynomial with power 1/3

Ans: (B)

6. For a two dimensional state-of-stress defined as σxx = σyy = τxy = S, the Mohr’s circle of stress has

(A)  center at (S, 0) and radius S

(B)  center at (0, 0) and radius S

(C)  center at (S, 0) and radius 0

(D)  center at (S/2, 0) and radius 2S

Ans: (A)

7. A specimen of steel has yield strength of 700 MPa. The specimen is subjected to a state of plane-stress with σ1 = σ2 = 500 MPa. The factor of safety according to the von-Mises theory of failure is _______

Ans: (1.4)

8. The inside and outside radii of a thick-walled cylindrical pressure vessel are denoted by a and b, respectively. If the vessel is subjected to an internal pressure P, then the magnitude of the radial stress σrr is

(A)  zero at r = a and maximum at r = b

(B)  maximum at r = a and zero at r = b

(C)  constant over the entire thickness

(D)  zero at both r = a and r = b

Ans: (B)

9. A metallic cylindrical casing of an exhaust pipe has inner radius 50 mm and wall thickness 7 mm. If the thermal conductivity of the material of the casing is 50 W/m-K, then the thermal resistance of the casing in K/kW is _____(up to three decimal places).

Ans: (0.41 to 0.42)

10. In Value Engineering approach, the value of the product is

(A)  inversely proportional to its functions and directly proportional to its cost

(B)  directly proportional to its functions and inversely proportional to its cost

(C)  inversely proportional to its functions as well as its cost

(D)  directly proportional to its functions as well as its cost

Ans: (B)

11. Match the ASME process charge symbols with their correct description

(A)  P-3, Q-4, R-1, S-5, T-2

(B)  P-4, Q-2, R-5, S-1, T-3

(C)  P-3, Q-2, R-5, S-1, T-4

(D)  P-1, Q-5, R-3, S-2, T-4

Ans: (C)

12. In Glass fiber Reinforce Plastic (GFRP) composites with long fibers, the role matrix is to

(P) support and transfer the stresses to the fibers

(Q) reduce propagation of cracks

(R) carry the entire load

(S) protect the fibers against damage

The correct statements are

(A)  P, Q and R

(B)  Q, R and S

(C)  P, Q and S

(D)  P, R and S

Ans: (C)

13. Turning, drilling, boring and milling are commonly used machining operations. Among these, the operation(s) performed by a single point cutting tool is (are)

(A)  turning only

(B)  drilling and milling only

(C)  turning and boring only

(D)  boring only

Ans: (C)

14. In chemical machining, the etch factor is expressed as

(A)   

(B)   

(C)   

(D)   

Ans: (A)

15. A Shewhart  was developed for an in-control process. Considering the probability of a point falling outside the 3σ control limits as 0.0026, the value of average run length for this chart is ______

Ans: (384 to 385)

16. Accuracy of measuring instrument is expressed as

(A)  true value – measured value

(B)     measured value – true value

(C) 

(D) 

Ans: (C)

17. The operating characteristic curves of three single sampling plans X, Y and Z with same lot size and acceptance number are shown in the Figure.

Considering the above operating characteristic curves, the correct relationship of the plans with respect to sample size is

(A)  sample size of X < sample size of Y < sample size of Z

(B)  sample size of X = sample size of Y = sample size of Z

(C)  sample size of X > sample size of Y > sample size of Z

(D)  sample size of X > sample size of Y < sample size of Z

Ans: (C)

18. In carbon dioxide molding process, the binder used is

(A)  Sodium bentonite

(B)  Calcium bentonite

(C)  Sodium silicate

(D)  Phenol formaldehyde

Ans: (C)

19. A steel wire of 2 mm diameter is to be drawn from a wire of 5 mm diameter. The value of true s train developed is _____(up to three decimal places).

Ans: (1.80 to 1.85)

20. In gas tungsten arc welding process, the material coated on pure tungsten electrode to enhance its current carrying capacity is

(A)  Titanium

(B)  Manganese

(C)  Radium

(D)  Thorium

Ans: (D)

21. In powder metallurgy, the process ‘atomization refers to a method of

(A)  producing powders

(B)  compaction of powders

(C)  sintering of powder compacts

(D)  blending of  metal powders

Ans: (A)

22. The ideal stress-strain behavior for a completely brittle material during tensile testing up to failure is described by

(A) 

(B) 

(C) 

(D) 

Ans: (B)

23. With reference to Iron-Carbon equilibrium phase diagram, the crystal structure of 0.3% plain carbon steel at 1, 100℃ is

(A)  HCP

(B)  BCT

(C)  BCC

(D)  FCC

Ans: (D)

24. If E is the modulus of elasticity in GPa, G is the shear modulus in GPa and v is the Poisson’s ratio of a linear elastic and isotropic material, the three terms are related as

(A)  E = G(1− 2v)

(B)  E = 2G(1 – v)

(C)  E = G(1 + 2v)

(D)  E = 2G(1 + v)

Ans: (D)

25. A machined surface with standard symbols indicating the surface texture is shown in the Figure. (All dimensions in the Figure are in micrometer).

The waviness height (in micrometer) of the surface is

(A)  1

(B)  50

(C)  60

(D)  120

Ans: (B)

26. The improper integral  converges to

(A)  0

(B)  1.0

(C)  0.5

(D)  2.0

Ans: (C)

27. The local minima of the function f(x) = x2 – x4 in the range −8 ≤ x ≤ 0.8 is located at

(A)   

(B)   

(C)   

(D)   

Ans: (A)

28. Runge-Kutta fourth order method is used to solve the differential equation  If the initial value y(0) = 2 and step-size is 0.1, then the value of y(0.1) is _______(up to three decimal places)

Ans: (2.2 to 2.3)

29. Two machines are defective in a lot of 10. A combination of four machines is to be picked at a time from the lot. The maximum number of combinations that can be obtained without any defective machine is ______

Ans: (70)

30. The simply-supported beam shown in the Figure is loaded symmetrically using two equal point loads P. The radius of curvature of deflection-curve is 15m for the portion of the beam that is subjected to pure bending. The vertical deflection (in mm) at point M, equidistant from both the supports, is _____(up to two decimal places).

Ans: (18.00 to 19.00)

31. A solid circular shaft is subjected to a bending moment M and torque T simultaneously. Neglecting the effects of stress concentration, the equivalent bending moment is expressed as

(A)   

(B)   

(C)   

(D)   

Ans: (A)

32. A pair of spur gears with 20° full-depth involute teeth is used to transmit 3.5 kW of power. The pinion rotates at 700 rpm and has pitch circle diameter of 100 mm. Assuming a single pair of teeth in contact, the total force acting on a gear tooth (in kN) is

(A)  0.347

(B)  0.954

(C)  1.016

(D)  1.302

Ans: (C)

33. A manometer is used for the pressure measurement in a closed tank. The three fluids f1, f2 and f3 have specific weights γ, 2γ and 0.5γ, respectively. The schematic arrangement with manometric readings and other dimensions are shown in the Figure. In order to ensure zero gauge pressure in the tank at the mid-height level (h/2), the height of the tank h(in m) is _______

Ans: (2.0)

34. A pipeline with variable cross-section contains water with specific weight 104N/m3. The flow conditions at two points 1 and 2 on the axis of the pipe are:

P1 = 3 bar,     V1 = 10 m/s

P2 = 1 bar,     V2 = 20 m/s

Consider frictional losses to be negligible. For no-flow condition between points 1 and 2(as shown in Figure), if the height z1 from the datum is 1 m, then the height z2(in m) is _______

(g = 9.81 m/s2)

Ans: (5.5 to 6.0)

35. A reversible heat engine (E) operating in a cycle interacts with three reservoirs 1, 2 and 3 maintained at temperatures T1 = 500 K, T2 = 400 K and T3 = 300 K, respectively. The engine receives 10 kJ of heat from reservoir 1 and rejects 3 kJ to reservoir 3. The net work output, Wnet(in kJ) from the engine is ______

Ans: (3)

36. A schematic diagram of peripheral milling is shown in the Figure.

If t is the depth of cut and d is the diameter of the milling cutter, then the length of approach (la) is expressed as

(A)   

(B)   

(C)   

(D)   

Ans: (C)

37. An electrical appliances showroom sells 2,400 ceiling fans in one year (52 weeks). The holding cost is 10% the cost of the ceiling fan. The cost of one ceiling fan is Rs. 600. The cost incurred for placing an order is Rs. 201. There is a lead time of 5 weeks. The economic order quantity (EOQ) and the reorder level, respectively (rounded to the next higher integer) are

(A)  231, 127

(B)  38, 231

(C)  127, 231

(D)  127, 13

Ans: (C)

38. In a calendar year, the demand forecast of motorbikes for the month of June is 200. The actual demand of motorbikes for the month of June and July are 300 and 350, respectively. If single exponential smoothing method with smoothing constant 0.7 is used, then the demand forecast for the month of August is _____

Ans: (326)

39. In a project, tasks, A, B, C, D, E, F, G, H, I and J are to be performed. The precedence relationships and the time required (in days) to complete the tasks are given in the Table.

The time required (in days) to complete the project along the critical path is ______

Ans: (48)

40. The potential production alternative for manufacturing a product along with their unit cost and monthly capacity are given in the Table.

The inventory at the end of July is 100 units. If the demand for the month of August is 620, then the minimum total cost (in Rs.) to meet the demand is _______

Ans: (2900)

41. The preparatory and miscellaneous codes used in CNC part programming and the functions are given in the Table.

The correct combinations of code and the respective function is

(A)  P-4, Q-1, R-3, S-2

(B)  P-4, Q-1, R-2, S-3

(C)  P-1, Q-4, R-3, S-2

(D)  P-2, Q-1, R-3, S-4

Ans: (A)

42. A surface of 30 mm × 30 mm of an iron block is machined using electrochemical machining process. The atomic weight and valency of iron of 55.85 and 2, respectively. The density o f iron is 7,860 kg/m3. If input current is 1,000 A and Faraday’s constant is 96,540 Coulombs, then the feed rate (in mm/min) is _______(up to two decimal places).

Ans: (2.40 to 2.50)

43. Quality control department of a company maintains ‘c’ chart to assess the quality of laptops. In this process, twenty laptops are examined randomly. The number of nonconformities observed per laptop is given in the Table.

Based on the data, the upper control limit for the ‘c’ chart is _______(up to two decimal places).

Ans: (11.00 to 11.20)

44. The Merchant circle diagram showing various forces associated with a cutting process using a wedge-shaped tool is given in the Figure.

The coefficient of friction can be estimated from the ratio

(A)   

(B)   

(C)   

(D)   

Ans: (D)

45. An air conditioner unit is expected to run continuously. The mean time between failures (MTBF) for this unit is 2,000 hours and the mean time to repair (MTTR) is 48 hours. The availability of the air conditioning unit is ______(up to three decimal places).

Ans: (0.970 to 0.980)

46. A firm manufactures capacitors using a specialized process. The desired specification for the capacitance is 40 ≠ 10 picofarads (pF). The process used is in statistical control. If the process mean is 41 pF and the estimated standard deviation is 3 pF, then the process capability index Cpk is _______

Ans: (1)

47. A metallic strip having thickness of 12 mm is to be rolled using two steel rolls, each of 800 mm diameter. It is assumed that there is no change in width of the strip during rolling. In order to achieve 10% reduction in cross-sectional area of the strip after rolling, the angle subtended (in degrees) by the deformation zone at the center of the roll is

(A)  1.84

(B)  3.14

(C)  6.84

(D)  8.23

Ans: (B)

48. An electron beam welding process uses 15 mA beam current at an accelerating voltage of 150 kV. The energy released per second by the beam (in J) is ______(up to one decimal place).

(1 Ampere = 6.28 × 1018 electrons per second, 1 eV= 1.6 × 1019 J)

Ans: (2250 to 2265)

49. In a machine shop, four jobs need to be assigned to four different machines. Each of the jobs is to be assigned to one machine only at a time. The time taken to complete the job in different machines is given in the Table.

In order ensure that the total time required to complete all the jobs is minimum, the optimal assignment of the job is

(A)  J1 ⇒ M4, J2 ⇒ M2, J3 ⇒ M3, J4 ⇒ M1

(B)  J1 ⇒ M2, J2 ⇒ M1, J3 ⇒ M4, J4 ⇒ M3

(C)  J1 ⇒ M2, J2 ⇒ M1, J3 ⇒ M3, J4 ⇒ M4

(D)  J1 ⇒ M4, J2 ⇒ M2, J3 ⇒ M1, J4 ⇒ M3

Ans: (B)

50. A hose coupling manufacturing company has production capacity of 2,500 units per year. The unit selling price of the item is Rs. 150/ The fixed cost of production is Rs. 80,000 and variable cost of production per unit its Rs. 70. If the company wishes to achieve a profit of Rs. 20,000 during the calendar year, then the minimum quantity to be produced is ______

Ans: (1250)

51. Schematic diagram of pouring basin and sprue of a gating system is shown in the Figure. Depth of molten metal in the pouring basin is 100 mm and the height of the sprue is 1,500 mm.

Consider the cross-section of the sprue is circular, the ratio d1 : d2 to avoid aspiration is

(A)  3 : 2

(B)  5 : 6

(C)  15 : 16

(D)  1 : 2

Ans: (D)

52. In a numerical control (NC) machine positioning system, the measures of precision are expressed by considering a single axis as shown in the Figure.

If σ is standard deviation of the error distribution, then lm and n are

(A)  l = Accuracy,   m = Repeatability,                   n = control resolution

(B)  l = Repeatability,      m = Accuracy       n = control resolution

(C)  l = Control resolution,                  m = Repeatability          n = Accuracy

(D)  l = Accuracy,   m = Control resolution, n = Repeatability

Ans: (A)

53. In a machining operation with turning tool, the tool life (T) is related to cutting speed v(m/s), feed f(mm) and depth of cut d(mm) as

T=Cv2.5f0.9d0.15

where, C is a constant. The suggested values for the cutting parameters are: v = 1.5 m/s, f = 0.25 mm and d = 3 mm for normal rough turning. If the operation is performed at twice the cutting speed and the other parameters remain unchanged, the corresponding percentage change in tool life is ______

Ans: (80 to 84)

54. The annual demand of wrist produced on an assembly line is 1,03,125 units. The line operates 50 weeks/year, 5 shifts/week and 7.5 hours/shift. The uptime efficiency of the line is 99%. The cycle time (Tc) of the assembly line (in minutes/unit) is _____(up to two decimal places).

Ans: (1.00 to 1.10)

55. In a gear manufacturing company, three orders P, Q and R are to be processed on a hobbing machine. The orders were received in the sequence P – Q – R. The Table indicates the process time remaining and production calendar due date for each order.

Considering today as the Day 10 in the production calendar of the Hobbing Shop, the sequence of the order scheduled using the ‘Critical Ratio’ rule is

(A)  P – Q – R

(B)  P – R – Q

(C)  Q – P – R

(D)  Q – R – P

Ans: (D)

56. She has a sharp tongue and it occasionally turn _______

(A)  hurtful

(B)  left

(C)  methodical

(D)  vital

Ans: (A)

57. I_____ made arrangements had I _______ informed earlier.

(A)  could have, been

(B)  would have, being

(C)  had, have

(D)  had been, been

Ans: (A)

58. In the summer, water consumption is known to decrease overall by 25%. A Water Board official states that in the summer household consumption decreases by 20%, while other consumption increases by 70%.

Which of the following statements is correct?

(A)  The ratio of household to other consumption is 8/17

(B)  The ratio of household to other consumption is 1/17

(C)  The ratio of household to other consumption is 17/8

(D)  There are errors in the official’s statement.

Ans: (D)

59. 40% of deaths on city roads may be attributed to drunken driving. The number of degrees needed to represents this as a slice of a pie chart is

(A)  120

(B)  144

(C)  160

(D)  212       

Ans: (B)

60. Some tables are shelves. Some shelves are chairs. All chairs are benches. Which of the following conclusions can be deduced from the preceding sentences?

i. At least one bench is a table

ii. At least one shelf is a bench

iii. At least one chair is a table

iv. All benches are chairs

(A)  Only i

(B)  Only ii

(C)  Only ii and iii

(D)  Only iv

Ans: (B)

61. ‘If you are looking for a history of India, or for an account of the rise and fall of the British Raj, or for the reason of the cleaving of the subcontinent into two mutually antagonistic parts and the effects this mutilation will have in the respective sections, and ultimately on Asia, you will not find it in these page; for though I have spent a lifetime in the country, I lived too near the seat of events, and was too intimately associated with the actors, to get the perspective needed for the impartial recording of these matters”.

Here, the word ‘antagonistic’ is closest in meaning to

(A)  impartial

(B)  argumentative

(C)  separated

(D)  hostile

Ans: (D)

62. S, T, U, V, W, X, Y, and Z are seated around a circular table. T’s neighbours are Y and V, Z is seated third to the left of T and second to the right of S,. U’s neighbours are S and Y; and T and W are not seated opposite each other. Who is third to the left of V?

(A)  X

(B)  W

(C)  U

(D)  T

Ans: (A)

63. Trucks (10 m long) and cars (5 m long) go on a single lane bridge.. There must be a gap of at least 20 m after each truck and a gap of at least 15 m after each car. Trucks and cars travel at a speed of 36 km/h. If cars and trucks go alternately, what is the maximum number of vehicles that can use the bridge in one hour?

(A)  1440

(B)  1200

(C)  720

(D)  600

Ans: (A)

64. There are 3 Indians and 3 Chinese in a group of 6 people. How many subgroups of this group can we choose so that every subgroup has at least one Indian?

(A)  56

(B)  52

(C)  48

(D)  44

Ans: (A)

65. A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at 25 m intervals in this plot.

The path from P to Q is best described by

(A)  Up-Down-Up-Down

(B)  Down-Up-Down-Up

(C)  Down-Up-Down

(D)  Up-Down-Up

Ans: (C)

Gate 2017 Physics Question Paper 5th Feb 2017 PDF Download

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Physics 5th Feb 2017

Subject Name: Physics

Duration : 180

Total Marks: 100

1. Identical charges q are placed at five vertices of a regular hexagon of side a. The magnitude of the electric field and the electrostatic potential at the centre of the hexagon are respectively

(A)   

(B)   

(C)   

(D)   

Ans: (C)

2. A parallel plate capacitor with square plates of side 1 m separated by 1 micro meter is filled with a medium of dielectric constant of 10. If the charges on the two plates are 1C and −1C, the voltage across the capacitor is _____kV. (upto two decimal places). (ε0 = 8.854 × 1012 F/m)

Ans: (11.25 to 11.34)

3. Light is incident from a medium of refractive index n = 1.5 onto vacuum. The smallest angle of incidence for which the light is not transmitted into vacuum is ____ degrees. (up to two decimal places).

Ans: (41.60 to 42.00)

4. A monochromatic plane wave in the free space with electric field amplitude of 1 V/m is normally incident on a fully reflecting mirror. The pressure exerted on the mirror is _______× 1012 (up to two decimal places) (ε0 = 8.854 × 1012 F/m).

Ans: (8.80 to 8.90)

5. The best resolution that a 7 bit A/D convertor with 5 V full scale can achieve is _____mV. (up to two decimal places).

Ans: (39.30 to 39.50)

6. In the figure given below, the input to the primary of the transformer is a voltage varying sinusoidally with time. The resistor R is connected to the centre tap of the secondary. Which one of the following plots represents the voltage across the resistor R as a function of time?

(A) 

(B) 

(C) 

(D) 

Ans: (A)

7. The atomic mass and mass density of Sodium are 23 and 0.968 g cm3, respectively. The number density of valence electrons is ______×1022 cm3. (Up to two decimal places.)

(Avogadro number, NA = 6.022 × 1023)

Ans: (2.50 to 2.55)

8. Consider a one-dimensional lattice with a weak periodic potential  The gap at the edge of the Brillouin zone  is :

(A)  U0

(B)  U0/2

(C)  2U0

(D)  U0/4

Ans: (A)

9. Consider a triatomic molecule of the shape shown in the figure below in three dimensions. The heat capacity of this molecule at high temperature (temperature much higher than the vibrational energy scales of the molecule but lower than its bond dissociation energies) is:

(A)   

(B)  3kB

(C)   

(D)  6kB

Ans: (D)

10. If the Lagrangian  is modified to  which one of the following is TRUE?

(A)  Both the canonical momentum and equation of motion do not change

(B)  Canonical momentum changes, equation of motion does not change

(C)  Canonical momentum does not change, equation of motion changes

(D)  Both the canonical momentum and equation of motion change

Ans: (B)

11. Two identical masses of 10 gm each are connected by a massless spring of spring constant 1 N/m. The non-zero angular eigenfrequency of the system is ______ rad/s. (up to two decimal places).

Ans: (14.10 to 14.20)

12. The phase space trajectory of an otherwise free particle bouncing between two hard walls elastically in one dimension is a

(A)  straight line

(B)  parabola

(C)  rectangle

(D)  circle

Ans: (C)

13. The Poisson bracket [x, xp + ypx] is equal to

(A)  −x

(B)  y

(C)  2px

(D)  py

Ans: (B)

14. The wavefunction of which orbital is spherically symmetric :

(A)  px

(B)  py

(C)  s

(D)  dxy

Ans: (C)

15. The contour integral  evaluated along a contour going from −∞ to +∞ along the real axis and closed in the lower half-plane by a half circle is equal to _____.(up to two decimal places).

Ans: (3.13 to 3.15)

16. The Compton wavelength of a proton is ____ fm. (up to two decimal places).

(mp = 1.67 × 1027 kg, h = 6.626 × 1034 Js, ,e = 1.602 × 1019 C, c = 3 × 108 ms1)

Ans: (1.30 to 1.34)

17. Which one of the following conservation laws is violated in the decay τ+ → μ+μ+μ

(A)  Angular momentum

(B)  Total Lepton number

(C)  Electric charge

(D)  Tau number

Ans: (D)

18. Electromagnetic interactions are :

(A)  C conserving

(B)  C non-conserving but CP conserving

(C)  CP non-conserving but CPT conserving

(D)  CPT non-conserving

Ans: (A)

19. A one dimensional simple oscillator with Hamiltonian is subjected to a small perturbation, H1 = αx + βx3 + γx4. The first order correction to the ground state energy is dependent on

(A)  only β

(B)  α and γ

(C)  α and β

(D)  only γ

Ans: (D)

20. For the Hamiltonian  where a0 ∈ R,  is a real vector, I is the 2 × 2 identity matrix, and  are the Pauli matrices, the ground state energy is

(A)  |b|

(B)  2a0 − |b|

(C)  a0 – |b|

(D)  a0

Ans: (C)

21. The coefficient of eikx in the Fourier expansion of u(x) = Asin2 (αx) for k = −2α is

(A)  A/4

(B)  −A/4

(C)  A/2

(D)  −A/2

Ans: (B)

22. The degeneracy of the third energy level of a 3-dimensional isotropic quantum harmonic oscillator is

(A)  6

(B)  12

(C)  8

(D)  10

Ans: (A)

23. The electronic ground state energy of the Hydrogen atom is −6 eV. The highest possible electronic energy eigenstable has an energy equal to

(A)  0

(B)  1 eV

(C)  +13.6 eV

(D)  ∞

Ans: (D)

24. A reversible Carnot engine is operated between temperatures T1 and T2 (T2 > T1) with a photon gas as the working substance. The efficiency of the engine is

(A)   

(B)   

(C)   

(D)   

Ans: (B)

25. In the nuclear reaction 13C6 + ve → 13N7 + X, the particle X is

(A)  an electron

(B)  an anti-electron

(C)  a muon

(D)  a pion

Ans: (A)

26. Three charges (2C, −1C, −1C) are placed at the vertices of an equilateral triangle of side 1m as shown in the figure. The component of the electric dipole moment about the marked origin along the  direction is ____ Cm.

27. An infinite solenoid carries a time varying current I(t) = At2, with A ≠ 0. The axis of the solenoid is along the  are the usual radial and polar directions in cylindrical polar coordinates.  is the magnetic field at a point outside the solenoid. Which one of the following statements is true?

(A)  Br = 0, Bθ = 0, Bz = 0

(B)  Br ≠ 0, Bθ ≠ 0, Bz = 0

(C)  Br ≠ 0, Bθ ≠ 0, Bz ≠ 0

(D)  Br = 0, Bθ = 0, Bz ≠ 0

Ans: (D)

28. A uniform volume charge density is placed inside a conductor (with resistivity 102 Ωm). The charge density becomes 1/(2.718) of its original value after time _____ femto seconds. (up to two decimal places) (ε0 = 8.854 × 1012 F/m)

Ans: (87.50 to 89.50)

29. Water freezes at 0℃ at atmospheric pressure (1.01 × 105 Pa). The densities of water and ice at this temperature and pressure are 1000 kg/m3 and 934 kg/m3 The latent heat of fusion is 3.34 × 105 J/kg. The pressure required for depressing the melting temperature of ice by 10℃ is _____ GPa. (up to two decimal places)

Ans: (0.15 to 0.19)

30. The minimum number of NAND gates required to construct an OR gate is

(A)  2

(B)  4

(C)  5

(D)  3

Ans: (D)

31. Consider a 2-dimensional electron gas with a density of 1019 m2. The Fermi energy of the system is _____ eV(up to two decimal places).

(me = 9.31 × 1031 kg, h = 6.626 × 1034 Js, e = 1.602 × 1019C)

Ans: (2.32 to 2.38)

32. The total energy of an inert-gas crystal is given by  , were R is the inter-atomic spacing in Angstroms. The equilibrium separation between the atoms is ______ Angstroms. (up to two decimal places).

Ans: (0.90 to 1.10)

33. Consider N non-interacting, distinguishable particles in a two-level system at temperature T. The energies of the levels are 0 and ε, where ε > 0. In the high temperature limit (kBT >> ε), what is the population of particles in the level with energy ε?

(A)  N/2

(B)  N

(C)  N/4

(D)  3N/4

Ans: (A)

34. A free electron of energy 1 eV is incident upon a one-dimensional finite potential step of h eight 0.75 eV. The probability of its reflection from the barrier is ______(up to two decimal places).

Ans: (0.10 to 0.12)

35. Consider a one-dimensional potential well of width 3 mm. Using the uncertainty principle (∆x∙∆p ≥ h/2), an estimate of the minimum depth of the well such that it has at least one bound state for an electron is (me = 9.31 × 1031 kg, h = 6.626 × 1034 J s, e = 1.602 × 1019 C):

(A)  1 μeV

(B)  1 meV

(C)  1 eV

(D)  1 MeV

Ans: (B)

36. Consider a metal with free electron density of 6 × 1022 cm3. The lowest frequency electromagnetic radiation to which this metal is transparent is 1.38 × 1016 If this metal had a free electron density of 1.8 × 1023 cm−3 instead, the lowest frequency electromagnetic radiation to which it would be transparent is _________× 1016 Hz. (up to two decimal places).

Ans: (2.35 to 2.45)

37. An object travels along the x-direction with velocity c/2 in a frame O. An observer in a frame O’ sees the same object travelling with velocity c/4. The relative velocity of Oʹ with respect to O in units of c is ______.(up to two decimal places).

Ans: (0.27 to 0.31)

38. The integral  is equal to ______.(up to two decimal places).

Ans: (0.43 to 0.45)

39. The imaginary part of an analytic complex function is v(x, y) = 2xy + 3y. The real part of the function is zero at the origin. The value of the real part of the function at 1 + i is _____.(up to two decimal places).

Ans: (2.90 to 3.10)

40. Let X be a column vector of dimension n > 1 with a t least one non-zero entry. The number of non-zero eigenvalues of the matrix M = XXT is

(A)  0

(B)  n

(C)  1

(D)  n – 1

Ans: (C)

41. JP for the ground state of the 13C6 nucleus is

(A)   

(B)   

(C)   

(D)   

Ans: (D)

42. A uniform solid cylinder is released on a horizontal surface with speed 5 m/s without any rotation (slipping without rolling). The cylinder eventually starts rolling without slipping. If the mass and radius of the cylinder are 10 gm and 1 cm respectively, the final linear velocity of the cylinder is ______ m/s. (up to two decimal places).

Ans: (3.30 to 3.35)

43. The energy density and pressure of a photon gas are given by u = aT4 and P = u/3, where T is the temperature and a is the radiation constant. The entropy per u nit volume is given by αaT3. The value of α is ______.(up to two decimal places).

Ans: (1.30 to 1.36)

44. Which one of the following gases of diatomic molecules is Raman, infrared, and NMR active?

(A)  1H – 1H

(B)  12C – 16O

(C)  1H – 35Cl

(D)  16O – 16O

Ans: (C)

45. The π+ decays at rest to μ+ and vμ. Assuming the neutrino to be massless, the momentum of the neutrino is ____ MeV/c. (up to decimal places)

(mπ = 139 MeV/c2, mμ = 105 MeV/c2).

Ans: (29.50 to 30.10)

46. Using Hund’s rule, the total angular momentum quantum number J for the electronic ground stat of the nitrogen atom is

(A)  1/2

(B)  3/2

(C)  0

(D)  1

Ans: (B)

47. Which one of the following operators is Hermitian?

(A)   

(B)   

(C)   

(D)   

Ans: (A)

48. The real space primitive lattice vectors are  The reciprocal space unit vectors  for this lattice are, respectively

(A)   

(B)   

(C)   

(D)   

Ans: (A)

49. Consider two particles and two non-degenerate quantum levels 1 and 2. Level 1 always contains a particle. Hence, what is the probability that level 2 also contains a particle for each of the two cases:

(i) when the two particles are distinguishable and (ii) when the two particles are bosons?

(A)  (i) 1/2 and (ii) 1/3

(B)  (i) 1/2 and (ii) 1/2

(C)  (i) 2/3 and (ii) 1/2

(D)  (i) 1 and (ii) 0

Ans: (C)

50. A person weighs wp at Earth’s north pole and we at the equator. Treating the Earth as a perfect sphere of radius 6400 km, the value 100 × (wp – we)/wp is _____. (up to two decimal places).

(Take g = 10 ms2).

Ans: (0.32 to 0.36)

51. The geometric cross-section of two colliding protons at large energies is very well estimated by the product of the effective sizes of each particle. This is closest to

(A)  10 b

(B)  10 mb

(C)  10 μb

(D)  10 pb

Ans: (B)

52. For the transistor amplifier circuit shown below with R1 = 10 kΩ, R2 = 10 kΩ, R3 = 1 kΩ, and β = 99. Neglecting the emitter diode resistance ,the input impedance of the amplifier looking into the base for small ac signal is _____kΩ. (up to two decimal places).

Ans: (4.75 to 5.01)

53. Consider an ideal operational amplifier as shown in the figure below with R1 = 5 kΩ, R2 = 1 kΩ, RL = 100 kΩ. For an applied input voltage V = 10 mV, current passing through R2 is ______μA. (up two decimal places).

Ans: (9.80 to 10.20)

54. Consider the differential equation dy/dx + ytan x) = cos(x). If y(0) = 0, y(π/3) is ______. (up to two decimal places).

Ans: (0.51 to 0.53)

55. Positronium is an atom made of an electron and a positron. Given the Bohr radius for the ground state of the Hydrogen atom to be 0.53 Angstroms, the Bohr radius for the ground state of posistronium is _____ Angstroms. (up to two decimal places).

Ans: (0.99 to 1.10)

56. The ninth and the tenth of this month are Monday and Tuesday _______.

(A)  figuratively

(B)  retrospectively

(C)  respectively

(D)  rightfully

Ans: (C)

57. It is _______ to read this year’s textbook ______ the last year’s

(A)  easier, than

(B)  most easy, than

(C)  easier, from

(D)  easiest, from

Ans: (A)

58. A rule states that in order to drink beer, one must be over 18 years old. In a bar, there are 4 people. P is 16 years old, Q is 25 years old, R is drinking milkshake and S is drinking a beer. What must be checked to ensure that the rule is being followed?

(A)  Only P’s drink

(B)  Only P’s drink and S’s age

(C)  Only S’s age

(D)  Only P’s drink, Q’s drink and S’s age

Ans: (B)

59. Fatima starts from point P, goes North for 3 km, and then East for 4 km to reach point Q. She then turns to face point P and goes 15 km in that direction. She then goes North for 6 km. How far is she from point P, and in which direction should she go to reach point P?

(A)  8 km, East

(B)  12 km, North

(C)  6 km, East

(D)  10 km, North

Ans: (A)

60. 500 students are taking one or more courses out of Chemistry, Physics and Mathematics. Registration records indicate course enrolment as follows: Chemistry (329), Physics (186), Mathematics (295), Chemistry and Physics (83), Chemistry and Mathematics (217), and Physics and Mathematics (63). How many students are taking all 3 subjects?

(A)  37

(B)  43

(C)  147

(D)  53

Ans: (D)

61. “If you are looking for a history of India, or for an account of the rise and fall of the British Raj, or for the reason of the cleaving of the subcontinent into two mutually antagonistic parts and the effects this mutilation will have in the respective sections, and ultimately on Asia, you will not find it in these pages; for though I have spent a lifetime in the country. I lived too near the seat of events, and was too intimately associated with the actors, to get the perspective needed for the impartial recording of these matters.”

Which of the following statements best reflects the author’s opinion?

(A)  An intimate association does not allow for the necessary perspective.

(B)  Matters are recorded with an impartial perspective.

(C)  An intimate association offers an impartial perspective.

(D)  Actors are typically associated with the impartial recording of matters.

Ans: (A)

62. Each of P, Q, R, S, W, X, Y and Z has been married at most once. X and Y are married and have two children P and Q. Z is the grandfather of the daughter S of P. Further, Z and W are married and are parents of R. Which one of the following must necessarily be FALSE?

(A)  X is the mother-in-law of R

(B)  P and R are not married to each other

(C)  P is a son of X and Y

(D)  Q cannot be married to R

Ans: (D)

63. 1200 men and 500 women can build a bridge in 2 weeks. 900 men and 250 women will take 3 weeks to build the same bridge. How many men will be needed to build the bridge in one week?

(A)  3000

(B)  3300

(C)  3600

(D)  3900

Ans: (C)

64. The number of 3-digit numbers such that the digit 1 is never to the immediate right of 2 is

(A)  781

(B)  791

(C)  881

(D)  891

Ans: (C)

65. A contour line joins locations having the same height above the mean sea level. The following is a contour plot of geographical region. Contour lines are shown at 25 m intervals in this plot.

Which of the following is the steepest path leaving from P?

(A)  P to Q

(B)  P to R

(C)  P to S

(D)  P to T

Ans: (B)

Gate 2017 Petroleum Engineering Question Paper 5th Feb 2017 PDF Download

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Petroleum Engineering 5th Feb 2017

Subject Name: Petroleum Engineering

Duration : 180

Total Marks: 100

1. If a vector  has components vx = 1, vy = 2, vz = 3, then its magnitude is ______. (write answer with two decimal places)

Ans: (3.70 to 3.79)

2. The value of  is _____.

3. If  is to be solved using the conditions y(0) = and y(1) = b, which of the following numerical method(s) can be used?

(A)  Euler with shooting method

(B)  Euler without shooting method

(C)  4th order Runge-Kutta with shooting method

(D)  Both (A) and (C)

Ans: (D)

4. The numerical method used to find the root of a non-linear algebraic equation, that converges quadratically, is :

(A)  Bisection method.

(B)  Regula-falsi method (Method of False Position).

(C)  Newton-Raphson method.

(D)  None of the above

Ans: (C)

5. Which one of the following curves shows a typical behavior of the producing gas oil ratio (GOR) with time for a reservoir under solution gas drive?

(A) 

(B) 

(C) 

(D) 

Ans: (D)

6. A student has written following possible causes of lost circulation during a drilling operation.

i. High salinity in the reservoir

ii. Fracture in the reservoir

iii. A fault encountered during drilling

iv. Low viscosity of the reservoir fluid

Which of the above statements are correct?

(A)  i, iv

(B)  ii, iii

(C)  i, iii

(D)  ii, iv

Ans: (B)

7. For water depth less than 8 m, which one of the following drilling vessels is the most suitable and economical?

(A)  Semi-submersible rig

(B)  Jack-up rig

(C)  Drilling barges

(D)  Drill ship

Ans: (C)

8. Which one of the following statements is correct for pseudo-steady state condition in a confined reservoir?

(A)  The pressure decline stops in the reservoir.

(B)  The pressure declines at the same rate across the reservoir.

(C)  The boundary pressure does not change.

(D)  The pressure starts increasing in the reservoir.

Ans: (B)

9. The roots of the equation  are :

(A)  1, 1, 2

(B)  1, 2, 3

(C)  1, 3, 4

(D)  1, 2, 4

Ans: (B)

10. The °API of a crude oil density 950 kg/m3 is ______.(write answer with two decimal places)

Ans: (17.00 to 18.00)

11. The differential equation 2xydx + (1 + x2)dy = 0, in which x is an independent variable and y is the dependent variable, is :

(A)  an ordinary differential equation of second order.

(B)  a first order nonlinear differential equation.

(C)  an exact differential equation.

(D)  a partial differential equation.

Ans: (C)

12. For the two marices , the product YX will be:

(A)   

(B)   

(C)   

(D)   

Ans: (A)

13. As per the Bharat IV norms, the maximum permissible limit of sulfur in diesel in ppm is :

(A)  10

(B)  50

(C)  100

(D)  500

Ans: (B)

14. The amount of methane gas evolved at 0℃ and 1 atm from the dissociation of 1 m3 of methane gas hydrate, is approximately:

(A)  equal to the volume of gas hydrate.

(B)  10 times the volume of gas hydrate.

(C)  160 times the volume of gas hydrate.

(D)  300 times the volume of gas hydrates.

Ans: (C)

15. For a centrifugal pump, the head developed by the pump is proportional to the :

(A)  speed of the impeller rotation.

(B)  square of speed of the impeller rotation.

(C)  cubic power of speed of the impeller rotation.

(D)  square root of speed of the impeller rotation.

Ans: (B)

16. Which of these is a must for petroleum generation and accumulation?

(A)  Source rocks

(B)  Porous reservoir rocks

(C)  Impermeable cap rocks

(D)  All of the above

Ans: (D)

17. The problem of viscous fingering is encountered when:

(A)  a low viscosity fluid is injected in a high viscosity fluid.

(B)  a high viscosity fluid is injected in a low viscosity fluid.

(C)  a fluid of equal viscosity but lower density is injected in a fluid of higher density.

(D)  none of the above

Ans: (A)

18. Which of these is NOT a sedimentary rock?

(A)  Shale

(B)  Sandstone

(C)  Carbonate

(D)  None of the above

Ans: (D)

19. The unbiased sample variance for the set of numbers: S={40, 45, 50, 55, 60} is ______.(write answer with one decimal place

Ans: (61.0 to 63.0)

20. If 5x + 2iy – ix + 7y = 2 + 3i, where  the values of two real numbers (x, y) are, respectively:

(A)  (−1, 1)

(B)  (1, −1)

(C)  (1, 1)

(D)  (−1, −1)

Ans: (A)

21. Pick the INCORRECT inequality, where z1, z2 and z3 are complex numbers.

(A)  |z1 + z2| ≤ |z1| + |z2|

(B)  |z1 − z2| ≥ |z1| − |z2|

(C)  |z1 − z2| ≤ |z1| − |z2|

(D)  |z1 + z2 + z| ≤ |z1| + |z2| + |z3|

Ans: (C)

22. Which of the following is NOT true? 

(A)   

(B)   

(C)   

(D)   

Ans: (D)

23. Which of the following is a potential environmental threat due to the cement-plug deterioration in an abandoned oil well?

(A)  Well bore could leak oil reservoir fluids into groundwater

(B)  Oil reservoir fluids could flow to the surface and contaminate surface soil

(C)  Oil reservoir fluids could discharge into navigable waters

(D)  All of the above

Ans: (D)

24. _______ is a mode of flame propagation in a pre-mixed gas, and drives a leading shock front into the quiescent, unburnt gas at supersonic velocity, immediately followed by a combustion zone.

(A)  Deflagration

(B)  Fire

(C)  Detonation

(D)  Ignition

Ans: (C)

25. Bio-Ga(BG), Coal Bed Methane (CBM) and Methane Gas Hydrate (MGH), if arranged in the order of increasing methane content, the correct order is :

(A)  BG, CBM, MGH

(B)  CBM, BG, MGH

(C)  CBM, MGH, BG

(D)  BG, MGH, CBM

Ans: (A)

26. For a velocity field given by  calculate the curl of  If the calculated vector is  then the value of c is _______

Ans: (−2.05 to −1.95)

27. Single step integration (step size = 0.5) of evaluated numerically using the Simpson’s 1/3 rule, is _______(write answer with three decimal places)

Ans: (0.720 to 0.730)

28. Solve  numerically from x = 0 to 1 using explicit, forward, first order Euler method with initial condition of y(0) = 1 and step size (h) of 0.2. The absolute value of error in y(1) calculated using analytical and numerical solution is _____% (calculate the error using analytical solution as the basis and use three decimal places)

Ans: (10.5 to 11.5)

29. Relative permeability curves are shown in the following figure for a water-oil system in a porous medium. Sw is water saturation and kr is relative permeability. Curve 1 is relative permeability of water and Curve 2 is relative permeability of oil. Assuming the porous medium is at irreducible water saturation initially, the maximum possible recovery of oil by water flooding is _____%. (write answer with one decimal place)

Ans: (72.0 to 75.0)

30. An oil reservoir of 1000 m2 area and thickness of 10 m has a porosity of 30%. The connate water saturation is 20%. Initial formation volume factor  Assuming average oil flow rate of 2 m3/day (at surface condition), the life of reservoir is _____ days.

Ans: (999.0 to 1001.0)

31. A self-flowing production well of depth 3,000 m having oil with density 850 kg/m3 is shut-in for workover job. The shut-in pressure at the surface is 70 × 105 N/m2. The density of the mud required to kill the well will be _____kg/m3. (G = 9.81 m/s2, write answer with one decimal place)

Ans: (1080.0 to 1095.0)

32. In a directional well, the kick off point has a true vertical depth (TVD) of 1000 m and the end of buildup section has a TVD of 1200 m. The buildup section for directional drilling has a horizontal displacement of 200 m, after which the tangent section has inclination of 45°. A driller monitors the well from the surface location of the well and sees that the target has horizontal departure of 1000 m. The T VD of the deepest point of the well is _____meters.

Ans: (1990 to 2010)

33. The figure below shows the pressure measured in a well at different depths. AB is cap, B is gas oil contact and C is water-oil contact. Density of gas in gas cap is 2 kg/m3, oil density is 800 kg/m3 and water density is 1000 kg/m3. The difference between pressure at point D and point B (PD – PB) is _____× 105 N/m2. (use g = 9.81 m/s2, write answer with one decimal place)

Ans: (7.5 to 8.2)

34. A laboratory air-brine capillary pressure of 1.20 × 105 N/m2 has been measured in a reservoir core sample at residual water saturation. The air-brine surface tension is 0.070 N/m, and the brine-oil interfacial tension for the reservoir fluid is 0.025 N/m. The density values of brine and oil are 1080 kg/m3 and 780 kg/m3, respectively. Take g = 9.81 m/s2, and assume identical wetting preferences for the core sample and reservoir. The height of the water-oil transition zone (up to the point of reservoir where connate water saturation is reached) from the free water level is ____meters. (write answer with two decimal places)

Ans: (14.20 to 14.90)

35. The eigenvalues for the matrix  are :

(A)  2 and 5

(B)  −2 and −5

(C)  −2 and 5

(D)  none of the above

Ans: (C)

36. The temperature time profile for a system is given as follows:  where T is temperature in ℃, and t is time in hours. The initial conditions are T(0) = 500℃. The temperature of the system after 1 hour is _____℃. (write answer with two decimal places)

Ans: (101.00 to 104.00)

37. A porous medium is blended with three types of sediment fractions, fine pebble gravel with porosity (ϕpebble = 38%), sand (ϕsand = 32%) and fine sand(ϕfine_sand = 30%). The three sediments are mixed in such proportions that the sand fills the pore volume of fine pebbles completely, and the fine sand fills the pore volume of sand completely. The total porosity of such an irregular system is ______%. (write answer with two decimal places)

Ans: (3.50 to 3.80)

38. Match the following

(P) Sandstone                   (I) Clastic rocks

(Q) Limestone         (II) Noncalstic rocks

(R) Shale

(S) Gypsum

(A)  P-I, Q-I, R-II, S-II

(B)  P-II, Q-II, R-I, S-I

(C)  P-I, Q-II, R-I, S-II

(D)  P-II, Q-I, R-II, S-I

Ans: (C)

39. Oil of density 900 lg/m3 is flowing at 100 m3/day through a horizontal pipeline having a diameter reduction from 0.1 m to 0.05 m as shown in the following figure. The kinetic energy pressure drop (P1 – P2) caused by the diameter change is _____N/m2. (Assume frictional losses to e negligible, write answer with one decimal place)

Ans: (140.0 to 150.0)

40. Match the following EOR techniques and the principle behind them:

(P) Surfactant flooding

(Q) Polymer flooding

(R) Steam flooding

(S) Sea water flooding

(I) Lower the viscosity of the oil phase

(II) Increase the viscosity of the aqueous phase

(III) Lower the oil-water interfacial tension

(IV) Influence the wettability of the rock

(A)  P-I, Q-II, R-III, S-IV

(B)  P-II, Q-III, R-IV, S-I

(C)  P-III, Q-II, R-I, S-IV

(D)  P-III, Q-I, R-II, S-IV

Ans: (C)

41. The viscosity – shear rate curve for a fluid is shown in the following plot. Which one of the following options best describes the behavior of the fluid in the regions I, II, and III, respectively?

(A)  Newtonian, Shear thinning, Shear thickening

(B)  Shear thinning, Newtonian, Shear thickening

(C)  Shear thickening, Newtonian, Shear thinning

(D)  Shear thinning, Shear thickening, Newtonian

Ans: (B)

42. The value of constant a for which :  is a valid probability density function, is (given, a ≥ 0):

(A)   

(B)   

(C)   

(D)   

Ans: (B)

43. where ,  would simplify to:

(A)  1 – i

(B)  1

(C)  −i

(D)  1 + i

Ans: (D)

44. A well of radius 0.25 m is drilled. Mud invasion in the formation caused a skin radius of 2 m and reduced the permeability of the damaged zone to 30 mD. Well test revealed that the skin factor of the damaged zone is 2.3. The permeability of the unaffected formation will be ______mD. (write answer the one decimal place)

Ans: (60.0 to 65.0)

45. The average reservoir pressure and fracture gradient of petroleum formation at a depth of 4,000 m are 30,000 kN/m2 and 16(kN/m2)/m, respectively. The density of the formation is 2290 kg/m3. If the reservoir pressure declines to 20,000 kN/m2 after a few years of production, the fracture gradient of the formation is ____(kN/m2)/m. (write answer with one decimal place)

Ans: (13.5 to 15.5)

46. Match the following:

(P) Gamma ray log           (I) Water saturation

(Q) Resistivity log            (II) Acoustic waves

(R) Cement bond log        (III) Permeability

(S) NMR log                     (IV) Lithology

(A)  P-IV, Q-I, R-II, S-III

(B)  P-I, Q-II, R-III, S-IV

(C)  P-I, Q-III, R-II, S-IV

(D)  P-IV, Q-II, R-I, S-III

Ans: (A)

47. The sonic log travel time in a loosely consolidated formation is 260 μs/m. The matrix and fluid travel times are 130 μs/m and 618 μs/m, respectively. A correction factor of 1.0 may be used in a Wyllie time average equation for simplification. The calculated formation porosity using the Wyllie time average equation is _____%. (write answer with two decimal places)

Ans: (25.00 to 28.00)

48. An oil emulsion having 15% water cut by weight is being treated in a horizontal heater-treater unit at the rate of 6000 kg/hr. The inlet temperature of the emulsion is 30℃ and operating temperature of the heater-treater is 40℃. The specific heat capacity of water and oil are 1 kcal/kg℃ and 0.5 kcal/kg℃, respectively. Assuming 10% of the total heat input is lost to the surroundings, the total heat energy required to break the emulsion in the heater-treater unit is ______kcal/hr. (write answer with one decimal place)

Ans: (38200.0 to 38500.0)

49. An oil well has a flowing bottom hole pressure of 3000 psi and the reservoir has an average pressure of 3250 psi. A pressure build-up test reveals that the slope of the straight line portion of Horner’s plot is 38.5 psi/cycle and skin factor of the well is 3. The flow efficiency of this well is _____. (write answer with two decimal places)

Ans: (0.55 to 0.65)

50. A pressure charged, casing pressure operated gas lift valve is installed at a depth of 200 m and the bellow pressure of this valve is 50 × 105 N/m2 under operating conditions. The tubing pressure is 30 × 105 N/m2 at the valve depth. The area of the bellow and the port are 6 and 0.6 cm2, respectively. The opening pressure of the gas lift valve under operating conditions is ______× 105 N/m2. (Write answer with one decimal place)

Ans: (50.0 to 54.0)

51. Match the following:

(P) Coal bed methane

(Q) Tight gas

(R) Gas hydrate

(S) Associated gas

(I) Requires natural or artificial fractures

(II) Exists in solid phase

(III) Gas absorbed on surface in micro-pores

(IV) Dissolved in crude oil

(A)  P-I, Q-II, R-III, S-IV

(B)  P-IV, Q-III, R-I, S-II

(C)  P-III, Q-I, R-II, S-IV

(D)  P-IV, Q-I, R-II, S-III

Ans: (C)

52. Match the following in the context of treatment of oil spills:

(P) Boom

(Q) Absorbent

(R) Skimmer

(S) Biostimulation

(I) Use of chemical fertilizers to enhance the rate of oil degradation by microbes

(II) Mechanized equipment for removing floating oil from water surface

(III) Floating physical barrier to divert oil to a recovery area

(IV) Oleophilic material to attract oil, which can be removed subsequently

(A)  P-I, Q-IV, R-II, S-III

(B)  P-III, Q-IV, R-II, S-I

(C)  P-III, Q-II, R-IV, S-I

(D)  P-I, Q-III, R-IV, S-II

Ans: (B)

53. Match the following:

(P) Aquifer

(Q) Aquitard

(R) Aquicludes

(I) Slows down the movement of water and not good for water (or CO2) injection

(II) Evaporite rocks, such as halide or anhydrite, retarding upward movement of water/CO2

(III) Prefrentially stores CO2 but not water

(IV) Rocks with sufficient permeability to conduct water, into which water (or CO2) may be injected

(A)  P-I, Q-III, R-IV

(B)  P-IV, Q-I, R-III

(C)  P-IV, Q-I, R-II

(D)  P-IV, Q-II, R-III

Ans: (C)

54. Synthetic Aperture Radar (SAR), used for oil spill monitoring and detection, is based on the:

(A)  dampening effect oil has on capillary and short ocean surface waves, as seen in the radar backscatter signal.

(B)  radar backscatter signal only from navigating ships.

(C)  frequency change in the radar backscatter signal from flights over the sea.

(D)  physical sample collection from random locations on the high seas.

Ans: (A)

55. The adjacent figure shows the phase diagram of free methane gas and methane hydrate for a pure water and pure methane system. Match the zone marked (I), (II), (III) and (IV) with different states of phases listed below.

(P) Methane hydrate + water + gas

(Q) Methane gas + water

(R) Methane gas + ice

(S) Methane hydrae + ice + gas

(A)  I-R, II-S, III-P, IV-Q

(B)  I-R, II-Q, III-P, IV-S

(C)  I-R, II-S, III-Q, IV-P

(D)  I-R, II-P, III-S, IV-Q

Ans: (C)

56. The ninth and the tenth of this month are Monday and Tuesday _______.

(A)  figuratively

(B)  retrospectively

(C)  respectively

(D)  rightfully

Ans: (C)

57. It is _______ to read this year’s textbook ______ the last year’s

(A)  easier, than

(B)  most easy, than

(C)  easier, from

(D)  easiest, from

Ans: (A)

58. A rule states that in order to drink beer, one must be over 18 years old. In a bar, there are 4 people. P is 16 years old, Q is 25 years old, R is drinking milkshake and S is drinking a beer. What must be checked to ensure that the rule is being followed?

(A)  Only P’s drink

(B)  Only P’s drink and S’s age

(C)  Only S’s age

(D)  Only P’s drink, Q’s drink and S’s age

Ans: (B)

59. Fatima starts from point P, goes North for 3 km, and then East for 4 km to reach point Q. She then turns to face point P and goes 15 km in that direction. She then goes North for 6 km. How far is she from point P, and in which direction should she go to reach point P?

(A)  8 km, East

(B)  12 km, North

(C)  6 km, East

(D)  10 km, North

Ans: (A)

60. 500 students are taking one or more courses out of Chemistry, Physics and Mathematics. Registration records indicate course enrolment as follows: Chemistry (329), Physics (186), Mathematics (295), Chemistry and Physics (83), Chemistry and Mathematics (217), and Physics and Mathematics (63). How many students are taking all 3 subjects?

(A)  37

(B)  43

(C)  147

(D)  53

Ans: (D)

61. “If you are looking for a history of India, or for an account of the rise and fall of the British Raj, or for the reason of the cleaving of the subcontinent into two mutually antagonistic parts and the effects this mutilation will have in the respective sections, and ultimately on Asia, you will not find it in these pages; for though I have spent a lifetime in the country. I lived too near the seat of events, and was too intimately associated with the actors, to get the perspective needed for the impartial recording of these matters.”

Which of the following statements best reflects the author’s opinion?

(A)  An intimate association does not allow for the necessary perspective.

(B)  Matters are recorded with an impartial perspective.

(C)  An intimate association offers an impartial perspective.

(D)  Actors are typically associated with the impartial recording of matters.

Ans: (A)

62. Each of P, Q, R, S, W, X, Y and Z has been married at most once. X and Y are married and have two children P and Q. Z is the grandfather of the daughter S of P. Further, Z and W are married and are parents of R. Which one of the following must necessarily be FALSE?

(A)  X is the mother-in-law of R

(B)  P and R are not married to each other

(C)  P is a son of X and Y

(D)  Q cannot be married to R

Ans: (D)

63. 1200 men and 500 women can build a bridge in 2 weeks. 900 men and 250 women will take 3 weeks to build the same bridge. How many men will be needed to build the bridge in one week?

(A)  3000

(B)  3300

(C)  3600

(D)  3900

Ans: (C)

64. The number of 3-digit numbers such that the digit 1 is never to the immediate right of 2 is

(A)  781

(B)  791

(C)  881

(D)  891

Ans: (C)

65. A contour line joins locations having the same height above the mean sea level. The following is a contour plot of geographical region. Contour lines are shown at 25 m intervals in this plot.

Which of the following is the steepest path leaving from P?

(A)  P to Q

(B)  P to R

(C)  P to S

(D)  P to T

Ans: (B)

Gate 2017 Metallurgical Engineering Question Paper 5th Feb 2017 PDF Download

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Metallurgical Engineering 5th Feb 2017

Subject Name: Metallurgical Engineering

Duration : 180

Total Marks: 100

1. For the matrix,  AAT is

(A) 

(B) 

(C) 

(D) 

Ans: (D)

2. The mean of a numerical data-se is  and the standard deviation is S. If a number K is added to each term in the data-set then the mean and standard deviation become.

(A)   

(B)   

(C)   

(D)   

Ans: (B)

3. If f(x) = e|x| then at x = 0, the function f(x) is

(A)  continuous and differentiable.

(B)  continuous but not differentiable.

(C)  neither continuous nor differentiable.

(D)  not continuous but differentiable.

Ans: (B)

4. The pressure (P) versus volume (V) diagram given below represents reversible isothermal curves at temperatures, T1, T2 and T3

Considering one mole of ideal gas for all the three isothermal processes, which one of the following is TRUE?

(A)  T1 > T2 > T3

(B)  T2 > T3 > T1

(C)  T3 > T1> T2

(D)  T2 > T1 > T3

Ans: (B)

5. For the electrochemical reaction, Cu2+ + Zn = Zn2+ + Cu, the standard cell potential at 25℃ and 1 atm pressure is:

(Given : E° (Cu2+/Cu) = 0.337 V and E° (Zn2+/Zn) = −0.763 V)

(A)  −0.426 V

(B)  0.426 V

(C)  0.55 V

(D)  1.1 V

Ans: (D)

6. The rate of dissolution of Al particles in liquid steel is proportional to concentration difference (∆C). ∆C is defined by:

(Given: (i) Cb = bulk concentration of dissolved Al in liquid steel, (ii) C* = saturation concentration of Al in liquid steel at the given temperature, (iii) Cm = Density of Al(Atomic weight of Al.)

(A)  C* − Cb

(B)  Cb – Cm

(C)     C* − Cm

(D) 

Ans: (A)

7. Hydrogen dissolves in Pd by the reaction H2 = 2[H]. At 300℃ and  the solubility of hydrogen in Pd is 1.64 × 104 mm3 (STP) per kg of Pd. At 300℃ and  the solubility of hydrogen in Pd in mm3 (STP) per kg of Pd is _________(answer up to one decimal place)

Ans: (4900 to 4940)

8. The sieve analysis of ground quartz particles is given in the table below :

Sieve size                          Mass fraction of ground product

(mm)                                retained on each sieve

4.76                                  0.0

3.36                                  0.2

2.38                                  0.4

1.68                                  0.3

1.19                                  0.08

<1.19                                0.02

The cumulative mass fraction of particles of size less than 1.68 mm is ____ (answer up to two decimal places)

Ans: (0.09 to 0.11)

9. The sequence of precipitation to each stable equilibrium during ageing of Al-4.5 wt.% Cu alloy is:

(A)  GP zone → θ’ → θ” → θ

(B)  GP zone → θ” → θ’ → θ

(C)  GP zone → θ → θ” → θ’

(D)  GP zone → θ” → θ → θ’

Ans: (B)

10. Tungsten powder is pressed at 150 MPa to green density of 55%. After sintering, the compact attains 86.5% of its theoretical density. Assuming uniform shrinkage, the linear shrinkage (in%) is _______ (answer up to two decimal places)

Ans: (13.30 to 15.50)

11. For a FCC metal, radius of the largest sphere that can fit in the tetrahedral void (in nm) is ______ (answer up to three decimal places)

(Given : lattice parameter = 0.401 nm)

Ans: (0.030 to 0.034)

12. In an iron-carbon alloy containing 0.35 wt.% C, the mass fraction of pearlite just below the eutectoid temperature is _____(answer up to two decimal places)

(Given: eutectoid composition = 0.8 wt.% carbon; and carbon content in ferrite is 0.025 wt.%)

Ans: (0.36 to 0.44)

13. A cubic metal has a density of 19000 kg.m3, lattice parameter of 0.4 nm and atomic weight of 183. The effective number of atoms in an unit cell of this metal is ______

Ans: (4)

14. Primary mechanisms of accommodating plastic strain at low temperatures in crystalline metals are:

(A)  twinning and dislocation-slip

(B)  dislocation-climb and dislocation-slip

(C)  dislocation-slip and diffusion

(D)  viscous-flow and dislocation-slip

Ans: (A)

15. Spherical α phase particles are depicted in the hypothetical microstructure section shown  below. Using the superimposed grid on the microstructure, the estimated volume fraction of α phase is _______(answer up to three decimal places)

Ans: (0.130 to 0.160)

16. A brittle material (Young’s modulus = 60 GPa and surface energy = 0.5 J.m2) has a surface crack of length 2 μ The fracture strength (in MPa) of this material is ________(answer up to two decimal places)

Ans: (95.00 to 125.00)

17. Both creep resistance and tensile strength of a metal can be enhanced by

(A)  increase in the grain size

(B)  decrease in the grain size

(C)  addition of dispersoids

(D)  annealing

Ans: (C)

18. Stress required to operate a Frank-Read source of length L is approximately given by:

(A) 

(B)   

(C)   

(D)   

Ans: (A)

19. The second peak in the powder X-ray diffraction pattern of a FCC metal occurs at a Bragg angle θ (in degrees) = _______(answer up to two decimal places)

(Given: λCuKα = 0.154 nm; lattice parameter of the metal = 0.36 nm)

Ans: (24.00 to 26.00)

20. A rod is elastically deformed by a uniaxial stress resulting in a strain of 0.02. If the Poisson’s ratio is 0.3, the volumetric strain is _______(answer up to three decimal places)

Ans: (0.006 to 0.010)

21. Four alloys, C1, C2, C3, C4, shown in the phase diagram are poured at temperature T1 in a mold. During solidification, which one of these alloys is expected to have the highest fluidity?

(A)  C1

(B)  C2

(C)  C3

(D)  C4

Ans: (C)

22. A material, which shows power law behavior,  is being wire drawn. The maximum strain per pass in annealed condition (assume ideal work and efficiency η = 1) is ______ (answer up to two decimal places)

Ans: (1.20 to 1.40)

23. Schematic diagram shows rolling of a slab. P and Q are points on the surface of the workpiece near entrance and exit, respectively. With reference to the work piece, which one of the following statements is TRUE?

(A)  Frictional force is along rolling direction at both P and Q

(B)  Frictional force is opposite to rolling direction at both P and Q.

(C)  Frictional force is along rolling direction at P and opposite to rolling direction at Q.

(D)  Frictional force is opposite to rolling direction at P and along rolling direction at Q.

Ans: (C)

24. Which one of the following manufacturing techniques is used for making window glass?

(A)  Investment casting

(B)  Patenting

(C)  Spray forming

(D)  Float-bath method

Ans: (D)

25. Dye penetrant test is based on the principle of

(A)  polarized sound wave sin liquid.

(B)  magnetic domain.

(C)  absorption of X-rays

(D)  capillary action.

Ans: (D)

26. Assume that the probability of South Africa against India is 1/3. If South Africa plays a 3 match cricket series against India, the probability that South Africa wins only one match is (assume that no matches are tied or abandoned)______(answer up to three decimal places)

Ans: (0.400 to 0.500)

27. The function f(x) = x3 – 3x has a minimum at x = _______

Ans: (1)

28. The definite integral, is to be evaluated numerically. Divide the integration interval into exactly 2 subintervals of equal length. Applying the trapezoidal rule, the approximate value of the integral is _______(answer up to two decimal places)

Ans: (0.70 to 0.80)

29. For the second order linear ordinary differential equation,

the following function is a solution:

y = eλx

Which one of the following statements is NOT TRUE?

(A)  λ has two values: one complex and one real

(B)  λ2 + pλ + q = 0

(C)  λ has two real values

(D)  λ has two complex values

Ans: (A)

30. Using the bisection method, the root of the equation x3 + x – 1 = 0 after thre iterations is ______(answer up to two decimal places)

(Assume starting values of x = −1 and +1)

Ans: (0.74 to 0.76)

31. T1 and T2 are the melting points of pure metal A and pure stoichiometric oxide AO2, respectively, and T1 < T2. The stoichiometric metal oxidation reaction A(s) + O2(g) = AO2(s) is in equilibrium at 1 atm pressure at temperature less than T1. If the  temperature increases, which schematic represents the correct standard free energy change versus temperature plot?

(A) 

(B) 

(C) 

(D) 

Ans: (C)

32. A continuous cast steel slab, 1 m × 1 m ×1 m, at 1298 K cools in air. The initial rate of heat loss (in kW) from the top surface of slab by radiation and convection is ______(answer up to two decimal places)

Given: (i) Ambient temperature = 298 K, (ii) emissivity of steel = 0.8, (iii) convective heat transfer coefficient = 4.6 W. m2. K1, (iv) Stefan-Blotzmann constant (σ) = 5.7 × 108 W.m2.K−4

Ans: (130.00 to 135.00)

33. The Pourbaix plot of the reaction Al3+ + 2H2O = AlO2 + 4H+ in potential (E) versus pH diagram is :

(A) 

(B) 

(C) 

(D) 

Ans: (C)

34. During the end blow period in LD steelmaking, the de-carburization rate is expressed by the equation :  . Here , c and c* are the instantaneous and equilibrium concentration of carbon in steel respectively, in units of wt.% Given that c* = 0.04 wt.% and c(t = 0 min) = 0.4 wt.%, the concentration of carbon in steel (in wt.%) at t = 1 min is ______(answer up to three decimal places)

Ans: (0.170 to 0.175)

35. CaCO3(s) dissociate in a closed system according to the reaction :

CaCO3(s) = CaO(s) + CO2(g)

Assuming the reaction is in thermodynamic equilibrium, the degree(s) of freedom, F = ____

Ans: (1)

36. A ladle containing molten steel is being discharged. The relevant forces are listed in Column I Match them with their corresponding expressions in Column II.

Column I               Column II

[P] Pressure force   [1] μUL

[Q] Inertial force      [2] ρgL3

[R] Gravity force     [3] ρU2L2

[S] Viscous force    [4] PL2

μ = viscosity, U = characteristic velocity, L = characteristic length,

g = acceleration due to gravity, P = pressure.

(A)  P-4; Q-3; R-2; S-1

(B)  P-1; Q-3; R-2; S-4

(C)  P-2; Q-3; R-4; S-1

(D)  P-4; Q-3; R-1; S-2

Ans: (A)

37. In primary steelmaking, dissolved oxygen (O) reacts with carbon (C) to produce CO(g), at 1 atm pressure according to the reaction: C + C = CO(g). The equilibrium constant for this reaction is:  where T is in Kelvin. Assuming Henrian activity coefficient of both O and C to be unity, the dissolved oxygen content (in wt.%) of a plain carbon steel melt with 0.7 wt.% C at 1600℃ is ______ (answer up to four decimal places)

Ans: (0.0010 to 0.0050)

38. A stoichiometric mixture of CO and pure oxygen at 1 atm and 25℃ flows into a combustion reactor. The molar flow rate of CO entering the reactor is 1 kg-mol.h−1. The adiabatic flame temperature (in K) for the combustion of CO with stoichiometric oxygen is:_____

Given:  CP(CO2) = 44 kJ.(kg-mol K)−1.

Ans: (6650.00 to 6750.00)

39. A solution contains 103 M of Fe3+ at 25℃. The solubility product of Fe(OH)3 is 1039. Assuming activity equals concentration, the minimum pH at which Fe3+ will precipitate as Fe(OH)3 is ______(answer up to two decimal places)

Ans: (1.80 to 2.20)

40. A zinc elctrowinning cell is being operated at a current of 400 A, voltage of 3.5 V, and a cathodic current efficiency of 90%. The specific energy consumption (in kJ.kg1 zinc) is _____

(Atomic weight of Zn = 65)

Ans: (11535.00 to 11580.00)

41. Pure metals A and B form two real binary solid solutions α and β at temperature T and pressure P. The free energy versus composition plots for both the solutions are shown below.

The condition for chemical equilibrium is:

(A)  Mole fraction of A in α = mole fraction of A in β and mole fraction of B in α = mole fraction of B in β

(B)  Mole fraction of B in α = mole fraction of A in β and mole fraction of A in α = mole fraction of B in β

(C)  Activity of A in α = activity of A in β and activity of B in α = activity of B in β

(D)  Activity of A in α = activity of B in β and activity of B in α = activity of A in β

Ans: (C)

42. Pure orthorhombic sulfur transforms to stable monoclinic sulfur above 368.5 K. Applying Third law of thermodynamics, the value of entropy (in J.K1 of transformation at 368.5 K is ______(answer up to two decimal places)

Given:

i. Entropy change associated with heating orthorhombic sulfur from 0 K to 368.5 K is 36.86 J.K1.

ii. Entropy change associated with cooling monoclinic sulfur from 368.5 K to 0 K is −37.8 J.K1.

Ans: (0.92 to 0.96)

43. For homogeneous nucleation of solid in a liquid of pure metal, the critical edge length (in nm) of a cube shaped nucleus is _____(answer up to two decimal places)

(Given : surface energy γ = 0.177 J.m2; change in volume free energy ∆GV = −2.8 × 108 J.m3)

Ans: (2.50 to 2.60)

44. Assuming the solid phases to be pure, the slope of line BC in the predominance area diagram schematically shown below is _____(answer up to two decimal places)

Ans: (−0.51 to −0.49)

45. For each of the crystallographic system listed in Group-I, match the corresponding minimum symmetric in Group-II

Group-I                           Group-II

[P] Tetragonal                 [1] 1 twofold rotation

[Q] Cubic                        [2] 1 three-fold rotation

[R] Monoclinic                 [3] 4 three-fold rotation

[S] Rhombohedral           [4] 1 four-fold rotation

(A)  P-3; Q-4; R-2; S-3

(B)  P-4; Q-3; R-2; S-1

(C)  P-1; Q-2; R-4; S-3

(D)  P-4; Q-3; R-1; S-2

Ans: (D)

46. Arrange the magnetic moment of neighboring atoms in a one-dimensional lattice in Group-I to the corresponding magnetic material in Group-II

(A)  P-4; Q-1; R-3; S-2

(B)  P-3; Q-4; R-1; S-2

(C)  P-2; Q-4; R-1; S-3

(D)  P-1; Q-2; R-3; S-4

Ans: (B)

47. For an intrinsic semiconductor , all room temperature electrical conductivity is 106Ω1. If the electron and hole mobilities are 0.75 and 0.06 m2V1s1 respectively, the intrinsic carrier concentration (per m3) at room temperature is:

(A)  5.1 × 1012

(B)  7.7 × 1012

(C)  8.3 × 1012

(D)  1.1 × 104

Ans: (B)

48. A steel component is subjected to fatigue loading : σ (maximum) = 200 MPa, σ(minimum) = 0. The component has an initial crack length of 1 mm. Propagation of crack is governed by  

where, the crack length a is in meters, N is the number of cycles and ∆K is in Mpa.m1/2. The length of the crack (in m) after one million cycles will be _____(answer up to three decimal  places)

Ans: (0.009 to 0.015)

49. During heat treatment of a cold worked metal, recrystallization is 20% complete after 100 s. The transformation (in %) in 400 s is ______(answer up to two decimal places)

(Assume Avrami exponent, n = 2)

Ans: (96.00 to 98.00)

50. At low temperature, two parallel edge dislocations lying on parallel slip planes are shown in different configurations below.

Configuration [P]            [1] Dislocations repel

Configuration [Q]            [2] Dislocations attract

Configuration [R]             [3] Dislocations are in stable equilibrium

Configuration [S]             [4] Dislocation are in unstable equilibrium

(A)  P-3, Q-2, R-4, S-1

(B)  P-4, Q-1, R-3, S-2

(C)  P-1, Q-3, R-2, S-4

(D)  P-2, Q-4, R-1, S-3

Ans: (A)

51. A single crystal of an FCC metal is subjected to a sufficiently large tensile stress along the [110] direction to activate some of the slip systems. Which one of the following slip systems will be activated.

(A)   

(B)   

(C)   

(D)   

Ans: (B)

52. A perfectly elastic-plastic material has a yield stress of 450 MPa and fractures at a strain of 0.45. The ratio of resilience to toughness for this material is _____(answer up to three decimal places)

(Given is Young’s modulus E = 4.5 GPa)

Ans: (0.110 to 0.140)

53. Total time for solidification of a cubic casting of dimensions 5.0 cm ×0 cm × 5.0 cm is 1.6 min. A cylindrical riser with diameter to height ratio 0.5 is required so that the time for solidification of riser is 3.2 min. Applying Chvorinov’s rule, the height of the riser (in cm) is ______(answer up to two decimal places)

(Assume that exponent (n) in Chvorinov’s equation is 2)

Ans: (11.00 to 12.50)

54. A 250 mm thick slab of a nickel alloy is subjected to cold rolling using a roll of diameter 450 mm. If the angle of bite during rolling is 10°, the maximum possible reduction (in mm) during rolling is ______(answer up to two decimal places)

Ans: (6.60 to 7.40)

55. W-Ni compact is prepared by liquid phase sintering at 1500℃. If the size of tungsten grains is 40 μm and the interfacial tungsten- tungsten and tungsten-nickel energies are 0.52 and 0.30 J.m2 respectively, the predicted average neck size (in μm) of sintered tungsten grain is :

(Melting points of tungsten and nickel are 3410℃ and 1453℃, respectively)

(A)  10

(B)  15

(C)  20

(D)  25

Ans: (C)

56. The ninth and the tenth of this month are Monday and Tuesday _______.

(A)  figuratively

(B)  retrospectively

(C)  respectively

(D)  rightfully

Ans: (C)

57. It is _______ to read this year’s textbook ______ the last year’s

(A)  easier, than

(B)  most easy, than

(C)  easier, from

(D)  easiest, from

Ans: (A)

58. A rule states that in order to drink beer, one must be over 18 years old. In a bar, there are 4 people. P is 16 years old, Q is 25 years old, R is drinking milkshake and S is drinking a beer. What must be checked to ensure that the rule is being followed?

(A)  Only P’s drink

(B)  Only P’s drink and S’s age

(C)  Only S’s age

(D)  Only P’s drink, Q’s drink and S’s age

Ans: (B)

59. Fatima starts from point P, goes North for 3 km, and then East for 4 km to reach point Q. She then turns to face point P and goes 15 km in that direction. She then goes North for 6 km. How far is she from point P, and in which direction should she go to reach point P?

(A)  8 km, East

(B)  12 km, North

(C)  6 km, East

(D)  10 km, North

Ans: (A)

60. 500 students are taking one or more courses out of Chemistry, Physics and Mathematics. Registration records indicate course enrolment as follows: Chemistry (329), Physics (186), Mathematics (295), Chemistry and Physics (83), Chemistry and Mathematics (217), and Physics and Mathematics (63). How many students are taking all 3 subjects?

(A)  37

(B)  43

(C)  147

(D)  53

Ans: (D)

61. “If you are looking for a history of India, or for an account of the rise and fall of the British Raj, or for the reason of the cleaving of the subcontinent into two mutually antagonistic parts and the effects this mutilation will have in the respective sections, and ultimately on Asia, you will not find it in these pages; for though I have spent a lifetime in the country. I lived too near the seat of events, and was too intimately associated with the actors, to get the perspective needed for the impartial recording of these matters.”

Which of the following statements best reflects the author’s opinion?

(A)  An intimate association does not allow for the necessary perspective.

(B)  Matters are recorded with an impartial perspective.

(C)  An intimate association offers an impartial perspective.

(D)  Actors are typically associated with the impartial recording of matters.

Ans: (A)

62. Each of P, Q, R, S, W, X, Y and Z has been married at most once. X and Y are married and have two children P and Q. Z is the grandfather of the daughter S of P. Further, Z and W are married and are parents of R. Which one of the following must necessarily be FALSE?

(A)  X is the mother-in-law of R

(B)  P and R are not married to each other

(C)  P is a son of X and Y

(D)  Q cannot be married to R

Ans: (D)

63. 1200 men and 500 women can build a bridge in 2 weeks. 900 men and 250 women will take 3 weeks to build the same bridge. How many men will be needed to build the bridge in one week?

(A)  3000

(B)  3300

(C)  3600

(D)  3900

Ans: (C)

64. The number of 3-digit numbers such that the digit 1 is never to the immediate right of 2 is

(A)  781

(B)  791

(C)  881

(D)  891

Ans: (C)

65. A contour line joins locations having the same height above the mean sea level. The following is a contour plot of geographical region. Contour lines are shown at 25 m intervals in this plot.

Which of the following is the steepest path leaving from P?

(A)  P to Q

(B)  P to R

(C)  P to S

(D)  P to T

Ans: (B)

Gate 2017 Mining Engineering Question Paper 12th Feb 2017 PDF Download

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Mining Engineering 12th Feb 2017

Subject Name: Mining Engineering

Duration : 180

Total Marks: 100

1. Which one of the following plots represents the relationship xy = c, where c is a positive constant

(A)  I

(B)  II

(C)  III

(D)  IV

Ans: (C)

2. F(y) and f(y) are the probability distribution function and density function respectively of continuous variable Y in the interval (0, ∞). Which one of the following is TRUE?

(A)   

(B)   

(C)   

(D)   

Ans: (B)

3. The position vector of a moving particle is given by  The acceleration of the particle in the direction of the motion is

(A)   

(B)   

(C)   

(D)   

Ans: (D)

4. The value of 

(A) 

(B) 

(C)  1

(D)  0

Ans: (A)

5. Components of a 2-D stress tensor in Cartesian coordinate are σxx = 5.0 MPa, σyy = −10.0 MPa, and τxy = 2.0 MPa. The traction vector  in MPa acting on a plane having outward normal  is

(A)   

(B)   

(C)   

(D)   

Ans: (B)

6. If only two members form a truss joint and no external load or support reaction is applied to the joint, the members

(A)  have infinite force

(B)  have equal but opposite force

(C)  are zero-force members

(D)  have unequal forces

Ans: (C)

7. A multi-pint borehole extensometer is used to monitor

(A)  convergence  between the roof and the floor

(B)  strain between fixed points along a borehole

(C)  strain between the anchor point and the reference point on the surface

(D)  changing distances between fixed points along a borehole

Ans: (D)

8. The failure load of a point load test specimen having diameter 45 mm is 6000 N. The uncorrected point load index in MPa is ______

Ans: (2.9 to 3.0)

9. The beam shown in the figure is hinged at one end and rested on a roller at the other end. The free body diagram of the system is

(A) 

(B) 

(C) 

(D) 

Ans: (C)

10. Mineral A and B are produced from a deposit. Mineral A and B will be called coproducts if

(A)  economics of mining depends upon the extraction of either mineral A or B

(B)  economics of mining depends upon the extraction of both the minerals A and B

(C)  mineral B is produced economically and mineral A is an additional benefit

(D)  minerals A and B are produced in equal quantity

Ans: (B)

11. Semi-variogam modeling is used for reserve estimation of mineral deposit by

(A)  polygonal method

(B)  distance weighting method

(C)  geostatistical method

(D)  nearest neighbor method

Ans: (C)

12. Which one of the following does NOT belong to the direct operating cost of mine?

(A)  Administrative cost

(B)  Royalty

(C)  Fuel cost

(D)  Explosive cost

Ans: (A)

13. Lane’s algorithm is applied to determine

(A)  mill cut-off grade

(B)  mine production rate

(C)  operating cost

(D)  ultimate pit

Ans: (A)

14. In an underground coal mine a driller, wearing personal protective equipment, was going to workplace along the travelling roadway. A piece of rock fell down from the roof and hit the person on head causing serious injury. The cause of accident is

(A)  unsafe act of the driller

(B)  job stress

(C)  unsafe act and unsafe condition

(D)  unsafe condition

Ans: (D)

15. In a PERT network, the “time estimates” of an activity are the following: Optimistic time – 2 days, Most likely time – 4 days, and Pessimistic time – 12 days. The expected time and standard deviation of the activity in days are respectively

(A)  6.0 and 2.78

(B)  5.0 and 1.66

(C)  6.00 and 1.66

(D)  5.0 and 2.78

Ans: (B)

16. The magnetic bearing of a line is 65°30ʹ. If the declination is 4°30ʹW, the true bearing of the line in degrees is _____

Ans: (60 to 62)

17. A vertical photograph of a 40 m high hill is taken from 4.4 km height. If the focal length of the camera is 15 cm, the scale of the photograph is _____

(A)  1 in 29067

(B)  1 in 7267

(C)  1 in 29050

(D)  1 in 9688

Ans: (A)

18. The operating conditions of a rotary rock drill are: applied thrust: 6.75 kN, revolution : 180 rpm, and penetration rate : 0.15 m/min. The work done per revolution in N-m is _____

Ans: (5.15 to 6.0)

19. The Absolute amount of energy and density of a booster and ANFO are given below.

The Relative bulk strength of booster is _______

Ans: (113 to 116 OR 1.13 to 1.16)

20. A deeply seated ore body dips at 70° having an average width of 60 m, The ore body, hanging wall, and footwall are competent. The suitable stoping method for this ore body is

(A)  Post pillar cut and fill

(B)  Shrinkage stoping

(C)  Transverse sublevel caving

(D)  Transverse sublevel open stoping

Ans: (D)

21. The results of the crossing point temperature experiments for coal A and B are shown in the figure.

The correct interpretation of the plot is that

(A)  coal A is more prone to spontaneous heating than coal B

(B)  coal B is more prone to spontaneous heating than coal A

(C)  coal A is more prone to coal dust explosion than coal B

(D)  coal B is more prone to coal dust explosion than coal A

Ans: (B)

22. The “yellow boy” formed due to acid mine drainage mainly consists of

(A)  Ferrous hydroxide

(B)  Ferrous sulfate

(C)  Ferric hydroxide

(D)  Ferric sulfate

Ans: (C)

23. A double ended ranging drum shearer is employed in a longwall mine of face length 150 m. The mining height is 3.5 m and depth of the web cut is 0.76 m. The cycle time for unidirectional cutting is 40 min. Considering bulk density of the coal to be 1.4 t/m3, hourly production from the face in tonne is ______

Ans: (835 to 840)

24. The strength of a stranded wire rope is proportional to

(A)  the diameter of the rope

(B)  square of the diameter of the rope

(C)  square root of the diameter of the rope

(D)  inverse of the diameter of the rope

Ans: (B)

25. A 20 m thick and 30 m wide confined aquifer has two monitoring wells spaced 500 m apart along the direction of groundwater flow. The difference in water level between the wells is 2 m. The hydraulic conductivity is 50 m/day. The rate of flow in m3/day is

(A)  4

(B)  12

(C)  40

(D)  120

Ans: (D)

26. The y intercept of the tangent of curve y = x3 – x2 + x – 1 at x = 1 is ____

Ans: (2.0)

27. A rectangle has two of its corners on the x axis and the other two on the parabola y = 12 – x2. The largest area of the rectangle is ______

Ans: (32)

28. The area of cross-section (x) of four rock samples and the respective applied loads (y) at failure under uniaxial loading are given below :

If the best fit line  y = 4.88 x represents the above data, the coefficient of determination (R2) of the best fit line is _____

Ans: (0.96 to 0.98)

29. The following reading refer to a reciprocal leveling at staff stations A and B respectively:

The reduced level (RL) of staff station B in m is ______

Ans: (123 to 124.5)

30. The areas within the contour lines of a proposed site for an overburden dump are as follows:

The total volume of overburden in cubic meter that could be dumped within the 120 m and 195 m contour levels is _______

Ans: (174765 to 174765)

31. Total ore mined from a sub-level open stope of a copper deposit is measured to be 100000 tonne. The ore recovery and ore dilution during stoping are 90% and 20% respectively. The in situ Cu grade of the ore in the stope is 0.65%. The selling price of copper is Rs. 400/kg of metal. Ignoring any other metal losses in the downstream process of the ore, the revenue generated by selling the ore in Crores of rupees is ______

Ans: (20 to 23)

32. The block grade model of an ore deposit is shown in the figure below. The relationship between block value per tone (Bv) in rupees and the block grade in percentage (x) is given below:

Bv = −38500 + 700 × x,     for x ≥ 55%

     = −300                            otherwise

The each square block contains 1000 tonne of material and the overall pit slope angle is 45°, the total value of pit determined by the floating cone algorithm in Lakhs of rupees is _____

Ans: (25 to 27)

33. A mine is being developed by bord and pillar method with a gallery size of 4.8 m ×4 m. The mine operates in 3 shifts per day and 6 faces are blasted per shift. The average pull per round of blast is 1.2 m and the bulk density of coal is 1.4 t/m3. If the OMS is 2.5, then the average manpower deployed in the development section per shift is ______

Ans: (46 to 47)

34. Consider the following linear programming problem:

Maximize Z = 6X + 10Y

Subject to X ≤ 4

                  Y ≤ 6

                 3X + 2Y ≤ 18

                 X ≥ 0,  Y≥0

The maximum value of the objective function is ______

Ans: (71 to 73)

35. A mining company having three mines A, B and C supplies coal to three power plants P, Q and R located close to the mines. The daily production capacities of the three mines in tonnes are 700, 1200 and 1100 respectively. The daily requirements at the power plants in tones are 1000, 1000, and 1000 respectively. The transportation costs in rupees per tonne is given in the matrix below:

The total cost of coal transportation in rupees from the three mines to three power plants using the least-cost method is ______

Ans: (65000 to 67000)

36. The series-parallel configuration of a system, consisting of 6 independent components A, B, C, D, E and F with their individual reliability, is

Shown in the figure :

The reliability of the system is _____

Ans: (0.96 to 0.97)

37. 500 coal miners were randomly selected from an underground coal mine. It was found that 50 workers experienced an injury in the year 2014. The distribution of injury based on younger age group (age ≤ 40 years) and older age group (age > 40 years) generated the following cross classification table.

The odd of injury for the younger age group compared to the older age group is _______

Ans: (1.6 to 1.7)

38. A bord and pillar panel is being planned at a depth of 300 m. The dimension of square pillar is 35 m centre-to-centre. The average unit weight of the overburden rock is 25 kN/m3. If the strength of the pillar is 14.0 MPa,the gallery width in m for a safety factor of 1.3 is _____

Ans: (5.5 to 6.0)

39. A sandstone sample having 15% moisture content and volume of 75 cm3 weighs 180 g. If the grain density is 2.6 g/cm3, porosity of the sample in % is _______

Ans: (19.5 to 20)

40. Let σ1 and σ3 are major and minor principal stresses respectively. The equation σ1 = f(σ3) denotes the failure envelop of a rock as shown in the figure. Match the zones (P, Q, R and S) with the legend code.

(A)  P-1, Q-2, R-4, S-3

(B)  P-3, Q-1, R-4, S-2

(C)  P-3, Q-1, R-2, S-4

(D)  P-1, Q-4, R-3, S-2

Ans: (B)

41. A blasted muck of mass m is being lifted from a shaft of diameter d by an arrangement of two pulleys as shown in the figure. Ignoring friction in the pulleys, as the height h decreases, tension in the ropes

(A)  increases

(B)  decreases

(C)  remains constant

(D)  increases until h > d, then decreases

Ans: (A)

42. The longitudinal section of stope is given in the figure. Match the different labeled stope features (P, Q, R, S and T) with their corresponding nomenclatures.

(A)  P-2, Q-3, R-1, S-5, T-4

(B)  P-5, Q-1, R-2, S-3, T-4

(C)  P-3, Q-5, R-4, S-2, T-1

(D)  P-1, Q-5, R-3, S-4, T-2

Ans: (C)

43. To break a volume of 30000 cubic meter of overburden per month in an open cast mine, the number of blast hole drills required for the following data is _____

Spacing and burden of blast holes : 6.0 m × 4.0 m

Hours scheduled per shift            : 5

Number of shifts per day             : 2

Weeks per month                         : 4

Drilling days per week                 : 5

Drilling rate                                : 30.67 m/h

Ans: (1 to 3)

44. Two inclined coal seams with their accesses are shown in the figure. Match the labeled access (P, Q, R, S) with their corresponding names.

(A)  P-4, Q-3, R-1, S-2

(B)  P-4, Q-3, R-2, S-1

(C)  P-3, Q-4, S-2, R-1

(D)  P-3, Q-4, R-2, S-1

Ans: (D)

45. Ground reaction curve (GRC) of a tunnel roof under hydrostatic stress field is given b y pg = 10 – 0.75u, where pg is the required support pressure in MPa and u is radial displacement in mm. A uniform support is installed at the boundary of the tunnel providing support reaction (SR) as ps = 1.5 – 3.0, for u ≥ 2 mm. Considering GRC = SR, the support pressure in MPa is _____

Ans: (5.5 to 6.0)

46. If the rank of the following matrix is less than 3, the values of x are 

(A)  1, −1/2

(B)  1, 1/2    

(C)  2, −1/4

(D)  2, −3/4

Ans: (A)

47. The discharge rate of a water pump is 0.25 m3/s. The diameter of the discharge and suction nozzles are 300 and 350 respectively. The measured pressure at the discharge end located 0.25 m above the centerline of the impeller is 150 kN/m2 and the pressure at the suction gage located at the centre line of the impeller 20 kN/m2. Specific weight of water is 9810 N/m3 The total dynamic head for the above installation in m is ______

Ans: (13.5 to 14.0)

48. In a mine, 200 and 250 persons are deployed in t he Panels A and B (shown in figure) respectively in the largest shift. The panel produce 400 and 500 tonne/day respectively. The resistances of panels A and B are 0.3 ns2m−8 and 0.4 Ns2m−8 respectively and the combined resistance of shaft and trunk airways is 0.5 Ns2m−8. The operating static pressure of the fan in Pa to provide the minimum air quantities in the panels as per CMR 1957 is ____

Ans: (1185 to 1189)

49. In an auxiliary ventilation system, a fan is installed inside a 100 m long and 600 mm diameter duct to ventilate a blind heading face. The frictional coefficient of the duct is 0.0066 Ns2m4 and the static pressure characteristic of the fan is represented by :

Ps = 5Q2 – 250Q + 1000

where, Ps is in Pa and Q is in m3/s. The quantity of air delivered by the fan in m3/s is _______

Ans: (2.5 to 2.8)

50. A stream flowing at 15 m3/s has a tributary feeding into it with a flow rate of 7 m3/s. The concentrations of chloride at the upstream of the junction and that of the tributary are 30 mg/L, and 50 mg/L respectively. Treating chloride as conservative substance and assuming complete mixing of two stream, the concentration of chloride in mg/L at the downstream is ______

Ans: (36 to 37)

51. A sample of mine water has 100 mg/L of Ca2+ and 10 mg/L of Mg2+. The equivalent weights of Ca2+ and Mg2+ are 20 mg/meq and 12.2 mg/meq respectively. The hardness of mine water in unit of mg/L as CaCO3 is _______

Ans: (290 to 292)

52. A 1.1 m wide belt conveyor carries materials of bulk density 1.35 t/m3 at a speed of 1.75 m/s. The average cross-sectional area of material is equal to w2/11, where w is the width of the belt in m. The carrying capacity of the conveyor in t/h is ______

Ans: (935 to 936)

53. In a book of 600 pages, there are 60 typographical errors. Assuming Poisson distribution for the number of errors per page, the probability of no errors ini randomly chosen 4 pages is ______

Ans: (0.66 to 0.68)

54. Match the special methods of shaft sinking with rock mass conditions and scope of application.

(A)  A-S-3, B-R-2, C-Q-1, D-P-4

(B)  A-P-2, B-Q-1, C-S-4, D-R-3

(C)  A-R-3, B-P-1, C-S-2, D-Q-4

(D)  A-S-4, B-Q-1, C-P-2, D-R-3

Ans: (D)

55. A wheel of radius 0.5 m rotates under a moment of 2000 N-m as shown in the figure. A block brake is used to stop the wheel. If the coefficient of static friction between the wheel and the block brake is 0.3, the smallest force of P in N required to stop the wheel is _______

Ans: (5975 to 5990)

56. The bacteria in milk are destroyed when it ____ heated to 80 degree Celsius.

(A)  would be

(B)  will be

(C)  is

(D)  was

Ans: (C)

57. _______ with someone else’s email account is now a very serious offence.

(A)  Involving

(B)  Assisting

(C)  Tampering

(D)  Incubating

Ans: (C)

58. Consider the following sentences:

All benches are beds. No bed is a bulb. Some bulbs are lamps.

Which of the following can be inferred?

i. Some beds are lamps.

ii. Some lamps are beds.

(A)  Only i

(B)  Only ii

(C)  Both i and ii

(D)  Neither i nor ii

Ans: (D)

59. If the radius of a right circular cone is increased by 50%, its volume increases by

(A)  75%

(B)  100%

(C)  125%

(D)  237.5%

Ans: (C)

60. The following sequence of numbers is arranged in increasing order: 1, x, x, x, y, y, 9, 16, 18. Given that the mean and median are equal, and are also equal to twice the mode, the value of y is

(A)  5

(B)  6

(C)  7

(D)  8

Ans: (D)

61. The old concert hall was demolished because of fears that the foundation would be affected by the construction of the new metro line in the area. Modern technology for underground metro construction tried to mitigate the impact of pressurized air pockets created by the excavation of large amounts of soil. But even with these safeguards, it was feared that the soil below the concert hall would not be stable.

From this, one can infer that

(A)  the foundations of old buildings create pressurized air pockets underground, which are difficult to handle during metro construction.

(B)  metro construction has to be done carefully considering its impact on the foundations of existing buildings.

(C)  old buildings in an area form an impossible hurdle to metro construction in that area.

(D)  pressurized air can be used to excavate large amounts of soil from underground areas.

Ans: (B)

62. Students applying for hostel rooms are allotted rooms in order of seniority. Students already staying in a room will move if they get a room in their preferred list. .Preferences of lower ranked applicants are ignored during allocation.

Given that data below, which room will Ajit stay in?

(A)  P

(B)  Q

(C)  R

(D)  S

Ans: (B)

63. The last digit (2171)7 + (2172)9 + (2173)11 + (2174)13 is

(A)  2

(B)  4

(C)  6

(D)  8

Ans: (B)

64. Two machines M1 and M2 are able to execute any of four jobs P, Q, R and S. The machines can perform one job on one object at a time. Jobs P, Q, R and S take 30 minutes, 20 minutes, 60 minutes and 15 minutes each respectively. There are 10 objects each requiring exactly 1 job. Job P is to be performed on 2 objects, Job Q on 3 objects, Job R on 1 object and Job S on 4 objects. What is the minimum time needed to complete all the jobs?

(A)  2 hours

(B)  2.5 hours

(C)  3 hours

(D)  3.5 hours

Ans: (A)

65. The bar graph below shows the output of five carpenters over one month, each of whom made different items of furniture: chairs, tables, and beds.

Consider the following statements.

i. The number of beds made by carpenter C2 is exactly the same as the number of tables made by carpenter C3.

ii. The total number of chairs made by all carpenters is less than the total number of tables.

Which one of the following is true?

(A)  Only i

(B)  Only ii

(C)  Both i and ii

(D)  Neither i nor ii

Ans: (C)

Gate 2017 Mechanical Engineering Question Paper 4th Feb 2017 Session 2 PDF Download

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Mechanical Engineering 4th Feb 2017 Session 2

Subject Name: Mechanical Engineering

Duration : 180

Total Marks: 100

1. A mass m of a perfect gas at pressure p1 and volume V1 undergoes an isothermal process. The final pressure is p2 and volume is V2. The work done on the system is considered positive. If R is the gas constant and T is the temperature, then the work done in the process is

(A)   

(B)   

(C)   

(D)   

Ans: (B)

2. Which one of the following statements is TRUE for the ultrasonic machining (USM) process?

(A) In USM, the tool vibrates at subsonic frequency.

(B) USM does not employ magnetostrictive transducer.

(C) USM is an excellent process for machining ductile materials.

(D) USM often uses a slurry comprising abrasive-particles and water.

Ans: (D)

3. The standard deviation of linear dimensions P and Q are 3μm, respectively. When assembled, the standard deviation (in μm) of the resulting linear dimension (P+Q) is ________

Ans: (5)

4. The emissive power of a blackbody is P. If its absolute temperature is doubled, the emissive power becomes.

(A)  2P

(B)  4P

(C)  8P

(D)  16P

Ans: (D)

5. The state of stress at a point is σx = σy = σz = τxz = τzx = τyz = τzy = 0 and τxy = τyx = 50MPa. The maximum normal stress (in MPa) at that point is _________

Ans: (49.9 to 50.1)

6. The determinant of a 2×2 matrix is 50. If one eigenvalue of the matrix is 10, the other eigenvalue is ___________

Ans: (5)

7. Which one of the following statement is TRUE?

(A) Both Pelton and Francis turbines are impulse turbines.

(B) Francis turbine is a reaction turbine but Kaplan turbine is an impulse turbine.

(C) Francis turbine is an axial – flow reaction turbine.

(D) Kaplan turbine is an axial – flow reaction turbine.

Ans: (D)

8. Two coins are tossed simultaneously. The probability (upto two decimal points accuracy) of getting at least one head is ____________

Ans: (0.75)

9. A cantilever beam of length L and flexural modulus EI is subjected to a point load P at the free end. The elastic strain energy stored in the beam due to bending (neglecting transverse shear)

(A)   

(B)   

(C)   

(D)   

Ans: (A)

10. It is desired to make a product having T-shaped cross-section from a rectangular aluminium block. Which one of the following processes is expected to provide the highest strength of the product?

(A)  Welding

(B)  Casting

(C)  Metal Forming

(D)  Machining

Ans: (C)

11. The heat loss from a fin is 6W. The effectiveness and efficiency of the fin are 3 and 0.75, respectively. The heat loss (in W) from the fin, keeping the entire fin surface at base temperature, is __________.

Ans: (7.9 to 8.1)

12. For a single server with Poisson arrival and exponential service time, the arrival rate is 12 per hour. Which one of the following service rates will provide a steady state finite queue length?

(A)  6 per hour

(B)  10 per hour

(C)  12 per hour

(D)  24 per hour

Ans: (D)

13. For the stability of a floating body the

(A) centre of buoyancy must coincide with the centre of gravity

(B) centre of buoyancy must be above the centre of gravity

(C) centre of gravity must be above the centre of buoyancy

(D) metacentre must be above the centre of gravity

Ans: (D)

14. The divergence of the vector −yi + xj __________

Ans: (0)

15. For a loaded cantilever beam of uniform cross-section, the bending moment (in N.mm) along the length is M(x) = 5x2+10x, where x is the distance (in mm) measured from the free end of the beam. The magnitude of shear force (in N) in the cross-section at x =10 mm is ________.

Ans: (110)

16. A sample of 15 data is a follows: 17, 18, 17, 17, 13, 18, 5, 5, 6, 7, 8, 9, 20, 17, 3. The mode of the data is

(A)  4

(B)  13

(C)  17

(D)  20

Ans: (C)

17. If a mass of moist air contained in a closed metallic vessel is heated, then its

(A) relative humidity decreases

(B) relative humidity increases

(C) specific humidity increases

(D) specific humidity decreases

Ans: (A)

18. In a slider-crank mechanism, the lengths of the crank and the connecting rod are 100mm and 160mm, respectively. The crank is rotating with an angular velocity of 10 radian/s counterclockwise. The magnitude of linear velocity (in m/s) of the piston at the instant corresponding to the configuration shown in the figure is _____________

Ans: (0.99 to 1.01)

19. A machine component made of a ductile material is subjected to a variable loading with σmin = −50 MPa and σmax = 50 MPa. If the corrected endurance limit and the yield strength for the material are σe = 100 MPa and σy = 300 MPa, the factor of safety is ______

Ans: (1.99 to 2.01)

20. The crystal structure of aluminium is

(A) body-centred cubic

(B) face-centred cubic

(C) close-packed hexagonal

(D) body-centred tetragonal

Ans: (B)

21. A steel bar is held by two fixed supports as shown in the figure and is subjected to an increases of temperature ∆T =100℃. and 200GPa, respectively, the magnitude of thermal stress (in MPa) induced in the bar is

Ans: (218 to 222)

22. The Laplace transform of  tet is

(A)   

(B)   

(C)   

(D)   

Ans: (B)

23. Consider a laminar flow at zero incidence over a flat plate. The shear stress at the wall is denoted by τw. The axial positions x1 and x2 on the plate are measured from the leading edge in the direction of flow. If x2 > x1, then

(A)   

(B)   

(C)   

(D)   

Ans: (C)

24. A mass m is attached to two identical springs having spring constant k as shown in the figure. The natural frequency ω of this single degree of freedom system is

(A)   

(B)   

(C)   

(D)   

Ans: (A)

25. Given the atomic weight of Fe is 56 and that of C is 12, the weight percentage of carbon in cementite (Fe3C) is _________.

Ans: (6.3 to 7.0)

26. In an orthogonal machining with a tool of 9° orthogonal rake angle, the uncut chip thickness is 0.2mm. The chip thickness fluctuates between 0.25 mm and 0.4 mm. The ratio of the maximum shear angle to the minimum shear angle during machining is ___________

Ans: (1.45 to 1.53)

27. A cylindrical pin of  diameter is electroplated. Plating thickness is 2.0±0.005 mm. Neglecting the gauge tolerance, the diameter (in mm, up to 3 decimal points accuracy) of the GO ring gauge to inspect the plated pin is _________.

Ans: (29.030 to 29.030)

28. A helical compression spring made of wire of circular cross-section is subjected to a compressive load. The maximum shear stress induced in the cross-section of the wire is 24 MPa. For the same compressive load, if both the wire diameter and the mean coil diameter are doubled, the maximum shear stress (in MPa) induced in the cross-section of the wire is _____.

Ans: (6)

29. In a counter-flow heat exchanger, water is heated at the rate of 1.5kg/s from 40°C to 80°C by an oil entering at 120°C and leaving at 60°C. The specific heats of water and oil are 4.2kJ/kg.K and 2kJ/kg.K respectively. The overall heat transfer coefficient is 400 W/m2.K. The required heat transfer surface area (in m2) is

(A)  0.104

(B)  0.022

(C)  10.4

(D)  21.84

Ans: (D)

30. The rod PQ of length L = √2 m, and uniformly distributed mass of M = 10 kg, is released from rest at the position shown in the figure. The ends slide along the frictionless faces OP and OQ. Assume acceleration due to gravity, g = 10 m/s2. The mass moment of inertia of the rod about its centre of mass and an axis perpendicular to the plane of the figure is (ML2/12). At this instant, the magnitude of angular acceleration (in radian/s2) of the rod is ____________

Ans: (7.25 to 7.75)

31. A steel plate, connected to a fixed channel using three identical bolts A, B and C, carries a load of 6kN as shown in the figure. Considering the effect of direct load and moment, the magnitude of resultant shear force (in kN) on bolt C is.

(A)  13

(B)  15

(C)  17

(D)  30

Ans: (C)

32. The volume and temperature of air (assumed to be an ideal gas) in a closed vessel is 2.87 m3 and 300K, respectively. The gauge pressure indicated by a manometer fitted to the wall of the vessel is 0.5bar. If the gas constant of air is R = 287 J/kg. K and the atmospheric pressure is 1 bar, the mass of air (in kg) in the vessel is

(A)  1.67

(B)  3.33

(C)  5.00

(D)  6.66

Ans: (C)

33. For the laminar flow of water over a sphere, the drag coefficient CF is defined as CF = F/(ρU2D2), where F is the drag force, ρ is the fluid density, U is the fluid velocity and D is the diameter of the sphere. The density of water is 1000 kg/m3. When the diameter of the sphere is 100mm and the fluid velocity is 2m/s, the drag coefficient is 0.5. If water now flows over another sphere of diameter 200mm under dynamically similar conditions, the drag force (in N) on this sphere is _____________

Ans: (19.9 to 20.1)

34. A rod of length 20mm is stretched to make a rod of length 40 mm. Subsequently, it is compressed to make a rod of final length 10mm. Consider the longitudinal tensile strain as positive and compressive strain as negative. The total true longitudinal strain in the rod is

(A)  −0.5

(B)  −0.69

(C)  −0.75

(D)  −1.0

Ans: (B)

35. A gear train shown in the figure consists of gears P, Q, R and S. Gear Q and gear R are mounted on the same shaft. All the gears are mounted on parallel shafts and the number of teeth of P, Q, R and S are 24, 45, 30 and 80, respectively. Gear P is rotating at 400 rpm. The speed (in rpm) of the gear S is _________.

Ans: (120)

36. In the Rankine cycle for a steam power plant the turbine entry and exit enthalpies are 2803 kJ/kg and 1800 kJ/kg, respectively. The enthalpies of water at pump entry and exit are 121 kJ/kg and 124 kJ/kg, respectively. The specific steam consumption (in kg/k W.h) of the cycle is ______

Ans: (3.5 to 3.7)

37. A calorically perfect gas (specific heat at constant pressure 1000 J/kg.K) enters and leaves a gas turbine with the same velocity. The temperatures of the gas at turbine entry and exit are 1100 K and 400 K. respectively. The power produced is 4.6 MW and heat escapes at the rate of 300 kJ/s through the turbine casing. The mass flow rate of the gas (in kg/s) through the turbine is.

(A)  6.14

(B)  7.00

(C)  7.50

(D)  8.00

Ans: (B)

38. Three masses are connected to a rotating shaft supported on bearings A and B as shown in the figure. The system is in a space where the gravitational effect is absent. Neglect the mass of shaft and rods connecting the masses. For m1 = 10kg, m2 = 5kg and m3 = 2.5 kg and for a shaft angular speed of 1000 radian/s, the magnitude of the bearing reaction (in N) at location B is _________.

Ans: (0)

39. A strip of 120 mm width and 8mm thickness is rolled between two 300 mm-diameter rolls to get a strip of 120 mm width and 7.2 mm thickness. The speed of the strip at the exit is 30 m/min. There is no front or back tension. Assuming uniform roll pressure of 200 MPa in the roll bite and 100% mechanical efficiency, the minimum total power (in kW) required to drive the two rolls is _________.

Ans: (9.4 to 9.8)

40. A product made in two factories p and Q, is transported to two destinations, R and S. The per unit costs of transportation (in Rupees) from factories to destinations are as per the following matrix:

Factory P produces 7 units and factory Q produces 9 units of the product. Each destination requires 8 units. If the north-west corner method provides the total transportation cost as X (in Rupees) and the optimized (the minimum) total transportation cost Y (in Rupees), then (X-Y), in Rupees, is

(A)  0

(B)  15

(C)  35

(D)  105

Ans: (A)

41. One kg of an ideal gas (gas constant R = 287 J/kg.K) undergoes an irreversible process from state-1 (1 bar, 300 K) to state -2 (2 bar, 300 K). The change in specific entropy (s2 – s1) of the gas (in J/kg. K) in the process is ___________

Ans: (−201 to −197)

42. A 60 mm-diameter water jet strikes a plate containing a hole of 40mm diameter as shown in the figure. Part of the jet passes through the hole horizontally, and the remaining is deflected vertically. The density of water is 1000 kg/m3. If velocities are as indicated in the figure, the magnitude of horizontal force (in N) required to hold the plate is _________

Ans: (627 to 629)

43. The arrangement shown in the figure measures the velocity V of a gas of density 1 kg/m3 flowing through a pipe. The acceleration due to gravity is 9.81 m/s2. If the manometric fluid is water (density 1000 kg/m3) and the velocity V is 20 m/s, the differential head h (in mm) between the two arms of the manometer is ____________

Ans: (19 to 21)

44. A metal ball of diameter 60mm is initially at 220 °C. The ball is suddenly cooled by an air jet of 20°C. The heat transfer coefficient is 200 W/m2.K and 9000kg/m3, respectively. The ball temperature (in °C) after 90 seconds will be approximately.

(A)  141

(B)  163

(C)  189

(D)  210

Ans: (A)

45. A single – plate clutch has a friction disc with inner and outer radii of 20mm and 40 mm, respectively. The friction lining in the disc is made in such a way that the coefficient of friction μ varies radially as μ = 0.01r, where r is in mm. The clutch needs to transmit a friction torque of 18.85kN.mm. As per uniform pressure theory, the pressure (in MPa) on the disc is _________

Ans: (0.49 to 0.51)

46. The surface integral  over the surface S of the sphere x2 + y2 + z2 = 9, where F=(x+y) i+ (x+z) j+(y+z) k and n is the unit outward surface normal, yields ______.

Ans: (225 to 227)

47. Block 2 slides outward on link 1 at a uniform velocity of 6 m/s as shown in the figure. Link 1 is rotating at a constant angular velocity of 20 radian/s counterclockwise. The magnitude of the total acceleration (in m/s2) of point P of the block with respect to fixed point O is ________

Ans: (243 to 244)

48. During the turning of a 20mm-diameter steel bar at a spindle speed of 400 rpm, a tool life of 20 minute is obtained. When the same bar is turned at 200 rpm, the tool life becomes 60 minute. Assume that Taylor‟s tool life equation is valid. When the bar is turned at 300 rpm, the tool life (in minute) is approximately.

(A)  25

(B)  32

(C)  40

(D)  50

Ans: (B)

49. Consider the matrix  whose eigenvectors corresponding to eigenvalues λ1 and λ2 are  respectively. The value of  is ______

Ans: (0)

50. The radius of gyration of a compound pendulum about the point of suspension is 100mm. The distance between the point of suspension and the centre of mass is 250mm. Considering the acceleration due to gravity as 9.81 m/s2, the natural frequency (in radian/s) of the compound pendulum is _________.

Ans: (15 to 16)

51. Consider the differential equation 3y”(x) + 27y(x) = 0 with initial conditions y(0) = 0 and y'(0) = 200. The value of y at x = 1 is ______

Ans: (93 to 95)

52. If f(z) = (x2 + ay2) + ibxy is a complex analytic function of z = x + iy, where , then

(A)  a = −1, b = −1

(B)  a = −1, b = 2

(C)  a = 1, b = 2

(D)  a = 2, b = 2

Ans: (B)

53. A project starts with activity A and ends with activity F. The precedence relation and durations of the activities are as per the following table:

The minimum project completion time (in days) is ______

Ans: (30)

54. Maximize Z = 5x1 + 3x2

Subject to

x1 + 2x12 ≤ 10,

x1 – x2 ≤ 8,

x1, x12 ≥ 0.

In the starting Simplex tableau, x1 and x2 are non-basic variables and the value of Z is zero. The value of Z in the next Simplex tableau is _________.

Ans: (40)

55. The principal stresses at a point in a critical section of a machine component are σ1 = 60MPa, σ2 = 5MPa and σ3 = −40 Mpa. For the material of the component, the tensile yield strength is σy = 200 MPa. According to the maximum shear stress theory, the factor of safety is

(A)  1.67

(B)  2.00

(C)  3.60

(D)  4.00

Ans: (B)

56. If you choose plan P, you will have to _______ plan Q, as these two are mutually _________.

(A) forgo, exclusive

(B) forget, inclusive

(C) accept, exhaustive

(D) adopt, intrusive

Ans: (A)

57. P looks at Q while Q looks at R. P is married, R is not. The number of people in which a married person is looking at an unmarried person is

(A)  0

(B)  1

(C)  2

(D)  Cannot be determined

Ans: (B)

58. If a and b are integers and a – b is even, which of the following must always be even?

(A)  ab

(B)  a2 + b2 + 1

(C)  a2 + b + 1

(D)  ab – b

Ans: (D)

59. A couple has 2 children. The probability that both children are boys if the older one is a boy is

(A)  1/4

(B)  1/3

(C)  1/2

(D)  1

Ans: (C)

60. The ways in which this game can be played __________ potentially infinite.

(A)  is

(B)  is being

(C)  are

(D)  are being

Ans: (C)

61. “If you are looking for a history of India, or for an account of the rise and fall of the British Raj, or for the reason of the cleaving of the subcontinent into two mutually antagonistic parts and the effects this mutilation will have in the respective sections, and ultimately on Asia, you will not find it in these pages; for though I have spent a lifetime in the country, I lived too near the seat of events, and was too intimately associated with the actors, to get the perspective needed for the impartial recording of these matters.”

Which of the following closest in meaning to “cleaving”?

(A)  Deteriorating

(B)  Arguing

(C)  Departing

(D)  Splitting

Ans: (D)

62. There 4 women P, Q, R, S, and 5 men V, W, X, Y, Z in a group. We are required to form pairs each consisting of one woman and one man. P is not to be paired with Z, and Y must necessarily be paired with someone. In how may ways can 4 such pairs be formed?

(A)  74

(B)  76

(C)  78

(D)  80

Ans: (C)

63. In the graph below, the concentration of a particular pollutant in a lake is plotted over (alternate) days of a month in winter (average temperature 10°C) and a month in summer (average temperature 30°C).

Consider the following statements based on the data shown above:

(i) Over the given months, the difference between the maximum and the minimum pollutant concentrations is the same in both winter and summer.

(ii) There are at last four days in the summer month such that the pollutant concentrations on those days are within 1 ppm of the pollutant concentrations on the corresponding days in the winter month.

Which one of the following options is correct?

(A)  Only i

(B)  Only ii

(C)  Both i and ii

(D)  Neither i nor ii

Ans: (B)

64. All people in a certain island are either „Knights‟ or „Knaves‟ and each person knows every other person’s identity. Knights NEVER lie, and knaves ALWAYS lie.

P says “Both of us are knights”. Q says “None of us are knaves”.

Which one of the following can be logically inferred from the above?

(A) Both P and Q are knights

(B) P is a knight; Q is a knave

(C) Both P and Q are knaves

(D) The identities of P, Q cannot be determined

Ans: (D)

65. X bullocks and Y tractors take 8 days to plough a field. If we halve the number of bullocks and double the number of tractors, it takes 5days to plough the same field. How many days will it take X bullocks alone to plough the field?

(A)  30

(B)  35

(C)  40

(D)  45

Ans: (A)

Gate 2017 Mechanical Engineering Question Paper 4th Feb 2017 Session 1 PDF Download

Graduate Aptitude Test in Engineering 2017

Question Paper Name: Mechanical Engineering 4th Feb 2017 Session 1

Subject Name: Mechanical Engineering

Duration : 180

Total Marks: 100

1. A motor driving a solid circular steel shaft transmits 40kW of power at 500 rpm. If the diameter of the shaft is 40 mm, the maximum shear stress in the shaft is ________MPa.

Ans: (60.79)

2. Consider the following partial differential equation for u(x,y) with the constat c > 1 :

Solution of this equation is

(A)  u(x, y) = f(x + cy)

(B)  u(x, y) = f(x – cy)

(C)  u(x, y) = f(cx + y)

(D)  u(x, y) = f(cx – y)

Ans: (B)

3. The following figure shows the velocity- time plot for a particle traveling along a straight line. The distance covered by the particle from t = 0 to t= 5 s is __________m.

Ans: (11)

4. The damping ratio for a viscously damped spring mass system, governed by the relationship  is given by

(A)   

(B)   

(C)   

(D)   

Ans: (B)

5. The differential equation  for y(x) with the two boundary conditions  has

(A)  no solution

(B)  exactly two solutions

(C)  exactly one solution

(D)  infinitely many solutions

Ans: (A)

6. Metric thread of 0.8 mm pitch is to be cut on a lathe. Pitch of the lead screw is 1.5 mm. If the spindle rotates at 1500 rpm, the speed of rotation of the lead screw (rpm) will be _________

Ans: (800)

7. The molar specific heat at constant volume of an ideal gas is equal to 2.5 times the universal gas constant (8.314 J/mol.K). When the temperature increases by 100K, the change in molar specific enthalpy is _______________ J/mol.

Ans: (2909.9)

8. A particle of unit mass is moving on a plane. Its trajectory, in polar coordinates, is given by r(t) = t2, θ(t) = t, where t is time. The kinetic energy of the particle at time t = 2 is

(A)  4

(B)  12

(C)  16

(D)  24

Ans: (C)

9. The Poisson’s ratio for a perfectly incompressible linear elastic material is

(A)  1

(B)  0.5

(C)  0

(D)  infinity

Ans: (B)

10. A heat pump absorbs 10 kW of heat from outside environment at 250 K while absorbing 15 kW of work. It delivers the heat to a room that must be kept warm at 300K. The Coefficient of Performance (COP) of the heat pump is ___________.

Ans: (1.66)

11. Which one of the following is NOT a rotating machine?

(A) Centrifugal pump

(B) Gear pump

(C) Jet pump

(D) Vane pump

Ans: (C)

12. Consider the schematic of a riveted lap joint subjected to tensile load F, as shown below. Let d be the diameter of the rivets, and Sf be the maximum permissible tensile stress in the plates. What should be the minimum value for the thickness of the plates to guard against tensile failure of the plates? Assume the plates to be identical.

(A)   

(B)   

(C)   

(D)   

Ans: (A)

13. Water (density =1000 kg/m3) at ambient temperature flows through a horizontal pipe of uniform cross section at the rate of 1 kg/s. If the pressure drop across the pipe is 100 kPa, the minimum power required to pump the water across the pipe, in watts, is _______

Ans: (100)

14. For steady flow of a viscous incompressible fluid through a circular pipe of constant diameter, the average velocity in the fully developed region is constant. Which one of the following statements about the average velocity in the developing region is TRUE?

(A) It increases until the flow is fully developed.

(B) It is constant and is equal to the average velocity in the fully developed region.

(C) It decreases until the flow is fully developed.

(D) It is constant but always lower than the average velocity in the fully developed region.

Ans: (B)

15. Cylindrical pins of diameter 15±020 mm are being produced on a machine. Statistical quality control tests show a mean of 14.995 mm and standard deviation of 0.004mm. The process capability index Cp is

(A)  0.833

(B)  1.667

(C)  3.333

(D)  3.750

Ans: (B)

16. The product of Eigen values of the matrix P is 

(A)  −6

(B)  2

(C)  6

(D)  −2

Ans: (B)

17. Match the processes with their characteristics.

(A) P – 2, Q – 3, R – 1, S – 4

(B) P – 3, Q – 2, R – 1, S – 4

(C) P – 3, Q – 2, R – 4, S – 1

(D) P – 2, Q – 4, R – 3, S – 1

Ans: (A)

18. The Value of  

(A)  0

(B)  3

(C)  1

(D)  −1

Ans: (D)

19. In an arc welding process, welding speed is doubled. Assuming all other process parameters to be constant, the cross sectional area of the weld bead will

(A) Increase by 25%

(B) Increase by 50%

(C) Reduce by 25%

(D) Reduce by 50%

Ans: (D)

20. A six-face fair dice is rolled a large number of times. The mean value of the outcomes is ______.

Ans: (3.5)

21. Consider the two dimensional velocity field given by  where a1, b1 , a2 and b2 are constants. Which one of the following conditions needs to be satisfied for the flow to be incompressible?

(A)  a1 + b1 = 0

(B)  a1 + b2 = 0

(C)  a2 + b2 = 0

(D)  a2 + b1 = 0

Ans: (B)

22. Consider a beam with circular cross-section of diameter d. The ratio of the second moment of area about the neutral axis to the section modulus of the area is.

(A)  d/2

(B)  πd/2

(C)  d

(D)  πd

Ans: (A)

23. Saturated steam at 100°C condenses on the outside of a tube. Cold fluid enters the tube at 20° C and exists at 50°C. The value of the Log Mean Temperature Difference (LMTD) is ________°C.

Ans: (63.82)

24. In a metal forming operation when the material has just started yielding, the principal stresses are σ1 = +180MPa, σ2 = −100MPa, σ3 = 0. Following Von Mises’ criterion, the yield stress is ________ MPa.

Ans: (245.76)

25. In the engineering stress-strain curve for mild steel, the Ultimate Tensile Strength (UTS) refers to

(A) Yield stress

(B) Proportional limit

(C) Maximum stress

(D) Fracture stress.

Ans: (C)

26. A parametric curve defined by  in the range 0 ≤ u ≤ 1 is rotated about the X – axis by 360 degrees. Area of the surface generated is

(A)  π/2

(B)  π

(C)  2π

(D)  4π

Ans: (C)

27. Assume that the surface roughness profile is triangular as shown schematically in the figure. If the peak to valley height is 20μm, The central line average surface roughness Ra (in μm) is

(A)  5

(B)  6.67

(C)  10

(D)  20

Ans: (A)

28. A thin uniform rigid bar of length L and mass M is hinged at point O, located at a distance of L / 3from one of its ends. The bar is further supported using springs, each of stiffness k, located at the two ends. A particle of mass m = M/4 is fixed at one end of the bar, as shown in the figure. For small rotations of the bar about O, the natural frequency of the systems is.

(A)   

(B)   

(C)   

(D)   

Ans: (B)

29. A point mass of 100 kg is dropped onto a massless elastic bar (cross-sectional area = 100 mm2, length = 1m, Young’s moduls = 100 GPa) from a height H of 10mm as shown (Figure is not to scale). If g = 10m/s2, the maximum compression of the elastic bar is _______ mm.

Ans: (1.51)

30. One kg of an ideal gas (gas constant, R = 400 J/kg.K; specific heat at constant volume, cv = 1000J/kg.K) n = at 1 bar, and 300 K is contained in a sealed rigid cylinder. During an adiabatic process, 100kJ of work is done on the system by a stirrer. The increase in entropy of the system is _________ J/K.

Ans: (287)

31. For an inline slider-crank mechanism, the lengths of the crank and connecting rod are 3m and 4m, respectively. At the instant when the connecting rod is perpendicular to the crank, if the velocity of the slider is 1m/s, the magnitude of angular velocity (upto 3 decimal points accuracy) of the crank is _________ radian/s.

Ans: (0.264)

32. In an epicyclic gear train, shown in the figure, the outer ring gear is fixed, while the sun gear rotates counterclockwise at 100rpm. Let the number of teeth on the sun, planet and outer gears to be 50, 25, and 100, respectively. The ratio of magnitudes of angular velocity of the planet gear to the angular velocity of the carrier arm is _________.

Ans: (3)

33. Moist air is treated as an ideal gas mixture of water vapor and dry air (molecular weight of air = 28.84 and molecular weight of water = 18). At a location, the total pressure is 100 kPa, the temperature is 30°C and the relative humidity is 55%. Given that the saturation pressure of water at 30°C is 4246 Pa, the mass of water vapor per kg of dry air is _____________ grams.

Ans: (14.87)

34. Following data refers to the jobs (P, Q, R, S) which have arrived at a machine for scheduling. The shortest possible average flow time is ___________ days.

Ans: (15)

35. Two models, P and Q, of a product earn profits of Rs. 100 and Rs. 80 per piece, respectively. Production times for P and Q are 5 hours and 3 hours, respectively, while the total production time available is 150 hours. For a total batch size of 40, to maximize profit, the number of units of P to be produced is ____________.

Ans: (15)

36. Circular arc on a part profile is being machined on a vertical CNC milling machine. CNC part program using metric units with absolute dimensions is listed below:

——————————–

N60 G01 X 30 Y 55 Z – 5 F 50

N70 G02 X 50 Y 35 R 20

N80 G01 Z 5

——————————–

The coordinates of the centre of the circular arc are :

(A)  (30, 55)

(B)  (50, 55)

(C)  (50, 35)

(D)  (30, 35)

Ans: (D)

37. Two black surfaces, AB and BC, of lengths 5m and 6m, respectively, are oriented as shown. Both surfaces extend infinitely into the third dimension. Given that view factor F12 = 0.5 T1 = 800 K, T2 = 600 K, Tsurrounding = 300 K and Stefan Boltzmann constant, σ = 5.67 × 10−8 W/(m2K4), the transfer rate from Surface 2 to the surrounding environment is ______kW.

Ans: (13.8)

38. Consider the matrix 

Which one of the following statements about P is INCORRECT?

(A) Determinant of P is equal to 1.

(B) P is orthogonal.

(C) Inverse of P is equal to its transpose.

(D) All Eigen values of P are real numbers

Ans: (D)

39. The Pressure ratio across a gas turbine (for air, specific heat at constant pressure, cp =1040J / kg.K and ratio of specific heats, γ =1.4) is 10. If the inlet temperature to the turbine is 1200K and the isentropic efficiency is 0.9, the gas temperature at turbine exit is ______ K.

Ans: (679.38)

40. An initially stress-free massless elastic beam of length L and circular cross-section with diameter d (d << L) is held fixed between two walls as shown. The beam material has Young’s modulus E and coefficient of thermal expansion α .

If the beam is slowly and uniformly heated, the temperature rise required to cause the beam to buckle is proportional to

(A)  d

(B)  d2

(C)  d3

(D)  d4

Ans: (B)

41. For the vector  the value of  is ______

Ans: (0)

42. A 10 mm deep cylindrical cup with diameter of 15mm is drawn from a circular blank. Neglecting the variation in the sheet thickness, the diameter (upto 2 decimal points accuracy) of the blank is _________ mm.

Ans: (28.72)

43. A machine element has an ultimate strength (σu) of 600 N/mm2, and endurance limit (σen) of 250 N/mm2. The fatigue curve for the element on log-log plot is shown below. If the element is to be designed for a finite of 10000 cycles, the maximum amplitude of a completely reversed operating stress is _________ N/mm2.

Ans: (386.19)

44. A sprue in a sand mould has a top diameter of 20mm and height of 200mm. The velocity of the molten metal at the entry of the sprue is 0.5m/s. Assume acceleration due to gravity as 9.8 m/s2 and neglect all losses. If the mould is well ventilated, the velocity (upto 3 decimal points accuracy) of the molten metal at the bottom of the sprue is ________ m/s.

Ans: (2.042)

45. Air contains 79% N2 and 21% O2 on a molar basis. Methane (CH4) is burned with 50% excess air than required stoichiometrically. Assuming complete combustion of methane, the molar percentage of N2 in the products is __________

Ans: (73.83)

46. P(0,3), Q(0.5, 4), and R (1,5) are three points on the curve defined by f(x). Numerical integration is carried out using both Trapezoidal rule and Simpson’s rule within limits x = 0 and x =1 for the curve. The difference between the two results will be.

(A)  0

(B)  0.25

(C)  0.5

(D)  1

Ans: (A)

47. Heat is generated uniformly in a long solid cylindrical rod (diameter = 10mm) at the rate of 4×107 W/m3. The thermal conductivity of the rod material is 25W/m.K. Under steady state conditions, the temperature difference between the centre and the surface of the rod is _________ °C.

Ans: (10)

48. Two disks A and B with identical mass (m) and radius (R) are initially at rest. They roll down from the top of identical inclined planes without slipping. Disk A has all of its mass concentrated at the rim, while Disk B has its mass uniformly distributed. At the bottom of the plane, the ratio of velocity of the center of disk A to the velocity of the center of disk B is.

(A)   

(B)   

(C)   

(D)   

Ans: (A)

49. A block of length 200mm is machined by a slab milling cutter 34mm in diameter. The depth of cut and table feed are set at 2mm and 18mm/minute, respectively. Considering the approach and the over travel of the cutter to be same, the minimum estimated machining time per pass is _____________ minutes.

Ans: (12)

50. A horizontal bar, fixed at one end (x = 0), has a length of 1 m, and cross-sectional area of 100 mm2. Its elastic modulus varies along its length as given by E(x) = 100ex GPa, Where x is the length coordinate (in m) along the axis of the bar. An axial tensile load of 10 kN is applied at the free end (x=1). The axial displacement of the free end is _______ mm.

Ans: (1.71)

51. Consider steady flow of an incompressible fluid through two long and straight pipes of diameters d1 and d2 arranged in series. Both pipes are of equal length and the flow is turbulent in both pipes. The friction factor for turbulent flow though pipes is of the form, f = K(Re)−n where K and n are known positive constants and Re is the Reynolds number. Neglecting minor losses, the ratio of the frictional pressure drop in pipe 1 to that in pipe 2,  is given by

(A)   

(B)   

(C)   

(D)   

Ans: (D)

52. The velocity profile inside the boundary layer for flow over a flat plate is given as  where U is the free stream velocity and δ is the local boundary layer thickness. If δ * is the local displacement thickness, the value of  is

(A)   

(B)   

(C)   

(D)   

Ans: (B)

53. For a steady flow, the velocity field is  The magnitude of the acceleration of a particle at (1, −1) is

(A)  2

(B)  1

(C)  2√5

(D)  0

Ans: (C)

54. Two cutting tools with tool life equations given below are being compared :

Tool 1L VT0.1 = 150

Tool 2: VT0.3 = 300

Where V is cutting speed in m/minute and T is tool life in minutes. The breakeven cutting speed beyond which Tool 2 will have a higher tool life is ____ m/minute.

Ans: (106.21)

55. A rectangular region in a solid is in a state of plane strain. The (x,y) coordinates of the corners of the under deformed rectangle are given by P(0,0), Q (4,0), S (0,3). The rectangle is subjected to uniform strains, εxx = 0.001, εyy = 0.002, γxy = 0.003. The deformed length of the elongated diagonal, up to three decimal places, is _____ units.

Ans: (5.013)

56. A right – angled cone (with base radius 5cm and height 12cm), as shown in the figure below, is rolled on the ground keeping the point P fixed until the point Q (at the base of the cone, as shown) touches the ground again.

By what angle (in radians) about P does the cone travel?

(A)   

(B)   

(C)   

(D)   

Ans: (D)

57. In a company with 100 employees, 45 earn Rs. 20,000 per month, 25 earn Rs. 30,000, 20 earn Rs. 40,000 8 earn Rs. 60,000, and 2 earn Rs. 150,000. The median of the salaries is

(A)  Rs. 20,000

(B)  Rs. 30,000

(C)  Rs. 32,300

(D)  Rs. 40,000

Ans: (B)

58. As the two speakers became increasingly agitated, the debate became __________.

(A)  lukewarm

(B)  poetic

(C)  forgiving

(D)  heated

Ans: (D)

59. P,Q, and R talk about S’s car collection. P states that S has at least 3 cars. Q believes that S has less than 3 cars. R indicates that to his knowledge, S has at least one Car. Only one of P, Q and R is right the number cars owned by S is.

(A)  0

(B)  1

(C)  3

(D)  Cannot be determined

Ans: (A)

60. He was one of my best __________ and I felt his loss _________.

(A) friend, keenly

(B) friends, keen

(C) friend, keener

(D) friends, keenly

Ans: (D)

61. Two very famous sportsmen Mark and Steve happened to be brothers, and played for country K. Mark teased James, an opponent from country E, “There is no way you are good enough to play for your country.’’ James replied, “Maybe not, but at least I am the best player in my own family.”

Which one of the following can be inferred from this conversation?

(A) Mark was known to play better than James

(B) Steve was known to play better than Mark

(C) James and Steve were good friends

(D) James played better than Steve

Ans: (B)

62. “Here, throughout the early 1820s, Stuart continued to fight his losing battle to allow his sepoys to wear their caste-marks and their own choice of facial hair on parade, being again reprimanded by the commander-in-chief. His retort that ‘A stronger instance than this of European prejudice with relation to this country has never come under my observations’ had no effect on his superiors.”

According to this paragraph, which of the statements below is most accurate?

(A)  Stuart’s commander – in chief was moved by this demonstration of his prejudice.

(B)  The Europeans were accommodating of the sepoys’ desire to weak their caste – marks.

(C)  Stuart’s losing battle’ refers to his inability to succeed in enabling sepoys to wear caste-marks.

(D)  The commander– in – Chief was exempt from the European preiudice that dictated how the sepoys were to dress.

Ans: (C)

63. The growth of bacteria (lactobacillus) in milk leads to curd formation. A minimum bacterial population density of 0.8(in suitable units) is needed to form curd. In the graph below, the population density of lactobacillus in 1 litre of milk is plotted as a function of time, at two different temperatures, 25°C and 37°C.

Consider the following statements based on the data shown above:

(i) The growth in bacterial population stops earlier at 37°C as compared to 25°C

(ii) The time taken for curd formation at 25°C is twice the time taken at 37°C

Which one of the following options is correct?

(A)  Only i

(B)  only ii

(C)  Both i and ii

(D)  Neither i nor ii

Ans: (A)

64. Let S1 be the plane figure consisting of the points (x,y) given by the inequalities |x – 1| ≤ 2 and |y + 2| ≤ Let S2 be the plane figure given by the inequalities x – y ≥ −2, y ≥ 1, and x ≤ 3 Let S be the union of S1 and S2. The area of S is

(A)  26

(B)  28

(C)  32

(D)  34

Ans: (C)

65. What is the sum of the missing digits in the subtraction problem below?

(A)  8

(B)  10

(C)  11

(D)  Cannot be determined

Ans: (D)