GATE Entrance Paper 2023

GATE Exam 2023 Chemistry (CY) Question Paper With Answer Key

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GATE-2023

CY: Chemistry

GA-General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. “I cannot support this proposal. My ________ will not permit it.”

(A)  conscious

(B)  consensus

(C)  conscience

(D)  consent

Answer: (C)

2. Courts : _______ : : Parliament : Legislature

(By word meaning)

(A)  Judiciary

(B)  Executive

(C)  Governmental

(D)  Legal

Answer: (A)

3. What is the smallest number with distinct digits whose digits add up to 45?

(A)  123555789

(B)  123457869

(C)  123456789

(D)  99999

Answer: (C)

4. In a class of 100 students,

(i) there are 30 students who neither like romantic movies nor comedy movies,

(ii) the number of students who like romantic movies is twice the number of students who like comedy movies, and

(iii) the number of students who like both romantic movies and comedy movies is 20.

How many students in the class like romantic movies?

(A)  40

(B)  20

(C)  60

(D)  30

Answer: (C)

5. How many rectangles are present in the given figure?

(A)  8

(B)  9

(C)  10

(D)  12

Answer: (C)

Q.6 – Q.10 Carry TWO marks Each

6. Forestland is a planet inhabited by different kinds of creatures. Among other creatures, it is populated by animals all of whom are ferocious. There are also creatures that have claws, and some that do not. All creatures that have claws are ferocious.

Based only on the information provided above, which one of the following options can be logically inferred with certainty?

(A)  All creatures with claws are animals.

(B)  Some creatures with claws are non-ferocious.

(C)  Some non-ferocious creatures have claws.

(D)  Some ferocious creatures are creatures with claws.

Answer: (D)

7. Which one of the following options represents the given graph?

(A)  f(x) = x2 2−|x|

(B)  f(x) = x 2−|x|

(C)  f(x) = |x|2−x

(D)  f(x) = x 2−x

Answer: (A)

8. Which one of the following options can be inferred from the given passage alone?

When I was a kid, I was partial to stories about other worlds and interplanetary travel. I used to imagine that I could just gaze off into space and be whisked to another planet.

[Excerpt from The Truth about Stories by T. King]

(A)  It is a child’s description of what he or she likes.

(B)  It is an adult’s memory of what he or she liked as a child.

(C)  The child in the passage read stories about interplanetary travel only in parts.

(D)  It teaches us that stories are good for children.

Answer: (B)

9. Out of 1000 individuals in a town, 100 unidentified individuals are covid positive. Due to lack of adequate covid-testing kits, the health authorities of the town devised a strategy to identify these covid-positive individuals. The strategy is to:

(i) Collect saliva samples from all 1000 individuals and randomly group them into sets of 5.

(ii) Mix the samples within each set and test the mixed sample for covid.

(iii) If the test done in (ii) gives a negative result, then declare all the 5 individuals to be covid negative.

(iv) If the test done in (ii) gives a positive result, then all the 5 individuals are separately tested for covid.

Given this strategy, no more than _______ testing kits will be required to identify all the 100 covid positive individuals irrespective of how they are grouped.

(A)  700

(B)  600

(C)  800

(D)  1000

Answer: (A)

10. A 100 cm × 32 cm rectangular sheet is folded 5 times. Each time the sheet is folded, the long edge aligns with its opposite side. Eventually, the folded sheet is a rectangle of dimensions 100 cm×1 cm.

The total number of creases visible when the sheet is unfolded is _______.

(A)  32

(B)  5

(C)  31

(D)  63

Answer: (C)

CY: Chemistry

Q.11 – Q.35 Carry ONE mark Each

11. The major product formed in the given reaction is

DME: 1,2-Dimethoxyethane

Answer: (A)

12. The compound which gives a fragment at m/z = 124[M + H]+ is

Answer: (B)

13. The major product formed in the given reaction is

Answer: (A)

14. The major product formed in the given reaction is

Answer: (A)

15. On irradiation using UV light (>300 nm), compounds X and Y, predominantly, undergo

(A)  X: Norrish type I reaction and Y: Norrish type II reaction

(B)  X: Norrish type II reaction and Y: Norrish type I reaction

(C)  Both X and Y: Norrish type I reaction

(D)  Both X and Y: Norrish type II reaction

Answer: (B)

16. The topicity relationship of Ha and Hb in X, Y and Z are, respectively,

(A)  Diastereotopic, Homotopic and Enantiotopic

(B)  Homotopic, Enantiotopic and Enantiotopic

(C)  Homotopic, Homotopic and Enantiotopic

(D)  Diastereotopic, Enantiotopic and Homotopic

Answer: (B)

17. Compound P was prepared based on a four-component reaction at room temperature in methanol. The required starting materials for the synthesis are

Answer: (A)

18. The major product formed in the following reaction is

Answer: (B)

19. The reaction of Ph3PCl2 with PhNH2 primarily produces

(A)  Ph3P=NPh

(B)  PhP=NPh

(C)  PhCl2P=NPh

(D)  Ph2ClP=NPh

Answer: (A)

20. Formation of [M(en)3]2+ from [M(H2O)6]2+ and three equivalents of ethylenediamine (en) is LEAST favored when M is

(A)  Co

(B)  Ni

(C)  Cu

(D)  Fe

Answer: (D)

21. Wacker oxidation of alkenes is catalyzed by a combination of

(A)  Pd(II) and Cu(II)

(B)  Co(II) and Cu(II)

(C)  Pd(II) and Ni(II)

(D)  Pd(II) and Co(II)

Answer: (A)

22. For the conversion of [Pt(L)Cl3]− to trans-[Pt(L)Cl2(H2O)], the trans-effect is LEAST when the ligand L is

(A)  H2O

(B)  NH3

(C)  DMSO

(D)  C2H4

Answer: (A)

23. The tetracoordinated copper center in the oxidized and reduced forms of plastocyanin exhibits longest bond with

(A)  cysteine-S and methionine-S, respectively

(B)  methionine-S and cysteine-S, respectively

(C)  cysteine-S and cysteine-S, respectively

(D)  methionine-S and methionine-S, respectively

Answer: (D)

24. The packing efficiency (in %) of spheres for a body-centered cubic (bcc) lattice is approximately

(A)  74

(B)  68

(C)  60

(D)  52

Answer: (B)

25. The magnitudes of CFSE in [M(H2O)6]n+ for Mn and Fe ions satisfy the relations

(A)  Mn2+ < Mn3+ and Fe2+ < Fe3+

(B)  Mn2+ > Mn3+ and Fe2+ > Fe3+

(C)  Mn2+ < Mn3+ and Fe2+ > Fe3+

(D)  Mn2+ > Mn3+ and Fe2+ < Fe3+

Answer: (C)

26. The organometallic catalyst for the following transformation is

Answer: (A)

27. Point group of naphthalene (C10H8) is

(A)  D2d

(B)  D2h

(C)  D3d

(D)  D­3h

Answer: (B)

28. The INCORRECT statement is

(A)  Zero-point energy of a quantum mechanical harmonic oscillator of frequency v is hv/2

(B)  Energy level of a quantum mechanical rigid rotor is inversely proportional to its moment of inertia

(C)  The time independent Schrödinger equation for Li2+ cannot be solved exactly

(D)  Total angular momentum of an atomic system is equal to the sum of orbital angular momentum and spin angular momentum

Answer: (C)

29. For an ideal gas, the molecular partition function in the canonical ensemble, that is proportional to the system volume (V), is the

(A)  vibrational partition function

(B)  rotational partition function

(C)  electronic partition function

(D)  translational partition function

Answer: (D)

30. Assertion (S): The total angular momentum for light atoms (low atomic number) is obtained by Russell-Saunders coupling, whereas jj-coupling is used for heavy atoms (high atomic number).

Reasoning (R): The spin-orbit interactions are weak in light atoms (low atomic number) and strong in heavy atoms (high atomic number).

The correct option is

(A)  S and R are true; and R is the correct reason for S

(B)  S and R are true; but R is NOT the correct reason for S

(C)  S is true but R is false

(D)  S is false but R is true

Answer: (A)

31. The acetolysis product(s) of the given reaction is(are)

Answer: (A, C)

32. Product(s) formed in the given reaction is(are)

Answer: (A, B, C)

33. The choice(s) that correctly identify radioisotopes (P, Q, R, S) shown in the following nuclear reaction is(are)

Answer: (A, B, D)

34. For the Lindemann-Hinshelwood mechanism of gas phase unimolecular reactions, the true statement(s) is(are)

(A)  Only molecules with three or more atoms can follow the Lindemann-Hinshelwood mechanism

(B)  Lindemann-Hinshelwood mechanism involves bimolecular elementary steps

(C)  The overall reaction is of second order at low pressure

(D)  The overall reaction is of second order at high pressure

Answer: (A, B, C)

35. The calculated magnetic moment of [Ce(NO3)5]2− is _______ BM. (rounded off to two decimal places)

(Given: atomic number of Ce is 58)

Answer: (2.51 to 2.55)

Q.36 – Q.65 Carry TWO marks Each

36. A compound, C15H16O2 , has the following spectral data;

1H NMR (ppm): 9.16 (s), 6.89 (d, J = 8 Hz), 6.64 (d, J = 8 Hz), 1.53 (s)

13C NMR (ppm): 154.7, 140.9, 127.1, 114.4, 40.7, 30.7

The structure of the compound is

Answer: (A)

37. The major product formed in the given reaction sequence is

Answer: (B)

38. E and F in the given reaction scheme are

Answer: (A)

39. M and N in the given reaction scheme are

NMO: N-Methylmorpholine-N-oxide

Answer: (C)

40. In the 1H NMR spectrum, multiplicity of the signal (bold and underlined H atom) in the following species is

(A)  I- pentet, II- quartet, III- doublet and IV- singlet

(B)  I- pentet, II- singlet, III- singlet and IV- doublet

(C)  I- triplet, II- triplet, III- doublet and IV- doublet

(D)  I- singlet, II- quartet, III- singlet and IV- singlet

Answer: (A)

41. The major product obtained by the treatment of (η5-C5H5)2Ni with Na/Hg in ethanol is

(A)  (η5-C5H5)( η3-C5H5)Ni

(B)  (η3-C5H5)2Ni

(C)  (η5-C5H5)( η3-C5H7)Ni

(D)  (η3-C5H7)2Ni

Answer: (C)

42. The number of shared corners of the constituent SiO4 units in orthosilicate, pyrosilicate, cyclic silicate and sheet silicate, respectively, are

(A)  0, 1, 2 and 3

(B)  2, 3, 0 and 1

(C)  0, 3, 1 and 2

(D)  1, 2, 3 and 0

Answer: (A)

43. Concentration of Q in a consecutive reaction  is given by  where [P]0 is the initial concentration of P.

If the value of k2 = 25 s−1, the value of k1 that leads to the longest waiting time for Q to reach its maximum is

(A)  k1 = 20 s−1

(B)  k1 = 25 s−1

(C)  k1 = 30 s−1

(D)  k1 = 35 s−1

Answer: (A)

44. The wave function for Be3+ in a certain state is given by  where N is the normalization constant, r is the distance of electron from the nucleus and 𝑎0 is the Bohr radius. The most probable distance of the electron from the nucleus in this state is

(A)  4a0

(B)  a0/4

(C)  8a0

(D)  a0/8

Answer: (B)

45. Match the following

(A)  P→III, Q→I, R→IV, S→II

(B)  P→III, Q→IV, R→II, S→I

(C)  P→IV, Q→I, R→III, S→II

(D)  P→II, Q→III, R→IV, S→I

Answer: (A)

46. In the scheme below,

Iα represents the intensity of the light absorbed. Assuming that the quantum yield of the first step is one, the steady state concentration of Q is given by

Answer: (A)

47. Product(s) formed in the given reaction sequence is(are)

Answer: (A, B)

48. Product(s) formed in the reaction below is(are)

Answer: (A, C)

49. The stereoisomer(s) of G giving the depicted product is(are)

Answer: (A, C)

50. Product(s) formed in the given reaction sequence is(are)

Answer: (A, C)

51. The reaction(s) in which inversion of configuration occur(s) is(are)

Answer: (A, B)

52. The correct statement(s) regarding myoglobin (Mb) and haemoglobin (Hb) is(are)

(A)  At low partial pressure of O2 (e.g., 5 kPa), the O2 affinity of Hb lowers upon lowering the pH

(B)  Binding of the first O2 molecule to Hb results in lower affinity for the binding of second O2 molecule

(C)  Metal center in deoxy-Mb is low-spin whereas it is high-spin in the case of oxy-Mb

(D)  One end of O2 binds to the metal center in oxy-Mb and the other end of the bound O2 is H-bonded with imidazole-NH of a distal histidine

Answer: (A, D)

53. The correct statement(s) regarding Co2(CO)8 is(are)

(A)  It reacts with Na to give Na[Co(CO)4]

(B)  It contains three bridging carbonyls

(C)  It can be prepared by reductive carbonylation of Co(OAc)2·4H2O

(D)  Two isomers exist in hexane solution

Answer: (A, C, D)

54. The compound(s) having [Xe]4f1 configuration is(are)

(Given the atomic numbers Ce:58, Lu:71, Pr:59 and Nd:60)

(A)  Na3[Ce(NO3)6]

(B)  Na3[LuCl6]

(C)  PrO2

(D)  Nd(NR2)3 (R = SiMe3)

Answer: (A, C)

55. The correct statement(s) for XeF2 is(are)

(A)  Its bonding is best explained by classical 2-centered-2-electron bonds

(B)  Its bonding is best explained by a non-classical 3-centered-4-electron bond

(C)  It contains nine lone pairs of electrons

(D)  Its point group is D∞h

Answer: (B, C, D)

56. For the non-dissociative adsorption of a gas on solid,

(i) the Freundlich isotherm is given by θ = kp1/n where θ is surface coverage, p is pressure, k and n are empirical constants; and

(ii) the BET isotherm is given by 

where p* and c empirical constants, and p < p*.

The correct statement(s) is(are)

(A)  At low surface coverage, the Langmuir isotherm reduces to the Freundlich isotherm with n = 1

(B)  At high surface coverage, the Langmuir isotherm reduces to the Freundlich isotherm with n = ∞

(C)  At very low pressure (p << p*), the BET isotherm reduces to the Langmuir isotherm

(D)  At very high pressure (p → p*), the BET isotherm reduces to the Langmuir isotherm

Answer: (A, B, C)

57. Two different enzyme catalysis reactions I and II have identical Y-intercepts for the Lineweaver-Burke (equation given below) plots. The slope for reaction I is twice than that of reaction II.

If the initial concentrations of enzymes in I and II are same, the correct statement(s) is(are)

where v and vmax are rate and maximum rate; KM is Michaelis-Menten constant, and [S] is substrate concentration.

(A)  Reactions I and II have same turn over number

(B)  Michaelis-Menten constants for reactions I and II are identical

(C)  Michaelis-Menten constant for reaction I is twice than that of reaction II

(D)  The rates of the elementary steps for reactions I and II are identical

Answer: (A, C)

58. The enthalpy change for the exothermic reaction between BeI2 and HgF2 is _______kJ mol−1 (rounded off to the nearest integer)

(Given: Bond dissociation energy (in kJ mol−1) for Be−F = 632, Be−I = 289, Hg−F = 268 and Hg−I = 145)

Answer: (-440 to -440)

59. Number of carbon atoms connected to the metal center in [W(C60)(CO)5] is _______ (rounded off to the nearest integer)

(Given: atomic number of W is 74)

Answer: (7 to 7)

60. Two-component solid-liquid system of naphthalene-benzene forms a simple eutectic mixture. Assuming that naphthalene-benzene forms an ideal solution, the mole fraction of naphthalene in benzene at 300 K and 1 bar is _______ (rounded off to two decimal places)

(Given: Freezing point (Tfp) and enthalpy of fusion (∆Hfus) of naphthalene are 353 K and 19.28 kJ mol−1, respectively and gas constant (R) =8.31 J K−1 mol−1)

Answer: (0.30 to 0.32)

61. The intrinsic viscosity of a sample of polystyrene in toluene is 84 cm3 g−1 at 30° It follows Mark-Houwink equation with empirical constant values of K = 1.05 × 10−2 cm3 g−1 and a = 0.75. The molecular weight of the polymer is ________ × 103 g mol−1 (rounded off to the nearest integer)

Answer: (158 to 160)

62. According to Debye-Hückel limiting law, the mean molal activity coefficient for 0.87 g K2SO4 (molar mass = 174 g mol−1) in 1 kg of water at 25°C is _________ (rounded off to two decimal places)

Answer: (0.74 to 0.76)

63. A solution is prepared by dissolving 128 g of naphthalene (C10H8) in 780 g of benzene (C6H6). The vapor pressure of pure benzene is 12.6 kPa at 25° Assuming that naphthalene in benzene is an ideal solution, the partial vapor pressure of benzene is _________ kPa (rounded off to two decimal places)

Answer: (11.34 to 11.47)

64. For the galvanic cell: H2 (g) | HCl (aq) | Cl2 (g)

the standard electromotive force (E0) value is given by

E0 = 1.73 – (1.25 × 10−3)T + (1.00 × 10−6)T2

where E0 is in Volts and T is in Kelvin.

For the cell reaction, the standard enthalpy change (∆rH0) at 300 K is _________ kJ mol−1(rounded off to the nearest integer)

(Given: Faraday constant, F = 96500 C mol−1)

Answer: (-164 to -154)

65. A solution of three non-interacting compounds P, Q, and R is taken in a cuvette of 1 cm path length. Their concentrations are [P] = 1 × 10−6 M, [Q] = 2 × 10−6 M, [R] = 3 × 10−6 M and the molar extinction coefficients at 300 nm are εP =1 × 105 M−1 cm−1, εQ = 2 × 105 M−1 cm−1 and εR = 3 × 105 M−1 cm−1. The % transmittance at 300 nm is __________ (rounded off to two decimal places)

Answer: (3.98 to 4.00)

GATE Exam 2023 Computer Science and Information Technology (CS) Question Paper With Answer Key

by

GATE-2023

CS: Computer Science and Information Technology

General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. We reached the station late, and _______ missed the train.

(A)  near

(B)  nearly

(C)  utterly

(D)  mostly

Answer: (B)

2. Kind : _______ : : Often : Frequently

(By word meaning)

(A)  Mean

(B)  Type

(C)  Cruel

(D)  Kindly

Answer: (MTA)

3. A series of natural numbers F­1, F2, F3, F4, F5, F6, F7, … obeys Fn+1 = Fn + Fn – 1 for all integers n ≥

If F6 = 37, and F7 = 60, then what is F1?

(A)  4

(B)  5

(C)  8

(D)  9

Answer: (A)

4. A survey for a certain year found that 90% of pregnant women received medical care at least once before giving birth. Of these women, 60% received medical care from doctors, while 40% received medical care from other healthcare providers.

Given this information, which one of the following statements can be inferred with certainty?

(A)  More than half of the pregnant women received medical care at least once from a doctor.

(B)  Less than half of the pregnant women received medical care at least once from a doctor.

(C)  More than half of the pregnant women received medical care at most once from a doctor.

(D)  Less than half of the pregnant women received medical care at most once from a doctor.

Answer: (A)

5. Looking at the surface of a smooth 3-dimensional object from the outside, which one of the following options is TRUE?

(A)  The surface of the object must be concave everywhere.

(B)  The surface of the object must be convex everywhere.

(C)  The surface of the object may be concave in some places and convex in other places.

(D)  The object can have edges, but no corners.

Answer: (C)

Q.6 – Q.10 Carry TWO marks Each

6. The country of Zombieland is in distress since more than 75% of its working population is suffering from serious health issues. Studies conducted by competent health experts concluded that a complete lack of physical exercise among its working population was one of the leading causes of their health issues. As one of the measures to address the problem, the Government of Zombieland has decided to provide monetary incentives to those who ride bicycles to work.

Based only on the information provided above, which one of the following statements can be logically inferred with certainty?

(A)  All the working population of Zombieland will henceforth ride bicycles to work.

(B)  Riding bicycles will ensure that all of the working population of Zombieland is free of health issues.

(C)  The health experts suggested to the Government of Zombieland to declare riding bicycles as mandatory.

(D)  The Government of Zombieland believes that riding bicycles is a form of physical exercise.

Answer: (D)

7. Consider two functions of time (t),

                             F(t) = 0.01 t2

                             g(t) = 4t

where 0 < t < ∞.

Now consider the following two statements:

(i) For some t > 0, g(t) > f(t)

(ii) There exists a T, such that f(t) > g(t) for all t > T.

Which one of the following options is TRUE?

(A)  only (i) is correct

(B)  only (ii) is correct

(C)  both (i) and (ii) are correct

(D)  neither (i) nor (ii) is correct

Answer: (C)

8. Which one of the following sentence sequences creates a coherent narrative?

(i) Once on the terrace, on her way to her small room in the corner, she notices the man right away.

(ii) She begins to pant by the time she has climbed all the stairs.

(iii) Mina has bought vegetables and rice at the market, so her bags are heavy.

(iv) He was leaning against the parapet, watching the traffic below.

(A)  (i), (ii), (iv), (iii)

(B)  (ii), (iii), (i), (iv)

(C)  (iv), (ii), (i), (iii)

(D)  (iii), (ii), (i), (iv)

Answer: (D)

9. f(x) and g(y) are functions of x and y, respectively, and f(x) = g(y) for all real values of x and y. Which one of the following options is necessarily TRUE for all x and y?

(A)  f(x) = 0 and g(y) = 0

(B)  f(x) = g(y) = constant

(C)  f(x) ≠ constant and g(y) ≠ constant

(D)  f(x) + g(y) = f(x) – g(y)

Answer: (B)

10. Which one of the options best describes the transformation of the 2-dimensional figure P to Q, and then to R, as shown?

(A)  Operation 1: A clockwise rotation by 90º about an axis perpendicular to the plane of the figure

Operation 2: A reflection along a horizontal line

(B)  Operation 1: A counter clockwise rotation by 90º about an axis perpendicular to the plane of the figure

Operation 2: A reflection along a horizontal line

(C)  Operation 1: A clockwise rotation by 90º about an axis perpendicular to the plane of the figure

Operation 2: A reflection along a vertical line

(D)  Operation 1: A counter clockwise rotation by 180º about an axis perpendicular to the plane of the figure

Operation 2: A reflection along a vertical line

Answer: (A)

CS: Computer Science and Information Technology

Q.11 – Q.35 Carry ONE mark each.

11. Consider the following statements regarding the front-end and back-end of a compiler.

S1: The front-end includes phases that are independent of the target hardware.

S2: The back-end includes phases that are specific to the target hardware.

S3: The back-end includes phases that are specific to the programming language used in the source code.

Identify the CORRECT option.

(A)  Only S1 is TRUE.

(B)  Only S1 and S2 are TRUE.

(C)  S1, S2, and S3 are all TRUE.

(D)  Only S1 and S3 are TRUE.

Answer: (B)

12. Which one of the following sequences when stored in an array at locations A[1], . . . , A[10] forms a max-heap?

(A)  23, 17, 10, 6, 13, 14, 1, 5, 7, 12

(B)  23, 17, 14, 7, 13, 10, 1, 5, 6, 12

(C)  23, 17, 14, 6, 13, 10, 1, 5, 7, 15

(D)  23, 14, 17, 1, 10, 13, 16, 12, 7, 5

Answer: (B)

13. Let SLLdel be a function that deletes a node in a singly-linked list given a pointer to the node and a pointer to the head of the list. Similarly, let DLLdel be another function that deletes a node in a doubly-linked list given a pointer to the node and a pointer to the head of the list.

Let n denote the number of nodes in each of the linked lists. Which one of the following choices is TRUE about the worst-case time complexity of SLLdel and DLLdel?

(A)  SLLdel is O(1) and DLLdel is O(n)

(B)  Both SLLdel and DLLdel are O(log(n))

(C)  Both SLLdel and DLLdel are O(1)

(D)  SLLdel is O(n) and DLLdel is O(1)

Answer: (D)

14. Consider the Deterministic Finite-state Automaton (DFA) 𝒜 shown below. The DFA runs on the alphabet {0, 1}, and has the set of states {s, p, q, r}, with s being the start state and p being the only final state.

Which one of the following regular expressions correctly describes the language accepted by A?

(A)  1(0∗11)∗

(B)  0(0 + 1)∗

(C)  1(0 + 11)∗

(D)  1(110∗)∗

Answer: (C)

15. The Lucas sequence Ln is defined by the recurrence relation:

Ln = Ln – 1 + Ln – 2, for n ≥ 3,

with L1 = 1 and L2 = 3.

Which one of the options given is TRUE?

Answer: (A)

16. Which one of the options given below refers to the degree (or arity) of a relation in relational database systems?

(A)  Number of attributes of its relation schema.

(B)  Number of tuples stored in the relation.

(C)  Number of entries in the relation.

(D)  Number of distinct domains of its relation schema.

Answer: (A)

17. Suppose two hosts are connected by a point-to-point link and they are configured to use Stop-and-Wait protocol for reliable data transfer. Identify in which one of the following scenarios, the utilization of the link is the lowest.

(A)  Longer link length and lower transmission rate

(B)  Longer link length and higher transmission rate

(C)  Shorter link length and lower transmission rate

(D)  Shorter link length and higher transmission rate

Answer: (B)

18. Let

Let det(A) and det(B) denote the determinants of the matrices A and B, respectively.

Which one of the options given below is TRUE?

(A)  det(A) = det(B)

(B)  det(B) = −det(A)

(C)  det(A) = 0

(D)  det(AB) = det(A)+det(B)

Answer: (B)

19. Consider the following definition of a lexical token id for an identifier in a programming language, using extended regular expressions:

Answer: (C)

20. An algorithm has to store several keys generated by an adversary in a hash table. The adversary is malicious who tries to maximize the number of collisions. Let k be the number of keys, m be the number of slots in the hash table, and k > m.

Which one of the following is the best hashing strategy to counteract the adversary?

(A)  Division method, i.e., use the hash function h(k) = k mod m.

(B)  Multiplication method, i.e., use the hash function  where A is a carefully chosen constant.

(C)  Universal hashing method.

(D)  If k is a prime number, use Division method. Otherwise, use Multiplication method.

Answer: (C)

21. The output of a 2-input multiplexer is connected back to one of its inputs as shown in the figure.

Match the functional equivalence of this circuit to one of the following options.

(A)  D Flip-flop

(B)  D Latch

(C)  Half-adder

(D)  Demultiplexer

Answer: (B)

22. Which one or more of the following need to be saved on a context switch from one thread (T1) of a process to another thread (T2) of the same process?

(A)  Page table base register

(B)  Stack pointer

(C)  Program counter

(D)  General purpose registers

Answer: (B, C, D)

23. Which one or more of the following options guarantee that a computer system will transition from user mode to kernel mode?

(A)  Function Call

(B)  malloc Call

(C)  Page Fault

(D)  System Call

Answer: (C, D)

24. Which of the following statements is/are CORRECT?

(A)  The intersection of two regular languages is regular.

(B)  The intersection of two context-free languages is context-free.

(C)  The intersection of two recursive languages is recursive.

(D)  The intersection of two recursively enumerable languages is recursively enumerable.

Answer: (A, C, D)

25. Which of the following statements is/are INCORRECT about the OSPF (Open Shortest Path First) routing protocol used in the Internet?

(A)  OSPF implements Bellman-Ford algorithm to find shortest paths.

(B)  OSPF uses Dijkstra’s shortest path algorithm to implement least-cost path routing.

(C)  OSPF is used as an inter-domain routing protocol.

(D)  OSPF implements hierarchical routing.

Answer: (A, C)

26. Geetha has a conjecture about integers, which is of the form

∀x(P(x) ⟹ ∃yQ(x, y),

where P is a statement about integers, and Q is a statement about pairs of integers. Which of the following (one or more) option(s) would imply Geetha’s conjecture?

(A)  ∃x(P(x) ˄ ∀yQ(x, y))

(B)  ∀x∀yQ(x, y)

(C)  ∃y∀x(P(x) ⟹ Q(x, y))

(D)  ∃x(P(x) ˄ ∃yQ(x, y))

Answer: (B, C)

27. Which one or more of the following CPU scheduling algorithms can potentially cause starvation?

(A)  First-in First-Out

(B)  Round Robin

(C)  Priority Scheduling

(D)  Shortest Job First

Answer: (A, C, D or C, D)

28. Let

f(x) = x3 + 15x2 – 3x – 36

be a real-valued function.

Which of the following statements is/are TRUE?

(A)  f(x) does not have a local maximum.

(B)  f(x) has a local maximum.

(C)  f(x) does not have a local minimum.

(D)  f(x) has a local minimum.

Answer: (B, D)

29. Let f and g be functions of natural numbers given by f(n) = n and g(n) = n2. Which of the following statements is/are TRUE?

(A)  f ∈ O(g)

(B)  f ∈ Ω(g)

(C)  f ∈ o(g)

(D)  f ∈ Θ(g)

Answer: (A, C)

30. Let A be the adjacency matrix of the graph with vertices {1, 2, 3, 4, 5}.

Let λ1, λ2, λ3, λ4, and λ5 be the five eigenvalues of A. Note that these eigenvalues need not be distinct.

The value of λ1 + λ2 + λ3 + λ4 + λ5 = _______.

Answer: (2 to 2 OR 4 to 4)

31. The value of the definite integral

is ___________. (Rounded off to the nearest integer)

Answer: (0 to 0)

32. A particular number is written as 132 in radix-4 representation. The same number in radix-5 representation is _________.

Answer: (110 to 110)

33. Consider a 3-stage pipelined processor having a delay of 10 ns (nanoseconds), 20 ns, and 14 ns, for the first, second, and the third stages, respectively. Assume that there is no other delay and the processor does not suffer from any pipeline hazards. Also assume that one instruction is fetched every cycle.

The total execution time for executing 100 instructions on this processor is ___________ ns.

Answer: (2040 to 2040)

34. A keyboard connected to a computer is used at a rate of 1 keystroke per second. The computer system polls the keyboard every 10 ms (milli seconds) to check for a keystroke and consumes 100 μs (micro seconds) for each poll. If it is determined after polling that a key has been pressed, the system consumes an additional 200 μs to process the keystroke. Let T1 denote the fraction of a second spent in polling and processing a keystroke.

In an alternative implementation, the system uses interrupts instead of polling. An interrupt is raised for every keystroke. It takes a total of 1 ms for servicing an interrupt and processing a keystroke. Let T2 denote the fraction of a second spent in servicing the interrupt and processing a keystroke.

The ratio T1/T2 is _________. (Rounded off to one decimal place)

Answer: (10.2 to 10.2)

35. The integer value printed by the ANSI-C program given below is ________.

Answer: (7 to 7)

Q.36 – Q.65 Carry TWO mark each.

36. Consider the following program:

Which one of the following options represents the activation tree corresponding to the main function?

Answer: (A)

37. Consider the control flow graph shown.

Which one of the following choices correctly lists the set of live variables at the exit point of each basic block?

(A)  B1: {}, B2: {a}, B3: {a}, B4: {a}

(B)  B1: {i, j}, B2: {a}, B3: {a}, B4: {i}

(C)  B1: {a, i, j}, B2: {a, i, j}, B3: {a, i}, B4: {a}

(D)  B1: {a, i, j}, B2: {a, j}, B3: {a, j}, B4: {a, i, j}

Answer: (D)

38. Consider the two functions incr and decr shown below.

There are 5 threads each invoking incr once, and 3 threads each invoking decr once, on the same shared variable X. The initial value of X is 10.

Suppose there are two implementations of the semaphore s, as follows:

I-1: s is a binary semaphore initialized to 1.

I-2: s is a counting semaphore initialized to 2.

Let V1, V2 be the values of X at the end of execution of all the threads with

implementations I-1, I-2, respectively.

Which one of the following choices corresponds to the minimum possible values of

V1, V2, respectively?

(A)  15, 7

(B)  7, 7

(C)  12, 7

(D)  12, 8

Answer: (C)

39. Consider the context-free grammar G below

S → aSb | X

X → aX | Xb |a| b,

where S and X are non-terminals, and a and b are terminal symbols. The starting non-terminal is S.

Which one of the following statements is CORRECT?

(A)  The language generated by G is (a + b)∗

(B)  The language generated by G is a∗(a + b)b∗

(C)  The language generated by G is a∗b∗(a + b)

(D)  The language generated by G is not a regular language

Answer: (B)

40. Consider the pushdown automaton (PDA) P below, which runs on the input alphabet {a, b}, has stack alphabet {⊥, A}, and has three states {s, p, q}, with s being the start state. A transition from state u to state v, labelled c/X/γ, where c is an input symbol, or ϵ, X is a stack symbol, and γ is a string of stack symbols, represents the fact that in state u, the PDA can read c from the input, with X on the top of its stack, pop X from the stack, push in the string γ on the stack, and go to state v. In the initial configuration, the stack has only the symbol ⊥ in it. The PDA accepts by empty stack.

Which one of the following options correctly describes the language accepted by P?

(A)  {ambn|1 ≤ m and n < m}

(B)  {ambn | 0 ≤ n ≤ m}

(C)  {ambn | 0 ≤ m and 0 ≤ n}

(D)  {am| 0 ≤ m}∪ {bn|0 ≤ n}

Answer: (A)

41. Consider the given C-code and its corresponding assembly code, with a few operands U1–U4 being unknown. Some useful information as well as the semantics of each unique assembly instruction is annotated as inline comments in the code. The memory is byte-addressable.

Which one of the following options is a CORRECT replacement for operands in the position (U1, U2, U3, U4) in the above assembly code?

(A)  (8, 4, 1, L02)

(B)  (3, 4, 4, L01)

(C)  (8, 1, 1, L02)

(D)  (3, 1, 1, L01)

Answer: (B)

42. A 4 kilobyte (KB) byte-addressable memory is realized using four 1 KB memory blocks. Two input address lines (IA4 and IA3) are connected to the chip select (CS) port of these memory blocks through a decoder as shown in the figure. The remaining ten input address lines from IA11–IA0 are connected to the address port of these blocks. The chip select (CS) is active high.

The input memory addresses (IA11–IA0), in decimal, for the starting locations (Addr = 0) of each block (indicated as X1, X2, X3, X4 in the figure) are among the options given below. Which one of the following options is CORRECT?

(A)  (0, 1, 2, 3)

(B)  (0, 1024, 2048, 3072)

(C)  (0, 8, 16, 24)

(D)  (0, 0, 0, 0)

Answer: (C)

43. Consider a sequential digital circuit consisting of T flip-flops and D flip-flops as shown in the figure. CLKIN is the clock input to the circuit. At the beginning, Q1, Q2 and Q3 have values 0, 1 and 1, respectively.

Which one of the given values of (Q1, Q2, Q3) can NEVER be obtained with this digital circuit?

(A)  (0, 0, 1)

(B)  (1, 0, 0)

(C)  (1, 0, 1)

(D)  (1, 1, 1)

Answer: (A)

44. A Boolean digital circuit is composed using two 4-input multiplexers (M1 and M2) and one 2-input multiplexer (M3) as shown in the figure. X0–X7 are the inputs of the multiplexers M1 and M2 and could be connected to either 0 or 1. The select lines of the multiplexers are connected to Boolean variables A, B and C as shown.

Which one of the following set of values of (X0, X1, X2, X3, X4, X5, X6, X7) will realise the Boolean function 

(A)  (1, 1, 0, 0, 1, 1, 1, 0)

(B)  (1, 1, 0, 0, 1, 1, 0, 1)

(C)  (1, 1, 0, 1, 1, 1, 0, 0)

(D)  (0, 0, 1, 1, 0, 1, 1, 1)

Answer: (C)

45. Consider the IEEE-754 single precision floating point numbers P=0xC1800000 and Q=0x3F5C2EF4.

Which one of the following corresponds to the product of these numbers (i.e., P × Q), represented in the IEEE-754 single precision format?

(A)  0x404C2EF4

(B)  0x405C2EF4

(C)  0xC15C2EF4

(D)  0xC14C2EF4

Answer: (C)

46. Let A be a priority queue for maintaining a set of elements. Suppose A is implemented using a max-heap data structure. The operation Extract-Max(A) extracts and deletes the maximum element from A. The operation Insert(A, key) inserts a new element key in A. The properties of a max-heap are preserved at the end of each of these operations.

When A contains n elements, which one of the following statements about the worst case running time of these two operations is TRUE?

(A)  Both Extract-Max(A) and Insert(A, key) run in O(1).

(B)  Both Extract-Max(A) and Insert(A, key) run in O(log(n)).

(C)  Extract-Max(A) runs in O(1) whereas Insert(A, key) runs in O(n).

(D)  Extract-Max(A) runs in O(1) whereas Insert(A, key) runs in O(log(n)).

Answer: (B)

47. Consider the C function foo and the binary tree shown.

When foo is called with a pointer to the root node of the given binary tree, what will it print?

(A)  3 8 5 13 11 10

(B)  3 5 8 10 11 13

(C)  3 8 16 13 24 50

(D)  3 16 8 50 24 13

Answer: (C)

48. Let U = {1, 2, . . . , n}, where n is a large positive integer greater than 1000. Let k be a positive integer less than n. Let A,B be subsets of U with |A| = |B| = k and A ∩ B = ∅. We say that a permutation of U separates A from B if one of the following is true.

– All members of A appear in the permutation before any of the members of B.

– All members of B appear in the permutation before any of the members of A.

How many permutations of U separate A from B?

Answer: (D)

49. Let f : A → B be an onto (or surjective) function, where A and B are nonempty sets. Define an equivalence relation ∼ on the set A as

a1 ∼ a2 if f(a1) = f(a2) ,

where a1, a2 ∈ A. Let E = {[x] : x ∈ A} be the set of all the equivalence classes under ∼. Define a new mapping F :E →B as

F([x]) = f(x), for all the equivalence classes [x] in E.

Which of the following statements is/are TRUE?

(A)  F is NOT well-defined.

(B)  F is an onto (or surjective) function.

(C)  F is a one-to-one (or injective) function.

(D)  F is a bijective function.

Answer: (B, C, D)

50. Suppose you are asked to design a new reliable byte-stream transport protocol like TCP. This protocol, named myTCP, runs over a 100 Mbps network with Round Trip Time of 150 milliseconds and the maximum segment lifetime of 2 minutes.

Which of the following is/are valid lengths of the Sequence Number field in the myTCP header?

(A)  30 bits

(B)  32 bits

(C)  34 bits

(D)  36 bits

Answer: (B, C, D)

51. Let X be a set and 2X denote the powerset of X.

Define a binary operation Δ on 2X as follows:

A∆B = (A – B) ∪ (B – A).

Let H = (2X, Δ). Which of the following statements about H is/are correct?

(A)  H is a group.

(B)  Every element in H has an inverse, but H is NOT a group.

(C)  For every A ∈ 2X, the inverse of A is the complement of A.

(D)  For every A ∈ 2X, the inverse of A is A.

Answer: (A, D)

52. Suppose in a web browser, you click on the gate-2023.in URL. The browser cache is empty. The IP address for this URL is not cached in your local host, so a DNS lookup is triggered (by the local DNS server deployed on your local host) over the 3-tier DNS hierarchy in an iterative mode. No resource records are cached anywhere across all DNS servers.

Let RTT denote the round trip time between your local host and DNS servers

in the DNS hierarchy. The round trip time between the local host and the web server hosting www.gate-2023.in is also equal to RTT. The HTML file associated with the URL is small enough to have negligible transmission time and negligible rendering time by your web browser, which references 10 equally small objects on the same web server.

Which of the following statements is/are CORRECT about the minimum elapsed time between clicking on the URL and your browser fully rendering it?

(A)  7 RTTs, in case of non-persistent HTTP with 5 parallel TCP connections.

(B)  5 RTTs, in case of persistent HTTP with pipelining.

(C)  9 RTTs, in case of non-persistent HTTP with 5 parallel TCP connections.

(D)  6 RTTs, in case of persistent HTTP with pipelining.

Answer: (C, D)

53. Consider a random experiment where two fair coins are tossed. Let A be the event that denotes HEAD on both the throws, B be the event that denotes HEAD on the first throw, and C be the event that denotes HEAD on the second throw. Which of the following statements is/are TRUE?

(A)  A and B are independent.

(B)  A and C are independent.

(C)  B and C are independent.

(D)  Prob(B|C) = Prob(B)

Answer: (C, D)

54. Consider functions Function 1 and Function 2 expressed in pseudocode as follows:

Let f1(n) and f2(n) denote the number of times the statement “x = x + 1” is executed in Function 1 and Function 2, respectively.

Which of the following statements is/are TRUE?

(A)  f1(n) ∈ Θ(f2(n))

(B)  f1(n) ∈ o(f2(n))

(C)  f1(n) ∈ ω(f2(n))

(D)  f1(n) ∈ O(n)

Answer: (A, D)

55. Let G be a simple, finite, undirected graph with vertex set {v1, . . . , vn}. Let Δ(G) denote the maximum degree of G and let ℕ = {1, 2, . . .} denote the set of all possible colors. Color the vertices of G using the following greedy strategy:

for i = 1, . . . , n

color(vi) ← min{j ∈ ℕ : no neighbour of vi is colored j}

Which of the following statements is/are TRUE?

(A)  This procedure results in a proper vertex coloring of G.

(B)  The number of colors used is at most Δ(G) + 1.

(C)  The number of colors used is at most Δ(G).

(D)  The number of colors used is equal to the chromatic number of G.

Answer: (A, B)

56. Let U = {1, 2, 3}. Let 2U denote the powerset of U. Consider an undirected graph G whose vertex set is 2U. For any A,B ∈ 2U, (A,B) is an edge in G if and only if (i) A = B, and (ii) either A B or B A. For any vertex A in G, the set of all possible orderings in which the vertices of G can be visited in a Breadth First Search (BFS) starting from A is denoted by B(A).

If ∅ denotes the empty set, then the cardinality of B(∅) is ________.

Answer: (5040 to 5040)

57. Consider the following two-dimensional array D in the C programming language, which is stored in row-major order:

int D[128][128];

Demand paging is used for allocating memory and each physical page frame holds 512 elements of the array D. The Least Recently Used (LRU) page-replacement policy is used by the operating system. A total of 30 physical page frames are allocated to a process which executes the following code snippet:

The number of page faults generated during the execution of this code snippet is ________.

Answer: (4096 to 4096)

58. Consider a computer system with 57-bit virtual addressing using multi-level tree-structured page tables with L levels for virtual to physical address translation. The page size is 4 KB (1 KB = 1024 B) and a page table entry at any of the levels occupies 8 bytes.

The value of L is _______.

Answer: (5 to 5)

59. Consider a sequence a of elements a0 = 1, a1 = 5, a2 = 7, a3 = 8, a4 = 9, and a5 = 2. The following operations are performed on a stack S and a queue Q, both of which are initially empty.

I: push the elements of a from a0 to a5 in that order into S.

II: enqueue the elements of a from a0 to a5 in that order into Q.

III: pop an element from S.

IV: dequeue an element from Q.

V: pop an element from S.

VI: dequeue an element from Q.

VII: dequeue an element from Q and push the same element into S.

VIII: Repeat operation VII three times.

IX: pop an element from S.

X: pop an element from S.

The top element of S after executing the above operations is ________.

Answer: (8 to 8)

60. Consider the syntax directed translation given by the following grammar and semantic rules. Here N, I, F and B are non-terminals. N is the starting non-terminal, and #, 0 and 1 are lexical tokens corresponding to input letters “#”, “0” and “1”, respectively. X.val denotes the synthesized attribute (a numeric value) associated with a non-terminal X. I1 and F1 denote occurrences of I and F on the right hand side of a production, respectively. For the tokens 0 and 1, 0.val = 0 and 1.val = 1.

The value computed by the translation scheme for the input string

10 # 011

is __________. (Rounded off to three decimal places)

Answer: (2.374 to 2.376)

61. Consider the following table named Student in a relational database. The primary key of this table is rollNum.

The SQL query below is executed on this database.

The number of rows returned by the query is ______.

Answer: (2 to 2)

62. Consider a database of fixed-length records, stored as an ordered file. The database has 25,000 records, with each record being 100 bytes, of which the primary key occupies 15 bytes. The data file is block-aligned in that each data record is fully contained within a block. The database is indexed by a primary index file, which is also stored as a block-aligned ordered file. The figure below depicts this indexing scheme.

Suppose the block size of the file system is 1024 bytes, and a pointer to a block occupies 5 bytes. The system uses binary search on the index file to search for a record with a given key. You may assume that a binary search on an index file of b blocks takes  block accesses in the worst case.

Given a key, the number of block accesses required to identify the block in the data file that may contain a record with the key, in the worst case, is _______.

Answer: (6 to 6)

63. Consider the language L over the alphabet {0, 1}, given below:

L = {w ∈ {0, 1}∗ | w does not contain three or more consecutive 1’s}.

The minimum number of states in a Deterministic Finite-State Automaton (DFA) for L is _______.

Answer: (4 to 4)

64. An 8-way set associative cache of size 64 KB (1 KB = 1024 bytes) is used in a system with 32-bit address. The address is sub-divided into TAG, INDEX, and BLOCK OFFSET.

The number of bits in the TAG is ______.

Answer: (19 to 19)

65. The forwarding table of a router is shown below.

A packet addressed to a destination address 200.150.68.118 arrives at the router. It will be forwarded to the interface with ID _______.

Answer: (3 to 3)

GATE Exam 2023 Chemical Engineering (CH) Question Paper With Answer Key

by

GATE-2023

CH: Chemical Engineering

GA-General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. “You are delaying the completion of the task. Send _______ contributions at the earliest.”

(A)  you are

(B)  your

(C)  you’re

(D)  yore

Answer: (B)

2. References : ______ : : Guidelines : Implement

(By word meaning)

(A)  Sight

(B)  Site

(C)  Cite

(D)  Plagiarise      

Answer: (C)

3. In the given figure, PQRS is a parallelogram with PS = 7 cm, PT = 4 cm and PV = 5 cm. What is the length of RS in cm? (The diagram is representative.)

(A)  20/7

(B)  28/5

(C)  9/2

(D)  35/4

Answer: (B)

4. In 2022, June Huh was awarded the Fields medal, which is the highest prize in Mathematics.

When he was younger, he was also a poet. He did not win any medals in the International Mathematics Olympiads. He dropped out of college.

Based only on the above information, which one of the following statements can be logically inferred with certainty?

(A)  Every Fields medalist has won a medal in an International Mathematics Olympiad.

(B)  Everyone who has dropped out of college has won the Fields medal.

(C)  All Fields medalists are part-time poets.

(D)  Some Fields medalists have dropped out of college.

Answer: (D)

5. A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is a mirror image of the other part about that line.

The given figure consists of 16 unit squares arranged as shown. In addition to the three black squares, what is the minimum number of squares that must be coloured black, such that both PQ and MN form lines of symmetry? (The figure is representative)

(A)  3

(B)  4

(C)  5

(D)  6

Answer: (C)

Q.6 – Q.10 Carry TWO marks Each

6. Human beings are one among many creatures that inhabit an imagined world. In this imagined world, some creatures are cruel. If in this imagined world, it is given that the statement “Some human beings are not cruel creatures” is FALSE, then which of the following set of statement(s) can be logically inferred with certainty?

(i) All human beings are cruel creatures.

(ii) Some human beings are cruel creatures.

(iii) Some creatures that are cruel are human beings.

(iv) No human beings are cruel creatures.

(A)  only (i)

(B)  only (iii) and (iv)

(C)  only (i) and (ii)

(D)  (i), (ii) and (iii)

Answer: (D)

7. To construct a wall, sand and cement are mixed in the ratio of 3:1. The cost of sand and that of cement are in the ratio of 1:2.

If the total cost of sand and cement to construct the wall is 1000 rupees, then what is the cost (in rupees) of cement used?

(A)  400

(B)  600

(C)  800

(D)  200

Answer: (A)

8. The World Bank has declared that it does not plan to offer new financing to Sri Lanka, which is battling its worst economic crisis in decades, until the country has an adequate macroeconomic policy framework in place. In a statement, the World Bank said Sri Lanka needed to adopt structural reforms that focus on economic stabilisation and tackle the root causes of its crisis. The latter has starved it of foreign exchange and led to shortages of food, fuel, and medicines. The bank is repurposing resources under existing loans to help alleviate shortages of essential items such as medicine, cooking gas, fertiliser, meals for children, and cash for vulnerable households.

Based only on the above passage, which one of the following statements can be inferred with certainty?

(A)  According to the World Bank, the root cause of Sri Lanka’s economic crisis is that it does not have enough foreign exchange.

(B)  The World Bank has stated that it will advise the Sri Lankan government about how to tackle the root causes of its economic crisis.

(C)  According to the World Bank, Sri Lanka does not yet have an adequate macroeconomic policy framework.

(D)  The World Bank has stated that it will provide Sri Lanka with additional funds for essentials such as food, fuel, and medicines.

Answer: (C)

9. The coefficient of x4 in the polynomial (x − 1)3 (x − 2)3 is equal to _______.

(A)  33

(B)  −3

(C)  30

(D)  21

Answer: (A)

10. Which one of the following shapes can be used to tile (completely cover by repeating) a flat plane, extending to infinity in all directions, without leaving any empty spaces in between them? The copies of the shape used to tile are identical and are not allowed to overlap.

(A)  circle

(B)  regular octagon

(C)  regular pentagon

(D)  rhombus

Answer: (D)

CH: Chemical Engineering

Q.11 – Q.35 Carry ONE mark Each

11. Which one of the following is the CORRECT value of y, as defined by the expression given below?

(A)  1

(B)  2

(C)  0

(D)  ∞

Answer: (B)

12. The vector  is defined as

Which one of the following is the CORRECT value of divergence of  evaluated at the point (x, y, z) = (3, 2, 1)?

(A)  0

(B)  3

(C)  14

(D)  13

Answer: (D)

13. Given that

where z1 = 2 + 3i and z2 = −2 + 3i with i = √−1, which one of the following options is CORRECT?

(A)  F < 0

(B)  F < 1

(C)  F > 1

(D)  F = 1

Answer: (B)

14. For a two-dimensional plane, the unit vectors,  of the polar coordinate system and  of the Cartesian coordinate system, are related by the following two equations.

Which one of the following is the CORRECT value of 

(A)  1

(B) 

(C) 

(D) 

Answer: (D)

15. Which one of the following statements related to octane number is NOT correct?

(A)  Linear alkanes with higher carbon number have higher octane number.

(B)  Branching in linear alkanes increases their octane number.

(C)  Catalytic reforming of hydrocarbons increases their octane number.

(D)  Gasoline quality is measured in terms of octane number.

Answer: (A)

16. Which one of the following options represents the major components of oleum?

(A)  Sulfuric acid and nitric acid

(B)  Concentrated sulfuric acid and petroleum jelly

(C)  Sulfuric acid and hydrochloric acid

(D)  Sulfuric acid and sulfur trioxide

Answer: (D)

17. For a reversible endothermic chemical reaction with constant heat of reaction over the operating temperature range, K is the thermodynamic equilibrium constant. Which one of the following figures shows the CORRECT dependence of K on temperature T?

Answer: (A)

18. Nitrile rubber is manufactured via polymerization process. Which one of the following options is the CORRECT pair of monomers used in this process?

(A)  Acrylonitrile and styrene

(B)  Acrylonitrile and butadiene

(C)  Butadiene and styrene

(D)  Butadiene and isoprene

Answer: (B)

19. John and Jane independently performed a thermodynamic experiment, in which X and Y represent the initial and final thermodynamic states of the system, respectively. John performed the experiment under reversible conditions, for which the change in entropy of the system was ∆Srev. Jane performed the experiment under irreversible conditions, for which the change in entropy of the system was ∆Sirr. Which one of the following relationships is CORRECT?

(A)  ∆Srev = ∆Sirr

(B)  ∆Srev > ∆Sirr

(C)  ∆Srev < ∆Sirr

(D)  ∆Srev = 2∆Sirr

Answer: (A)

20. For a packed-bed comprising of uniform-sized spherical particles of diameter Dp, the pressure drop across the bed is given by the Kozeny-Carman equation when the particle Reynolds number (Rep) < 1. Under this condition, minimum fluidization velocity is proportional to Dpn. Which one of the following is the CORRECT value of exponent n?

(A)  2

(B)  −1

(C)  −2

(D)  1

Answer: (A)

21. Match the quantities in Group 1 with their units in Group 2 listed in the table below.

(A)  P-II, Q-I, R-IV, S-III

(B)  P-I, Q-II, R-III, S-IV

(C)  P-III, Q-IV, R-II, S-I

(D)  P-IV, Q-I, R-III, S-II

Answer: (A)

22. A slab of thickness L, as shown in the figure below, has cross-sectional area A and constant thermal conductivity k. T1 and T2 are the temperatures at x = 0 and x = L, respectively. Which one of the following options is the CORRECT expression of the thermal resistance for steady-state one-dimensional heat conduction?

(A)  L/kA

(B)  k/LA

(C) 

(D)  A/Lk

Answer: (A)

23. Spray dryers have many advantages. Which one of the following is NOT an advantage of a typical spray dryer?

(A)  Has short drying time

(B)  Produces hollow spherical particles

(C)  Has high heat efficiency

(D)  Is suitable for heat sensitive materials

Answer: (C)

24. Which one of the following quantities of a flowing fluid is measured using a rotameter?

(A)  Static pressure

(B)  Dynamic pressure

(C)  Volumetric flow rate

(D)  Viscosity

Answer: (C)

25. A liquid surge tank has Fin and Fout as the inlet and outlet flow rates respectively, as shown in the figure below. Fout is proportional to the square root of the liquid level ℎ. The cross-sectional area of the tank is 20 cm2. Density of the liquid is constant everywhere in the system. At steady state, Fin = Fout =10 cm3s−1 and h = 16 cm. The variation of h with Fin is approximated as a first order transfer function. Which one of the following is the CORRECT value of the time constant (in seconds) of this system?

(A)  20

(B)  32

(C)  64

(D)  128

Answer: (C)

26. A packed distillation column, with vapor having an average molecular weight of 45 kg.kmol−1, density of 2 kg.m−3 and a molar flow rate of 0.1 kmol.s−1, has a flooding velocity of 0.15 m.s−1. The column is designed to operate at 60 % of the flooding velocity. Which one of the following is the CORRECT value for the column diameter (in m)?

(A)  5/√π

(B)  5√π

(C)  4π

(D)  10/√π

Answer: (D)

27. An isothermal jacketed continous stirred tank reactor (CSTR) operating at 150°C is shown in the figure below. The cold feed entering the system at 30 oC is preheated to a temperature T (T < 150°C) using a heat exchanger HX1. This preheated feed is further heated to 150°C using the utility heater HX2. The mass flow rate and heat capacity are same for all the process streams, and the overall heat transfer coefficient is independent of temperature. Which one of the following statements is the CORRECT action to take if it is desired to increase the value of T?

(A)  Increase both heat transfer area of HX1 and heat duty of HX2.

(B)  Decrease both heat transfer area of HX1 and heat duty of HX2.

(C)  Increase the heat transfer area of HX1 and decrease the heat duty of HX2.

(D)  Decrease the heat transfer area of HX1 and increase the heat duty of HX2.

Answer: (C)

28. Consider a system where a Carnot engine is operating between a source and a sink. Which of the following statements about this system is/are NOT correct?

(A)  This engine is reversible.

(B)  The engine efficiency is independent of the source and sink temperatures.

(C)  This engine has the highest efficiency among all engines that operate between the same source and sink.

(D)  The total entropy of this system increases at the completion of each cycle of the engine.

Answer: (B, D)

29. For a fully developed turbulent flow of an incompressible Newtonian fluid through a pipe of constant diameter, which of the following statements is/are CORRECT?

(A)  Reynolds stress, averaged over a sufficiently long time, is zero everywhere inside the pipe.

(B)  Reynolds stress at the pipe wall is zero.

(C)  Average velocity of the fluid is half of its center-line velocity.

(D)  Average pressure gradient in the flow direction is constant.

Answer: (B, D)

30. Given that E (in W.m−2) is the total hemispherical emissive power of a surface maintained at a certain temperature, which of the following statements is/are CORRECT?

(A)  E does not depend on the direction of the emission.

(B)  E depends on the viewfactor.

(C)  E depends on the wavelength of the emission.

(D)  E does not depend on the frequency of the emission.

Answer: (-1 to -1)

31. The position x(t) of a particle, at constant ω, is described by the equation

The initial conditions are x(t = 0) = 1 and  The position of the particle at t = (3π/ω) is __________ (in integer).

Answer: (199.5 to 200.5)

32. Burning of methane in a combustor yields carbon monoxide, carbon dioxide, and water vapor. Methane is fed to the combustor at 100 mol.hr−1, of which 50 % reacts. The theoretical oxygen requirement (in mol.hr−1) is ________ (rounded off to one decimal place).

Answer: (1.01 to 1.03)

33. The viscosity of an incompressible Newtonian fluid is measured using a capillary tube of diameter 0.5 mm and length 1.5 m. The fluid flow is laminar, steady and fully developed. For a flow rate of 1 cm3s−1, the pressure drop across the length of the tube is 1 MPa. If the viscosity of the fluid is k × 10−3s, the value of k is ___________ (rounded off to two decimal places).

Answer: (3 to 3)

34. A liquid L containing a dissolved gas S is stripped in a countercurrent operation using a pure carrier gas V. The liquid phase inlet and outlet mole fractions of S are 0.1 and 0.01, respectively. The equilibrium distribution of S between V and L is governed by ye = xe, where ye and xe are the mole fractions of S in V and L, respectively. The molar feed rate of the carrier gas stream is twice as that of the liquid stream. Under dilute solution conditions, the minimum number of ideal stages required is __________ (in integer).

Answer: (1.17 to 1.19)

35. In a binary gas-liquid system, NA,EMD is the molar flux of a gas A for equimolar counter diffusion with a liquid B. NA,UMD is the molar flux of A for steady one-component diffusion through stagnant B. Using the mole fraction of A in the bulk of the gas phase as 0.2 and that at the gas-liquid interface as 0.1 for both the modes of diffusion, the ratio of NA,UMD to NA,EMD is equal to ______ (rounded off to two decimal places).

Answer: (A)

Q.36 – Q.65 Carry TWO marks Each

36. An exhibition was held in a hall on 15 August 2022 between 3 PM and 4 PM during which any person was allowed to enter only once. Visitors who entered before 3:40 PM exited the hall exactly after 20 minutes from their time of entry. Visitors who entered at or after 3:40 PM, exited exactly at 4 PM. The probability distribution of the arrival time of any visitor is uniform between 3 PM and 4 PM. Two persons X and Y entered the exhibition hall independent of each other. Which one of the following values is the probability that their visits to the exhibition overlapped with each other?

(A)  5/9

(B)  4/9

(C)  2/9

(D)  7/9

Answer: (B)

37. Simpson’s one-third rule is used to estimate the definite integral

with an interval length of 0.5. Which one of the following is the CORRECT estimate of I obtained using this rule?

Answer: (B)

38. Match the products in Group 1 with the manufacturing processes in Group 2 listed in the table below.

(A)  P-III, Q-IV, R-I, S-II

(B)  P-III, Q-I, R-IV, S-II

(C)  P-IV, Q-I, R-II, S-III

(D)  P-I, Q-IV, R-II, S-III

Answer: (A)

39. Match the reactions in Group 1 with the catalysts in Group 2 listed in the table below.

(A)  P-III, Q-IV, R-II, S-I

(B)  P-III, Q-IV, R-I, S-II

(C)  P-IV, Q-II, R-I, S-III

(D)  P-IV, Q-III, R-I, S-II

Answer: (B)

40. Water in a container at 290 K is exposed to air containing 3 % CO2 by volume. Air behaves like an ideal gas and is maintained at 100 kPa pressure. The liquid phase comprising of dissolved CO2 in water behaves like an ideal solution. Use Henry’s constant of CO2 dissolved in water at 290 K as 12 MPa. Under equilibrium conditions, which one of the following is the CORRECT value of the mole fraction of CO2 dissolved in water?

(A)  2.9 × 10−4

(B)  0.9 × 10−4

(C)  2.5 × 10−4

(D)  0.5 × 10−4

Answer: (C)

41. The enthalpy (H, in J.mol−1) of a binary liquid system at constant temperature and pressure is given as

H = 40x1 + 60x2 + x1x2(4x1 + 2x2),

where x1 and x2 represent the mole fractions of species 1 and 2 in the liquid, respectively. Which one of the following is the CORRECT value of the partial molar enthalpy of species 1 at infinite dilution, 

(A)  100

(B)  42

(C)  64

(D)  40

Answer: (B)

42. Which one of the following represents the CORRECT effects of concentration polarization in a reverse osmosis process?

(A)  Reduced water flux and reduced solute rejection

(B)  Increased water flux and increased solute rejection

(C)  Reduced water flux and increased solute rejection

(D)  Increased water flux and reduced solute rejection

Answer: (A)

43. CO and H2 participate in a catalytic reaction. The partial pressures (in atm) of the reacting species CO and H2 in the feed stream are pCO and pH2, respectively. While CO undergoes molecular adsorption, H2 adsorbs via dissociative adsorption, that is, as hydrogen atoms. The equilibrium constants (in atm−1) corresponding to adsorption of CO and H2 to the catalyst sites are KCO and KH2, respectively. Total molar concentration of active sites per unit mass of the catalyst is Ct (in mol.(g cat)−1). Both the adsorption steps are at equilibrium. Which one of the following expressions is the CORRECT ratio of the concentration of catalyst sites occupied by CO to that by hydrogen atoms?

Answer: (A)

44. A cascade control strategy is shown in the figure below. The transfer function between the output (y) and the secondary disturbance (d2) is defined as 

Which one of the following is the CORRECT expression for the transfer function Gd2(s)?

Answer: (A)

45. Level (h) in a steam boiler is controlled by manipulating the flow rate (F) of the make-up (fresh) water using a proportional (P) controller. The transfer function between the output and the manipulated input is

The measurement and valve transfer functions are both equal to 1. A process engineer wants to tune the controller so that the closed-loop response gives decaying oscillations under servo mode. Which one of the following is the CORRECT value of the controller gain to be used by the engineer?

(A)  0.25

(B)  2

(C)  4

(D)  6

Answer: (B)

46. Which of the following statements is/are CORRECT?

(A)  Bond number includes surface tension.

(B)  Jakob number includes latent heat.

(C)  Prandtl number includes liquid-vapor density difference.

(D)  Biot number includes gravity.

Answer: (A, B)

47. If a matrix M is defined as  the sum of all the eigenvalues of M3 is equal to ________ (in integer).

Answer: (4160 to 4160)

48. The first derivative of the function  evaluated at r = 1 is ________ (in integer).

Answer: (-24 to -24)

49. Wet air containing 10 mole percent water vapor is dried by continuously passing it through a column of CaCl2 The pellets remove 50 percent of water from wet air entering the column. The mole percent of water vapor in the product stream exiting the column is ___________ (rounded off to two decimal places).

Answer: (5.20 to 5.30)

50. Orsat analysis showing the composition (in mol %, on a dry basis) of a stack gas is given in the table below. The humidity measurement reveals that the mole fraction of H2O in the stack gas is 0.07. The mole fraction of N2 calculated on a wet basis is ________ (rounded off to two decimal places).

Answer: (0.59 to 0.62)

51. A pump draws water (density =1000 kg.m−3) at a steady rate of 10 kg.s−1. The pressures at the suction and discharge sides of the pump are −20 kPa (gauge) and 350 kPa (gauge), respectively. The pipe diameters at the suction and discharge side are 70 mm and 50 mm, respectively. The suction and discharge lines are at the same elevation, and the pump operates at an efficiency of 80 %. Neglecting frictional losses in the system, the power (in kW) required to drive the pump is ______ (rounded off to two decimal places).

Answer: (4.70 to 4.78)

52. A cylindrical tank with a diameter of 500 mm contains water (density =1 g.cm−3) upto a height ℎ. A 5 mm diameter round nozzle, whose center is 1 cm above the base of the tank, has its exit open to the atmosphere as shown in the schematic below. The pressure above the water level in the tank is maintained at 2 bar (absolute). Neglect all frictional and entry/exit losses. Use acceleration due to gravity as 10 m.s−2 and atmospheric pressure as 1 bar. The absolute value of initial  when h = 51 cm is equal to _______ (round off to two decimal places).

Answer: (1.40 to 1.50)

53. A large tank is filled with water (density =1 g.cm−3) upto a height of 5 m. A 100 μm diameter solid spherical particle (density =0.8 g.cm−3) is released at the bottom of the tank. The particle attains its terminal velocity (vt) after traveling to a certain height in the tank. Use acceleration due to gravity as 10 m.s−2 and water viscosity as 10−3s . Neglect wall effects on the particle. If Stokes law is applicable, the absolute value of vt (in mm.s−1) is ____________ (rounded off to two decimal places).

Answer: (1.00 to 1.20)

54. A fluid is flowing steadily under laminar conditions over a thin rectangular plate at temperature Ts as shown in the figure below. The velocity and temperature of the free stream are u∞ and T∞, respectively. When the fluid flow is only in the x- direction, hx is the local heat transfer coefficient. Similarly, when the fluid flow is only in the y-direction, hy is the corresponding local heat transfer coefficient. Use the correlation Nu = 0.332 (Re)1/2 (Pr)1/3 for the local heat transfer coefficient, where, Nu, Re, and Pr, respectively are the appropriate Nusselt, Reynolds and Prandtl numbers. The average heat transfer coefficients are defined as  and  If w = 1 m and l = 4 m, the value of the ratio of   is ________ (in integer).

Answer: (2 to 2)

55. A perfectly insulated, concentric tube countercurrent heat exchanger is used to cool lubricating oil using water as a coolant (see figure below). Oil enters the outer annulus at a mass flow rate of 2 kg.s−1 with a temperature of 100°C and leaves at 40° Water enters the inner tube at a mass flow rate of 1 kg.s−1 with a temperature of 20°C and leaves at 80°C. Use specific heats of oil and water as 2089 J.kg−1K−1 and 4178 J.kg−1K−1, respectively. There is no phase change in both the streams. Under steady-state conditions, the number of transfer units (NTU) is _______ (in integer).

Answer: (3 to 3)

56. Partially saturated air at 1 bar and 50°C is contacted with water in an adiabatic saturator. The air is cooled and humidified to saturation, and exits at 25°C with an absolute humidity of 0.02 kg water per kg dry air. Use latent heat of vaporization of water as 2450 kJ.kg−1, and average specific heat capacity for dry air and water, respectively as 1.01 kJ.kg−1K−1 and 4.18 kJ.kg−1K−1. If the absolute humidity of air entering the adiabatic saturator is H × 10−3 kg water per kg dry air, the value of H is __________ (rounded off to two decimal places).

Answer: (9.10 to 9.50)

57. Distillation of a non-reactive binary mixture with components A and B is carried out in a batch still as shown in the figure below. The initial charge of the mixture in the still is 1 kmol. The initial and final amounts of 𝐴 in the still are 0.1 kmol and 0.01 kmol, respectively. Use a constant relative volatility of 4.5. The mole fraction of 𝐵 remaining in the vessel is _______ (rounded off to three decimal places).

Answer: (0.002 to 0.004 OR 0.981 to 0.983)

58. Fresh catalyst is loaded into a reactor before the start of the following catalytic reaction.

A → products

The catalyst gets deactivated over time. The instantaneous activity a(t), at time t, is defined as the ratio of the rate of reaction −rꞌA(t) (mol.(g cat)−1hr−1) to the rate of reaction with fresh catalyst. Controlled experimental measurements led to an empirical correlation

−rꞌA(t) = −0.5t + 10

where t is in hours. The activity of the catalyst at t = 10 hr is _______ (rounded off to one decimal place).

Answer: (0.5 to 0.5)

59. A unimolecular, irreversible liquid-phase reaction

A → P

was carried out in an ideal batch reactor at temperature T. The rate of the reaction (−rA) measured at different conversions XA is given in the table below. This reaction is also carried out in an ideal continuous stirred tank reactor (CSTR) at the same temperature T with a feed concentration of 1 mol.m−3, under steady-state conditions. For a conversion of 0.8, the space time (in s) of the CSTR is __________ (in integer).

Answer: (16 to 16)

60. An irreversible liquid-phase second-order reaction  with rate constant k = 0.2 liter.mol−1min−1, is carried out in an isothermal non-ideal reactor. A tracer experiment conducted on this reactor resulted in a residence time distribution (𝐸-curve) as shown in the figure below. The areas of the rectangles (i), (ii), and (iii) are equal. Pure A at a concentration of 1.5 mol.liter−1 is fed to the reactor. The segregated model mimics the nonideality of this reactor. The percentage conversion of A at the exit of the reactor is ______ (rounded off to the nearest integer).

Answer: (71 to 73)

61. The outlet concentration CA of a plug flow reactor (PFR) is controlled by manipulating the inlet concentration CA0. The following transfer function describes the dynamics of this PFR.

In the above equation, V = 1 m3, F = 0.1 m3min−1 and k = 0.5 min−1. The measurement and valve transfer functions are both equal to 1. The ultimate gain, defined as the proportional controller gain that produces sustained oscillations, for this system is _______ (rounded off to one decimal place).

Answer: (148.0 to 148.8)

62. The transfer function of a measuring instrument is 

At time t = 0, a step change of +1 unit is introduced in the input of this instrument. The time taken by the instrument to show an increase of 1 unit in its output is _____ (rounded off to two decimal places).

Answer: (6.99 to 7.19)

63. A design engineer needs to purchase a membrane module (M) for a plant. Details about the two available options, M1 and M2, are given in the table below. The overall plant has an expected life of 7 years. If the interest rate is 8 % per annum, compounded annually, the difference in the net present value (NPV) of these two options, in lakhs of rupees, is ______ (rounded off to one decimal place).

Answer: (-4.8 to -4.6 OR 4.6 to 4.8)

64. The purchase cost of a new distillation column is Rs.10 lakhs with an installation factor of 5.8. The cost of the capital is to be annualized over a period of 6 years at a fixed rate of interest of 5 % per annum, compounded annually. The annual cost (in lakhs of rupees) of the installed capital is _______ (rounded off to one decimal place).

Answer: (11.0 to 11.8)

65. Pumps A and B are being considered for purchase in a chemical plant. Cost details for these two pumps are given in the table below. The interest rate is 10 % per annum, compounded annually. For both the pumps to have the same capitalized cost, the salvage value (in Rs.) of pump B should be ______ (rounded off to the nearest integer).

Answer: (2080 to 2300)

GATE Exam 2023 Civil Engineering (CE-2) Question Paper With Answer Key

by

GATE-2023

CE2: Civil Engineering

GA-General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. The line ran _______ the page, right through the centre, and divided the page into two.

(A)  across

(B)  of

(C)  between

(D)  about

Answer: (A)

2. Kind : ________ : : Often : Seldom

(By word meaning)

(A)  Cruel

(B)  Variety

(C)  Type           

(D)  Kindred

Answer: (A)

3. In how many ways can cells in a 3 × 3 grid be shaded, such that each row and each column have exactly one shaded cell? An example of one valid shading is shown.

(A)  2

(B)  9

(C)  3

(D)  6

Answer: (D)

4. There are 4 red, 5 green, and 6 blue balls inside a box. If N number of balls are picked simultaneously, what is the smallest value of N that guarantees there will be at least two balls of the same colour?

One cannot see the colour of the balls until they are picked.

(A)  4

(B)  15

(C)  5

(D)  2

Answer: (A)

5. Consider a circle with its centre at the origin (O), as shown. Two operations are allowed on the circle.

Operation 1: Scale independently along the x and y axes.

Operation 2: Rotation in any direction about the origin.

Which figure among the options can be achieved through a combination of these two operations on the given circle?

Answer: (A)

Q.6 – Q.10 Carry TWO marks Each

6. Elvesland is a country that has peculiar beliefs and practices. They express almost all their emotions by gifting flowers. For instance, if anyone gifts a white flower to someone, then it is always taken to be a declaration of one’s love for that person. In a similar manner, the gifting of a yellow flower to someone often means that one is angry with that person.

Based only on the information provided above, which one of the following sets of statement(s) can be logically inferred with certainty?

(i) In Elvesland, one always declares one’s love by gifting a white flower.

(ii) In Elvesland, all emotions are declared by gifting flowers.

(iii) In Elvesland, sometimes one expresses one’s anger by gifting a flower that is not yellow.

(iv) In Elvesland, sometimes one expresses one’s love by gifting a white flower.

(A)  only (ii)

(B)  (i), (ii) and (iii)

(C)  (i), (iii) and (iv)

(D)  only (iv)

Answer: (D)

7. Three husband-wife pairs are to be seated at a circular table that has six identical chairs. Seating arrangements are defined only by the relative position of the people. How many seating arrangements are possible such that every husband sits next to his wife?

(A)  16

(B)  4

(C)  120

(D)  720

Answer: (A)

8. Based only on the following passage, which one of the options can be inferred with certainty?

When the congregation sang together, Apenyo would also join, though her little screams were not quite audible because of the group singing. But whenever there was a special number, trouble would begin; Apenyo would try singing along, much to the embarrassment of her mother. After two or three such mortifying Sunday evenings, the mother stopped going to church altogether until Apenyo became older and learnt to behave.

At home too, Apenyo never kept quiet; she hummed or made up silly songs to sing by herself, which annoyed her mother at times but most often made her become pensive. She was by now convinced that her daughter had inherited her love of singing from her father who had died unexpectedly away from home.

[Excerpt from These Hills Called Home by Temsula Ao]

(A)  The mother was embarrassed about her daughter’s singing at home.

(B)  The mother’s feelings about her daughter’s singing at home were only of annoyance.

(C)  The mother was not sure if Apenyo had inherited her love of singing from her father.

(D)  When Apenyo hummed at home, her mother tended to become thoughtful.

Answer: (D)

9. If x satisfies the equation  then x is equal to _____.

(A)  1/2

(B)  log16 8

(C)  2/3

(D)  log4 8

Answer: (C)

10. Consider a spherical globe rotating about an axis passing through its poles. There are three points P, Q, and R situated respectively on the equator, the north pole, and midway between the equator and the north pole in the northern hemisphere. Let P, Q, and R move with speeds vP , vQ, and vR, respectively.

Which one of the following options is CORRECT?

(A)  vP < vR < vQ

(B)  vP < vQ < vR

(C)  vP > vR > vQ

(D)  vP = vR ≠ vQ

Answer: (C)

CE2: Civil Engineering

Q.11 – Q.35 Carry ONE mark Each

11. Let ϕ be a scalar field, and u be a vector field. Which of the following identities is true for div (ϕ u)?

(A)  div(ϕu) = ϕdiv(u) + u ∙ grad(ϕ)

(B)  div(ϕu) = ϕdiv(u) + u × grad(ϕ)

(C)  div(ϕu) = ϕgrad(u) + u ∙ grad(ϕ)

(D)  div(ϕu) = ϕgrad(u) + u × grad(ϕ)

Answer: (A)

12. Which of the following probability distribution functions (PDFs) has the mean greater than the median?

(A)  Function 1

(B)  Function 2

(C)  Function 3

(D)  Function 4

Answer: (B)

13. A remote village has exactly 1000 vehicles with sequential registration numbers starting from 1000. Out of the total vehicles, 30% are without pollution clearance certificate. Further, even- and odd-numbered vehicles are operated on even- and odd-numbered dates, respectively.

If 100 vehicles are chosen at random on an even-numbered date, the number of vehicles expected without pollution clearance certificate is ______.

(A)  15

(B)  30

(C)  50

(D)  70

Answer: (B)

14. A circular solid shaft of span L = 5 m is fixed at one end and free at the other end. A torque T = 100 kN.m is applied at the free end. The shear modulus and polar moment of inertia of the section are denoted as G and J, respectively. The torsional rigidity GJ is 50,000 kN.m2/rad. The following are reported for this shaft:

Statement i) The rotation at the free end is 0.01 rad

Statement ii) The torsional strain energy is 1.0 kN.m

With reference to the above statements, which of the following is true?

(A)  Both the statements are correct

(B)  Statement i) is correct, but Statement ii) is wrong

(C)  Statement i) is wrong, but Statement ii) is correct

(D)  Both the statements are wrong

Answer: (B)

15. M20 concrete as per IS 456: 2000 refers to concrete with a design mix having ________

(A)  an average cube strength of 20 MPa

(B)  an average cylinder strength of 20 MPa

(C)  a 5-percentile cube strength of 20 MPa

(D)  a 5-percentile cylinder strength of 20 MPa

Answer: (C)

16. When a simply-supported elastic beam of span L and flexural rigidity EI (E is the modulus of elasticity and I is the moment of inertia of the section) is loaded with a uniformly distributed load w per unit length, the deflection at the mid-span is 

If the load on one half of the span is now removed, the mid-span deflection _______.

(A)  reduces to Δ0/2

(B)  reduces to a value less than Δ0/2

(C)  reduces to a value greater than Δ0/2

(D)  remains unchanged at Δ0

Answer: (A)

17. Muller-Breslau principle is used in analysis of structures for _____________.

(A)  drawing an influence line diagram for any force response in the structure

(B)  writing the virtual work expression to get the equilibrium equation

(C)  superposing the load effects to get the total force response in the structure

(D)  relating the deflection between two points in a member with the curvature diagram in-between

Answer: (A)

18. A standard penetration test (SPT) was carried out at a location by using a manually operated hammer dropping system with 50% efficiency. The recorded SPT value at a particular depth is 28. If an automatic hammer dropping system with 70% efficiency is used at the same location, the recorded SPT value will be _________.

(A)  28

(B)  20

(C)  40

(D)  25

Answer: (B)

19. A vertical sheet pile wall is installed in an anisotropic soil having coefficient of horizontal permeability, kH and coefficient of vertical permeability, kV. In order to draw the flow net for the isotropic condition, the embedment depth of the wall should be scaled by a factor of ______, without changing the horizontal scale.

Answer: (A)

20. Identify the cross-drainage work in the figure.

(A)  Super passage

(B)  Aqueduct

(C)  Siphon aqueduct

(D)  Level crossing

Answer: (A)

21. Which one of the following options provides the correct match of the terms listed in Column-1 and Column-2?

(A)  P-IV, Q-V, R-III

(B)  P-III, Q-IV, R-I

(C)  P-IV, Q-III, R-II

(D)  P-III, Q-I, R-IV

Answer: (A)

22. In the context of Municipal Solid Waste Management, ‘Haul’ in ‘Hauled Container System operated in conventional mode’ includes the _________.

(A)  time spent by the transport truck at the disposal site

(B)  time spent by the transport truck in traveling between a pickup point and the disposal site with a loaded container

(C)  time spent by the transport truck in picking up a loaded container at a pickup point

(D)  time spent by the transport truck in driving from the depot to the first pickup point

Answer: (B)

23. Which of the following is equal to the stopping sight distance?

(A)  (braking distance required to come to stop) + (distance travelled during the perception-reaction time)

(B)  (braking distance required to come to stop) – (distance travelled during the perception-reaction time)

(C)  (braking distance required to come to stop)

(D)  (distance travelled during the perception-reaction time)

Answer: (A)

24. The magnetic bearing of the sun for a location at noon is 183˚ 30ˊ. If the sun is exactly on the geographic meridian at noon, the magnetic declination of the location is _______.

(A)  3˚ 30ʹ W

(B)  3˚ 30ʹ E

(C)  93˚ 30ʹ W

(D)  93˚ 30ʹ E

Answer: (A)

25. For the matrix

which of the following statements is/are TRUE?

(A)  [A]{x} = {b} has a unique solution

(B)  [A]{x} = {b} does not have a unique solution

(C)  [A] has three linearly independent eigenvectors

(D)  [A] is a positive definite matrix

Answer: (B, C)

26. In the frame shown in the figure (not to scale), all four members (AB, BC, CD, and AD) have the same length and same constant flexural rigidity. All the joints A, B, C, and D are rigid joints. The midpoints of AB, BC, CD, and AD, are denoted by E, F, G, and H, respectively. The frame is in unstable equilibrium under the shown forces of magnitude 𝑃 acting at E and G. Which of the following statements is/are TRUE?

(A)  Shear forces at H and F are zero

(B)  Horizontal displacements at H and F are zero

(C)  Vertical displacements at H and F are zero

(D)  Slopes at E, F, G, and H are zero

Answer: (A, B, D)

27. With regard to the shear design of RCC beams, which of the following statements is/are TRUE?

(A)  Excessive shear reinforcement can lead to compression failure in concrete

(B)  Beams without shear reinforcement, even if adequately designed for flexure, can have brittle failure

(C)  The main (longitudinal) reinforcement plays no role in the shear resistance of beam

(D)  As per IS456:2000, the nominal shear stress in the beams of varying depth depends on both the design shear force as well as the design bending moment

Answer: (A, B, D)

28. The reason(s) of the nonuniform elastic settlement profile below a flexible footing, resting on a cohesionless soil while subjected to uniform loading, is/are:

(A)  Variation of friction angle along the width of the footing

(B)  Variation of soil stiffness along the width of the footing

(C)  Variation of friction angle along the depth of the footing

(D)  Variation of soil stiffness along the depth of the footing

Answer: (B)

29. Which of the following is/are NOT active disinfectant(s) in water treatment?

(A)  •OH (hydroxyl radical)

(B)  O3 (ozone)

(C)  OCl− (hypochlorite ion)

(D)  Cl− (chloride ion)

Answer: (D)

30. As per the Indian Roads Congress guidelines (IRC 86: 2018), extra widening depends on which of the following parameters?

(A)  Horizontal curve radius

(B)  Superelevation

(C)  Number of lanes

(D)  Longitudinal gradient

Answer: (A, C)

31. The steady-state temperature distribution in a square plate ABCD is governed by the 2-dimensional Laplace equation. The side AB is kept at a temperature of 100°C and the other three sides are kept at a temperature of 0 °C. Ignoring the effect of discontinuities in the boundary conditions at the corners, the steady-state temperature at the center of the plate is obtained as T0°C. Due to symmetry, the steady-state temperature at the center will be same (T0°C), when any one side of the square is kept at a temperature of 100°C and the remaining three sides are kept at a temperature of 0°C. Using the principle of superposition, the value of T0 is ____________ (rounded off to two decimal places).

Answer: (24.90 to 25.10)

32. An unconfined compression strength test was conducted on a cohesive soil. The test specimen failed at an axial stress of 76 kPa. The undrained cohesion (in kPa, in integer) of the soil is _________.

Answer: (38 to 38)

33. The pressure in a pipe at X is to be measured by an open manometer as shown in figure. Fluid A is oil with a specific gravity of 0.8 and Fluid B is mercury with a specific gravity of 13.6. The absolute pressure at X is __________ kN/m2 (round off to one decimal place).

[Assume density of water as 1000 kg/m3 and acceleration due to gravity as 9.81 m/s2 and atmospheric pressure as 101.3 kN/m2]

Answer: (140.0 to 141.0)

34. For the elevation and temperature data given in the table, the existing lapse rate in the environment is _______ ℃/100 m (round off to two decimal places).

Answer: (0.84 to 0.85)

35. If the size of the ground area is 6 km × 3 km and the corresponding photo size in the aerial photograph is 30 cm × 15 cm, then the scale of the photograph is 1 : ________ (in integer).

Answer: (20000 to 20000)

Q.36 – Q.65 Carry TWO marks Each

36. The solution of the differential equation is expressed as y = C1e2.5x + C2eα x + C3eβx, where C1, C2, C3, α, and β are constants, with α and β being distinct and not equal to 2.5. Which of the following options is correct for the values of α and β ?

(A)  1 and 2

(B)  −1 and −2

(C)  2 and 3

(D)  −2 and −3

Answer: (A)

37. Two vectors  and  belong to the null space of a 4×4 matrix of rank 2. Which one of the following vectors also belongs to the null space?

Answer: (A)

38. Cholesky decomposition is carried out on the following square matrix [A].

Let lij and aij be the (i, j)th elements of matrices [L] and [A], respectively. If the element l22 of the decomposed lower triangular matrix [L] is 1.968, what is the value (rounded off to the nearest integer) of the element a22?

(A)  5

(B)  7

(C)  9

(D)  11

Answer: (B)

39. In a two-dimensional stress analysis, the state of stress at a point is shown in the figure. The values of length of PQ, QR, and RP are 4, 3, and 5 units, respectively. The principal stresses are _________. (round off to one decimal place)

(A)  σx = 26.7 MPa, σy = 172.5 MPa

(B)  σx = 54.0 MPa, σy = 128.5 MPa

(C)  σx = 67.5 MPa, σy = 213.3 MPa

(D)  σx = 16.0 MPa, σy = 138.5 MPa

Answer: (C)

40. Two plates are connected by fillet welds of size 10 mm and subjected to tension, as shown in the figure. The thickness of each plate is 12 mm. The yield stress and the ultimate stress of steel under tension are 250 MPa and 410 MPa, respectively. The welding is done in the workshop (partial safety factor, γmw = 1.25). As per the Limit State Method of IS 800: 2007, what is the minimum length (in mm, rounded off to the nearest higher multiple of 5 mm) required of each weld to transmit a factored force P equal to 275 kN?

(A)  100

(B)  105

(C)  110

(D)  115 

Answer: (B)

41. In the given figure, Point O indicates the stress point of a soil element at initial non-hydrostatic stress condition. For the stress path (OP), which of the following loading conditions is correct?

(A)  σv is increasing and σh is constant

(B)  σv is constant and σh is increasing 

(C)  σv is increasing and σh is decreasing

(D)  σv is decreasing and σh is increasing

Answer: (A)

42. The figure shows a vertical retaining wall with backfill consisting of cohesive-frictional soil and a failure plane developed due to passive earth pressure. The forces acting on the failure wedge are: P as the reaction force between the wall and the soil, R as the reaction force on the failure plane, C as the cohesive force along the failure plane and W as the weight of the failure wedge. Assuming that there is no adhesion between the wall and the wedge, identify the most appropriate force polygon for the wedge.

Answer: (C)

43. A compound symmetrical open channel section as shown in the figure has a maximum of ________ critical depth(s).

(A)  3

(B)  2

(C)  1

(D)  0

Answer: (A)

44. The critical flow condition in a channel is given by ________.

Note: α – kinetic energy correction factor; Q – discharge; Ac – cross-sectional area of flow at critical flow condition; Tc – top width of flow at critical flow condition; g – acceleration due to gravity]

Answer: (A)

45. Match the following air pollutants with the most appropriate adverse health effects:

(A)  (P) – (II), (Q) – (I), (R) – (IV), (S) – (III)

(B)  (P) – (IV), (Q) – (I), (R) – (III), (S) – (II)

(C)  (P) – (III), (Q) – (I), (R) – (II), (S) – (IV)

(D)  (P) – (IV), (Q) – (I), (R) – (II), (S) – (III)

Answer: (D)

46. A delivery agent is at a location R. To deliver the order, she is instructed to travel to location P along straight-line paths of RC, CA, AB and BP of 5 km each. The direction of each path is given in the table below as whole circle bearings. Assume that the latitude (L) and departure (D) of R is (0, 0) km. What is the latitude and departure of P (in km, rounded off to one decimal place)?

(A)  L = 2.5; D = 5.0

(B)  L = 0.0; D = 5.0

(C)  L = 5.0; D = 2.5

(D)  L = 0.0; D = 0.0

Answer: (B)

47. Which of the following statements is/are TRUE?

(A)  The thickness of a turbulent boundary layer on a flat plate kept parallel to the flow direction is proportional to the square root of the distance from the leading edge

(B)  If the streamlines and equipotential lines of a source are interchanged with each other, the resulting flow will be a sink

(C)  For a curved surface immersed in a stationary liquid, the vertical component of the force on the curved surface is equal to the weight of the liquid above it

(D)  For flow through circular pipes, the momentum correction factor for laminar flow is larger than that for turbulent flow

Answer: (C, D)

48. In the context of water and wastewater treatments, the correct statements are:

(A)  particulate matter may shield microorganisms during disinfection

(B)  ammonia decreases chlorine demand

(C)  phosphorous stimulates algal and aquatic growth

(D)  calcium and magnesium increase hardness and total dissolved solids

Answer: (A, C, D)

49. Which of the following statements is/are TRUE for the aerobic composting of sewage sludge?

(A)  Bulking agent is added during the composting process to reduce the porosity of the solid mixture

(B)  Leachate can be generated during composting

(C)  Actinomycetes are involved in the process

(D)  In-vessel composting systems cannot be operated in the plug-flow mode

Answer: (B, C)

50. The figure presents the time-space diagram for when the traffic on a highway is suddenly stopped for a certain time and then released. Which of the following statements are true?

(A)  Speed is higher in Region R than in Region P

(B)  Volume is lower in Region Q than in Region P

(C)  Volume is higher in Region R than in Region P

(D)  Density is higher in Region Q than in Region R

Answer: (B, C, D)

51. Consider the Marshall method of mix design for bituminous mix. With the increase in bitumen content, which of the following statements is/are TRUE?

(A)  the Stability decreases initially and then increases

(B)  the Flow increases monotonically

(C)  the air voids (VA) increases initially and then decreases

(D)  the voids filled with bitumen (VFB) increases monotonically

Answer: (B, D)

52. A 5 cm long metal rod AB was initially at a uniform temperature of T0 °C. Thereafter, temperature at both the ends are maintained at 0 °C. Neglecting the heat transfer from the lateral surface of the rod, the heat transfer in the rod is governed by the one-dimensional diffusion equation  where D is the thermal diffusivity of the metal, given as 1.0 cm2/s.

The temperature distribution in the rod is obtained as  where x is in cm measured from A to B with x = 0 at A, t is in s, Cn are constants in °C, T is in °C, and β is in s−1.

The value of β (in s−1, rounded off to three decimal places) is ___________.

Answer: (0.394 to 0.396)

53. A beam is subjected to a system of coplanar forces as shown in the figure. The magnitude of vertical reaction at Support P is ________N (round off to one decimal place).

Answer: (195.0 to 200.0)

54. For the frame shown in the figure (not to scale), all members (AB, BC, CD, GB, and CH) have the same length, L and flexural rigidity, EI. The joints at B and C are rigid joints, and the supports A and D are fixed supports. Beams GB and CH carry uniformly distributed loads of w per unit length. The magnitude of the moment reaction at A is wL2/k. What is the value of k (in integer)? _________

Answer: (6 to 6)

55. Consider the singly reinforced section of a cantilever concrete beam under bending, as shown in the figure (M25 grade concrete, Fe415 grade steel). The stress block parameters for the section at ultimate limit state, as per IS 456: 2000 notations, are given. The ultimate moment of resistance for the section by the Limit State Method is __________ kN.m (round off to one decimal place).

Note: Here, As is the total area of tension steel bars, b is the width of the section, d is the effective depth of the bars, fck is the characteristic compressive cube strength of concrete, fy is the yield stress of steel, and xu is the depth of neutral axis.]

Answer: (295.0 to 305.0)

56. A 2D thin plate with modulus of elasticity, E = 1.0 N/m2, and Poisson’s ratio, μ = 0.5, is in plane stress condition. The displacement field in the plate is given by u = Cx2y and 𝑣=0, where u and v are displacements (in m) along the X and Y directions, respectively, and C is a constant (in m−2). The distances x and y along X and Y, respectively, are in m. The stress in the X direction is σXX = 40 xy N/m2, and the shear stress is τXY = αx2 N/m2. What is the value of 𝛼 (in N/m4, in integer)? ___________

Answer: (5 to 5)

57. An idealised frame supports a load as shown in the figure. The horizontal component of the force transferred from the horizontal member PQ to the vertical member RS at P is __________ N (round off to one decimal place).

Answer: (17.5 to 18.5)

58. A square footing is to be designed to carry a column load of 500 kN which is resting on a soil stratum having the following average properties: bulk unit weight = 19 kN/m3; angle of internal friction = 0° and cohesion = 25 kPa. Considering the depth of the footing as 1 m and adopting Meyerhof’s bearing capacity theory with a factor of safety of 3, the width of the footing (in m) is _____________ (round off to one decimal place)

[Assume the applicable shape and depth factor values as unity; ground water level at greater depth.]

Answer: (3.0 to 3.5)

59. A circular pile of diameter 0.6 m and length 8 m was constructed in a cohesive soil stratum having the following properties: bulk unit weight = 19 kN/m3; angle of internal friction = 0° and cohesion = 25 kPa.

The allowable load the pile can carry with a factor of safety of 3 is __________ kN (round off to one decimal place).

[Adopt: Adhesion factor, α = 1.0 and Bearing capacity factor, Nc = 9.0]

Answer: (145.0 to 149.0)

60. For the flow setup shown in the figure (not to scale), the hydraulic conductivities of the two soil samples, Soil 1 and Soil 2, are 10 mm/s and 1 mm/s, respectively. Assume the unit weight of water as 10 kN/m3 and ignore the velocity head. At steady state, what is the total head (in m, rounded off to two decimal places) at any point located at the junction of the two samples? ____________

Answer: (4.50 to 4.60)

61. A consolidated drained (CD) triaxial test was carried out on a sand sample with the known effective shear strength parameters, cʹ = 0 and ϕʹ = 30°. In the test, prior to the failure, when the sample was undergoing axial compression under constant cell pressure, the drainage valve was accidentally closed. At the failure, 360 kPa deviatoric stress was recorded along with 70 kPa pore water pressure. If the test is repeated without such error, and no back pressure is applied in either of the tests, what is the deviatoric stress (in kPa, in integer) at the failure? ________

Answer: (500 to 500)

62. The annual rainfall recorded at these gauges in a particular year are given below.

Using the Thiessen polygon method, what is the average rainfall (in mm, rounded off to two decimal places) over the catchment in that year? ___________

Answer: (912.28 to 912.82)

63. The cross-section of a small river is sub-divided into seven segments of width 1.5 m each. The average depth, and velocity at different depths were measured during a field campaign at the middle of each segment width. The discharge computed by the velocity area method for the given data is ___________ m3/s (round off to one decimal place).

Answer: (8.4 to 8.6)

64. The theoretical aerobic oxidation of biomass (C5H7O2N) is given below:

C5H7O2N + 5O2 → 5CO2 + NH3 + 2H2O

The biochemical oxidation of biomass is assumed as a first-order reaction with a rate constant of 0.23/d at 20ºC (logarithm to base e). Neglecting the second-stage oxygen demand from its biochemical oxidation, the ratio of BOD5 at 20ºC to total organic carbon (TOC) of biomass is ________ (round off to two decimal places).

[Consider the atomic weights of C, H, O and N as 12 g/mol, 1 g/mol, 16 g/mol and 14 g/mol, respectively]

Answer: (1.80 to 2.00)

65. A system of seven river segments is shown in the schematic diagram. The Ri’s, Qi’s, and Ci’s (i = 1 to 7) are the river segments, their corresponding flow rates, and concentrations of a conservative pollutant, respectively. Assume complete mixing at the intersections, no additional water loss or gain in the system, and steady state condition. Given: Q1 = 5 m3/s ; Q2 = 15 m3/s ; Q4 = 3 m3/s ; Q6 = 8 m3/s ; C1 = 8 kg/m3 ; C2 = 12 kg/m3 ; C6 = 10 kg/m3. What is the steady state concentration (in kg/m3, rounded off to two decimal place) of the pollutant in the river segment 7 ? ___________

Answer: (10.58 to 10.78)

GATE Exam 2023 Civil Engineering (CE-1) Question Paper With Answer Key

by

GATE-2023

CE1: Civil Engineering

GA-General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. “I have not yet decided what I will do this evening; I ______ visit a friend.”

(A)  mite

(B)  would

(C)  might

(D)  didn’t

Answer: (C)

2. Eject : Insert : : Advance : _______

(By word meaning)

(A)  Advent

(B)  Progress

(C)  Retreat

(D)  Loan

Answer: (C)

3. In the given figure, PQRSTV is a regular hexagon with each side of length 5 cm. A circle is drawn with its centre at V such that it passes through P. What is the area (in cm2) of the shaded region? (The diagram is representative)

(A)  25π/3

(B)  20π/3

(C)  6π

(D)  7π

Answer: (A)

4. A duck named Donald Duck says “All ducks always lie.”

Based only on the information above, which one of the following statements can be logically inferred with certainty?

(A)  Donald Duck always lies.

(B)  Donald Duck always tells the truth.

(C)  Donald Duck’s statement is true.

(D)  Donald Duck’s statement is false.

Answer: (D)

5. A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is a mirror image of the other part about that line.

The figure below consists of 20 unit squares arranged as shown. In addition to the given black squares, upto 5 more may be coloured black. Which one among the following options depicts the minimum number of boxes that must be coloured black to achieve two lines of symmetry? (The figure is representative)

(A)  d

(B)  c, d, i

(C)  c, i

(D)  c, d, i, f, g

Answer: (B)

Q.6 – Q.10 Carry TWO marks Each

6. Based only on the truth of the statement ‘Some humans are intelligent’, which one of the following options can be logically inferred with certainty?

(A)  No human is intelligent.

(B)  All humans are intelligent.

(C)  Some non-humans are intelligent.

(D)  Some intelligent beings are humans.

Answer: (D)

7. Which one of the options can be inferred about the mean, median, and mode for the given probability distribution (i.e. probability mass function), P(x), of a variable x?

(A)  mean = median ≠ mode

(B)  mean = median = mode

(C)  mean ≠ median = mode

(D)  mean ≠ mode = median

Answer: (A)

8. The James Webb telescope, recently launched in space, is giving humankind unprecedented access to the depths of time by imaging very old stars formed almost 13 billion years ago. Astrophysicists and cosmologists believe that this odyssey in space may even shed light on the existence of dark matter. Dark matter is supposed to interact only via the gravitational interaction and not through the electromagnetic-, the weak- or the strong-interaction. This may justify the epithet “dark” in dark matter.

Based on the above paragraph, which one of the following statements is FALSE?

(A)  No other telescope has captured images of stars older than those captured by the James Webb telescope.

(B)  People other than astrophysicists and cosmologists may also believe in the existence of dark matter.

(C)  The James Webb telescope could be of use in the research on dark matter.

(D)  If dark matter was known to interact via the strong-interaction, then the epithet “dark” would be justified.

Answer: (D)

9. Let a = 30! , b = 50! , and c = 100! . Consider the following numbers:

loga c, logc a, logb a, loga b

Which one of the following inequalities is CORRECT?

(A)  logc a < logb a < loga b < loga c

(B)  logc a < loga b < logb a < logb c

(C)  logc a < logb a < loga c < loga b         

(D)  logb a < logc a < loga b < loga c

Answer: (A)

10. A square of side length 4 cm is given. The boundary of the shaded region is defined by one semi-circle on the top and two circular arcs at the bottom, each of radius 2 cm, as shown.

The area of the shaded region is _______ cm2.

(A)  8

(B)  4

(C)  12

(D)  10

Answer: (A)

CE1: Civil Engineering

Q.11 – Q.35 Carry ONE mark Each

11. For the integral

which of the following statements is TRUE?

(A)  I = 0

(B)  I = 2

(C)  I = −2

(D)  The integral does not converge

Answer: (D)

12. A hanger is made of two bars of different sizes. Each bar has a square cross-section. The hanger is loaded by three-point loads in the mid vertical plane as shown in the figure. Ignore the self-weight of the hanger. What is the maximum tensile stress in N/mm2 anywhere in the hanger without considering stress concentration effects?

(A)  15.0

(B)  25.0

(C)  35.0

(D)  45.0

Answer: (B)

  1. Creep of concrete under compression is defined as the _________.

(A)  increase in the magnitude of strain under constant stress

(B)  increase in the magnitude of stress under constant strain

(C)  decrease in the magnitude of strain under constant stress

(D)  decrease in the magnitude of stress under constant strain

Answer: (A)

14. A singly reinforced concrete beam of balanced section is made of M20 grade concrete and Fe415 grade steel bars. The magnitudes of the maximum compressive strain in concrete and the tensile strain in the bars at ultimate state under flexure, as per IS 456: 2000 are _______, respectively. (round off to four decimal places)

(A)  0.0035 and 0.0038

(B)  0.0020 and 0.0018

(C)  0.0035 and 0.0041

(D)  0.0020 and 0.0031

Answer: (A)

15. In cement concrete mix design, with the increase in water-cement ratio, which one of the following statements is TRUE?

(A)  Compressive strength decreases but workability increases

(B)  Compressive strength increases but workability decreases

(C)  Both compressive strength and workability decrease

(D)  Both compressive strength and workability increase

Answer: (A)

16. The specific gravity of a soil is 2.60. The soil is at 50% degree of saturation with a water content of 15%. The void ratio of the soil is _______.

(A)  0.35

(B)  0.78

(C)  0.87

(D)  1.28

Answer: (B)

17. A group of 9 friction piles are arranged in a square grid maintaining equal spacing in all directions. Each pile is of diameter 300 mm and length 7 m. Assume that the soil is cohesionless with effective friction angle ϕ′=32°. What is the center-to-center spacing of the piles (in m) for the pile group efficiency of 60%?

(A)  0.582

(B)  0.486

(C)  0.391

(D)  0.677

Answer: (MTA)

18. A possible slope failure is shown in the figure. Three soil samples are taken from different locations (I, II and III) of the potential failure plane. Which is the most appropriate shear strength test for each of the sample to identify the failure mechanism? Identify the correct combination from the following options:

P: Triaxial compression test

Q: Triaxial extension test

R: Direct shear or shear box test

S: Vane shear test

(A)  I-Q, II-R, III-P

(B)  I-R, II-P, III-Q

(C)  I-S, II-Q, III-R

(D)  I-P, II-R, III-Q

Answer: (A)

19. When a supercritical stream enters a mild-sloped (M) channel section, the type of flow profile would become _______.

(A)  M1

(B)  M2

(C)  M3

(D)  M1 and M2

Answer: (C)

20. Which one of the following statements is TRUE for Greenhouse Gas (GHG) in the atmosphere?

(A)  GHG absorbs the incoming short wavelength solar radiation to the earth surface, and allows the long wavelength radiation coming from the earth surface to pass through

(B)  GHG allows the incoming long wavelength solar radiation to pass through to the earth surface, and absorbs the short wavelength radiation coming from the earth surface

(C)  GHG allows the incoming long wavelength solar radiation to pass through to the earth surface, and allows the short wavelength radiation coming from the earth surface to pass through

(D)  GHG allows the incoming short wavelength solar radiation to pass through to the earth surface, and absorbs the long wavelength radiation coming from the earth surface

Answer: (D)

21. G1 and G2 are the slopes of the approach and departure grades of a vertical curve, respectively.

Given |G1| < |G2| and |G1| ≠ |G2| ≠ 0

Statement 1: +G1 followed by +G2 results in a sag vertical curve.

Statement 2: −G1 followed by −G2 results in a sag vertical curve.

Statement 3: +G1 followed by −G2 results in a crest vertical curve.

Which option amongst the following is true?

(A)  Statement 1 and Statement 3 are correct; Statement 2 is wrong

(B)  Statement 1 and Statement 2 are correct; Statement 3 is wrong

(C)  Statement 1 is correct; Statement 2 and Statement 3 are wrong

(D)  Statement 2 is correct; Statement 1 and Statement 3 are wrong

Answer: (A)

22. The direct and reversed zenith angles observed by a theodolite are 56o 00′ 00″ and 303o 00′ 00″, respectively. What is the vertical collimation correction?

(A)  +1° 00′ 00″

(B)  −1° 00′ 00″

(C)  −0° 30′ 00″

(D)  +0° 30′ 00″

Answer: (D)

23. A student is scanning his 10 inch × 10 inch certificate at 600 dots per inch (dpi) to convert it to raster. What is the percentage reduction in number of pixels if the same certificate is scanned at 300 dpi?

(A)  62

(B)  88

(C)  75

(D)  50

Answer: (C)

24. If M is an arbitrary real n × n matrix, then which of the following matrices will have non-negative eigenvalues?

(A)  M2

(B)  MMT

(C)  MTM

(D)  (MT)2

Answer: (B, C)

25. The following function is defined over the interval [−L, L]:

f(x) = px4 + qx5.

If it is expressed as a Fourier series,

which options amongst the following are true?

(A)  an, n = 1, 2 …, ∞ depend on p

(B)  an, n = 1, 2 …, ∞ depend on q

(C)  bn, n = 1, 2 …, ∞ depend on p

(D)  bn, n = 1, 2 …, ∞ depend on q

Answer: (B, C)

26. Consider the following three structures:

Which of the following statements is/are TRUE?

(A)  Structure I is unstable

(B)  Structure II is unstable

(C)  Structure III is unstable

(D)  All three structures are stable

Answer: (A, B, C)

27. Identify the waterborne diseases caused by viral pathogens:

(A)  Acute anterior poliomyelitis

(B)  Cholera

(C)  Infectious hepatitis

(D)  Typhoid fever

Answer: (A, C)

28. Which of the following statements is/are TRUE for the Refuse-Derived Fuel (RDF) in the context of Municipal Solid Waste (MSW) management?

(A)  Higher Heating Value (HHV) of the unprocessed MSW is higher than the HHV of RDF processed from the same MSW

(B)  RDF can be made in the powdered form

(C)  Inorganic fraction of MSW is mostly converted to RDF

(D)  RDF cannot be used in conjunction with oil

Answer: (B)

29. The probabilities of occurrences of two independent events A and B are 0.5 and 0.8, respectively. What is the probability of occurrence of at least A or B (rounded off to one decimal place)? ______

Answer: (0.9 to 0.9)

30. In the differential equation  α is a positive constant. If y = 1.0 at x = 0.0, and y = 0.8 at x = 1.0, the value of α is _______ (rounded off to three decimal places).

Answer: (0.445 to 0.447)

31. Consider the fillet-welded lap joint shown in the figure (not to scale). The length of the weld shown is the effective length. The welded surfaces meet at right angle. The weld size is 8 mm, and the permissible stress in the weld is 120 MPa. What is the safe load P (in kN, rounded off to one decimal place) that can be transmitted by this welded joint? ____________

Answer: (134.0 to 136.0)

32. A drained direct shear test was carried out on a sandy soil. Under a normal stress of 50 kPa, the test specimen failed at a shear stress of 35 kPa. The angle of internal friction of the sample is ________ degree (round off to the nearest integer).

Answer: (35 to 35)

33. A canal supplies water to an area growing wheat over 100 hectares. The duration between the first and last watering is 120 days, and the total depth of water required by the crop is 35 cm. The most intense watering is required over a period of 30 days and requires a total depth of water equal to 12 cm. Assuming precipitation to be negligible and neglecting all losses, the minimum discharge (in m3/s, rounded off to three decimal places) in the canal to satisfy the crop requirement is ___________.

Answer: (0.045 to 0.047)

34. The ordinates of a one-hour unit hydrograph for a catchment are given below:

Using the principle of superposition, a D-hour unit hydrograph for the catchment was derived from this one-hour unit hydrograph. The ordinates of the D-hour unit hydrograph were obtained as 3 m3/s at t = 1 hour and 10 m3/s at t = 2 hour. The value of D (in integer) is _____________.

Answer: (3 to 3)

35. For a horizontal curve, the radius of a circular curve is obtained as 300 m with the design speed as 15 m/s. If the allowable jerk is 0.75 m/s3, what is the minimum length (in m, in integer) of the transition curve? _________

Answer: (15 to 15 OR 26 to 27)

Q.36 – Q.65 Carry TWO marks Each

36. A function f(x), that is smooth and convex-shaped between interval (x­l, xu) is shown in the figure. This function is observed at odd number of regularly spaced If the area under the function is computed numerically, then ________

(A)  the numerical value of the area obtained using the trapezoidal rule will be less than the actual

(B)  the numerical value of the area obtained using the trapezoidal rule will be more than the actual

(C)  the numerical value of the area obtained using the trapezoidal rule will be exactly equal to the actual

(D)  with the given details, the numerical value of area cannot be obtained using trapezoidal rule

Answer: (A)

37. Consider a doubly reinforced RCC beam with the option of using either Fe250 plain bars or Fe500 deformed bars in the compression zone. The modulus of elasticity of steel is 2 × 105 N/mm2. As per IS456:2000, in which type(s) of the bars, the stress in the compression steel (fsc) can reach the design strength (0.87 fy) at the limit state of collapse?

(A)  Fe250 plain bars only

(B)  Fe500 deformed bars only

(C)  Both Fe250 plain bars and Fe500 deformed bars

(D)  Neither Fe250 plain bars nor Fe500 deformed bars

Answer: (A)

38. Consider the horizontal axis passing through the centroid of the steel beam cross-section shown in the figure. What is the shape factor (rounded off to one decimal place) for the cross-section?

(A)  1.5

(B)  1.7

(C)  1.3

(D)  2.0

Answer: (B)

39. Consider the pin-jointed truss shown in the figure (not to scale). All members have the same axial rigidity, AE. Members QR, RS, and ST have the same length L. Angles QBT, RCT, SDT are all 90°. Angles BQT, CRT, DST are all 30°. The joint T carries a vertical load P. The vertical deflection of joint T is  What is the value of k?

(A)  1.5

(B)  4.5

(C)  3.0

(D)  9.0

Answer: (B)

40. With reference to the compaction test conducted on soils, which of the following is INCORRECT?

(A)  Peak point of the compaction curve gives the maximum dry unit weight and optimum moisture content

(B)  With increase in the compaction effort, the maximum dry unit weight increases

(C)  With increase in the compaction effort, the optimum moisture content decreases

(D)  Compaction curve crosses the zero-air-voids curve

Answer: (D)

41. Consider that a force P is acting on the surface of a half-space (Boussinesq’s problem). The expression for the vertical stress (σz) at any point (r, z), within the half-space is given as,

where, r is the radial distance, and z is the depth with downward direction taken as positive. At any given r, there is a variation of σz along z, and at a specific z, the value of σz will be maximum. What is the locus of the maximum σz?

Answer: (A)

42. A square footing of size 2.5 m × 2.5 m is placed 1.0 m below the ground surface on a cohesionless homogeneous soil stratum. Considering that the groundwater table is located at the base of the footing, the unit weights of soil above and below the groundwater table are 18 kN/m3 and 20 kN/m3, respectively, and the bearing capacity factor Nq is 58, the net ultimate bearing capacity of the soil is estimated as 1706 kPa (unit weight of water = 10 kN/m3).

Earlier, a plate load test was carried out with a circular plate of 30 cm diameter in the same foundation pit during a dry season, when the water table was located beyond the plate influence zone. Using Terzaghi’s bearing capacity formulation, what is the ultimate bearing capacity (in kPa) of the plate?

(A)  110.16

(B)  61.20

(C)  204.00

(D)  163.20

Answer: (A)

43. A very wide rectangular channel carries a discharge (Q) of 70 m3/s per meter width. Its bed slope changes from 0.0001 to 0.0009 at a point P, as shown in the figure (not to scale). The Manning’s roughness coefficient of the channel is 0.01. What water surface profile(s) exist(s) near the point P?

(A)  M2 and S2

(B)  M2 only

(C)  S2 only

(D)  S2 and hydraulic jump

Answer: (A)

44. A jet of water having a velocity of 20 m/s strikes a series of plates fixed radially on a wheel revolving in the same direction as the jet at 15 m/s. What is the percentage efficiency of the plates? (round off to one decimal place)

(A)  37.5

(B)  66.7

(C)  50.0

(D)  88.9

Answer: (A)

45. In the following table, identify the correct set of associations between the entries in Column-1 and Column-2.

(A)  P-II, Q-I, S-III

(B)  Q-III, R-II, S-IV

(C)  P-IV, R-I, S-II

(D)  P-III, Q-I, R-IV

Answer: (D)

46. A plot of speed-density relationship (linear) of two roads (Road A and Road B) is shown in the figure.

If the capacity of Road A is CA and the capacity of Road B is CB, what is CA/CB?

(A)  kA/kB

(B)  uA/uB

(C)  kAuA/kBuB

(D)  kAuB/kBuA

Answer: (A, B, D)

47. For the matrix

which of the following statements is/are TRUE?

(A)  The eigenvalues of [A]T are same as the eigenvalues of [A]

(B)  The eigenvalues of [A]−1 are the reciprocals of the eigenvalues of [A]

(C)  The eigenvectors of [A]T are same as the eigenvectors of [A]

(D)  The eigenvectors of [A]−1 are same as the eigenvectors of [A]

Answer: (A, B, D)

48. For the function f(x) = ex|sin x|; x ∈ ℝ, which of the following statements is/are TRUE?

(A)  The function is continuous at all x

(B)  The function is differentiable at all x

(C)  The function is periodic

(D)  The function is bounded

Answer: (A)

49. Consider the beam shown in the figure (not to scale), on a hinge support at end A and a roller support at end B. The beam has a constant flexural rigidity, and is subjected to the external moments of magnitude 𝑀 at one-third spans, as shown in the figure. Which of the following statements is/are TRUE?

(A)  Support reactions are zero

(B)  Shear force is zero everywhere

(C)  Bending moment is zero everywhere

(D)  Deflection is zero everywhere

Answer: (A, B)

50. Which of the following statements is/are TRUE in relation to the Maximum Mixing Depth (or Height) ‘Dmax’ in the atmosphere?

(A)  Dmax is always equal to the height of the layer of unstable air

(B)  Ventilation coefficient depends on Dmax

(C)  A smaller Dmax will have a smaller air pollution potential if other meteorological conditions remain same

(D)  Vertical dispersion of pollutants occurs up to Dmax

Answer: (B, D)

51. Which of the following options match the test reporting conventions with the given material tests in the table?

(A)  (P) – (VI); (Q) – (I); (R) – (II); (S) – (VII)

(B)  (P) – (VI); (Q) – (III); (R) – (IV); (S) – (V)

(C)  (P) – (VI); (Q) – (I); (R) – (II); (S) – (V)

(D)  (P) – (VI); (Q) – (III); (R) – (IV); (S) – (VII)

Answer: (B, C)

52. The differential equation,

is solved by employing a backward difference scheme within the finite difference framework. The value of u at the (n – 1)th time-step, for some n, is 1.75. The corresponding time (t) is 3.14 s. Each time step is 0.01 s long. Then, the value of (un – un – 1) is __________ (round off to three decimal places).

Answer: (-0.152 to -0.149)

53. The infinitesimal element shown in the figure (not to scale) represents the state of stress at a point in a body. What is the magnitude of the maximum principal stress (in N/mm2, in integer) at the point? _________

Answer: (7 to 7)

54. An idealised bridge truss is shown in the figure. The force in Member U2L3 is _________ kN (round off to one decimal place).

Answer: (13.5 to 14.5)

55. The cross-section of a girder is shown in the figure (not to scale). The section is symmetric about a vertical axis (Y-Y). The moment of inertia of the section about the horizontal axis (X-X) passing through the centroid is ________ cm4 (round off to nearest integer).

Answer: (464000 to 472000)

56. A soil having the average properties, bulk unit weight = 19 kN/m3; angle of internal friction = 25° and cohesion = 15 kPa, is being formed on a rock slope existing at an inclination of 35° with the horizontal. The critical height (in m) of the soil formation up to which it would be stable without any failure is _________ (round off to one decimal place).

[Assume the soil is being formed parallel to the rock bedding plane and there is no ground water effect.]

Answer: (4.8 to 5.2)

57. A smooth vertical retaining wall supporting layered soils is shown in figure. According to Rankine’s earth pressure theory, the lateral active earth pressure acting at the base of the wall is ________ kPa (round off to one decimal place).

Answer: (34.0 to 37.0)

58. A vertical trench is excavated in a clayey soil deposit having a surcharge load of 30 kPa. A fluid of unit weight 12 kN/m3 is poured in the trench to prevent collapse as the excavation proceeds. Assume that the fluid is not seeping through the soil deposit. If the undrained cohesion of the clay deposit is 20 kPa and saturated unit weight is 18 kN/m3, what is the maximum depth of unsupported excavation (in m, rounded off to two decimal places)? ________

Answer: (3.30 to 3.35)

59. A 12-hour storm occurs over a catchment and results in a direct runoff depth of 100 mm. The time-distribution of the rainfall intensity is shown in the figure (not to scale). The ϕ-index of the storm is (in mm, rounded off to two decimal places) __________.

Answer: (MTA)

60. A hydraulic jump occurs in a 1.0 m wide horizontal, frictionless, rectangular channel, with a pre-jump depth of 0.2 m and a post-jump depth of 1.0 m. The value of g may be taken as 10 m/s2. The values of the specific force at the pre-jump and post-jump sections are same and are equal to (in m3, rounded off to two decimal places) _____________.

Answer: (0.60 to 0.64)

61. In Horton’s equation fitted to the infiltration data for a soil, the initial infiltration capacity is 10 mm/h; final infiltration capacity is 5 mm/h; and the exponential decay constant is 0.5 /h. Assuming that the infiltration takes place at capacity rates, the total infiltration depth (in mm) from a uniform storm of duration 12 h __________. (round off to one decimal place)

Answer: (69.7 to 70.1)

62. The composition and energy content of a representative solid waste sample are given in the table. If the moisture content of the waste is 26%, the energy content of the solid waste on dry-weight basis is __________ MJ/kg (round off to one decimal place).

Answer: (18.0 to 19.0)

63. A flocculator tank has a volume of 2800 m3. The temperature of water in the tank is 15°C, and the average velocity gradient maintained in the tank is 100/s. The temperature of water is reduced to 5°C, but all other operating conditions including the power input are maintained as the same. The decrease in the average velocity gradient (in %) due to the reduction in water temperature is _______ (round off to nearest integer).

[Consider dynamic viscosity of water at 15°C and 5°C as 1.139 × 10−3 N-s/m2 and 1.518 × 10−3 N-s/m2, respectively]

Answer: (12 to 15)

64. The wastewater inflow to an activated sludge plant is 0.5 m3/s, and the plant is to be operated with a food to microorganism ratio of 0.2 mg/mg-d. The concentration of influent biodegradable organic matter of the wastewater to the plant (after primary settling) is 150 mg/L, and the mixed liquor volatile suspended solids concentration to be maintained in the plant is 2000 mg/L. Assuming that complete removal of biodegradable organic matter in the tank, the volume of aeration tank (in m3, in integer) required for the plant is _________.

Answer: (16200 to 16200)

65. Trigonometric levelling was carried out from two stations P and Q to find the reduced level (R. L.) of the top of hillock, as shown in the table. The distance between Stations P and Q is 55 m. Assume Stations P and Q, and the hillock are in the same vertical plane. The R. L. of the top of the hillock (in m) is ________ (round off to three decimal places).

Answer: (137.500 to 137.730)

GATE Exam 2023 Biotechnology (BT) Question Paper With Answer Key

by

GATE-2023

BT: Biotechnology

General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. “You are delaying the completion of the task. Send _______ contributions at the earliest.”

(A)  you are

(B)  your

(C)  you’re

(D)  yore

Answer: (B)

2. References : ______ : : Guidelines : Implement

(By word meaning)

(A)  Sight

(B)  Site

(C)  Cite

(D)  Plagiarise      

Answer: (C)

3. In the given figure, PQRS is a parallelogram with PS = 7 cm, PT = 4 cm and PV = 5 cm. What is the length of RS in cm? (The diagram is representative.)

(A)  20/7

(B)  28/5

(C)  9/2

(D)  35/4

Answer: (B)

4. In 2022, June Huh was awarded the Fields medal, which is the highest prize in Mathematics.

When he was younger, he was also a poet. He did not win any medals in the International Mathematics Olympiads. He dropped out of college.

Based only on the above information, which one of the following statements can be logically inferred with certainty?

(A)  Every Fields medalist has won a medal in an International Mathematics Olympiad.

(B)  Everyone who has dropped out of college has won the Fields medal.

(C)  All Fields medalists are part-time poets.

(D)  Some Fields medalists have dropped out of college.

Answer: (D)

5. A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is a mirror image of the other part about that line.

The given figure consists of 16 unit squares arranged as shown. In addition to the three black squares, what is the minimum number of squares that must be coloured black, such that both PQ and MN form lines of symmetry? (The figure is representative)

(A)  3

(B)  4

(C)  5

(D)  6

Answer: (C)

Q.6 – Q.10 Carry TWO marks Each

6. Human beings are one among many creatures that inhabit an imagined world. In this imagined world, some creatures are cruel. If in this imagined world, it is given that the statement “Some human beings are not cruel creatures” is FALSE, then which of the following set of statement(s) can be logically inferred with certainty?

(i) All human beings are cruel creatures.

(ii) Some human beings are cruel creatures.

(iii) Some creatures that are cruel are human beings.

(iv) No human beings are cruel creatures.

(A)  only (i)

(B)  only (iii) and (iv)

(C)  only (i) and (ii)

(D)  (i), (ii) and (iii)

Answer: (D)

7. To construct a wall, sand and cement are mixed in the ratio of 3:1. The cost of sand and that of cement are in the ratio of 1:2.

If the total cost of sand and cement to construct the wall is 1000 rupees, then what is the cost (in rupees) of cement used?

(A)  400

(B)  600

(C)  800

(D)  200

Answer: (A)

8. The World Bank has declared that it does not plan to offer new financing to Sri Lanka, which is battling its worst economic crisis in decades, until the country has an adequate macroeconomic policy framework in place. In a statement, the World Bank said Sri Lanka needed to adopt structural reforms that focus on economic stabilisation and tackle the root causes of its crisis. The latter has starved it of foreign exchange and led to shortages of food, fuel, and medicines. The bank is repurposing resources under existing loans to help alleviate shortages of essential items such as medicine, cooking gas, fertiliser, meals for children, and cash for vulnerable households.

Based only on the above passage, which one of the following statements can be inferred with certainty?

(A)  According to the World Bank, the root cause of Sri Lanka’s economic crisis is that it does not have enough foreign exchange.

(B)  The World Bank has stated that it will advise the Sri Lankan government about how to tackle the root causes of its economic crisis.

(C)  According to the World Bank, Sri Lanka does not yet have an adequate macroeconomic policy framework.

(D)  The World Bank has stated that it will provide Sri Lanka with additional funds for essentials such as food, fuel, and medicines.

Answer: (C)

9. The coefficient of x4 in the polynomial (x − 1)3 (x − 2)3 is equal to _______.

(A)  33

(B)  −3

(C)  30

(D)  21

Answer: (A)

10. Which one of the following shapes can be used to tile (completely cover by repeating) a flat plane, extending to infinity in all directions, without leaving any empty spaces in between them? The copies of the shape used to tile are identical and are not allowed to overlap.

(A)  circle

(B)  regular octagon

(C)  regular pentagon

(D)  rhombus

Answer: (D)

BT: Biotechnology

Q.11 – Q.35 Carry ONE mark Each

11. Eukaryotic transcription is carried out by

(A)  DNA-dependent RNA polymerase

(B)  DNA-dependent DNA polymerase

(C)  RNA-dependent DNA polymerase

(D)  RNA-dependent RNA polymerase

Answer: (A)

12. Acetylcholine released by the parasympathetic nerves has which one of the following functions in the heart pacemaker cells?

(A)  It binds to GPCR and activates G protein to slow the heart rate

(B)  It stimulates GABA-activated ion-channel coupled receptor to increase the heart rate

(C)  It binds to GPCR and inhibits G protein to slow the heart rate

(D)  It inhibits GABA-activated ion-channel coupled receptor to increase the heart rate

Answer: (A)

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

Assertion [a]: In multicellular organisms, cells of different lineages have different gene expression profiles.

Reason [r]: Alternative splicing is the only mechanism to generate protein diversity.

(A)  Both [a] and [r] are false

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

(C)  Both [a] and [r] are true but [r] is not the correct reason for [a]

(D)  [a] is true but [r] is false

Answer: (D)

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

Assertion [a]: Chromosome mutations can change the structure of chromosomes.

Reason [r]: All chromosome mutations arise due to nondisjunction of chromosomes during mitosis or meiosis.

(A)  Both [a] and [r] are false

(B)  [a] is true but [r] is false

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

(D)  Both [a] and [r] are true but [r] is not the correct reason for [a]

Answer: (B)

15. C-value paradox refers to

(A)  the lack of correlation between genome size and genetic complexity of an organism

(B)  the presence of genetic sequences that propagate themselves within a genome

(C)  the coexistence of multiple alleles at a genetic locus

(D)  the concept that two or more genes may have the same function

Answer: (A)

16. Which one of the following drugs is NOT an immune checkpoint inhibitor?

(A)  Ipilimumab

(B)  Pembrolizumab

(C)  Nivolumab

(D)  Trastuzumab

Answer: (D)

17. Dendritic cells are involved in cross-presentation of antigens. Which of the following protein(s) is(are) required for cross-presentation?

(P) Basic leucine zipper ATF-like transcription factor 3 (BATF3)

(Q) Membrane associated ring-CH-type finger 1 (MARCH-1)

(R) Solute carrier family 10 member 1 (SLC10A1)

(S) Class II-associated invariant chain peptide (CLIP)

(A)  P only

(B)  P and R only

(C)  P, Q and R only

(D)  S only

Answer: (A)

18. Which one of the following is required for the development of B-cells in the bone marrow?

(A)  Stromal cells

(B)  Dendritic cells

(C)  Kupffer cells

(D)  NK cells

Answer: (A)

19. Which one of the following statements is TRUE about leghemoglobin?

(A)  It binds oxygen to protect nitrogenase

(B)  It binds hemoglobin to protect oxygenase

(C)  It binds oxygen to protect hydrogenase

(D)  It binds oxygen to protect oxygenase

Answer: (A)

20. The correct sequence of events during bacteriophage infection of a bacterial cell is

(A)  landing → attachment → tail contraction → penetration and unplugging → DNA ejection

(B)  attachment → landing → penetration and unplugging → tail contraction → DNA ejection

(C)  landing → tail contraction → attachment → DNA ejection → penetration and unplugging

(D)  attachment → tail contraction → landing → penetration and unplugging → DNA ejection

Answer: (A)

21. Intracellular proteins are targeted for proteolytic degradation in proteasomes upon conjugation with

(A)  ubiquitin

(B)  integrin

(C)  peptidase

(D)  calreticulin

Answer: (A)

22. In ELISA, which of the following enzymes are conjugated to antibodies for detection of the analyte?

(P) Alkaline phosphatase

(Q) Trypsinase

(R) Horseradish peroxidase

(S) Amylase

(A)  P and R

(B)  P and Q

(C)  Q and S

(D)  R and S

Answer: (A)

23. In hybridoma technology, which one of the following enzymes is absent in the myeloma cells that are used for monoclonal antibody production?

(A)  Hypoxanthine-guanine phosphoribosyltransferase

(B)  Alanine aminotransferase

(C)  Triose phosphate isomerase

(D)  Glycosyltransferase

Answer: (A)

24. Which of the following methods are used for detection of DNA and RNA, respectively?

(A)  Southern and Northern blotting

(B)  Southern and Western blotting

(C)  Northern and Southern blotting

(D)  Northern and Western blotting

Answer: (A)

25. Match the types of RNA in Group I with their corresponding function in Group II.

(A)  P-3, Q-4, R-2, S-1

(B)  P-3, Q-4, R-1, S-2

(C)  P-4, Q-3, R-2, S-1

(D)  P-2, Q-1, R-4, S-3

Answer: (A)

26. Which one of the following programs is used for finding distantly related (or remote) protein homologs?

(A)  BLASTN

(B)  BLASTX

(C)  PSI-BLAST

(D)  TBLASTX

Answer: (C)

27. Which one of the following is used for global alignment of two protein sequences?

(A)  Chou-Fasman method

(B)  Garnier-Osguthorpe-Robson (GOR) method

(C)  Needleman-Wunsch algorithm

(D)  Smith-Waterman algorithm

Answer: (C)

28. Which one of the following methods CANNOT be used to determine the secondary structure content of a protein?

(A)  Circular dichroism spectroscopy

(B)  Fourier transform infrared spectroscopy

(C)  Mass spectrometry

(D)  X-ray crystallography

Answer: (C)

29. Which one of the following plant growth regulators facilitate adventitious root formation?

(A)  Auxin

(B)  Zeatin

(C)  Dihydrozeatin

(D)  Kinetin

Answer: (A)

30. Fabry disease in humans is a X-linked disease. The probability (in percentage) for a phenotypically normal father and a carrier mother to have a son with Fabry disease is __________.

Answer: (25 to 25)

31. The value of  is _________.

Answer: (6 to 6)

32. A series (S) is given as

S = 1 + 3 + 5 + 7 + 9 + ……

The sum of the first 50 terms of S is __________.

Answer: (2500 to 2500)

33. Two fair six-sided dice are thrown. The probability of getting 12 as the product of

the numbers on the dice (rounded off to two decimal places) is __________.

Answer: (0.10 to 0.12)

34. If 73x = 216, the value of 7−x (rounded off to three decimal places) is ____________.

Answer: (0.166 to 0.168)

35. The distance between the two points of intersection of x2 + y = 7 and x + y = 7 (rounded off to two decimal places) is ____________.

Answer: (1.40 to 1.42)

Q.36 – Q.65 Carry TWO marks Each

36. Match the immune tolerance mechanisms in Group I with their respective outcomes in Group II.

(A)  P-3, Q-1, R-4, S-2

(B)  P-4, Q-3, R-1, S-2

(C)  P-3, Q-4, R-2, S-1

(D)  P-3, Q-2, R-4, S-1

Answer: (A)

37. Match the type of bacteria in Group I with their respective growth properties in Group II.

(A)  P-3, Q-4, R-1, S-2

(B)  P-2, Q-3, R-4, S-1

(C)  P-3, Q-1, R-2, S-4

(D)  P-4, Q-3, R-1, S-2

Answer: (A)

38. Match the virus in Group I with the type of genome it contains in Group II.

(A)  P-3, Q-4, R-1, S-2

(B)  P-2, Q-1, R-4, S-3

(C)  P-4, Q-3, R-2, S-1

(D)  P-1, Q-4, R-2, S-3

Answer: (A)

39. The event(s) that lead(s) to inactivation of tumor suppressor genes in cancer cells is(are)

(A)  gene amplification

(B)  promoter methylation

(C)  loss of heterozygosity

(D)  histone acetylation

Answer: (B, C)

40. Methylation of CpG islands near the promoter of a gene can inhibit transcription by

(A)  preventing RNA polymerase binding

(B)  facilitating repressor binding

(C)  facilitating heterochromatin formation

(D)  inducing euchromatin formation

Answer: (A, B, C)

41. Which of the following statement(s) is(are) TRUE about induced pluripotent stem cells?

(A)  They can self-renew

(B)  They require specific signals to maintain their stemness

(C)  They cannot be genetically manipulated

(D)  They can form organoids in vitro

Answer: (A, B, D)

42. Which of the following statement(s) is(are) TRUE about fluoroquinolone drugs?

(A)  They contain quinolone ring(s)

(B)  They inhibit RNA polymerase

(C)  They bind to bacterial topoisomerase

(D)  They bind to 23S rRNA within the 50S ribosome subunit

Answer: (A, C)

43. Which of the following is(are) plant protoplast fusogenic agent(s)?

(A)  Sodium nitrate

(B)  Polyvinyl alcohol

(C)  Polyethylene glycol

(D)  Bromoxynil

Answer: (A, B, C)

44. Direct DNA transfer method(s) used for plant genetic engineering is(are)

(A)  microparticle bombardment

(B)  electroporation

(C)  polyethylene glycol treatment

(D)  Agrobacterium-mediated transformation

Answer: (A, B, C)

45. Which of the following vector(s) is(are) used to clone a DNA fragment of size 220 kb?

(A)  Bacterial artificial chromosome

(B)  Yeast artificial chromosome

(C)  Cosmids

(D)  pUC19 plasmid

Answer: (A, B)

46. The following reaction represents biomass synthesis from hexadecane

C16H34 + 12.5O2 + 2.13NH3 → 10.6CH1.66O0.27N0.27 + 5.37CO2 + 11.4H2O

where CH1.66O0.27N0.27 represents the biomass. The value of respiratory quotient (rounded off to two decimal places) is __________.

Answer: (0.41 to 0.44)

47. Temperature of a reaction with an activation energy value of 15kcal .mol−1 is increased from 300 K to 310 K. If the value of the ideal gas constant (R) is 1.9872 cal.mol−1.K−1, the ratio of the reaction rate constants (k310/k300) (rounded off to two decimal places) is _______.

Answer: (2.24 to 2.26)

48. E. coli is cultivated in a chemostat operated at a dilution rate of 0.2 h−1 values of biomass yield due to oxygen consumption and the steady state biomass concentration are 0.2g.g−1 and 10 g.L−1, respectively. The oxygen transfer rate (in g.L−1.h−1) is ________.

Answer: (10 to 10)

49. Aqueous two-phase extraction is used to recover α-amylase from a solution. A polypropylene glycol-dextran mixture is added and the solution separates into upper and lower phases. The partition coefficient is 4.0 and the ratio of upper to lower phase volume is 5.0. The enzyme recovery or yield (in percentage, rounded off to the nearest integer) is __________.

Answer: (94 to 96)

50. E. coli cultivated at 298 K uptakes an uncharged compound (A) by passive diffusion. The intracellular and extracellular concentrations of A are 0.001 M and 0.1 M, respectively. If the value of the ideal gas constant R is 1.9872 cal.mol−1.K−1, the free-energy change (in kcal.mol−1) for this passive diffusion of A (rounded off to two decimal places) is _______.

Answer: (-2.74 to -2.71)

51. If there are three unrooted trees for four protein sequences, the number of rooted

trees for the same number of sequences is ___________.

Answer: (15 to 15)

52. The number of different possible ways of forming five intramolecular disulfide

bonds with ten cysteine residues of a protein is __________.

Answer: (945 to 945)

53. The following schematic diagram shows a chemostat with cell recycle

where F0 and Fr are the volumetric flow rates (in L.h−1) of feed and recycle streams, respectively. X1, X0 and X are the cell concentrations (in g.L−1) in the reactor, recycle-stream and product-stream, respectively. If  and X1 is 7.3 g.L−1, the value of X (in g.L−1, rounded off to one decimal place) is _________.

Answer: (4.6 to 4.9)

54. An enzyme (E) catalyzes the biochemical reaction A → B with kcat equal to 500 s−1. If the initial reaction velocity (V0) is 10 μs−1 at the total enzyme concentration [Et] of 30 nM and substrate concentration [A] of 40 μM, the value of Km(in μM) is _________.

Answer: (20 to 20)

55. DNA sample collected from an unidentified bacterial species (Y) contains 13% of adenine. The G+C content (in percentage) of Y is _________.

Answer: (74 to 74)

56. If 1000 bp of a double-helical DNA weighs 1 × 10−18 gm and distance between two bp is 0.34 nm , the total amount of DNA (in mg, rounded off to one decimal place) required to stretch from Earth to Moon (assuming the distance between Earth and Moon to be 3,74,000 km) is __________.

Answer: (1.0 to 1.2)

57. A protein has three identical sites arranged at the vertices of an equilateral triangle. If one site is filled with a dye (donor), the measured quantum yield (ϕD) is 0.5. Filling one site with a donor dye and a second site with an acceptor dye results in ϕD of 0.25. The measured ϕD of one site filled with donor and the other two sites filled with acceptor dye (rounded off to three decimal places) is __________.

Answer: (0.165 to 0.168)

58. If  the value of |A4 + 3A2 – 5A + 6I| is _______.

Answer: (10551 to 10551)

59. If  the value of fʹ(x) at x = 0 is _________.

Answer: (-2 to -2)

60. If f(2) = 5 and (f(x))(f(x + 1)) = 3 for all real values of x, the value of f(10) is __________.

Answer: (5 to 5)

61. Ten playing cards numbered 1, 2, 3, …., 10 are placed face down on a table. One card is drawn at random, its number recorded, and then replaced face down. A card is drawn again at random. The probability that the number on the second draw is greater than the number on the first draw (rounded off to two decimal places) is __________.

Answer: (0.45 to 0.45)

62. The values of the consistency index ‘ K ’ and the flow behavior index ‘ n ’ of a dilatant fluid are 0.415 (in CGS units) and 1.23, respectively. The value of the apparent viscosity (in g.cm−1.s−1) of this fluid at a shear rate of 60 s−1 (rounded off to the nearest integer) is ________.

Answer: (1 to 1)

63. An evaporator is insulated using glass wool material of 0.15 m thickness. The inner most surface and the outer surface of the insulation are at 700°C and 80°C, respectively. The mean thermal conductivity of the glass wool under these conditions is 0.29 W.m−1.K−1. The rate of heat loss (in W) through 1.2 m2 of the evaporator wall surface (rounded off to the nearest integer) is _________.

Answer: (1437 to 1439)

64. A proportional controller is used to control the temperature of an autoclave from 60°C to 130° If the proportional band setting of the controller is 25%, the proportional gain value is _________.

Answer: (4 to 4)

65. A dNTP master-mix is prepared by combining 40 μL of each 20 mM dNTP stock (dATP, dCTP, dGTP and dTTP). 4 μL of this dNTP master-mix is added to a PCR mix and the final volume is adjusted to 50 μ The concentration (in μM) of total dNTPs in the PCR mix is _________.

Answer: (1600 to 1600)

GATE Exam 2023 Biomedical Engineering (BM) Question Paper With Answer Key

by

GATE-2023

BM: Biomedical Engineering

General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. “I cannot support this proposal. My ________ will not permit it.”

(A)  conscious

(B)  consensus

(C)  conscience

(D)  consent

Answer: (C)

2. Courts : _______ : : Parliament : Legislature

(By word meaning)

(A)  Judiciary

(B)  Executive

(C)  Governmental

(D)  Legal

Answer: (A)

3. What is the smallest number with distinct digits whose digits add up to 45?

(A)  123555789

(B)  123457869

(C)  123456789

(D)  99999

Answer: (C)

4. In a class of 100 students,

(i) there are 30 students who neither like romantic movies nor comedy movies,

(ii) the number of students who like romantic movies is twice the number of students who like comedy movies, and

(iii) the number of students who like both romantic movies and comedy movies is 20.

How many students in the class like romantic movies?

(A)  40

(B)  20

(C)  60

(D)  30

Answer: (C)

5. How many rectangles are present in the given figure?

(A)  8

(B)  9

(C)  10

(D)  12

Answer: (C)

Q.6 – Q.10 Carry TWO marks Each

6. Forestland is a planet inhabited by different kinds of creatures. Among other creatures, it is populated by animals all of whom are ferocious. There are also creatures that have claws, and some that do not. All creatures that have claws are ferocious.

Based only on the information provided above, which one of the following options can be logically inferred with certainty?

(A)  All creatures with claws are animals.

(B)  Some creatures with claws are non-ferocious.

(C)  Some non-ferocious creatures have claws.

(D)  Some ferocious creatures are creatures with claws.

Answer: (D)

7. Which one of the following options represents the given graph?

(A)  f(x) = x22−|x|

(B)  f(x) = x 2−|x|

(C)  f(x) = |x|2−x

(D)  f(x) = x 2−x

Answer: (A)

8. Which one of the following options can be inferred from the given passage alone?

When I was a kid, I was partial to stories about other worlds and interplanetary travel. I used to imagine that I could just gaze off into space and be whisked to another planet.

[Excerpt from The Truth about Stories by T. King]

(A)  It is a child’s description of what he or she likes.

(B)  It is an adult’s memory of what he or she liked as a child.

(C)  The child in the passage read stories about interplanetary travel only in parts.

(D)  It teaches us that stories are good for children.

Answer: (B)

9. Out of 1000 individuals in a town, 100 unidentified individuals are covid positive. Due to lack of adequate covid-testing kits, the health authorities of the town devised a strategy to identify these covid-positive individuals. The strategy is to:

(i) Collect saliva samples from all 1000 individuals and randomly group them into sets of 5.

(ii) Mix the samples within each set and test the mixed sample for covid.

(iii) If the test done in (ii) gives a negative result, then declare all the 5 individuals to be covid negative.

(iv) If the test done in (ii) gives a positive result, then all the 5 individuals are separately tested for covid.

Given this strategy, no more than _______ testing kits will be required to identify all the 100 covid positive individuals irrespective of how they are grouped.

(A)  700

(B)  600

(C)  800

(D)  1000

Answer: (A)

10. A 100 cm × 32 cm rectangular sheet is folded 5 times. Each time the sheet is folded, the long edge aligns with its opposite side. Eventually, the folded sheet is a rectangle of dimensions 100 cm×1 cm.

The total number of creases visible when the sheet is unfolded is _______.

(A)  32

(B)  5

(C)  31

(D)  63

Answer: (C)

BM: Biomedical Engineering

Q.11 – Q.35 Carry ONE mark Each

11. What is the magnitude of the difference between the mean and the median of the dataset {1, 2, 3, 4, 6, 8}?

(A)  0

(B)  1

(C)  0.5

(D)  0.25

Answer: (C)

12. For a Binomial random variable X, E(X) and Var(X) are the expectation and variance, respectively. Which one of the following statements CANNOT be true?

(A)  E(X) = 20 and Var(X) = 16

(B)  E(X) = 6 and Var(X) = 5.4

(C)  E(X) = 10 and Var(X) = 15

(D)  E(X) = 64 and Var(X) = 12.8

Answer: (C)

13. is a 2 × 2 matrix. Which one of the following statements is TRUE?

(A)  Q is equal to its transpose.

(B)  Q is equal to its inverse.

(C)  Q is of full rank.

(D)  Q has linearly dependent columns.

Answer: (C)

14. Which one of the following vectors is an eigenvector corresponding to the eigenvalue = 1 for the matrix A?

Answer: (D)

15. For the function f(x, y) = ex cos (y), what is the value of  (x = 0, y = π/2)?

(A)  0

(B)  1

(C)  −1

(D)  eπ/2

Answer: (C)

16. For the circuit given below, choose the angular frequency ω0 (in rad/s) at which the voltage across the capacitor has maximum amplitude?

(A)  1000

(B)  100

(C)  1

(D)  0

Answer: (D)

17. A finite impulse response (FIR) filter has only two non-zero samples in its impulse response h[n], namely h[0] = h[1] = 1. The Discrete Time Fourier Transform (DTFT) of h[n] equals H(ejω), as a function of the normalized angular frequency ω. For the range |ω| ≤ π, |H(ejω)| is equal to ________.

(A)  2|cos(ω)|

(B)  2|sin(ω)|

(C)  2|cos(ω/2)|

(D)  2|sin(ω/2)|

Answer: (C)

18. An 8 bit successive approximation Analog to Digital Converter (ADC) has a clock frequency of 1 MHz. Assume that the start conversion and end conversion signals occupy one clock cycle each. Among the following options, what is the maximum frequency that this ADC can sample without aliasing?

(A)  0.9 kHz

(B)  9.9 kHz

(C)  49.9 kHz

(D)  99.9 kHz

Answer: (C)

19. In the following circuit with an ideal operational amplifier, the capacitance of the parallel plate capacitor C is given by the expression C = (ϵA/x), where ϵ is the dielectric constant of the medium between the capacitor plates, and A is the cross-sectional area. In the above relation, x is the separation between the two parallel plates, given by x = x0 + kt, where t is time; x0 and k are positive non-zero constants. If the input voltage vi is constant, then the output voltage v0 is given by _______.

(A)  RviCk/x

(B)  RviC/kx

(C)  vik/RCx

(D)  0

Answer: (A)

20. Which one of the following techniques makes use of Korotkoff sounds?

(A)  Sphygmomanometry

(B)  Audiometry

(C)  Spirometry

(D)  Tonometry

Answer: (A)

21. The pulmonary artery and pulmonary vein ________.

(A)  carry deoxygenated blood and oxygenated blood, respectively

(B)  carry oxygenated blood and deoxygenated blood, respectively

(C)  both carry oxygenated blood

(D)  both carry deoxygenated blood

Answer: (A)

22. Which one of the following bridges CANNOT be used for measuring inductance?

(A)  Schering Bridge

(B)  Maxwell Wien Bridge

(C)  Hay Bridge

(D)  Series Owen Bridge

Answer: (A)

23. A polychromatic beam of X-Rays has an energy spectrum as shown in Figure P below. Which of the following graphs (in the options A to D) depicts the energy spectrum after passing through a human body? In each figure, the horizontal axis represents Energy in keV and the vertical axis represents Relative X-ray Intensity.

Answer: (B)

24. M, L and T correspond to dimensions representing mass, length and time, respectively. What is the dimension of viscosity?

(A)  M1L−2T−1

(B)  M1L−1T−1

(C)  M1L−1T1

(D)  M1L−2T−2

Answer: (B)

25. Choose the option that has the biomaterials arranged in order of decreasing tensile strength.

(PMMA : poly-methyl-methacrylate)

(A)  Human compact bone > PMMA bone cement > Polymer foams > Graphite-epoxy

(B)  Human compact bone > Graphite-epoxy > PMMA bone cement > Polymer foams

(C)  Graphite-epoxy > Human compact bone > PMMA bone cement > Polymer foams

(D)  PMMA bone cement > Human compact bone > Polymer foams > Graphite-epoxy

Answer: (C)

26. A causal, discrete time system is described by the difference equation

y[n] = 0.5y[n – 1] + x[n], for all n,

where 𝑦[𝑛] denotes the output sequence and x[n] denotes the input sequence. Which of the following statements is/are TRUE?

(A)  The system has an impulse response described by 0.5n u[−n] where u[n] is the unit step sequence.

(B)  The system is stable in the bounded input, bounded output sense.

(C)  The system has an infinite number of non-zero samples in its impulse response.

(D)  The system has a finite number of non-zero samples in its impulse response.

Answer: (B, C)

27. Which of the following constituents is/are NOT normally found in serum obtained from human blood?

(A)  Platelets

(B)  Albumin

(C)  Glucose

(D)  Fibrinogen

Answer: (A, D)

28. Q, R, S are Boolean variables and ⊕ is the XOR operator. Select the CORRECT option(s).

(A)  (Q ⊕ R) ⊕ S = Q ⊕ (R ⊕ S)

(B)  (Q ⊕ R) ⊕ S = 0 when any two of the Boolean variables (Q, R, S) are 0 and the third variable is 1

(C)  (Q ⊕ R) ⊕ S = 1 when Q = R = S = 1

(D)  ((Q ⊕ R) ⊕(R ⊕ S) )⊕(Q ⊕ S) = 1

Answer: (A, C)

29. In the human pancreas, which cell types secrete insulin and glucagon?

(A)  Alpha cells and delta cells, respectively

(B)  Beta cells and delta cells, respectively

(C)  Alpha cells and beta cells, respectively

(D)  Beta cells and alpha cells, respectively

Answer: (D)

30. In the following circuit, the switch S is open for t < 0 and closed for t ≥ 0. What is the steady state voltage (in Volts) across the capacitor when the switch is closed? (Round off the answer to one decimal place.)

Answer: (6.9 to 7.1)

31. For a tissue with Young’s modulus of 3.6 kPa and Poisson’s ratio of 0.2, what is the value of its shear modulus (in kPa)? (Round off the answer to one decimal place.)

Answer: (1.5 to 1.5)

32. In the circuit shown below, the amplitudes of the voltage across the resistor and the capacitor are equal. What is the value of the angular frequency ω0 (in rad/s)? (Round off the answer to one decimal place.)

Answer: (9.9 to 10.1)

33. A continuous time, band limited signal x(t) has its Fourier transform described by:

The signal is uniformly sampled at a sampling rate of 600 Hz. The Fourier transform of the sampled signal is XS(f). What is the value of   (Round off the answer to one decimal place.)

Answer: (1.9 to 2.1)

34. At time t, the cardiac dipole is oriented at – 45° (minus forty five degrees) to the horizontal axis. The magnitude of the dipole is 3 mV. Assuming Einthoven frontal plane configuration, what is the magnitude (in mV) of the electrical signal in lead II? (Round off the answer to two decimal places.)

Answer: (2.8 to 3.0)

35. A 5 MHz ultrasound transducer is being used to measure the velocity of blood. When the transducer is placed at an angle of 45° to the direction of blood flow, a frequency shift of 200 Hz is observed in the echo. Assume that the velocity of sound is 1500 m/s. What is the velocity (in cm/s) of the blood flow? (Round off the answer to one decimal place.)

Answer: (4.1 to 4.3)

Q.36 – Q.65 Carry TWO marks Each

36. The time-dependent growth of a bacterial population is governed by the equation

where x is the population size at time t. The initial population size is x0 = 100 at t = 0. As t → ∞, the population size of bacteria asymptotically approaches __________.

(A)  150

(B)  200

(C)  300

(D)  500

Answer: (B)

37. A 20 mV DC signal has been superimposed with a 10 mV RMS band-limited Gaussian noise with a flat spectrum upto 5 kHz. If an integrating voltmeter is used to measure this DC signal, what is the minimum averaging time (in seconds) required to yield a 99 % accurate result with 95 % certainty?

(A)  0.1

(B)  1.0

(C)  5.0

(D)  10.0

Answer: (B)

38. In the circuit below, the two DC voltage sources have voltages of value V1 and V2. The expression for the power dissipated in the 60 kΩ resistor is proportional to _________.

(A)  (V1 + V2)2

(B)  (3V1 + V2)2

(C)  (2V1 + V2)2

(D)  (V1 + 2V2)2

Answer: (C)

39. The Laplace transform of x­1(t) = e−t u(t) is X1(s), where u(t) is the unit step function. The Laplace transform of x2(t) = etu(−t) is X2(s). Which one of the following statements is TRUE?

(A)  The region of convergence of X­1(s) is Re(s) > 0.

(B)  The region of convergence of X2(s) is confined to the left  half-plane of s.

(C)  The region of convergence of X1(s) is confined to the right half-plane of 𝑠.

(D)  The imaginary axis in the s-plane is included in both the region of convergence of X­1(s) and the region of convergence of X2(s).

Answer: (D)

40. A circular disc of radius R (in cm) has a uniform absorption coefficient of 1 cm−1. Consider a single ray passing through the disc in the plane of the disc. The shortest distance from the center of the disc to the ray is 𝑡 (in cm). If Ii is the intensity of the incident ray and I0 is the intensity of the transmitted ray, then log(Ii/I0) is given by _________.

(A) 

(B)  2R

(C)  1

(D) 

Answer: (A)

41. The free induction decay (FID) in the MRI of an object can be approximated as

Here Gx and Gy are pulses of identical period and are in-phase. By changing the amplitude of the pulses, one can obtain the two dimensional Fourier transform of the object __________.

(A)  over radial lines in (Kx, Ky)

(B)  over a parabolic contour in (Kx, Ky) space

(C)  along Ky only

(D)  along Kx only

Answer: (A)

42. In the circuit shown below, it is observed that the amplitude of the voltage across the resistor is the same as the amplitude of the source voltage. What is the angular frequency ω0 (in rad/s)?

(A)  104

(B)  103

(C)  103π

(D)  104π

Answer: (A)

43. In a biomaterial, formation of hydrogen bonds on alcoholic groups will lead to a _________.

(A)  shift in the infra-red peak around 1700 cm–1

(B)  shift in the infra-red peak around 2800 cm–1

(C)  broadening of the infra-red peak around 3500 cm–1

(D)  disappearance of the infra-red peak around 1700 cm–1

Answer: (C)

44. In the circuit shown below, the input voltage is sinusoidal and 2.5 V peak to peak. The capacitors are 20 μF each. Assume that the knee voltage of the diodes is 0 V and RL is very large (almost infinite). Which one of the following options is closest to the peak to peak voltage across RL, after a large number of cycles?

(A)  1.25 V

(B)  2.50 V

(C)  5.00 V

(D)  10.0 V

Answer: (C)

45. An ultrasound plane wave of amplitude P0 hits the semi-infinite boundary of two media having acoustic impedances Z1 and Z2. The sum of the amplitudes of the reflected and the incident waves at the boundary is equal to ________.

Answer: (A)

46. In the circuit given below, what should be the value of the resistance R for maximum dissipation of power in R?

(A)  1.2 kΩ

(B)  2.2 kΩ

(C)  3.2 kΩ

(D)  4.2 kΩ

Answer: (B)

47. Two sequences x1[n] and x2[n] are described as follows:

x1[0] = x2[0] = 1

x­1[1] = x2[2] = 2

x1[2] = x2[1] = 1

x1[n] = x2[n] = 0 for all n < 0 and n > 2

If x[n] is obtained by convolving x1[n] with x2[n], which of the following equations is/are TRUE?

(A)  x[2] = x[3]

(B)  x[1] = 2

(C)  x[4] = 3

(D)  x[2] = 5

Answer: (A, D)

48. The function  of a complex variable Z is integrated on a closed contour in an anti-clockwise direction. For which of the following contours, does this integral have a non-zero value?

(A)  |Z – 2| = 0.01

(B)  |Z – 1| = 0.1

(C)  |Z – 3| = 5

(D)  |Z| = 2

Answer: (B, C, D)

49. The continuous time signal x(t) is described by

If y(t) represents x(t) convolved with itself, which of the following statements is/are TRUE?

(A)  y(t) = 0 for all t < 0

(B)  y(t) = 0 for all t > 1

(C)  y(t) = 0 for all t > 3

(D) 

Answer: (A, C, D)

50. Which of the following relations is/are CORRECT in terms of various lung volume measurements?

(A)  Vital capacity minus expiratory reserve volume equals inspiratory capacity.

(B)  Vital capacity plus expiratory reserve volume equals inspiratory capacity.

(C)  Total lung capacity equals the sum of inspiratory capacity and functional residual capacity.

(D)  Functional residual capacity is the difference between expiratory reserve volume and residual volume.

Answer: (A, C)

51. Assuming the operational amplifier in the circuit shown below to be ideal, which of the following properties hold(s) TRUE for the circuit?

(A)  It acts as a voltage follower.

(B)  It is bistable.

(C)  It is astable.

(D)  The output voltage is at saturation.

Answer: (B, D)

52. A water insoluble polymeric biomaterial can become water soluble in vivo by which of the following mechanisms?

(A)  Cleavage of crosslinks between water soluble polymer chains

(B)  Cleavage of side chains leading to formation of non-polar groups

(C)  Cleavage of backbone linkages between polymer repeat units leading to the formation of polar groups

(D)  Enzymatic degradation of crosslinks between water soluble polymer chains

Answer: (A, C, D)

53. For the function f(x) = x4 – x2, which of the following statements is/are TRUE?

(A)  The function is symmetric about x = 0.

(B)  The minimum value of the function is –0.5.

(C)  The function has two minima.

(D)  The function is an odd function.

Answer: (A, C)

54. A system is described by the following differential equation

where time (t) is in seconds. If x(t) is the unit step input applied at t = 0 s to this system, the magnitude of the output at t = 1 s is _______. (Round off the answer to two decimal places.)

Answer: (5.80 to 6.00)

55. The resistance of a thermistor is 1 kΩ at 25 °C and 500 Ω at 50 °C. Find the temperature coefficient of resistance (in units of °C –1) at 35 °C. (Round off the answer to three decimal places.)

Answer: (-0.03 to -0.025)

56. A normally incident X-ray of energy 140 keV passes through a tissue phantom and is detected by the detector as shown in the figure below. The phantom consists of tissue P with an absorption coefficient of 1 cm–1 and a thickness of 1 cm, and tissue Q with an absorption coefficient of 10 cm–1 and a thickness of 2 cm. Calculate the intensity (in μeV) detected by the detector. (Round off the answer to one decimal place.)

Answer: (106.0 to 106.4)

57. A two-dimensional square plate (20 mm sides) contains a homogeneous circular inclusion of 5 mm diameter in it. A parallel beam of X-rays (beam width 30 mm) is used in a tomography system to determine the location of the inclusion. What is the minimum number of views required to approximately determine the location of the inclusion?

Answer: (2 to 2)

58. Calculate the reciprocal of the coefficient of z3 in the Taylor series expansion of the function f(z) = sin(z) around z = 0. (Provide the answer as an integer.)

Answer: (-6 to -6)

59. In a cell viability experiment, 10,000 cells were cultured in the absence and presence of a compound Q for 24 h. The absorbance of a dye associated with cellular metabolic activity was measured at a wavelength of 570 nm at 24 h. The measured absorbances were 0.8 a.u. in the absence of the compound Q, and 0.5 a.u. in its presence.

If the dye gives an absorbance (at 570 nm) of 0.1 a.u. in the absence of cells, what is the percentage cell growth inhibition caused by the compound Q? (Round off the answer to one decimal place.)

Answer: (42.0 to 44.0)

60. The volume percentage of oxygen in inspired air is 20 % and that of expired air is 16 %. A person is breathing at a rate of 12 breaths per minute. Each breath is 500 ml in volume. The cardiac output is 5 liters per minute.

Assuming ideal, healthy lung and cardiac conditions, what is the change in percentage of oxygen in blood over 1 minute? (Round off the answer to one decimal place.)

Answer: (4.8 to 4.8)

61. The intracellular and extracellular concentrations (in mM) of three important ions are given in the table below. The relative permeability of the cell membrane to each ion is provided. Universal gas constant is 8.31 J/(mol.K) and Faraday’s constant is 96500 C/mol.

What is the absolute value of the resting membrane potential (in mV) across the cell membrane at 27 °C? (Round off the answer to one decimal place.)

Answer: (82.6 to 86.0)

62. A metallic strain gauge with negligible piezoresistive effect is subjected to a strain of 50 × 10−6. For the metal, Young’s Modulus = 80 GPa and Poisson’s Ratio = 0.42. What is the change in resistance (in mΩ), if the unstrained resistance of the strain gauge is 200 Ω ? (Round off the answer to one decimal place.)

Answer: (18.4 to 18.4)

63. Consider the total hip joint prosthesis as shown in the figure. The geometric parameters of the prosthesis are such that L1 = 40 mm, L2 = 60 mm, θ1 = 45°, θ2 = 90°. Assume that, when standing symmetrically on both feet, a joint reaction force of 400 N is acting vertically at the femoral head (point A) due to the body weight of the subject. Calculate the magnitude of the moment (in Nm) about point C. (Round off the answer to one decimal place.)

Answer: (11.0 to 12.0)

64. A Wheatstone bridge strain gauge transducer is constructed on a diaphragm in such a way that when a force is applied on the diaphragm, the resistors R1 and R4 will be in compression, and the resistors R2 and R3 will be in tension.

The bridge excitation voltage (Ein) is 10 Volts. If all the resistors have a resistance of 200 Ω in the absence of any force, and each resistance changes by 20 Ω upon application of a force, what is the output voltage Vout (in Volts) from the Wheatstone bridge? (Round off your answer to the nearest integer.)

Answer: (-1 to -1 OR 1 to 1)

65. A stone is thrown from an elevation of 2 m above ground level, at an angle of 30° to the horizontal axis. If the stone hits the ground at a horizontal distance of 6 m from the point of release, at what speed (in m/s) was the stone thrown? Use g = 10 m/s2 and assume that there is no air resistance. (Round off your answer to one decimal place.)

Answer: (6.3 to 6.9)

GATE Exam 2023 Architecture and Planning (AR) Question Paper With Answer Key

by

GATE-2023

AR: Architecture and Planning

General Aptitude.

Q.1 – Q.5 Carry ONE mark each.

1. He did not manage to fix the car himself, so he _______ in the garage.

(A)  got it fixed

(B)  getting it fixed

(C)  gets fixed

(D)  got fixed

Answer: (A)

2. Planting : Seed : : Raising : _____

(By word meaning)

(A)  Child

(B)  Temperature

(C)  Height

(D)  Lift

Answer: (A)

3. A certain country has 504 universities and 25951 colleges. These are categorised into Grades I, II, and III as shown in the given pie charts.

What is the percentage, correct to one decimal place, of higher education institutions (colleges and universities) that fall into Grade III?

(A)  22.7

(B)  23.7

(C)  15.0

(D)  66.8

Answer: (A)

4. The minute-hand and second-hand of a clock cross each other _______ times between 09:15:00 AM and 09:45:00 AM on a day.

(A)  30

(B)  15

(C)  29

(D)  31

Answer: (A)

5. The symbols  are to be filled, one in each box, as shown below.

The rules for filling in the four symbols are as follows.

(1) Every row and every column must contain each of the four symbols.

(2) Every 2 × 2 square delineated by bold lines must contain each of the four symbols.

Which symbol will occupy the box marked with ‘?’ in the partially filled figure?

Answer: (B)

Q.6 – Q.10 Carry TWO marks Each

6. In a recently held parent-teacher meeting, the teachers had very few complaints about Ravi. After all, Ravi was a hardworking and kind student. Incidentally, almost all of Ravi’s friends at school were hardworking and kind too. But the teachers drew attention to Ravi’s complete lack of interest in sports. The teachers believed that, along with some of his friends who showed similar disinterest in sports, Ravi needed to engage in some sports for his overall development.

Based only on the information provided above, which one of the following statements can be logically inferred with certainty?

(A)  All of Ravi’s friends are hardworking and kind.

(B)  No one who is not a friend of Ravi is hardworking and kind.

(C)  None of Ravi’s friends are interested in sports.

(D)  Some of Ravi’s friends are hardworking and kind.

Answer: (D)

7. Consider the following inequalities

p2 – 4q < 4

3p + 2q < 6

where p and q are positive integers.

The value of (p + q) is ______.

(A)  2

(B)  1

(C)  3

(D)  4

Answer: (A)

8. Which one of the sentence sequences in the given options creates a coherent narrative?

(i) I could not bring myself to knock.

(ii) There was a murmur of unfamiliar voices coming from the big drawing room and the door was firmly shut.

(iii) The passage was dark for a bit, but then it suddenly opened into a bright kitchen.

(iv) I decided I would rather wander down the passage.

(A)  (iv), (i), (iii), (ii)

(B)  (iii), (i), (ii), (iv)

(C)  (ii), (i), (iv), (iii)

(D)  (i), (iii), (ii), (iv)

Answer: (C)

9. How many pairs of sets (S,T) are possible among the subsets of {1, 2, 3, 4, 5, 6} that satisfy the condition that S is a subset of T?

(A)  729

(B)  728

(C)  665

(D)  664

Answer: (A)

10. An opaque pyramid (shown below), with a square base and isosceles faces, is suspended in the path of a parallel beam of light, such that its shadow is cast on a screen oriented perpendicular to the direction of the light beam. The pyramid can be reoriented in any direction within the light beam. Under these conditions, which one of the shadows P, Q, R, and S is NOT possible?

(A)  P

(B)  Q

(C)  R

(D)  S

Answer: (B)

AR: Architecture and Planning

PART A: Common FOR ALL CANDIDATES

Q.11 – Q.28 Carry ONE mark Each

11. The triad of secondary colours in the additive colour system is _________.

(A)  Cyan, Magenta, Yellow

(B)  Red, Green, Blue

(C)  Purple, Green, Orange

(D)  Magenta, Blue, Yellow

Answer: (A)

12. The criterion that is specifically mentioned in Special Conditions of Contract (SCC) is__________.

(A)  Scope and performance of the work

(B)  Site mobilization advance

(C)  Labour regulation

(D)  Arbitration and law

Answer: (MTA)

13. The command employed in AutoCAD® to create a mesh from a line or curve that is swept along a straight path (as shown in the figure below) is _________.

(A)  TABSURF

(B)  REVSURF

(C)  RULESURF

(D)  EDGESURF

Answer: (A)

14. As per the Burra Charter (2013) ‘Cultural Significance’ means __________ for past, present or future generations.

(A)  historic, aesthetic, scientific, social or spiritual value

(B)  archaeological, architectural, environmental, cultural value

(C)  natural, cultural, mixed, intangible heritage

(D)  heritage value, authenticity, integrity

Answer: (A)

15. As per URDPFI (2015), the density range (in persons per Hectare) suggested for overall planning approach for small towns in hill areas is ________.

(A)  20-30

(B)  45-75

(C)  100-125

(D)  125-150

Answer: (B)

16. In ecology, the term ‘niche’ refers to ______.

(A)  the ways in which species interact with biotic and abiotic factors of the environment

(B)  only the abiotic factors such as temperature and rainfall

(C)  the gradient change of physiochemical characteristics between two ecosystems

(D)  the zone of junction or a transition area between two biomes

Answer: (A)

17. Lowry’s model of Metropolis (1964) includes two _____________ spatial interaction models.

(A)  Singly constrained

(B)  Doubly constrained

(C)  Unconstraine

(D)  Triply constrained

Answer: (A)

18. Select the method(s) that involve(s) a pairwise comparison matrix for quantifying the weights of decision criteria.

(A)  Analytical hierarchy process

(B)  Exploratory factor analysis

(C)  Latent class analysis

(D)  Multiple linear regression

Answer: (A)

19. Select the micro-organism which is NOT an enteric pathogen.

(A)  Staphylococcus aureus

(B)  Vibrio cholerae

(C)  Escherichia coli

(D)  Salmonella typhi

Answer: (A)

20. Select the publication by Ministry of Statistics and Programme Implementation (MoSPI) related to Environmental Accounts as per UN-SEEA framework.

(A)  EnviStats India 2022

(B)  Energy Conservation Building Code 2017

(C)  Eco Niwas Samhita 2018

(D)  Climate Change 2022: Impacts, Adaptation and Vulnerability

Answer: (A)

21. Ebenezer Howard suggested the maximum population of ‘Garden City’ as________ persons.

(A)  10,000

(B)  22,000

(C)  32,000

(D)  58,000

Answer: (C)

22. In eighteenth century English gardens, __________was used to eliminate visual boundaries between the garden and the landscape.

(A)  Stroll garden

(B)  Sunken fence

(C)  Topiary

(D)  Qanat

Answer: (B)

23. The figure below shows the spatial arrangement of rooms in a building with access from the exterior, marked as ‘entry’. Identify the appropriate diagram showing the access to rooms starting from the entry.

Answer: (B)

24. In high-rise buildings, the method adopted to prevent ingress of smoke in an enclosed fire staircase is _________.

(A)  Polarization

(B)  Pressurization

(C)  Perpetuation

(D)  Fumigation

Answer: (B)

25. Select the Act which stipulates prohibited area of 100 m around centrally protected monuments in India.

(A)  The Antiquities and Art Treasures Act, 1972

(B)  The AMASR (Amendment and Validation) Act, 2010

(C)  Urban Land (Ceiling and Regulation) Act, 1976

(D)  Environment Protection Act, 1986

Answer: (B)

26. Select the option(s) which include(s) a pair of ‘Gestalt’ principles.

(A)  Proximity and Similarity

(B)  Continuity and Closure

(C)  Grain and Texture

(D)  Scale and Proportion

Answer: (A, B)

27. Select the option(s) which is/are NOT considered as primary air pollutant(s).

(A)  Suspended particulate matter

(B)  Oxides of nitrogen

(C)  Volatile organic compounds

(D)  Peroxyacetyl Nitrate

Answer: (D)

28. Select the Biosphere Reserve(s) in India which is/are listed in the ‘Man and the Biosphere’ program of UNESCO.

(A)  Sunderban

(B)  Sena Oura

(C)  Majang Forest

(D)  Gulf of Mannar

Answer: (A, D)

Q.29 – Q.49 Carry TWO marks Each

29. Match the buildings in Group I with their dominant spatial pattern in Group II.

(A)  P-1, Q-3, R-2, S-5

(B)  P-5, Q-3, R-1, S-4

(C)  P-3, Q-4, R-1, S-5

(D)  P-1, Q-4, R-2, S-3

Answer: (A)

30. Match the Parts of Residential Buildings in Group-I with their respective minimum width (in m) in Group-II as per the National Building Code 2016

(A)  P-2, Q-1, R-5, S-3

(B)  P-5, Q-3, R-4, S-1

(C)  P-2, Q-3, R-5, S-4

(D)  P-5, Q-1, R-4, S-3

Answer: (D)

31. Match the following City Planning concepts in Group-I with their proponents in Group-II

(A)  P-2, Q-4, R-5, S-3

(B)  P-3, Q-4, R-5, S-2

(C)  P-3, Q-2, R-1, S-4

(D)  P-1, Q-5, R-3, S-2

Answer: (B)

32. With reference to planning and design of housing, identify the correct statements.

(P) Gross population density is higher than net population density

(Q) Gross population density is lower than net population density

(R) Net population density is directly proportional to area of the plot

(S) Net population density is inversely proportional to area of the plot

(A)  Both Q and S are correct

(B)  Both Q and R are correct

(C)  Both P and R are correct

(D)  Both P and S are correct

Answer: (A)

33. Match the Mission in Group I with their objectives in Group II.

(A)  P-3, Q-5, R-4, S-1

(B)  P-2, Q-5, R-4, S-3

(C)  P-3, Q-4, R-5, S-1

(D)  P-2, Q-5, R-3, S-4

Answer: (A)

34. Select the option(s) that is/are listed among the Sustainable Development Goals as articulated by the United Nations.

(A)  Globalization and Free Trade

(B)  Sustainable Cities and Communities

(C)  Protection of Indigenous Culture and Architecture

(D)  Good Health and Well-being

Answer: (B, D)

35. Select the statement(s) that are TRUE regarding ‘Building Security Services’.

(A)  ‘Radio Frequency Identification Device’ is used for electronic access control system.

(B)  ‘Magnetic Loop Detector’ is used for fire detection system.

(C)  ‘Infrared Sensor’ is used in public broadcasting system.

(D)  ‘Iris Scan’ is a type of biometric access control system.

Answer: (A, D)

36. Select the statement(s) that are TRUE regarding ‘Quality and Cost-Based Selection (QCBS)’ system for tendering.

(A)  Financial bid is opened before technical bid.

(B)  Earnest Money Deposit (EMD) is submitted before the opening of technical bid.

(C)  Technically qualified bidder with lowest financial bid is always awarded the job.

(D)  A composite scoring system considering both the financial and technical bids is adopted for awarding the job.

Answer: (B, D)

37. Design of septic tank requires consideration of space for the following item(s).

(A)  Settling of incoming sewage

(B)  Storage of digested sludge

(C)  Installation of liner to allow seepage of effluent

(D)  Digestion of the settled sludge

Answer: (A, B, D)

38. Select the place(s) which have adopted the “star pattern” of the French Garden in the design of its /their urban form(s).

(A)  Versailles

(B)  Washington D.C.

(C)  Islamabad

(D)  Jaipur

Answer: (A, B)

39. Select the parameter(s) required for determining peak rates of runoff using the Rational formula.

(A)  Intensity of rainfall

(B)  Coefficient of runoff

(C)  Velocity of flow

(D)  Hydraulic mean depth of flow

Answer: (A, B)

40. As per Solid Waste Management Rules 2016 (Ministry of Environment, Forest and Climate, Govt. of India) select the correct statement(s).

(A)  “dry waste” means waste other than bio-degradable waste and inert street sweepings.

(B)  “combustible waste” means biodegradable, recyclable, reusable, hazardous solid waste having maximum calorific value of 800 kcal/kg.

(C)  “domestic hazardous waste” includes expired medicine, CFL bulbs, discarded paint drums.

(D)  “biodegradable waste” means any inorganic material that cannot be degraded by micro-organisms into simpler stable compounds.

Answer: (A, C)

41. Select the correct statement(s) from the following.

(A)  Introduction of automobiles led to urban sprawl.

(B)  Compact cities show relatively higher carbon emissions.

(C)  Land use and transportation planning is inter-dependent on each other.

(D)  Addition of a transport mode in an urban area does not change accessibility.

Answer: (A, C)

42. Choose the correct statement(s) with regard to composting.

(A)  It produces natural soil amendment and enhances the effectiveness of fertilizer.

(B)  Warm temperature of tropical regions is least suitable for composting.

(C)  Composting is an aerobic thermophilic process.

(D)  Windrow composting and in-vessel composting are two of the common composting methods.

Answer: (A, C, D)

43. Select the item(s) that are NOT stipulated as obligatory function(s) of the urban local bodies as per the 12th Schedule of the Indian Constitution.

(A)  Urban poverty alleviation

(B)  Promotion of cultural, educational and aesthetic aspects

(C)  Special measures for disaster mitigation

(D)  Prevention of cruelty to animals

Answer: (C)

44. The annual precipitation recorded in a town is 400 mm. Rainwater is being collected from the flat roof of a building, and then treated to potable standards, and stored. Water loss due to evaporation, transmission and treatment is 40 percent of the total harvested volume. The roof area is 500 sq.m. There are 3 occupants, with average daily water demand as 200 lpcd. The stored rainwater will be adequate for the household’s daily use for ________ days [in integer].

Answer: (200 to 200)

45. A primary school is having 8 class rooms, each having internal dimensions of 15m × 10m × 4m (height). Only the internal walls of all the class rooms are proposed to be painted. Assume a deduction of 10% internal wall area due to doors, windows etc. The specification suggests two coats of paint application. The spreading rates of the selected paint during base coat and finish coat are 4.5 l/sq.m and 2.5 l/sq.m respectively. The amount of paint (in liters) required for the job will be _______ [in integer].

Answer: (10080 to 10080)

46. A construction project consists of four activities. The quantity of work, manpower requirement, and the productivity of the activities are listed in the table below. The interrelationship between the activities are also mentioned in the table. The construction project will start on January 29. Assume no holidays for the entire duration of the project. The project will finish on February _____ [mention date in number].

Answer: (17 to 17)

47. For a privately developed group housing project, the ratio of total number of dwelling units of HIG: MIG: LIG is 3:2:1. The proposed average size of HIG, MIG and LIG units in sq.m are 100, 60 and 30 respectively. The ratio of the total built up area between (MIG + LIG) to HIG will be 1: ______ [in integer].

Answer: (2 to 2)

48. The surface development of a three dimensional object is shown in the figure below. The dotted lines indicate the folds. The dimensions given in the figure are in centimeter. The volume of the three-dimensional object (in cu.cm) is_________ [ rounded off to one decimal place].

Answer: (25.5 to 25.5)

49. A residential housing project is designed in a plot measuring 1 hectare. The car parking area is equally distributed between the ground floor and the basement. Considering the data given below, the number of cars accommodated in the basement will be________ [in integer].

Data:

FAR consumed = 2.0 Car parking area is exempted from built up area for FAR calculations. One car parking to be given for each 100 sq.m of built up area. Area required for accommodating each car in ground floor = 15 sq.m Area required for accommodating each car in basement = 25 sq.m

Answer: (75 to 75)

PART B1: FOR Architecture CANDIDATES ONLY

Q.50 – Q.56 Carry ONE mark Each

50. As per the CPWD Specifications (2019), the material used for cleaning marble flooring after polishing is__________.

(A)  Oxalic Acid

(B)  Caustic Soda

(C)  Bleaching Power

(D)  White Cement

Answer: (A)

51. The proportion of the sides of a traditional Japanese tatami mat is _______.

(A)  1 : 1.414

(B)  1 : 1.5

(C)  1 : 2

(D)  1 : 1.618

Answer: (C)

52. As per IS:4954 – 1964, the acceptable noise level (in dB) for urban residential areas is____________.

(A)  35-45

(B)  65-75

(C)  20-30

(D)  15-25

Answer: (A)

53. Identify the Indian tribe that is associated with the vernacular dwelling illustrated in the image below.

(A)  Bhotia, Uttarakhand

(B)  Toda, Tamil Nadu

(C)  Naga, Nagaland

(D)  Kutia Kondh, Odisha

Answer: (B)

54. Thermal diffusivity of a wall is influenced by the choice of building material. Identify the statement(s) that is/are correct.

(A)  Thermal diffusivity is inversely proportional to thermal conductivity.

(B)  Increase in specific heat capacity increases the thermal diffusivity.

(C)  Materials with low thermal diffusivity have a high amplitude dampening effect.

(D)  Thermal diffusivity is inversely proportional to the density of material.

Answer: (C, D)

55. Select the statement(s) which are NOT correct with respect to burnt clay bricks.

(A)  Lime (<10% of clay) in carbonated form lowers the fusion point of bricks.

(B)  Magnesia (>1% of clay) imparts red colour to the bricks.

(C)  Iron Pyrites tend to oxidize and decompose the brick during burning.

(D)  Alkalis (alkaline salts) when present in excess (>10% of clay) decrease the probability of efflorescence.

Answer: (B, D)

56. Select the example(s) of Art Nouveau architecture.

(A)  Basilica of the Sagrada Familia, Barcelona

(B)  Chrysler Building, New York

(C)  Eiffel Tower, Paris

(D)  Mackintosh Building of the Glasgow School of Art, Glasgow

Answer: (A, D)

Q.57 – Q.65 Carry TWO marks Each

57. Match the buildings in Group I with their architectural feature in Group II.

(A)  P-2, Q-1, R-3, S-5

(B)  P-1, Q-2, R-4, S-3

(C)  P-3, Q-1, R-5, S-2

(D)  P-2, Q-3, R-4, S-5

Answer: (A)

58. Match the architects in Group I with their key architectural ideas in Group II.

(A)  P-2, Q-5, R-1, S-3

(B)  P-4, Q-1, R-3, S-5

(C)  P-2, Q-1, R-5, S-3

(D)  P-4, Q-5, R-1, S-2

Answer: (A)

59. Match the pump types in Group-I with their key components in Group-II.

(A)  P-2, Q-1, R-3, S-5

(B)  P-1, Q-2, R-5, S-3

(C)  P-2, Q-5, R-4, S-1

(D)  P-1, Q-2, R-3, S-4

Answer: (A)

60. Match the geometric forms in Group I with the buildings in Group II.

(A)  P-5, Q-3, R-4, S-2

(B)  P-3, Q-5, R-2, S-4

(C)  P-5, Q-3, R-1, S-4

(D)  P-3, Q-1, R-4, S-2

Answer: (A)

61. Match the instruments in Group I with the physical quantities they measure in Group II.

(A)  P-5, Q-2, R-1, S-3

(B)  P-2, Q-3, R-1, S-4

(C)  P-2, Q-3, R-1, S-5

(D)  P-5, Q-1, R-2, S-4

Answer: (B)

62. Match the terms in Group I with their associated items in Group II.

(A)  P-1, Q-4, R-5, S-2

(B)  P-4, Q-3, R-1, S-2

(C)  P-1, Q-5, R-4, S-2

(D)  P-4, Q-2, R-1, S-5

Answer: (C)

63. Choose the correct statement(s) from the following:

(A)  Waste water from sinks, baths, etc. enters through the top inlet of a gully trap, while foul water from sweeping of rooms or courtyards enters from side inlet.

(B)  Anti-siphon traps have a reduced water-way at the inlet side, while the outlet being larger prevents the pipe from filling full and causing siphonic action.

(C)  Intercepting traps prevent foul gases from street sewer to enter into the house.

(D)  P, Q and S traps are classified according to their shape.

Answer: (C, D)

64. A steel wire of 5.65 mm diameter and 50 m length is used for a hoisting crane. The wire is used to vertically lift a weight of 200 kg attached to its lowest end. Assume the Young’s Modulus of Elasticity of Steel as 2 × 105 N/mm2 and gravitational acceleration as 10 m/sec2. The elongation of the steel wire (in mm ) will be ____ [rounded off to two decimal places].

Answer: (19.75 to 20.15)

65. A simply supported RCC beam of span 4 m is supporting a brick wall over its entire span. The brick wall is 250 mm thick and 2 m high. The RCC beam has a depth of 600 mm and width of 250 mm. The density of brick masonry and RCC can be assumed as 18 KN/m3 and 25 KN/m3 Considering the load of the wall and self-weight of the RCC beam, the maximum bending moment in the beam (in KN-m) will be _______ [rounded off to two decimal places].

Answer: (25.4 to 25.6)

PART B2: FOR Planning CANDIDATES ONLY

Q.66 – Q.72 Carry ONE mark Each

66. Select the most appropriate scale to measure Attitude, Opinion and Perception.

(A)  Likert scale

(B)  Ratio scale

(C)  Richter scale

(D)  Armstrong scale

Answer: (A)

67. Jal Shakti Abhiyan initiated by the Ministry of Jal Shakti does NOT include ____.

(A)  Water conservation and rain water harvesting

(B)  Renovation of traditional water bodies

(C)  Hydroelectric power generation

(D)  Intensive afforestation

Answer: (C)

68. Select the correct sequence of activities for transit-operation planning process.

(A)  Network Route Design → Timetable Development → Vehicle Scheduling → Crew Scheduling

(B)  Timetable Development → Crew Scheduling → Vehicle Scheduling → Network route design

(C)  Vehicle Scheduling → Crew Scheduling → Network Route Design → Timetable Development

(D)  Crew Scheduling → Vehicle Scheduling → Timetable Development → Network Route Design

Answer: (A)

69. Select the correct sequence of steps for designing the operation of a signalized intersection.

(A)  Signal Phasing → Green Allocation → Cycle Length Selection

(B)  Green Allocation → Cycle Length Selection → Signal Phasing

(C)  Cycle Length Selection → Signal Phasing → Green Allocation

(D)  Signal Phasing → Cycle Length Selection → Green Allocation

Answer: (D)

70. Considering the following statements (P, Q, and R), select the correct option.

(P) Prediction of travel demand depends on target year modal alternatives.

(Q) Prediction of travel demand depends on target year population.

(R) Prediction of travel demand depends on target year land use.

(A)  Only P is correct

(B)  Only P & R are correct

(C)  Only Q & R are correct

(D)  P, Q, and R are all correct

Answer: (D)

71. During Covid-19 pandemic, the ARHC scheme was launched in 2021 by the Government of India to address the problems of poor urban migrants. The term ARHC refers to__________.

(A)  Accessible Rural Health Centre

(B)  Affordable Rental Housing Complexes

(C)  Affordable Rentals for Homeless Citizens

(D)  Accessible Rural Housing Complexes

Answer: (B)

72. Choose the non-probability sampling method where the sample is taken from a group of people easy to contact or reach.

(A)  Simple random sampling

(B)  Snowball sampling

(C)  Convenience sampling

(D)  Stratified random sampling

Answer: (C)

Q.73 – Q.81 Carry TWO marks Each

73. Match the items in Group-I with the most appropriate stages of travel demand modelling in Group-II.

(A)  P-4, Q-3, R-2, S-1

(B)  P-3, Q-4, R-5, S-1

(C)  P-4, Q-3, R-1, S-5

(D)  P-3, Q-4, R-2, S-5

Answer: (A)

74. Match the Acts in Group-I with the corresponding organizations empowered by the Act in Group-II.

(A)  P-4, Q-1, R-2, S-3

(B)  P-2, Q-3, R-4, S-5

(C)  P-3, Q-1, R-4, S-5

(D)  P-3, Q-1, R-5, S-2

Answer: (C)

75. As per IRC 11:1962, separate bicycle tracks may be provided when the peak hour ________.

Which of the following statement(s) can be used to correctly fill in the blank?

(P) Bicycle traffic is 400 bicycles/hour or more and the volume of motorized vehicles is 100-200 vehicles/hour

(Q) Bicycle traffic is 100 bicycles/hour or more and the volume of motorized vehicles exceed 200 vehicles/hour

(R) Bicycle traffic is 100-200 bicycles/hour and the volume of motorized vehicle is 100-200 vehicles/hour

(A)  Only P & Q

(B)  Only P & R

(C)  Only R

(D)  P, Q & R

Answer: (A)

76. As per URDPFI Guidelines (2015), match the following settlement types in Group-I to their population range in Group-II.

(A)  P-5, Q-2, R-3, S-1

(B)  P-2, Q-4, R-1, S-5

(C)  P-5, Q-4, R-1, S-2

(D)  P-4, Q-2, R-3, S-5

Answer: (A)

77. Match the application areas in Group I with the Satellites/Satellite sensors in Group II.

(A)  P-5, Q-3, R-4, S-1

(B)  P-3, Q-5, R-1, S-4

(C)  P-5, Q-2, R-4, S-3

(D)  P-2, Q-3, R-5, S-1

Answer: (A)

78. Select the institution(s) that are mandated as per the 73rd Constitutional Amendment Act, 1992 of India.

(A)  Panchayat

(B)  Municipal council

(C)  Ward committee

(D)  Gram Sabha

Answer: (A, D)

79. Select the method(s) that can be used for landuse classification based on satellite images.

(A)  Maximum Likelihood

(B)  Northwest Corner Method

(C)  K Means

(D)  ANN

Answer: (A, C, D)

80. The figure below shows a contour diagram and two points (A & B) on the continuously ascending surface. The horizontal projection of AB is 200 m long, and the gradient of AB is 1 in 25. The constant contour interval (in m) is ______ [in integer].

Answer: (2 to 2)

81. A given zone is characterized in the following tables in terms of household size, and vehicle ownership. Table I shows the trip rates of households, and Table II shows the household composition. For households of size two and above, having one or more vehicles, the total daily home-based trips made are __________ [in integer].

Answer: (2350 to 2350)

GATE Exam 2023 Agricultural Engineering (AG) Question Paper With Answer Key

by

GATE-2023

AG: Agricultural Engineering

GA-General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. “You are delaying the completion of the task. Send _______ contributions at the earliest.”

(A)  you are

(B)  your

(C)  you’re

(D)  yore

Answer: (B)

2. References : ______ : : Guidelines : Implement

(By word meaning)

(A)  Sight

(B)  Site

(C)  Cite

(D)  Plagiarise

Answer: (C)

3. In the given figure, PQRS is a parallelogram with PS = 7 cm, PT = 4 cm and PV = 5 cm. What is the length of RS in cm? (The diagram is representative.)

(A)  20/7

(B)  28/5

(C)  9/2

(D)  35/4

Answer: (B)

4. In 2022, June Huh was awarded the Fields medal, which is the highest prize in Mathematics.

When he was younger, he was also a poet. He did not win any medals in the International Mathematics Olympiads. He dropped out of college.

Based only on the above information, which one of the following statements can be logically inferred with certainty?

(A)  Every Fields medalist has won a medal in an International Mathematics Olympiad.

(B)  Everyone who has dropped out of college has won the Fields medal.

(C)  All Fields medalists are part-time poets.

(D)  Some Fields medalists have dropped out of college.

Answer: (D)

5. A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is a mirror image of the other part about that line.

The given figure consists of 16 unit squares arranged as shown. In addition to the three black squares, what is the minimum number of squares that must be coloured black, such that both PQ and MN form lines of symmetry? (The figure is representative)

(A)  3

(B)  4

(C)  5

(D)  6

Answer: (C)

Q.6 – Q.10 Carry TWO marks Each

6. Human beings are one among many creatures that inhabit an imagined world. In this imagined world, some creatures are cruel. If in this imagined world, it is given that the statement “Some human beings are not cruel creatures” is FALSE, then which of the following set of statement(s) can be logically inferred with certainty?

(i) All human beings are cruel creatures.

(ii) Some human beings are cruel creatures.

(iii) Some creatures that are cruel are human beings.

(iv) No human beings are cruel creatures.

(A)  only (i)

(B)  only (iii) and (iv)      

(C)  only (i) and (ii)

(D)  (i), (ii) and (iii)

Answer: (D)

7. To construct a wall, sand and cement are mixed in the ratio of 3:1. The cost of sand and that of cement are in the ratio of 1:2.

If the total cost of sand and cement to construct the wall is 1000 rupees, then what is the cost (in rupees) of cement used?

(A)  400

(B)  600

(C)  800

(D)  200

Answer: (A)

8. The World Bank has declared that it does not plan to offer new financing to Sri Lanka, which is battling its worst economic crisis in decades, until the country has an adequate macroeconomic policy framework in place. In a statement, the World Bank said Sri Lanka needed to adopt structural reforms that focus on economic stabilisation and tackle the root causes of its crisis. The latter has starved it of foreign exchange and led to shortages of food, fuel, and medicines. The bank is repurposing resources under existing loans to help alleviate shortages of essential items such as medicine, cooking gas, fertiliser, meals for children, and cash for vulnerable households.

Based only on the above passage, which one of the following statements can be inferred with certainty?

(A)  According to the World Bank, the root cause of Sri Lanka’s economic crisis is that it does not have enough foreign exchange.

(B)  The World Bank has stated that it will advise the Sri Lankan government about how to tackle the root causes of its economic crisis.

(C)  According to the World Bank, Sri Lanka does not yet have an adequate macroeconomic policy framework.

(D)  The World Bank has stated that it will provide Sri Lanka with additional funds for essentials such as food, fuel, and medicines.

Answer: (C)

9. The coefficient of x4 in the polynomial (x – 1)3 (x – 2)3 is equal to _______.

(A)  33

(B)  −3

(C)  30

(D)  21

Answer: (A)

10. Which one of the following shapes can be used to tile (completely cover by repeating) a flat plane, extending to infinity in all directions, without leaving any empty spaces in between them? The copies of the shape used to tile are identical and are not allowed to overlap.

(A)  circle

(B)  regular octagon

(C)  regular pentagon

(D)  rhombus

Answer: (D)

AG: Agricultural Engineering

Q.11 – Q.35 Carry ONE mark Each

11. If A and B are square matrices of order 3 such that |B|=−1, |B|=3, then |3AB| equals

(A)  -81

(B)  -27

(C)  -9

(D)  81

Answer: (A)

12. is equal to

(A)  0

(B)  1/2

(C)  1

(D)  2

Answer: (B)

13. The value of  is

(A)  0

(B)  1

(C)  2

(D)  3

Answer: (C)

14. y = aemx + be−mx is the solution of the differential equation

Answer: (D)

15. In rotary tiller, the total energy requirement for carrying out tillage will decrease if

(A)  the bite length is increased

(B)  the bite length is decreased

(C)  the cone index of soil is higher

(D)  forward speed of the machine is reduced

Answer: (A)

16. The effectiveness of the turbocharger of a diesel engine increases when

(A)  the ambient temperature increases

(B)  the pressure ratio across the compressor decreases

(C)  the load on the engine increases

(D)  the displacement volume of the engine decreases

Answer: (C)

17. In a thresher, the cylinder separation efficiency can be improved by increasing

(A)  cylinder diameter

(B)  cylinder speed

(C)  cylinder-concave clearance

(D)  feed rate

Answer: (B)

18. In a 4-stroke single cylinder diesel engine, the inlet valve opens at 10⁰ before TDC and closes at 40⁰ after BDC. The exhaust valve opens at 25⁰ before BDC and closes at 15⁰ after TDC. The percentage of time for which both the valves remain closed in one cycle of the engine is

(A)  32.29

(B)  40.97

(C)  46.53

(D)  75.01

Answer: (B)

19. The torque available at maximum power developed by the tractor is 150 N m. If the reserve torque is 20%, the peak torque that can be developed by the tractor in N m is

(A)  100

(B)  120

(C)  180

(D)  210

Answer: (C)

20. The statement which is not correct for the porous medium is

(A)  Seepage velocity is always greater than the Darcy’s velocity

(B)  Darcy’s velocity is not exclusively controlled by soil porosity

(C)  Seepage velocity increases with increasing surface ponding of water

(D)  Darcy’s velocity in unsaturated soil is always greater than that in saturated soil

Answer: (D)

21. A sprinkler irrigation system has been designed for a crop with the water application rate of 1.17 cm h−1 and sprinkler discharge of 1.3 L s−1. The coefficient of discharge and uniformity coefficient are 0.9 and 0.8, respectively. If the sprinkler spacing along the lateral is 20 m, the lateral spacing in m is

(A)  14.4

(B)  16.0

(C)  18.0

(D)  20.0

Answer: (D)

22. The average discharge, operating pressure and emitter constant of a drip emitter are 4 L h−1, 110 kPa and 0.3, respectively. The type of emitter is

(A)  orifice

(B)  long path

(C)  pressure compensating

(D)  disc

Answer: (A)

23. If the departure and latitude of a line are 70 m and −130 m, respectively, then the whole circle bearing of the line in degrees is

(A)  28

(B)  62

(C)  152

(D)  208

Answer: (C)

24. Match the Columns:

(A)  1 – c, 2 – b, 3 – a, 4 – e, 5 – d

(B)  1 – c, 2 – d, 3 – a, 4 – e, 5 – b

(C)  1 – d, 2 – c, 3 – e, 4 – a, 5 – b

(D)  1 – c, 2 – d, 3 – a, 4 – b, 5 – e

Answer: (B)

25. The information needed for estimating the design flood using Rational formula is

(A)  cumulative infiltration

(B)  antecedent moisture condition of soil

(C)  shape factor of the catchment

(D)  time of concentration of the catchment

Answer: (D)

26. The microbial death kinetics for a food suspension follows the equation:

where No= initial microbial load, N = microbial load after time t, tl = lag time and D = decimal reduction time.

The correct statement for this equation is

(A)  the time required to reduce 10% of the initial population is lag time.

(B)  the time required to reduce the initial 90% of population is lag time

(C)  time required to kill the first 90% population is lower than D value at the same temperature

(D)  lag time approaches D value as N0 becomes smaller and temperature decreases.

Answer: (B)

27. If the diameter of fat globule in a cream separator is reduced to half and the rotational speed of the centrifuge increased to three times, the terminal settling velocity of fat globule is

(A)  decreased to 0.44 times

(B)  increased to 0.44 times

(C)  decreased to 2.25 times

(D)  increased to 2.25 times

Answer: (D)

28. The log mean temperature difference (LMTD) correction factor is not required during heat transfer rate calculation in

(A)  plate heat exchanger

(B)  1 shell pass and 1 tube pass heat exchanger

(C)  1 shell pass and 2 tube pass heat exchanger

(D)  2 shell pass and 4 tube pass heat exchanger

Answer: (B)

29. Identify the dimensionless parameter(s) from the following:

(A)  Cone index

(B)  Puddling index

(C)  Performance index

(D)  Reel index

Answer: (B, D)

30. The probability that a storm event with a return period of 20 years will occur once in 5-year period is __________(rounded off to 2 decimal places).

Answer: (0.19 to 0.21)

31. Considering declining balance method, the constant rate of depreciation at which the value of the tractor will come down to 50% of its purchase price at the end of 4th year in per cent is _________ (rounded off to 2 decimal places).

Answer: (15.80 to 16.00)

32. A trapezoidal grassed waterway with side slope (H:V) of 1:1 carries a design discharge of 1 m3 s−1. The bed slope and Manning’s roughness coefficient of this channel are 1% and 0.04, respectively. The design depth of the best hydraulic trapezoidal grassed waterway section in m is ________ (rounded off to 2 decimal places).

Answer: (0.66 to 0.69)

33. The minimum fluidization height of 1.20 m is maintained during fluidized bed drying of carrots. The bed diameter of the fluidized bed dryer is 0.6 m. If mass and solid density of carrots are 250 kg and 1040 kg m−3, respectively, then the porosity of the bed at the minimum fluidization condition is ____________ (rounded off to 3 decimal places, Consider π = 3.14).

Answer: (0.290 to 0.296)

34. The lighter liquid layer and the interphase layer in a basket centrifuge, rotating at a speed of 1000 rpm, are 0.1025 m and 0.105 m away from the center, respectively. Considering the densities of lighter and heavier liquids as 920 kg m−3 and 1015 kg m−3, the differential pressure in horizontal direction required to maintain the interphase layer in kPa is ___________ (rounded off to 3 decimal places, Consider π = 3.14).

Answer: (2.610 to 2.620)

35. The upstream and downstream pressures in a homogenizer during homogenization of milk are maintained at 250 bar and 10 bar, respectively. If density of milk is 1030 kg m−3, then the velocity at which milk comes out of the homogenizing valve in m s−1 is ___________ (rounded off to 3 decimal places).

Answer: (215.850 to 215.900)

Q.36 – Q.65 Carry TWO marks Each

36. If  and (A + B)2, then the values of a and b are:

(A)  a = 4, b = 1

(B)  a = 1, b = 4

(C)  a = 0, b = 4

(D)  a = 2, b = 4

Answer: (B)

37. A vector  is passing through the origin of a 3-D frame. Considering the tendency of rotation in the counter clockwise direction as positive, the moment about a point A : (3, 4, 8) is

Answer: (D)

38. A vertical disc plough with 5 discs is operated at a depth of 0.15 m. The disc angle and disc diameter are 40⁰ and 0.6 m, respectively. If overlap between two consecutive discs is 0.12 m at 0.15 m depth of cut, the total width of cut at the specified depth in m is

(A)  1.19

(B)  1.55

(C)  2.11

(D)  2.36

Answer: (A)

39. In a 9 × 20 cm fluted roller type seed drill, each fluted roller is discharging 4.25 g of seed per revolution of fluted roller shaft. The fluted roller shaft rotates once for two complete rotation of the ground drive wheel of the seed drill. The rolling diameter of the ground drive wheel is 0.35 m. Considering no skid of the ground drive wheel, the seed rate in kg ha−1 is

Consider π = 3.14

(A)  96.62

(B)  141.55

(C)  187.35

(D)  386.42

Answer: (A)

40. A field sprayer with 12 nozzles fitted to the boom at a spacing of 0.5 m is used for spraying at a height of 0.75 m from the ground. The angle of spraying is 75⁰. If the height of spraying is reduced to 0.6 m, the change in swath in m is

(A)  0.23

(B)  0.48

(C)  0.65

(D)  0.91

Answer: (A)

41. The ordinates of a 6-hour S-hydrograph of a catchment are given in Table below. The catchment has phi-index of 0.25 cm h−1 and base flow of 10.5 m3 s−1. The peak of the flood hydrograph generated from this catchment due to a storm of 45 mm received during the first 6 h in m3 s−1 is

(A)  259.5

(B)  270.0

(C)  280.5

(D)  349.5

Answer: (C)

42. It is planned to provide irrigation in a crop field having field capacity and permanent wilting point of the soil as 0.21 cm3 cm−3 and 0.09 cm3 cm−3, respectively. The crop root zone depth is 0.90 m. The growing period of this crop is 1st January to 31st March, during which the observed reference evapotranspiration (ETr), effective rainfall (Pe) and crop coefficients (Kc) are listed below. Considering management allowable deficit (MAD) for this crop as 50%, the average irrigation interval during the growing period in days is

(A)  4

(B)  6

(C)  8

(D)  11

Answer: (B)

43. The infiltration capacity of a basin is described by the Horton’s equation, I = 2 + e−3t, where I is in cm h−1 and the duration, t is in hours. If the duration of the storm event is 2 hours, the depth of the infiltration in the last 1 hour of the storm event in mm is

(A)  5

(B)  10

(C)  20

(D)  25

Answer: (C)

44. In a juice filtration process, solid concentration per m3 of filtrate is 0.2 kg. During filtration of 12.49 m3 of juice, 0.02 m thick cake (porosity of 0.32) is deposited. If 2.5 kg of solid is collected in 180 s, the pressure drop across the cake in kPa is

[Absolute viscosity of juice is 2.12 ×10−3 kg m-1 s−1, and specific cake resistance is 1.2 × 108 m kg−1]

(A)  0.18

(B)  1.81  

(C)  18.06

(D)  180.60

Answer: (C)

45. Cheese is packed in a bilayer plastic package made up of low density polyethylene (LDPE) and polyethylene terephthalate (PET). The thickness of LDPE and PET in the package are 1.5 mm and 1.3 mm, respectively. The surface area of the plastic package is 6.25 cm2. The partial pressure difference of oxygen across the package wall is 0.30 atm. The permeability coefficient of oxygen in LDPE and PET are 4.18 × 10−8 cm3 cm cm−2 s−1 atm−1 and 1.67 × 10−10 cm3 cm cm−2 s−1 atm-1, respectively. If the food gets spoiled when it absorbs 0.025 ml of oxygen, then the shelf life of food in days is

(A)  121

(B)  103

(C)  73

(D)  61

Answer: (A)

46. The rotor shaft of an ice cream freezer consists of 3 scraper blades. The temperature difference between the ice cream mix and the refrigerant during freezing of ice cream is 30 ⁰C. Density and latent heat of fusion of ice are 917 kg m−3 and 335 kJ kg−1, respectively. The overall heat transfer coefficient is 2000 kJ m−2 h−1 °C−1. If the maximum thickness of ice formed before being scraped off is 10 μm, the minimum speed of the scraper shaft in rpm is

(A)  88

(B)  109

(C)  121

(D)  149

Answer: (B)

47. The percentage absolute humidity of air becomes equal to the percentage relative humidity, when

(A)  absolute humidity of air is equal to relative humidity

(B)  saturated humidity of air is equal to relative humidity

(C)  air is almost or completely dry

(D)  air is almost or completely saturated

Answer: (C, D)

48. Dimensionless numbers play an important role in correlating transfer coefficients during forced convection. In relation to the dimensionless numbers, the correct statement(s) is/are

(A)  Prandtl number in heat transfer is analogous to Schmidt number in mass transfer

(B)  Small value of Prandtl number signifies lower thermal diffusion as compared to momentum diffusion

(C)  Prandtl number is the ratio of momentum diffusivity to the thermal diffusivity of the fluid

(D)  Lewis number is the product of Schmidt number and Prandtl number

Answer: (A, C)

49. In a locality ‘A’, the probability of a convective storm event is 0.7 with a density function,  The probability of tropical cyclone-induced storm in the same location is given by the density function  The probability of occurring more than 1 unit of storm event is _________ (rounded off to 2 decimal places).

Answer: (0.28 to 0.32)

50. Given that  and y = 1, when x = 0. Using Runge-Kutta fourth order method, the value of y at x = 0.2 is ________ (rounded off to 3 decimal places).

Answer: (1.264 to 1.265)

51. A power operated chaff cutter with a mean cutting radius of 0.25 m is fitted with two cutting knives and is rotating at 300 rpm. Thirty maize stalks with a mean diameter of 12 mm are fed through the throat at a time. The dynamic shear strength of the stalk is 0.05 N mm−2. The mass and radius of gyration of the flywheel (including knives) are 40 kg and 0.27 m, respectively. The total shaft power requirement in kW is _________ (rounded off to 2 decimal places).

Answer: (2.70 to 2.85)

52. A two-wheel drive tractor with a total weight of 24 kN has a static weight distribution of 30% and 70% at the front and rear axles, respectively. When the tractor is operated on a level ground of pure sand, the maximum tractive force developed is 13 kN. If external weight of 1.5 kN is added to the rear axle, neglecting weight transfer, the change in maximum tractive force in kN is _________ (rounded off to 2 decimal places).

Answer: (1.15 to 1.20)

53. A 4-stroke diesel engine can be operated with either diesel (heating value 45 MJ kg−1) or biodiesel blend, B20 (heating value 42.1 MJ kg−1). The brake specific fuel consumption of the engine when operated with diesel and B20 is 260 g kW−1 h−1 and 310 g kW−1 h−1, respectively. For developing a brake power of 20 kW, the change in brake thermal efficiency of the engine when B20 is used in place of diesel is ________ (rounded off to 2 decimal places).

Answer: (3.15 to 3.25 OR 0.3 to 0.3)

54. A solar photovoltaic system is used to generate power from total solar radiations varying from 400 to 750 W m−2. The maximum conversion efficiency of solar photovoltaic system is 14%. The open circuit voltage, short circuit current and fill factor of solar cells are 21.6 V, 3.22 A and 0.72, respectively. To generate maximum power, the minimum cell area required in m2 is _________ (rounded off to 3 decimal places).

Answer: (0.885 to 0.895)

55. A single disc clutch is used to transmit 10 kW power at 1400 rpm. The axial pressure exerted on the contact surface is 0.07 N mm−2 and the coefficient of friction is 0.25. Considering the ratio of diameter to face width of the clutch lining as 8 and assuming uniform wear theory, the required face width of friction lining in mm is ___________ (rounded off to 2 decimal places).

Answer: (26.75 to 26.90)

56. In a tractor seat system, the chassis frequency and seat suspension damping rate are 20 rad s−1 and 400 N m−1 s, respectively. The critical damping rate of tractor seat system is 1600 N m−1 If the combined mass of the seat and operator is 80 kg, the transmissibility of vibration is _________ (rounded off to 2 decimal places).

Answer: (0.43 to 0.46)

57. Two cylindrical reservoirs ‘A’ and ‘B’ are connected by a 30 m long pipe of 250 mm internal diameter as shown in Figure below. The Darcy-Weisbach friction factor for the pipe is 0.025. Initially the reservoir ‘A’ was full at the indicated level and reservoir ‘B’ was empty. If the entrance and exit losses in this pipe are neglected, the time required to empty the reservoir ‘A’ in hour is _________ (rounded off to 3 decimal places).

Consider π = 3.14 and acceleration due to gravity, g = 9.81 m s−2.

Answer: (3.30 to 3.40)

58. A homogenous anisotropic earthen dam of height 52 m with a free board of 2 m is constructed on an impermeable foundation. The horizontal and vertical hydraulic conductivities of soil used for the construction of the dam are 4.5 × 10−8 m s−1 and 2.0 × 10−8 m s−1, respectively. There are 6 flow channels and 25 equipotential drops in a square flow net drawn in the transformed dam section. If the downstream dam side is dry, the quantity of seepage per unit length through the dam in m3 day−1 m−1 is __________ (rounded off to 3 decimal places).

Answer: (0.030 to 0.032)

59. A salt affected crop field is to be leached with irrigation water having salt concentration of 3.5 meq L−1. Salt concentration in the saturation extract of soil is 15.2 meq L−1. Leaching efficiency of the field is 55%. In the month of March, the observed reference evapotranspiration and effective rainfall in this area are 150 mm and 75 mm, respectively. If the average crop coefficient in this month is 1.05, the leaching requirement for the entire month in mm is _________ (rounded off to 2 decimal places).

Answer: (19.50 to 19.55)

60. A 10 m long concrete pipe is required to carry a peak discharge of 1.0 m3 s−1 in a drop inlet spillway with a head of 4 m. The entrance loss coefficient is 0.5 and the friction loss coefficient is 0.02. Consider acceleration due to gravity = 9.81 m s−2. The neutral slope of the water level in per cent is _________ (rounded off to 2 decimal places).

Answer: (4.69 to 4.80)

61. Discharge from a centrifugal pump operating at 1000 rpm with a total head of 30 m is 300 L min−1. The pump efficiency is 65%. If speed of the pump is increased to 1200 rpm, the power required to operate the pump in kW is ____________ (rounded off to 2 decimal places).

Consider acceleration due to gravity = 9.81 m s−2.

Answer: (3.90 to 4.00)

62. A 0.30 m diameter well penetrates an unconfined aquifer with a saturated depth of 40 m. After 8 hours of pumping at a steady rate of 0.03 m3 s−1, the drawdown in two observation wells located at 20 m and 50 m away from the pumping well are found to be 3 m and 2 m, respectively. The drawdown in the pumping well in m is _________ (rounded off to 1 decimal place, Consider π = 3.14).

Answer: (8.6 to 8.8)

63. The apparent wall shear stress in a 0.6 m long pipe line carrying refined oil is 12.5 Pa. If the pressure drop along the length is 300 Pa and flow rate is 0.25 m3 s−1, the absolute viscosity of oil in 10−3 Pa s is ______________ (rounded off to 3 decimal places).

Answer: (4.902 to 4.908)

64. The carrot slices (water activity = 0.89) are to be preserved using osmo-dehydration. Addition of salt (NaCl) to 20% sucrose solution (water activity = 0.987) reduces the water activity to 0.85. Percentage of NaCl added to the solution is ______________ (rounded off to 2 decimal places).

Consider molecular mass of Sucrose = 342 and molecular mass of NaCl = 58.44

Answer: (16.40 to 16.60)

65. A copper ball and a steel ball having diameters d1 and d2, respectively, are initially at a uniform temperature of 200⁰C. Both the balls are exposed to the atmosphere at 30⁰C. If both the balls attain a temperature of 120⁰C after equal exposure duration, then the ratio of d1 to d2 is _____________ (rounded off to 3 decimal places).

Assume Biot Number to be less than 0.1. The thermo-physical properties of copper and steel are given below:

Answer: (MTA)

GATE Exam 2023 Aerospace Engineering (AE) Question Paper With Answer Key

by

GATE-2023

AE: Aerospace Engineering

GA-General Aptitude

Q.1 – Q.5 Carry ONE mark each.

1. “You are delaying the completion of the task. Send _______ contributions at the earliest.”

(A)  you are

(B)  your

(C)  you’re

(D)  yore

Answer: (B)

2. References : ______ : : Guidelines : Implement

(By word meaning)

(A)  Sight

(B)  Site

(C)  Cite

(D)  Plagiarise      

Answer: (C)

3. In the given figure, PQRS is a parallelogram with PS = 7 cm, PT = 4 cm and PV = 5 cm. What is the length of RS in cm? (The diagram is representative.)

(A)  20/7

(B)  28/5

(C)  9/2

(D)  35/4

Answer: (B)

4. In 2022, June Huh was awarded the Fields medal, which is the highest prize in Mathematics.

When he was younger, he was also a poet. He did not win any medals in the International Mathematics Olympiads. He dropped out of college.

Based only on the above information, which one of the following statements can be logically inferred with certainty?

(A)  Every Fields medalist has won a medal in an International Mathematics Olympiad.

(B)  Everyone who has dropped out of college has won the Fields medal.

(C)  All Fields medalists are part-time poets.

(D)  Some Fields medalists have dropped out of college.

Answer: (D)

5. A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is a mirror image of the other part about that line.

The given figure consists of 16 unit squares arranged as shown. In addition to the three black squares, what is the minimum number of squares that must be coloured black, such that both PQ and MN form lines of symmetry? (The figure is representative)

(A)  3

(B)  4

(C)  5

(D)  6

Answer: (C)

Q.6 – Q.10 Carry TWO marks Each

6. Human beings are one among many creatures that inhabit an imagined world. In this imagined world, some creatures are cruel. If in this imagined world, it is given that the statement “Some human beings are not cruel creatures” is FALSE, then which of the following set of statement(s) can be logically inferred with certainty?

(i) All human beings are cruel creatures.

(ii) Some human beings are cruel creatures.

(iii) Some creatures that are cruel are human beings.

(iv) No human beings are cruel creatures.

(A)  only (i)

(B)  only (iii) and (iv)

(C)  only (i) and (ii)

(D)  (i), (ii) and (iii)

Answer: (D)

7. To construct a wall, sand and cement are mixed in the ratio of 3:1. The cost of sand and that of cement are in the ratio of 1:2.

If the total cost of sand and cement to construct the wall is 1000 rupees, then what is the cost (in rupees) of cement used?

(A)  400

(B)  600

(C)  800

(D)  200

Answer: (A)

8. The World Bank has declared that it does not plan to offer new financing to Sri Lanka, which is battling its worst economic crisis in decades, until the country has an adequate macroeconomic policy framework in place. In a statement, the World Bank said Sri Lanka needed to adopt structural reforms that focus on economic stabilisation and tackle the root causes of its crisis. The latter has starved it of foreign exchange and led to shortages of food, fuel, and medicines. The bank is repurposing resources under existing loans to help alleviate shortages of essential items such as medicine, cooking gas, fertiliser, meals for children, and cash for vulnerable households.

Based only on the above passage, which one of the following statements can be inferred with certainty?

(A)  According to the World Bank, the root cause of Sri Lanka’s economic crisis is that it does not have enough foreign exchange.

(B)  The World Bank has stated that it will advise the Sri Lankan government about how to tackle the root causes of its economic crisis.

(C)  According to the World Bank, Sri Lanka does not yet have an adequate macroeconomic policy framework.

(D)  The World Bank has stated that it will provide Sri Lanka with additional funds for essentials such as food, fuel, and medicines.

Answer: (C)

9. The coefficient of x4 in the polynomial (x − 1)3 (x − 2)3 is equal to _______.

(A)  33

(B)  −3

(C)  30

(D)  21

Answer: (A)

10. Which one of the following shapes can be used to tile (completely cover by repeating) a flat plane, extending to infinity in all directions, without leaving any empty spaces in between them? The copies of the shape used to tile are identical and are not allowed to overlap.

(A)  circle

(B)  regular octagon

(C)  regular pentagon

(D)  rhombus

Answer: (D)

AE: Aerospace Engineering

Q.11 – Q.35 Carry ONE mark Each

11. The direction in which a scalar field ϕ(x, y, z) has the largest rate of change at any point with position vector

Answer: (A)

12. If a monotonic and continuous function y = f(x) has only one root in the interval x1 < x < x2, then

(A)  f(x1)f(x2) > 0

(B)  f(x1)f(x2) = 0

(C)  f(x1)f(x2) < 0

(D)  f(x1) – f(x2) = 0

Answer: (C)

13. Consider the one-dimensional wave equation  for −∞ < x < ∞, t ≥ For an initial condition  the solution at t = 1 is

Answer: (A)

14. A two-dimensional potential flow solution for flow past an airfoil has a streamline pattern as shown in the figure. Which of the following conditions is additionally required to satisfy the Kutta condition?

(A)  Addition of a source of strength Q > 0

(B)  Addition of a source of strength Q < 0

(C)  Addition of a circulation of strength Γ > 0 (counter-clockwise)

(D)  Addition of a circulation of strength Γ < 0 (clockwise)

Answer: (D)

15. Consider the Blasius solution for the incompressible laminar flat plate boundary layer. Among the following options, select the correct relation for the development of the momentum thickness θ with distance x from the leading edge along the length of the plate.

(A)  θ ∝ x2/3

(B)  θ ∝ x1/2

(C)  θ ∝ x1/7

(D)  θ ∝ x−2/3

Answer: (B)

16. In a two-dimensional potential flow, the doublet is a limit of the superposition of

(A)  a uniform stream and a source

(B)  a source and a sink of equal strength

(C)  a uniform stream and a sink

(D)  a source and a vortex

Answer: (B)

17. An ideal glider has drag characteristics given by  where  is the induced drag coefficient, CL is the lift coefficient, and K is a constant. For maximum range of the glider, the ratio  is

(A)  1

(B)  1/3

(C)  3

(D)  3/2

Answer: (A)

18. The figures shown in the options are schematics of airfoil shapes (not to scale). For a civilian transport aircraft designed for a cruise Mach number of 0.8, which among them is aerodynamically best suited as a wing section?

Answer: (D)

19. For a longitudinally statically stable aircraft, which one of the following represents the relationship between the coefficient of pitching moment about the center of gravity Cmcg and absolute angle of attack αa ?

(Note : nose-up moment is positive.)

Answer: (D)

20. In a single-spool aviation turbojet engine, which of the following is the correct relationship between the total work output WT of a 2-stage axial turbine and the total work required WC by a 6-stage axial compressor, neglecting losses?

(A)  WT = 2WC

(B)  WT = 6WC

(C)  WT = WC

(D)  WT = 3WC

Answer: (C)

21. For a stage of a 50% reaction ideal axial flow compressor (symmetrical blading), select the correct statement from the options given.

(A)  The stagnation enthalpy rise across the rotor is 50% of the rise across the stage.

(B)  The static enthalpy rise across the rotor is 50% of the rise across the stage.

(C)  Axial velocity component of the flow at the rotor exit is 50% of that at the rotor entry.

(D)  The static pressure rise across the rotor is 50% of the rise across the stator.

Answer: (B)

22. An aircraft is cruising with a forward speed Va and the jet exhaust speed relative to the engine at the exit is Vj. If Vj/Va = 2, what is the propulsive efficiency?

(A)  0.50

(B)  1.00

(C)  0.33

(D)  0.67

Answer: (D)

23. Consider the four basic symmetrical flight loading conditions corresponding to the corners of a typical V-n diagram. For one of these flight loading conditions, it is observed that (i) the compressive bending stresses have a maximum value in the bottom aft region (see figure) of the wing cross-section; and (ii) the tensile bending stresses are maximum in the upper forward region (see figure) of the wing cross-section. For the preceding observations, select the corresponding flight loading condition from the options given.

(A)  Positive high angle of attack

(B)  Positive low angle of attack

(C)  Negative high angle of attack

(D)  Negative low angle of attack

Answer: (D)

24. Which one of the following figures represents the qualitative variation of absolute deceleration |dV/dt| with altitude h(measured from the mean sea level) for a space vehicle undergoing a ballistic entry into the Earth’s atmosphere?

Answer: (D)

25. Which of the following statement(s) is/are true about harmonically excited forced vibration of a single degree-of-freedom linear spring-mass-damper system?

(A)  The total response of the mass is a combination of free vibration transient and steady-state response.

(B)  The free vibration transient dies out with time for each of the three possible conditions of damping (under-damped, critically damped, and over-damped).

(C)  The steady-state periodic response is dependent on the initial conditions at the time of application of external forcing.

(D)  The rate of decay of free vibration transient response depends on the mass, spring stiffness and damping constant.

Answer: (A, B, D)

26. Which of the following statement(s) is/are true about the state of stress in a plane?

(A)  Maximum or major principal stress is algebraically the largest direct stress at a point.

(B)  The magnitude of minor principal stress cannot be greater than the magnitude of major principal stress.

(C)  The planes of maximum shear stress are inclined at 90 degrees to the principal axes.

(D)  The normal stresses along the planes of maximum shear stress are equal.

Answer: (A, D)

27. The normal stresses along the planes of maximum shear stress are equal.

(A)  For a rectangular planform wing, the dimensions of the ribs DO NOT depend on their spanwise position in the wing.

(B)  Ribs increase the column buckling stress of longitudinal stiffeners connected to them.

(C)  Ribs increase plate buckling stress of the skin panels.

(D)  Ribs help in maintaining aerodynamic shape of the wing.

Answer: (B, C, D)

28. From the options given, select all that are true for turbofan engines with afterburners.

(A)  Turning afterburner ON increases specific fuel consumption.

(B)  Turbofan engines with afterburners have variable area nozzles.

(C)  Turning afterburner ON decreases specific fuel consumption.

(D)  Turning afterburner ON increases stagnation pressure across the engine.

Answer: (A, B)

29. Which of the following statement(s) is/are true with respect to eigenvalues and eigenvectors of a matrix?

(A)  The sum of the eigenvalues of a matrix equals the sum of the elements of the principal diagonal.

(B)  If λ is an eigenvalue of a matrix A, then 1/λ is always an eigenvalue of its transpose (AT).

(C)  If λ is an eigenvalue of an orthogonal matrix A, then 1/λ is also an eigenvalue of A.

(D)  If a matrix has n distinct eigenvalues, it also has n independent eigenvectors.

Answer: (A, C, D)

30. For studying wing vibrations, a wing of mass M and finite dimensions has been idealized by assuming it to be supported using a linear spring of equivalent stiffness k and a torsional spring of equivalent stiffness kθ as shown in the figure.

The centre of gravity (CG) of the wing idealized as an airfoil is marked in the figure. The number of degree(s) of freedom for this idealized wing vibration model is _________. (Answer in integer)

Answer: (2 to 2)

31. The system of equations

x – 2y + αz = 0

2x + y – 4z = 0

x – y + z = 0

has a non-trivial solution for α = _______. (Answer integer)

Answer: (3 to 3)

32. An airplane weighting 40 kN is landing on a horizontal runway during which it is retarded by an arresting cable mechanism. The tension in the arresting cable at a given instant, as shown in the figure, is 100 kN. Assuming that the thrust from the engine continues to balance airplane drag, the magnitude of horizontal load factor is ________. (round off to one decimal place)

Answer: (2.4 to 2.6)

33. The ratio of the speed of sound in H2 (molecular weight 2 kg/kmol) to that in N2 (molecular weight 28 kg/kmol) at temperature 300 K and pressure 2 bar is ____. (round off to two decimal places)

Answer: (3.5 to 4.0)

34. Airplane A and Airplane B are cruising at altitudes of 2 km and 4 km, respectively. The free stream density and static pressure at altitude 2 km are 1.01 kg/m3 and 79.50 kPa, respectively, and at altitude 4 km, they are 0.82 kg/m3 and 61.70 kPa, respectively. The differential pressure reading from the pitot-static tubes is 3 kPa for both the airplanes. Assuming incompressible flow, the ratio of

cruise speeds of Airplane A to Airplane B is ______. (round off to two decimal places)

Answer: (0.89 to 0.91)

35. A supersonic vehicle powered by a ramjet engine is cruising at a speed of 1000 m/s. The ramjet engine burns hydrogen in a subsonic combustor to produce thrust. The heat of combustion for hydrogen is 120 MJ/kg. The overall efficiency of the engine η0, defined as the ratio of propulsive power to the total heat release in the combustor, is 40%. Taking acceleration due to gravity g0 = 10 m/s2, the specific impulse of the engine is __________ seconds.

(round off to the nearest integer).

Answer: (4800 to 4900)

Q.36 – Q.65 Carry TWO marks Each

36. Given the function y(x) = (x + 3) (x – 2), for −4 < x < 4. What is the value of x at which the function has a minimum?

(A)  −3/2

(B)  −1/2

(C)  1/2

(D)  3/2

Answer: (B)

37. A supersonic aircraft has an air intake ramp that can be rotated about the leading edge O such that the shock from the leading edge meets the cowl lip as shown in the figure. Select all the correct statement(s) as per oblique shock theory when the flight Mach number M is increased.

(A)  It is always possible to find a ramp setting θRAMP such that the shock still meets the cowl lip (βSHOCK remains the same).

(B)  If θRAMP is held fixed, the shock angle βSHOCK will increase.

(C)  If M exceeds a critical value, it would NOT be possible to find a ramp setting θRAMP such that the shock still meets the cowl lip (βSHOCK­ remains the same).

(D)  Shock angle βSHOCK < sin−1(1/M)

Answer: (A)

38. Two missiles A and B powered by solid rocket motors have identical specific impulse, liftoff mass of 5600 kg each, and burn durations of tA = 30 s and tB = 70 s, respectively. The propellant mass flow rates,  for missiles A and B, respectively, are given by

Neglecting gravity and aerodynamic forces, the relationship between the final velocities VA and VB of missiles A and B, respectively, is given by

(A)  VA = 4.1 VB

(B)  VA = VB

(C)  VA = 0.5 VB

(D)  VA = 0.7 VB

Answer: (C)

39. A perfect gas stored in a large reservoir exhausts into the atmosphere through a convergent duct. The reservoir pressure is P0 and temperature is T0. The jet emerges from the nozzle at choked conditions with average velocity u, Mach number M, pressure p, temperature T, and density ρ. If the reservoir pressure is increased, then

(A)  u, M, p, T and ρ increase

(B)  u, p, T, and ρ increase, but M remains the same

(C)  u, M and T remain the same, but p and ρ increase

(D)  u, M, T and ρ remain the same but p increases

Answer: (C)

40. Consider a general aviation airplane with weight 10 kN and a wing planform area of 15 m2. The drag coefficient of the airplane is given as CD = CD0 + KCL2 with CD0 = 0.025 and K = 0.05. For level flight at an altitude where the density is 0.60 kg/m3 and thrust 1 kN, the maximum cruise speed is

(rounded off to the nearest integer)

(A)  87 m/s

(B)  30 m/s

(C)  36 m/s

(D)  101 m/s

Answer: (A)

41. A scramjet engine features an intake, isolator, combustor, and a nozzle, as shown in the schematic. Station 3 indicates the combustor entry point. Assume stagnation enthalpy to be constant between Stations 1 and 3, and air to be a calorically perfect gas with specific heat ratio γ. Select the correct expression for Mach number M3 at the inlet to the combustor from the options given.

Answer: (B)

42. Consider the equation  where a and ω are constant. Given y = 1 at x = 0, select all correct statement(s) from the following is x → ∞.

(A)  y → 0 if a ≠ 0

(B)  y → 1 if a = 0

(C)  y → A exp(|a|x) if a < 0; A is a constant

(D)  y → B sin (ωx + C) if a > 0; B and C are constants

Answer: (C, D)

43. Given the vectors

which of the following statement(s) is/are TRUE?

(A)  Vectors  are coplanar

(B)  The scalar triple product of the vectors  is zero

(C)   are perpendicular

(D)  is parallel to 

Answer: (A, B)

44. Consider a one-dimensional inviscid supersonic flow in a diverging duct with heat addition (Qin) as shown. Which of the following statement(s) is/are always TRUE?

(A)  Mach number, M2 > M1

(B)  Stagnation pressure, P10 > P20

(C)  Static pressure, P2 > P1

(D)  Stagnation temperature, T10 < T20

Answer: (B, D)

45. Consider the International Standard Atmosphere (ISA) with h being the geopotential altitude (in km) and dT/dh being the temperature gradient (in K/m). Which of the following combination(s) of (h, dT/dh) is/are as per ISA?

(A)  (7, −6.5 × 10−3)

(B)  (9, 4 × 10−3)

(C)  (15, 0)

(D)  (35, 3 × 10−3)

Answer: (A, C, D)

46. For an airfoil, which of the relations given about the critical Mach number Mcr and drag divergence Mach number Mdd is/are correct?

(A)  Mcr < Mdd

(B)  Mcr < 1.0

(C)  Mdd < 1.0

(D)  Mcr > 1.0

Answer: (A, B, C)

47. Which of the following statement(s) about the elastic flexural buckling load of columns is/are correct?

(A)  The buckling load increases with increase in flexural rigidity of the column.

(B)  The buckling load increases with increase in the length of the column.

(C)  The boundary conditions of the column affect the buckling load.

(D)  The buckling load is NOT directly dependent on the density of the material used

for the column.

Answer: (A, C, D)

48. The thickness of a uniform hollow circular shaft is equal to the difference between the outer radius and the inner radius. The ratio of the inner diameter to outer diameter of the shaft is 0.5. For the shaft reacting to an applied torque, the ratio of the maximum shear stress τ to the maximum shear stress τthin – wall obtained using the thin-wall approximation is _________. (round off to one decimal place)

Answer: (1.1 to 1.3)

49. A rigid bar AB is subjected to a uniformly distributed load of 100 N/m as shown in the figure. The bar is supported by rod CD, with A, C, and D as pin joints. The rod CD has axial stiffness of 40 N/mm. The vertical deflection at point D is __________ mm. (round off to nearest integer)

Answer: (10 to 10)

50. A cantilever beam of length 2a is loaded at the tip with force F as shown in the figure. The beam is supported in the middle by a roller with a pin. The magnitude of moment reaction at the built-in end of the beam is α Fa, where α is ______ . (round off to one decimal place)

Answer: (0.5 to 0.5)

51. A single degree-of-freedom spring-mass-damper system has viscous damping ratio of 0.1. The mass is given an initial displacement of 10 cm without imparting any velocity. After exactly two complete cycles of oscillation (i.e., after time 2Td, where Td is the period of the damped vibration), the amplitude of the displacement is ______ cm. (round off to two decimal place)

Answer: (2.80 to 2.86)

52. The shear flow distribution in a single cell, thin-walled beam under the action of an arbitrary shear load Sy applied at the shear centre S is shown in the figure. The cell has horizontal symmetry with booms marked by 1 to 4 that carry direct stresses. The shear modulus G is the same for all the walls, and the area of the cell is 135000 mm2. With respect to the point O marked in the figure, the distance to the shear centre S is ______ mm. (round off to the nearest integer)

Answer: (196 to 198)

53. Consider a thin-walled cylindrical pressure vessel made of an alloy with yield strength of 300 MPa. The vessel has end caps to contain the pressure. The ratio of radius of the vessel to its wall thickness is 100. As per the von Mises yield criterion, the internal pressure that would cause the failure of the vessel is _____ MPa. (round off to two decimal places)

Answer: (3.40 to 3.50)

54. Consider the differential equation

with initial conditions  at x = 1. The value of y at x = 2 is ______. (round off to two decimal places)

Answer: (0.24 to 0.26)

55. The operating characteristic of a pump were measured to be CP = qΦ2, where power coefficient  is the flow coefficient, a is a constant, D is a length scale, ω is the rotation rate, ρ is fluid density, and P is the power required. The flow coefficient is a dimensionless volume flow rate scaled with ω and D. Assuming that the flow rate remains the same, if the rotation rate is increased to 1.25 ω, the power changes to α The value of α is ______. (round off to two decimal places)

Answer: (1.24 to 1.26)

56. A thin cambered airfoil has lift coefficient c1 = 0 at an angle of attack α = −1°. Assuming that stall occurs at much larger α, the c1 at α = 4° is _______. (round off to two decimal places)

Answer: (0.55 to 0.57)

57. In a potential flow, a uniform stream of strength U directed along the x-axis and four line sources (2-dimensional) of strengths π/2, −π/3, π/4, −π/5 are placed along the x-axis at x = 0, 1, 2, and 3, respectively. The strength of an additional line source to be placed at x = 4 such that a closed streamline encircles all five sources is ________. (round off to two decimal places).

Answer: (-0.69 to -0.67)

58. Enstrophy is defined as the square of the magnitude of vorticity.

For the three-dimensional velocity field

the enstrophy at location (1, 1, 1) is _______.

(round off to two decimal places)

Answer: (12.61 to 12.81)

59. An airplane with wing planform area of 20 m2 and weight 8 kN is flying straight and level with a speed of 100 m/s. The total drag coefficient is 0.026 and the air density is 0.7 kg/m3. The total thrust required to introduce a steady climb angle of 0.1 radians is ______ N. (round off to the nearest integer)

Answer: (2615 to 2625)

60. The maximum permissible load factor and the maximum lift force coefficient for an airplane is 7 and 2, respectively. For a wing loading of 6500 N/m2 and air density 1.23 kg/m3, the speed yielding the highest possible turn rate in the vertical plane is ___________ m/s. (round off to the nearest integer)

Answer: (190 to 195)

61. A gas turbine combustor is burning methane and air at an equivalence ratio ϕ = 0.5, where  and [F/A]stoich is the ratio of mass flow rate of fuel to the mass flow rate of air at stoichiometry. If the air flow rate is  then the mass flow rate of methane is ______ kg/s. (round off to two decimal places)

Answer: (0.57 to 0.60)

62. The universal gravitational constant is 11 6.67 × 10−11Nm2/kg2. For a planet of mass 6.4169 × 1023 kg and radius 3390 km, the escape velocity is _____ km/s.

(round off to one decimal place).

Answer: (4.9 to 5.1)

63. A satellite is in a circular orbit around Earth with a time period of 90 minutes. The radius of Earth is 6370 km, mass of Earth is 5.98 ×1024 kg and the universal gravitational constant is 6.67 × 10−11 Nm2/kg2. The altitude of the satellite above mean sea level is ______ km. (round off to the nearest integer)

Answer: (260 to 300)

64. A centrifugal air compressor has inlet root diameter of 0.25 m and the outlet diameter of the impeller is 0.6 m. The pressure ratio is 5.0. The air at the inlet of the rotor is at 1 atm and 25° The polytropic efficiency is 0.8 and slip factor is 0.92. Use Cp = 1.004 kJ/kg-K and γ = 1.4. The impeller speed in revolutions per minute (RPM) is ________. (round off to the nearest integer)

Answer: (15948 to 16048)

65. Consider a cryogenic liquid rocket engine using an expander cycle with liquid hydrogen and liquid oxygen as the two propellants. The mass flow rate of hydrogen  into the combustion chamber is 32 kg/s, and the mass flow rate of oxygen  into the chamber is such that  The combustion of hydrogen and oxygen is at stoichiometry. Assuming that the rate of the forward reaction is much larger than that of the reverse reaction, the rate of formation of H2O is _______ kmol/s. (round off to the nearest integer)

Answer: (16 to 16)

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