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
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)
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.
(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 _______.
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).
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:
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).
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 ? ___________
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)
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?
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).
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?
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
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 _________.
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.)
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.
(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.
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].
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:
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)
1. Writing too many things on the ________ while teaching could make the students get _________.
(A) bored / board
(B) board / bored
(C) board / board
(D) bored / bored
Answer: (B)
2. Which one of the following is a representation (not to scale and in bold) of all values of x satisfying the inequality on the real number line?
Answer: (C)
3. If f(x) = 2 ln (√ex), what is the area bounded by f(x) for the interval [0, 2]on the x-axis?
(A) 1/2
(B) 1
(C) 2
(D) 4
Answer: (C)
4. A person was born on the fifth Monday of February in a particular year.
Which one of the following statements is correct based on the aboveinformation?
(A) The 2nd February of that year is a Tuesday
(B) There will be five Sundays in the month of February in that year
(C) The 1st February of that year is a Sunday
(D) All Mondays of February in that year have even dates
Answer: (A)
5.
Which one of the groups given below can be assembled to get the shape that isshown above using each piece only once without overlapping with each other?(rotation and translation operations may be used).
Answer: (B OR C)
Q.6 – Q. 10 Carry TWO marks each.
6. Fish belonging to species S in the deep sea have skins that are extremely black (ultra-black skin). This helps them not only to avoid predators but also sneakily attack their prey. However, having this extra layer of black pigment results in lower collagen on their skin, making their skin more fragile.
Which one of the following is the CORRECT logical inference based on theinformation in the above passage?
(A) Having ultra-black skin is only advantageous to species S
(B) Species S with lower collagen in their skin are at an advantage because it helpsthem avoid predators
(C) Having ultra-black skin has both advantages and disadvantages to species S
(D) Having ultra-black skin is only disadvantageous to species S but advantageousonly to their predators
Answer: (C)
7. For the past m days, the average daily production at a company was 100 units per day.
If today’s production of 180 units changes the average to 110 units per day,what is the value of m?
(A) 18
(B) 10
(C) 7
(D) 5
Answer: (C)
8. Consider the following functions for non-zero positive integers, p and q.
Which one of the following options is correct based on the above?
(A) f(2,2) = g(2,2)
(B) f(g(2,2), 2) < f(2, g(2,2)
(C) g(2,1) ≠ f(2,1)
(D) f(3,2) >g(3,2)
Answer: (A)
9. Four cities P, Q, R and S are connected through one-way routes as shown in the figure. The travel time between any two connected cities is one hour. The boxes beside each city name describe the starting time of first train of the day and their frequency of operation. For example, from city P, the first trains of the day startat 8 AM with a frequency of 90 minutes to each of R and S. A person does not spend additional time at any city other than the waiting time for the next connecting train.
If the person starts from R at 7 AM and is required to visit S and return to R,what is the minimum time required?
(A) 6 hours 30 minutes
(B) 3 hours 45 minutes
(C) 4 hours 30 minutes
(D) 5 hours 15 minutes
Answer: (A)
10. Equal sized circular regions are shaded in a square sheet of paper of 1 cm side length. Two cases, case M and case N, are considered as shown in the figures below. In the case M, four circles are shaded in the square sheet and in the case N, nine circles are shaded in the square sheet as shown.
What is the ratio of the areas of unshaded regions of case M to that of case N?
(A) 2 : 3
(B) 1 : 1
(C) 3 : 2
(D) 2 : 1
Answer: (B)
Aerospace Engineering
Q.11 – Q.35 Carry ONE mark Each
11. The equation of the straight line representing the tangent to the curve y = x2 at the point (1,1) is
(A) y = 2x – 2
(B) x = 2y – 1
(C) y – 1 = 2(x – 1)
(D) x – 1 = 2(y – 1)
Answer: (C)
12. Let be the unit vectors in the x, y and z directions, respectively. If the vector is rotated about positive by 135°, one gets
Answer: (D)
13. Let x be a real number and i = √−Then the real part of cos(ix) is
(A) sinh x
(B) cosh x
(C) cos x
(D) sin x
Answer: (B)
14. The point of maximum entropy on a Fanno-curve in a Temperature-Entropy (T-s) diagram represents the
(A) maximum flow Mach number
(B) minimum flow Mach number
(C) sonic Mach number
(D) normal shock in the flow
Answer: (C)
15. Consider a two-dimensional potential flow over a cylinder. If the freestream speed is U∞, the maximum speed on the cylinder surface is
(A) U∞/2
(B) 3U∞/2
(C) 2U∞,
(D) 4U∞/3
Answer: (C)
16. Consider steady, two-dimensional, incompressible flow over a non-porous flat plate as shown in the figure. For the control volume PQRS, the speed, u∞, at section PQ is uniform and the speed at section RS is given by where 𝑛 is a positive integer. The value of A0 for which the flow through section PS will vanish is:
Answer: (B)
17. Consider the velocity distribution, u(y) shown in the figure. For two adjacent fluid layers L1 and L2, the viscous force exerted by L1 on L2 is
(A) to the right
(B) to the left
(C) vertically upwards
(D) vertically downwards
Answer: (B)
18. The service ceiling of an airplane is the altitude
(A) at which maximum rate of climb is 100 m/min
(B) beyond which theoretically the airplane cannot sustain level flight
(C) at which maximum power is required for flight
(D) at which maximum rate of climb is 100 ft/min
Answer: (D)
19. Regarding the horizontal tail of a conventional airplane, which one of the following statements is true?
(A) It contributes to
(B) It makes
(C) It makes
(D) It makes
Answer: (A)
20. A beam with a symmetrical T-shaped cross-section, as shown in the figure, is subjected to pure bending. The maximum magnitude of the normal stress is realised:
(A) only at the top fibres of the cross-section
(B) only at the bottom fibres of the cross-section
(C) both at the top and bottom fibres of the cross-section
(D) only at the centroidal fibres of the cross-section
Answer: (B)
21. A three-member truss is simply supported at Q and R, and loaded at P by a horizontal force F as shown. The force in QR is
(A) 0
(B) F(tensile)
(C) F/√2 (compressive)
(D) √2F (tensile)
Answer: (B)
22. The closed thin-walled rectangular channel shown in figure (i) is opened by introducing a sharp cut at the center of the bottom edge, as shown in figure (ii). Which one of the following statements is correct?
(A) Centroids of (i) and (ii) coincide while shear centers do not
(B) Shear centers of (i) and (ii) coincide while centroids do not
(C) Both centroids and shear centers of (i) and (ii) coincide
(D) Neither centroids nor shear centers of (i) and (ii) coincide
Answer: (A)
23. The region of highest static temperature in a rocket engine and the region of highest heat flux are ____________, respectively.
(A) nozzle throat and nozzle entry
(B) combustion chamber and nozzle throat
(C) nozzle exit and nozzle throat
(D) nozzle throat and combustion chamber
Answer: (B)
24. If are three mutually perpendicular unit vectors, then can take
(A) 0
(B) 1
(C) −1
(D) ∞
Answer: (B, C)
25. Across an oblique shock wave in a calorifically perfect gas,
(A) the stagnation enthalpy changes
(B) the stagnation entropy changes
(C) the stagnation temperature changes
(D) the speed of sound changes
Answer: (B, D)
26. NACA 2412 airfoil has
(A) 4% maximum camber with respect to chord
(B) maximum camber at 40% chord
(C) 12% maximum thickness to chord ratio
(D) maximum camber at 20% chord
Answer: (B, C)
27. For International Standard Atmosphere (ISA) up to 11 km, which of the following statement(s) is/are true?
(A) The hydrostatic/ aerostatic equation is used
(B) The temperature lapse rate is taken as−10−2 K/m
(C) The sea level conditions are taken as: pressure, ps = 1.01325 × 105 Pa; temperature, Ts = 300 K; density, ρs = 1.225 kg/m3
(D) Air is treated as a perfect gas
Answer: (A, D)
28. Let σ and τ represent the normal stress and shear stress on a plane, respectively. The Mohr circle(s) that may possibly represent the state of stress at points in a beam of rectangular cross-section under pure bending is/are:
Answer: (B, C)
29. An isotropic linear elastic material point under plane strain condition in the x-y plane always obeys:
(A) out-of-plane normal strain,ϵzz = 0
(B) out-of-plane normal stress,σzz = 0
(C) out-of-plane shear stress,τxz = 0
(D) out-of-plane shear strain, γxz = 0
Answer: (A, C, D)
30. A high-pressure-ratio multistage axial compressor encounters an extreme loading mismatch during starting. Which of the following technique(s) can be used to alleviate this problem?
(A) Blade cooling
(B) Variable angle stator vanes
(C) Blow-off valves
(D) Multi-spool shaft
Answer: (B, C, D)
31. The arc length of the parametric curve: x = cos θ, y = sin θ, z = θ from θ = 0 to θ = 2π is equal to ________ (round off to one decimal place).
Answer: (8.6 to 9.1)
32. An unpowered glider is flying at a glide angle of 10 degrees. Its lift-to-drag ratio is _______ (round off to two decimal places).
Answer: (5.5 to 5.80)
33. The two-dimensional plane-stress state at a point is:
σxx = 110 MPa; σyy = 30 MPa; τxy = 40 MPa.
The normal stress, σn, on a plane inclined 45° as shown in the figure is _____MPa(round off to the nearest integer).
Answer: (109 to 111)
34. In a static test, a turbofan engine with bypass ratio of 9 has core hot exhaust speed 1.5 times that of fan exhaust speed. The engine is operated at a fuel to air ratio of f = 0.03. Both the fan and the core streams have no pressure thrust. The ratio of fan thrust to thrust from the core engine is _______ (round off to one decimal place).
Answer: (5.7 to 6.0)
35. In a single stage turbine, the hot gases come out of stator/ nozzle at a speed of 500 m/s and at an angle of 70 degrees with the turbine axis as shown. The design speed of the rotor blade is 250 m/s at the mean blade radius. The rotor blade angle, β, at the leading edge is ________ degrees (round off to one decimal place).
Answer: (51.5 to 52.6)
Q.36 – Q.65 Carry TWO marks Each
36. The height of a right circular cone of maximum volume that can be enclosed within a hollow sphere of radius R is
Answer: (C)
37. Consider the differential equation
The boundary conditions are y = 0 and at x = 0.
Then the value of y at x = 1/2 is
(A) 0
(B) √e
(C) √e/2
(D)
Answer: (C)
38. Consider the partial differential equation where x, y are real.
If f(x, y) = a(x) b(y), where a(x) and b(y) are real functions, which one of the following statements can be true?
(A) a(x) is a periodic function and b(y) is a linear function
(B) both a(x) and b(y) are exponential functions
(C) a(x) is a periodic function and b(y) is an exponential function
(D) both a(x) and b(y) are periodic functions
Answer: (C)
39. A cylindrical object of diameter 900 mm is designed to move axially in air at 60 m/s. Its drag is estimated on a geometrically half-scaled model in water, assuming flow similarity.
Coefficients of dynamic viscosity and densities for air and water are1.86 × 10−5 Pa-s, 1.2 kg/m3and 1.01 × 10−3 Pa-s, 1000 kg/m3 respectively.
Drag measured for the model is 2280 N. Drag experienced by the full-scale objectis ____ N (rounded off to the nearest integer).
(A) 322
(B) 644
(C) 1288
(D) 2576
Answer: (B)
40. Consider a conventional subsonic fixed-wing airplane. 𝑒 is the Oswald efficiency factor and AR is the aspect ratio. Corresponding to the minimum which of the following relations is true?
Answer: (B)
41. A horizontal load F is applied at point R on a two-member truss, as shown in the figure. Both the members are prismatic with cross-sectional area, A0, and made of the same material with Young’s modulus E.
The horizontal displacement of point R is:
Answer: (C)
42. Which of the following is NOT always true for a combustion process taking place in a closed system?
(A) Total number of atoms is conserved
(B) Total number of molecules is conserved
(C) Total number of atoms of each element is conserved
(D) Total mass is conserved
Answer: (B)
43. The real function 𝑦 = sin2(|x|) is
(A) continuous for all x
(B) differentiable for all x
(C) not continuous at x = 0
(D) not differentiable at x = 0
Answer: (A, B)
44. A convergent nozzle fed from a constant pressure, constant temperature reservoir, is discharging air to atmosphere at 1 bar (absolute) with choked flow at the exit (marked as Q).
Flow through the nozzle can be assumed to be isentropic.
If the exit area of the nozzle is increased while all the reservoir parameters and ambient conditions remain the same, then at steady state
(A) the nozzle will remain choked
(B) the nozzle will be un-choked
(C) the Mach number at section P will increase
(D) the Mach number at section P will decrease
Answer: (A, C)
45. For a conventional airplane in straight, level, constant velocity flight condition, which of the following condition(s) is/are possible on Euler angles (ϕ, θ, ψ), angle of attack (α) and the sideslip angle (β)?
(A) ϕ = 0°, θ = 2°, ψ = 0°, α = 2°, β = 0°
(B) ϕ = 5°, θ = 0°, ψ = 0°, α = 2°, β = 0°
(C) ϕ = 0°, θ = 3°, ψ = 0°, α = 3°, β = 5°
(D) ϕ = 0°, θ = 5°, ψ = 0°, α = 2°, β = 5°
Answer: (A)
46. Consider a high Earth-orbiting satellite of angular momentum per unit mass and eccentricity e.
The mass of the Earth is M and G is the universal gravitational constant.
The distance between the satellite’s center of mass and the Earth’s center of mass is r, the true anomaly is θ, and the phase angle is zero.
Which of the following statements is/are true?
(A) The trajectory equation is
(B) The trajectory equation is
(C) is conserved
(D) The sum of potential energy and kinetic energy of the satellite is conserved
Answer: (B, C, D)
47. A rocket operates at an absolute chamber pressure of 20 bar to produce thrust, F1. The hot exhaust is optimally expanded to 1 bar (absolute pressure) using a convergent-divergent nozzle with exit to throat area ratio (Ae/At) of 3.5 and thrust coefficient, CF, 1 = 1.42.
The same rocket when operated at an absolute chamber pressure of 50 barproduces thrust F2 and the thrust coefficient is CF, 2.
Which of the following statement(s) is/are correct?
Answer: (B, D)
48. is a vector field where are the base vectors of a cartesian coordinate system.
Using the Gauss divergence theorem, the value of the outward flux of the vectorfield over the surface of a sphere of unit radius centered at the origin is________(rounded off to one decimal place).
Answer: (7.4 to 7.7)
49. The largest eigenvalue of the given matrix is _____.
Answer: (2 to 2)
50. A rotational velocity field in an air flow is given as with a = 10 s−1, b = 20 s−1.
The air density is 1.0 kg/m3 and the pressure at (x, y) = (0 m, 0 m) is 100 kPa.
Neglecting gravity, the pressure at (x, y) = (6 m, 8 m) is _____ kPa (rounded off to nearest integer).
Answer: (88 to 91)
51. Consider a circulation distribution over a finite wing given by the equation below.
The wingspan 𝑏 is 10 m, the maximum circulationΓ0is 20 m2/s, density of air is1.2 kg/m3 and the free stream speed is 80 m/s.
The lift over the wing is ______N (rounded off to the nearest integer).
Answer: (9500 to 9800)
52. Consider a solid cylinder housed inside another cylinder as shown in the figure.Radius of the inner cylinder is 1 m and itsheight is 2 m. The gap between thecylinders is 5 mm and is filled with a fluid of viscosity 10−4 Pa-s.
The inner cylinder is rotating at a constant angular speed of 5 rad/s while the outercylinder is stationary. Friction at thebottom surfaces can be ignored. Velocityprofile in the vertical gap between thecylinders can be assumed to be linear.
The driving moment required for the rotating motion of the inner cylinder is____________ Nm (rounded off to two decimal places).
Answer: (1.24 to 1.28)
53. In a converging duct, area and velocity at section P are 1 m2 and 15 m/s,respectively. The temperature of the fluid is 300 K.
Air flow through the nozzle can be assumed to be inviscid and isothermal.
Characteristic gas constant is 287 J/(kg-K) and ratio of specific heats is 1.4 for air.
To ensure that the air flow remains incompressible (Mach number, M ≤ 0.3) in the duct, the minimum area required at section Q is _____ m2 (rounded off to two decimal places).
Answer: (0.14 to 0.15)
54. Consider a thin symmetric airfoil at 2 degree angle of attack in a uniform flow at 50 m/s. The pitching moment coefficient about its leading edge is _____ (rounded off to three decimal places).
Answer: (-0.057 to -0.053)
55. A convergent-divergent nozzle with adiabatic walls is designed for an exit Mach number of 2.3. It is discharging air to atmosphere under the conditions indicated in the figure.
Flow through the nozzle is inviscid, the characteristic gas constant for air is 287 J/kg-K), and γ = 1.4.
When the reservoir pressure is 25 bar (absolute), and temperature is 300 K, Prandtl-Meyer expansion waves appear at the nozzle exit as shown.
The minimum percentage change in the reservoir pressure required to eliminate the wave system at the nozzle exit under steady state is _______%.
Answer: (49 to 51 OR -51 to -49)
56. A conventional airplane of mass 5000 kg is doing a level turn of radius 1000 m at aconstant speed of 100 m/s at sea level.
Taking the acceleration due to gravity as 10 m/s2, the bank angle of the airplane is ______ degrees.
Answer: (44 to 46)
57. Given: The tip deflection and tip slope for a tip loaded cantilever of length L are: respectively, where N is the tip force and EI is the flexural rigidity.
A cantilever PQ of rectangular cross-section is subjected to transverse load, F, at its mid-point. Two cases are considered as shown in the figure. In Case I, the end Q is free and in Case II, Q is simply supported.
The ratio of the magnitude of the maximum bending stress at P in Case I to that in Case II is ________ (rounded off to one decimal place).
Answer: (2.6 to 2.7)
58. A simply supported Aluminium column of length 1 m and rectangular cross-section w × t with t ≤ w, is subjected to axial compressive loading.
Young’s modulus is 70 GPa. Yield stress under uniaxial compression is 120 MPa.
The value of 𝑡 at which the failure load for yielding and buckling coincide is ______ mm.
Answer: (43 to 48)
59. A 0.5 m long thin-walled circular shaft of radius 2 cm is to be designed for an axial load of 7.4 kN and a torque of 148 Nm applied at its tip, as shown in the figure.
The allowable stress under uniaxial tension is 100 MPa.
Using maximum principal stress criterion, the minimum thickness, t, of the shaft so that it does not fail is _____ mm (rounded off to the nearest integer).
Answer: (1 to 1)
60. A 10 kN axial load is applied eccentrically on a rod of square cross-section (1 cm× 1 cm) as shown in the figure.
The strains measured by the two strain gages attached to the top and bottom surfaces at a distance of 0.5 m from the tip areϵ1 = 0.0016 and ϵ2 = 0.0004, respectively.
The eccentricity in loading,e, is ______ mm.
Answer: (0.95 to 1.05)
61. For a thin-walled I section, the width of the two flanges as well as the web height are the same, i.e., 2𝑏 = 20 mm. Thickness is 0.6 mm. The second moment of area about a horizontal axis passing through the centroid is______ mm4.
Answer: (2700 to 2960)
62. A damper with damping coefficient, c, is attached to a mass of 5 kg and spring of stiffness 5 kN/m as shown in figure. The system undergoes under-damped oscillations.
If the ratio of the 3rd amplitude to the 4th amplitude of oscillations is 1.5, the value
ofc is ____ Ns/m (rounded off to the nearest integer).
Answer: (19 to 21)
63. A uniform rigid prismatic bar of total mass m is suspended from a ceiling by two identical springs as shown in figure.
Letω1 and ω2 be the natural frequencies of mode I and mode II respectively (ω1<ω2).
The value of ω2/ω1 is _________ (rounded off to one decimal place).
Answer: (1.7 to 1.8)
64. An ideal ramjet is to operate with exhaust gases optimally expanded to ambient pressure at an altitude where temperature is 220 K. The exhaust speed at the nozzle
exit is 1200 m/s at a temperature of 1100 K.
Given :γ = 1.4 at 220 K; R = 287 J/kg-K) for air
γ = 1.33 at 1100 K; R = 287 J/(kg-K) for exhaust gases.
The cruise speed of this ramjet is ________ m/s (rounded off to nearest integer).
Answer: (545 to 555)
65. A multistage axial compressor takes in air at 1 atm, 300 K and compresses it to a minimum of 5 atm.
The mean blade speed is 245 m/s and work coefficient, ∆Cθ/U is 0.55 for each stage. For air, use Cp = 1005 J/(kg-K), R = 287 J/(kg-K) and γ = 1.4.
If the compression is isentropic, the number of stages required is ___________(rounded off to the next higher integer).
Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. Gauri said that she can play the keyboard __________ her sister.
(A) as well as
(B) as better as
(C) as nicest as
(D) as worse as
Answer: (A)
2. A transparent square sheet shown above is folded along the dotted line. The folded sheet will look like ________.
Answer: (B)
3. If θ is the angle, in degrees, between the longest diagonal of the cube and any one of the edges of the cube, then, cos θ =
(A) 1/2
(B) 1/√3
(C) 1/√2
(D) √3/2
Answer: (B)
4. If then the value of x is:
(A) 2
(B) 4
(C) 6
(D) 8
Answer: (B)
5. Pen : Write :: Knife : _________
Which one of the following options maintains a similar logical relation in the above?
(A) Vegetables
(B) Sharp
(C) Cut
(D) Blunt
Answer: (C)
Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).
6. Listening to music during exercise improves exercise performance and reduces discomfort. Scientists researched whether listening to music while studying can help students learn better and the results were inconclusive. Students who needed external stimulation for studying fared worse while students who did not need any external stimulation benefited from music.
Which one of the following statements is the CORRECT inference of the above passage?
(A) Listening to music has no effect on learning and a positive effect on physical exercise.
(B) Listening to music has a clear positive effect both on physical exercise and on learning.
(C) Listening to music has a clear positive effect on physical exercise. Music has a positive effect on learning only in some students.
(D) Listening to music has a clear positive effect on learning in all students. Music has a positive effect only in some students who exercise.
Answer: (C)
7. A jigsaw puzzle has 2 pieces. One of the pieces is shown above. Which one of the given options for the missing piece when assembled will form a rectangle? The piece can be moved, rotated or flipped to assemble with the above piece.
Answer: (A)
8. The number of students in three classes is in the ratio 3:13:6. If 18 students are added to each class, the ratio changes to 15:35:21.
The total number of students in all the three classes in the beginning was:
(A) 22
(B) 66
(C) 88
(D) 110
Answer: (C)
9. The number of units of a product sold in three different years and the respective net profits are presented in the figure above. The cost/unit in Year 3 was ` 1, which was half the cost/unit in Year 2. The cost/unit in Year 3 was one-third of the cost/unit in Year 1. Taxes were paid on the selling price at 10%, 13% and 15% respectively for the three years. Net profit is calculated as the difference between the selling price and the sum of cost and taxes paid in that year.
The ratio of the selling price in Year 2 to the selling price in Year 3 is ________.
(A) 4:3
(B) 1:1
(C) 3:4
(D) 1:2
Answer: (A)
10. Six students P, Q, R, S, T and U, with distinct heights, compare their heights and make the following observations.
Observation I: S is taller than R.
Observation II: Q is the shortest of all.
Observation III: U is taller than only one student.
Observation IV: T is taller than S but is not the tallest.
The number of students that are taller than R is the same as the number of students shorter than ______.
(A) T
(B) R
(C) S
(D) P
Answer: (C)
Chemistry (XL-P)
1. The geometry of Fe(CO)5 is
(Given: Atomic number of Fe = 26)
(A) pentagonal planar
(B) square pyramidal
(C) trigonalbipyramidal
(D) trigonal pyramidal
Answer: (C)
2. The structure of the major product Q of the following reaction is
Answer: (A)
Q.3 – Q.5 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).
3. The time taken by a first order reaction to reach 90% completion is 20 s. The time taken for the reaction to reach 50% completion is ___________ s (rounded off to the closest integer).
Answer: (6 to 6)
4. The ground state energy of an electron in a hydrogen atom is –13.60 eV. The energy of the electron in the third excited state is _________eV (rounded off to two decimal places).
Answer: (-0.86 to -0.84)
5. A solution of a compound shows an absorbance of 0.42 at 275 nm in a cuvette with 0.1 dm light path. The molar absorptivity of the compound is ε275 = 8.4 × 103 M–1 cm–1. The concentration of the compound is ______× 10–5 M (rounded off to the closest integer).
Answer: (5 to 5)
Q.6 – Q.9 Multiple Choice Question (MCQ), carry TWO mark each (for each wronganswer: – 2/3).
6. The CORRECT order of acidity of the following compounds is
(A) II > I > III
(B) II > III > I
(C) III > II > I
(D) III > I > II
Answer: (B)
7. The O–O bond order in O22– species is
(A) 0.5
(B) 1.0
(C) 1.5
(D) 2.0
Answer: (B)
8. For a reaction, X → Products
Group I contains three plots of reactant concentrations as functions of time, where x = concentration of reactant X at time t; x0 = concentration of reactant X at initial time, t = 0. Group II gives a list of different orders of reaction. Match the plots with the order of the reaction.
(A) (P) – (1), (Q) – (2), (R) – (3)
(B) (P) – (3), (Q) – (2), (R) – (1)
(C) (P) – (2), (Q) – (3), (R) – (1)
(D) (P) – (2), (Q) – (1), (R) – (3)
Answer: (C)
9. The structure of the major product S of the following reaction is
Answer: (B)
Q.10 – Q.11 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).
10. The CORRECT combination(s) of Y and T for the following elimination reaction is(are)
Answer: (B; D)
11. Among the following, the diamagnetic species is(are)
(Given: Atomic numbers of Fe = 26, Co = 27, and Ni = 28)
(A) [CoF6]3−
(B) [Ni(H2O)6]2+
(C) [Fe(CN)6]4−
(D) [Co(NH3)6]3+
Answer: (C; D)
Q.12 – Q.15 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).
12. Given the following standard heats of formation, ∆fH⊖(P, g) = 314. 6 kJ mol−1, ∆fH⊖(PH3, g) = 5. 4 kJ mol−1, and ∆fH⊖ (H, g) = 218. 0 kJ mol−1, the average bond enthalpy of a P–H bond in PH3(g) is __________ kJ mol−1(rounded off to one decimal place).
Answer: (321.0 to 321.2)
13. The total number of possible geometrical isomer(s) for [PtBrCl(NH3)(py)]0 is _______.
(Given: py = Pyridine and atomic number of Pt = 78)
Answer: (3 to 3)
14. Given the standard reduction potentials and the potential of the following cell
at 25 °C is___________ V (rounded off to two decimal places).
(Given: Faraday constant = 96500 C mol−1, Gas constant R = 8.314 J K−1mol−1)
Answer: (3.00 to 3.02)
15. The freezing point of 80 g of acetic acid (freezing point constant 3.9 K kg mol−1) was lowered by 7.8 K due to the addition of 20 g of a compound. The molar mass of the compound is _____________ g mol−1 (rounded off to closest integer).
Answer: (125 to 125)
Biochemistry (XL-Q)
Q.1 – Q.10 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. Which one of the following molecules (~ 1mg/mL) do NOT absorb at 280 nm in an aqueous solution of pH 7.00 at room temperature?
(A) Poly deoxy-Guanylate (poly dG)
(B) Adenosine triphosphate
(C) Phenylalanine
(D) Tyrosine
Answer: (C)
2. A molecule that forms a donor-acceptor energy transfer pair with the dansyl group is ______
(A) Aspartate
(B) Histidine
(C) Lysine
(D) Tryptophan
Answer: (D)
3. The stationary phase used in gel filtration chromatography is composed of ___
(A) Blue dextran
(B) Carboxymethyl (CM) cellulose
(C) Diethylaminoethyl (DEAE) cellulose
(D) Sepharose
Answer: (D)
4. According to the “wobble hypothesis” inosine at the third position of the anticodon cannot form hydrogen bonds with ________
(A) Adenine
(B) Cytidine
(C) Guanine
(D) Uracil
Answer: (C)
5. pKa value of the guanidinium group of Arginine is _____
(A) 4.30
(B) 7.40
(C) 9.20
(D) 12.50
Answer: (D)
6. The non-coenzyme vitamin is ________
(A) Ascorbic acid
(B) Folic acid
(C) Nicotinic acid
(D) Thiamine
Answer: (MTA)
7. Telomerase has a function similar to __________
(A) DNA dependent DNA polymerase
(B) RNA polymerase
(C) DNA gyrase
(D) Reverse transcriptase
Answer: (D)
8. Which one of the following enzymes is used in Polymerase Chain Reaction ?
(A) Klenow fragment
(B) Taq polymerase
(C) T7 polymerase
(D) Primase
Answer: (B)
9. In hepatocytes, the detoxification of drugs occurs in ______
(A) Golgi apparatus
(B) Nucleolus
(C) Rough endoplasmic reticulum
(D) Smooth endoplasmic reticulum
Answer: (D)
10. Which one of the following antibiotics can form an ion channel in the bacterial membrane?
(A) Ampicillin
(B) Gramicidin A
(C) Gentamicin
(D) Rifampicin
Answer: (B)
Q.11 – Q.12 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).
11. Which one of the following cells lack hypoxanthine-guanine phosphoribosyltransferase (HGPRT)?
(A) B Cell
(B) T Cell
(C) Macrophage
(D) Myeloma Cell
Answer: (D)
12. Which of the following lipids is non-ionic?
(A) Sphingomyelin
(B) Galactocerebroside
(C) Lecithin
(D) Phosphatidyl inositol
Answer: (B)
Q.13 – Q.20 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).
13. Anti-B antibodies are present in the serum of ________
(A) Blood group A
(B) Blood group B
(C) Blood group AB
(D) Blood group O
Answer: (A; D)
14. Which of the following are energy requiring processes?
(A) Facilitated diffusion
(B) Active transport
(C) Nonmediated transport
(D) Na+/K+transport
Answer: (B; D)
15. Which of the following are correctly paired?
(A) Replication: DnaA
(B) Recombination: RecA
(C) DNA repair: Rho factor
(D) Transcription: Sigma factor
Answer: (A; B; D)
16. The high energy compound(s) is/are:
(A) Phosphoenol pyruvate
(B) Adenosine monophosphate
(C) 1,3-Bisphosphoglycerate
(D) Vitamin K
Answer: (A; C)
17. Given below are four plots obtained from separate experiments on enzyme inhibition kinetics. The velocity (v) of the reaction is plotted at varying concentrations of substrate (s) and inhibitor (I). The plot(s) corresponding to competitive inhibition is/are
(A) (i)
(B) (ii)
(C) (iii)
(D) (iv)
Answer: (A; C)
18. With respect to sodium dodecyl sulphate – polyacrylamide gel electrophoresis (SDS-PAGE), which of these statement(s) is/are true?
(A) Ethidium bromide is used to track the progress of electrophoretic mobility
(B) β-mercaptoethanol is used to reduce disulphide bonds
(C) The protein migrates towards the anode
(D) The lower molecular weight protein migrates slower than the larger molecularweight protein
Answer: (B; C)
19. In the plot given below, the solid line represents oxygen binding to hemoglobin under physiological conditions. The broken line represents the condition(s) of
(A) High CO2 concentration
(B) Increase in 2,3- Bisphosphoglycerate concentration
(C) High pH
(D) Loss of cooperativity
Answer: (C)
20. Considering the open chain forms, which of the following pair(s) represent/s an epimer?
(A) D-mannose and D-fructose
(B) D-glucose and D-mannose
(C) D-glucose and D-fructose
(D) D-galactose and D-glucose
Answer: (B; D)
Botany (XL-R)
Q.1 – Q.7 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. Wheat plants treated with prolonged cold temperature at the seedling stage flower earlier than the untreated control. Seeds collected from these treated individuals, however, give rise to plants that do not flower early. This phenomenon is called
(A) vernalization.
(B) temperature acclimation.
(C) photoperiodism.
(D) adaptation.
Answer: (A)
2. Which ONE of the following plant taxa contains vascular tissue (xylem and phloem) but not woody tissue?
(A) Oak
(B) Moss
(C) Pine
(D) Fern
Answer: (D)
3. Which ONE of the following statements regarding spores and gametes is CORRECT?
(A) Spores can directly undergo mitosis whereas gametes cannot.
(B) Gametes can directly undergo mitosis whereas spores cannot.
(C) Neither spores nor gametes can directly undergo mitosis.
(D) Both spores and gametes can directly undergo mitosis.
Answer: (A)
4. Which ONE of the following organelles controls gravitropism in the roots of higher plants?
(A) Chromoplast
(B) Amyloplast
(C) Chloroplast
(D) Etioplast
Answer: (B)
5. Phytoalexins play important role in plant defense against pathogens. Choose the INCORRECT option related to phytoalexins.
(A) Phytoalexins belong to secondary metabolites.
(B) Phytoalexins have antifungal activity.
(C) Phytoalexins are abundant in plants under normal condition.
(D) Different hosts produce phyallexins of varying chemical nature.
Answer: (C)
6. The figure shows the germination percentage of imbibed seeds treated with the given sequence of red (R) and far-red (F) light (each exposure lasting 5 min). The percentage of germination was scored after 72 hours in darkness at 25 °C. Based on this, which ONE of the following options is CORRECT?
(A) Red light induces seed germination whereas far-red light inhibits it.
(B) Red light inhibits seed germination whereas far-red light induces it.
(C) Both red and far-red light inhibit seed germination.
(D) Both red and far-red light induce seed germination.
Answer: (A)
7. The structures of four plant hormones are shown. Identify the CORRECT hormone that is responsible for bending of coleoptile of canary grass in response to unidirectional white light.
Answer: (A)
Q.8 – Q.9 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).
8. Which of the following cellular component(s) is/are NOT part(s) of cytoskeleton in Angiosperms?
(A) Microtubules
(B) Microfilaments
(C) Intermediate filaments
(D) Centrioles
Answer: (C; D)
9. Which of the following enzyme(s), when overexpressed, would result in rice grains with increased β-carotene content?
Q.10 Numerical Answer Type (NAT), carry ONE mark (no negative marks).
10. In spiral phyllotaxis, leaves are initiated sequentially on the meristem with two successive primordia being separated by golden angle. If a plant follows right-handed spiral phyllotaxis when looked down the meristem, then the angle between two successive leaves would be _________degrees (with correct sign, round off to one decimal place).
Answer: (137.4 to 137.6 OR -137.6 to -137.4)
Q.11 – Q. 15 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).
11. Match the cell/tissue types in GROUP I with their corresponding total DNA content in GROUP II of a typical diploid Angiosperm species and choose the CORRECT option (C denotes DNA content in haploid genome).
(A) P-1, Q-2, R-3, S-5
(B) P-2, Q-2, R-1, S-5
(C) P-1, Q-2, R-1, S-5
(D) P-2, Q-1, R-2, S-4
Answer: (B)
12. Match the modified organs in GROUP I with their corresponding prototypic forms in GROUP II and choose the CORRECT option.
(A) P-1, Q-2, R-2, S-1
(B) P-2, Q-1, R-1, S-2
(C) P-1, Q-2, R-1, S-2
(D) P-1, Q-1, R-2, S-1
Answer: (A)
13. The diagram describes the ABC model of flower patterning in Arabidopsis where the A, B and C functions are operational in the whorls (1+2), (2+3) and (3+4), respectively, in the wild-type flower. Removal of A or C function results in the floral organ arrangements as (carpel; stamen; stamen; carpel) or (sepal; petal; petal; sepal), respectively. Based on these observations, which ONE of the following molecular pathways is CORRECT for floral organ pattern generation? Arrow indicates activation and bar indicates inhibition.
Answer: (C)
14. Find the CORRECT match among the plant species in GROUP I, the predominant phytochemical in GROUP II and the economic/medical use in GROUP III.
(A) P-i-1, Q-ii-3, R-iii-4, S-v-5, T-iv-2
(B) P-ii-1, Q-iii-2, R-i-3, S-v-5, T-iv-4
(C) P-ii-1, Q-iii-2, R-v-4, S-i-3, T-iv-5
(D) P-i-2, Q-ii-3, R-iv-1, S-iii-5, T-v-4
Answer: (B)
15. Match the genetically modified crop in GROUP I with the corresponding genetic element in GROUP II.
(A) P-3, Q-1, R-4, S-2
(B) P-1, Q-3, R-2, S-4
(C) P-2, Q-1, R-4, S-3
(D) P-3, Q-2, R-4, S-1
Answer: (A)
Q.16 – Q.18 Multiple Select Question (MSQ), carry TWO mark each (no negative marks)
16. To understand the mechanism of systemic acquired resistance (SAR), a team of researchers isolated a mutant with reduced SAR response. Sequencing of this mutant revealed homozygous mutations in two genes, X and Y. Which of the following experiment(s) would test whether the mutant phenotype is caused by mutation in either or both the genes?
(A) Complement the mutant with X or Y and analyze the phenotype in each case.
(B) Complement the mutant with both X and Y and analyze the phenotype.
(C) Cross the mutant with wild-type and analyze the segregation pattern of thephenotype.
(D) Compare the expression of X and Y in mutant and wild-type plants.
Answer: (A; B; C)
17. The observations of an experiment on seed germination in various genotypes under different light conditions are given, where √ and X indicate germination and the lack of it, respectively.
(A) All the three light qualities– blue, red and far-red – are required for seedgermination.
(B) Any one of the three light qualities – blue, red and far-red – is sufficient toinduce seed germination.
(C) The CRY1, phyA and phyB proteins are required for blue, red and far-red lightperception, respectively.
(D) The VP1 protein is unlikely to be involved in light perception.
Answer: (B; D)
18. Which of the following option(s) is/are CORRECT in the context of hybrid plant generation using Barnase/Barstar-based male sterile lines?
(A) Barnase inhibits Barstar.
(B) Barstar inhibits Barnase.
(C) Barnase and Barstar are used to generate the male sterile line and the restorerline, respectively.
(D) Barnase and Barstar are used to generate the restorer line and the male sterileline, respectively.
Answer: (B; C)
Q.19 – Q.20 Numerical Answer Type (NAT), carry TWO mark each (no negative marks)
19. In a diploid plant species, the T allele produces tall individuals and is completely dominant over the t allele that produces short individuals. Similarly, the W allele produces round seeds and is completely dominant over the w allele that produces wrinkled seeds (assume T and W loci not linked). If a parent with TTWW genotype is crossed to another parent with ttww genotype, the fraction of the F2 population produced by the fusion of both recombinant gametes would be ___________. (Round-off to two decimal places.)
Answer: (0.25 to 0.25)
20. In a population of a diploid plant species obeying Hardy-Weinberg equilibrium, a locus regulating flower color has two alleles R and r. Individuals with RR, Rrand rr genotypes produce red, pink and white flowers, respectively. If the ratio of red, pink and white flower-producing individuals in the population is 6:3:1, then the frequency of r allele in the population would be __________%.
(Round-off to two decimal places.)
Answer: (25 to 25)
Microbiology (XL-S)
Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. Antonie van Leeuwenhoek observed several microscopic organisms under his hand-made microscope. He described them as
(A) Bacteria.
(B) Fungi.
(C) Animalcules.
(D) Bacteriophages.
Answer: (C)
2. Which ONE of the following pathways oxidizes 1 mole of glucose to 2 moles of pyruvic acid along with one mole each of ATP, NADH and NADPH, in Pseudomonas, but not in Bacillus spp.?
(A) Gluconeogenesis
(B) Embden-Meyerhoff Pathway (EMP)
(C) Entner-Doudoroff (ED) Pathway
(D) Pentose Phosphate Pathway (PPP)
Answer: (C)
3. Water balance in extreme halophiles such as Halobacterium is maintained by cell surface glycoproteins consisting of
(A) glycine and lysine.
(B) lysine and histidine.
(C) glycine.
(D) aspartate and glutamate.
Answer: (D)
4. Nocardia spp. are not amenable to the classical method of Gram staining due to the presence of
(A) N-acetyltalosaminuronic acid in the cell wall.
(B) thick peptidoglycan.
(C) mycolic acid.
(D) keto-deoxy-octulosonic acid.
Answer: (C)
5. Protists belonging to the genus Trichonympha thrive in the gut of termites. They help the termites use wood as a food source. This relationship is an example of
(A) parasitism.
(B) competition.
(C) commensalism.
(D) mutualism.
Answer: (D)
Q.6 – Q.9 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).
6. Which of the following is/are used as electron donor/s for CO2 reduction during photosynthesis in purple sulfur bacteria?
(A) Hydrogen sulfide
(B) Thiosulfates
(C) Methane
(D) Sulfates
Answer: (A; B)
7. Which of the following catalyze(s) substrate-level phosphorylation?
(A) ATP synthase
(B) Succinate thiokinase
(C) Phosphofructokinase
(D) Pyruvate kinase
Answer: (B; D)
8. Which of the following method(s) can be applied to identify a bacterial species?
(A) Fluorescent in situ hybridization (FISH)
(B) Polymerase chain reaction (PCR) followed by sequencing of the amplicon
(C) Gram staining
(D) Acid-fast staining
Answer: (A; B)
9. Which of the following event(s) would contribute to the induction of lac operon in a wild-type strain of E. coli?
(A) Accumulation of allolactose in the cell
(B) Direct binding of cAMP to the promoter DNA
(C) Binding of cAMP to a specific protein leading to its interaction with thepromoter
(D) Elimination of cAMP from the cell
Answer: (A; C)
Q.10 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).
10. One mole of a circular bacterial plasmid was digested with a high-fidelity restriction enzyme. The plasmid has five restriction sites for the enzyme used. The number of moles of fragments released upon cleavage at all sites is________.
Answer: (5 to 5)
Q.11 – Q.16 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).
11. Under anaerobic fermentative growth conditions, one mole of glucose yields 22 grams of Streptococcus faecalis or 8.6 grams of Zymomonasmobilis. The molar growth yield (YATP) for (i) S. faecalis and (ii) Z. mobilis will be
(A) (i) 11 and (ii) 4.3
(B) (i) 22 and (ii) 4.3
(C) (i) 22 and (ii) 8.6
(D) (i) 11 and (ii) 8.6
Answer: (D)
12. The order of abundance of quinones (ubiquinone [UQ], menaquinone [MQ] and demethylmenaquinone [DMQ]) in E. coli growing anaerobically on fumarate is
(A) UQ > DMQ > MQ
(B) MQ > DMQ >UQ
(C) MQ = DMQ > UQ
(D) MQ > UQ > DMQ
Answer: (B)
13. What is the number of ATPs generated per molecule of NADH during oxidative phosphorylation in E. coli via (i) NDH-1 and cytochrome bo complex or (ii) the NDH-2 and cytochrome bd complex? (Assume H+/ATP =3)
(A) (i) 2.00 and (ii) 3.67
(B) (i) 3.00 and (ii) 2.67
(C) (i) 2.70 and (ii) 0.67
(D) (i) 2.50 and (ii) 0.50
Answer: (C)
14. Match the Immunoglobulin classes with their function
(A) (i)- (s), (ii)-(p), (iii)-(q), (iv)-(r)
(B) (i)- (p), (ii)-(t), (iii)-(q), (iv)-(r)
(C) (i)- (q), (ii)-(p), (iii)-(t), (iv)-(r)
(D) (i)- (r), (ii)-(p), (iii)-(t), (iv)-(s)
Answer: (A)
15. The figure shows the profiles of quantitative real-time PCR (qRT-PCR) tests for SARS-CoV-2 conducted on the throat swab samples of three individuals (X, Y and Z). Tests were carried out under identical conditions. Dotted line represents the threshold fluorescent value. Identify the correct statement on the status of the COVID-19 tests of the individuals based on their qRT-PCR profiles.
(A) X and Y are negative; Z is positive
(B) X and Y are positive; There is no apparent difference in their viral load
(C) X and Y are positive; X has the highest viral load
(D) X and Y are positive; Y has the highest viral load
Answer: (C)
16. The rate of appearance of recombinant E. coli strains containing different genes after a mating between Hfr and F− strains is shown in the graph (left). The approximate location of different genes (p, q, r, s, t, x, and y) along the Hfr chromosome is also shown (right). Based on this information, identify the recombinants X, Y and Z.
(A) X is x+, Y is r+and Z is p
(B) X is p+, Y is r+and Z is x
(C) X is x+, Y is p+and Z is r
(D) X is p+, Y is x+and Z is r
Answer: (B)
Q.17 – Q.20 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).
17. The genome of a bacterium encodes for 10 different surface antigens, whose expression can be turned ‘ON’ or ‘OFF’ randomly and independently. The number of possible antigenic combinations is__________.
Answer: (1024 to 1024)
18. Suppose the mRNAs in a newly discovered bacteria are composed of only two distinct nucleotides (as opposed to four found in all known organisms). Considering that the organism has no nucleotide modification systems, the number of nucleotides required per codon to encode at least 20 distinct amino acids will be________.
Answer: (5 to 5)
19. The decimal reduction time (D) for reducing 1012 spores of Clostridium botulinum to 1 spore at 111°C will be_______ min (in integer). The D value is 0.2 min at 121°C. The increase in temperature required to change D to 1/10th of its initial value (Z value) is 10°C.
Answer: (24 to 24)
20. The generation time of E. coli is 30 minutes. For an exponentially growing culture, the initial number of bacteria required to reach a number of 109 in 2 hours is_________×107 (round off to two decimal places).
Answer: (6.20 to 6.30)
Zoology (XL-T)
Q.1 – Q.7 Multiple Choice Question (MCQ), carry ONE mark each (for each wronganswer: – 1/3).
1. Ichthyophis belongs to which of the following Class?
(A) Mammalia
(B) Reptilia
(C) Amphibia
(D) Aves
Answer: (C)
2. The two homologous genes occurring in different species are called
(A) paralogous
(B) orthologous
(C) pseudologous
(D) prologous
Answer: (B)
3. The expression of holandric genes causes which of the following genetic trait in humans?
(A) Haemophilia
(B) Sickle cell anaemia
(C) Down’s Syndrome
(D) Hypertrichosis
Answer: (D)
4. Assume that the anticodon for an unknown amino acid is 3ʹ AUG 5ʹ. The corresponding code on DNA sequence would be
(A) 3ʹ TAC 5ʹ
(B) 5ʹ TAG 3ʹ
(C) 3ʹ ATG 5ʹ
(D) 5ʹ ATG 3ʹ
Answer: (C)
5. The Organ of Corti is found in which of the following parts of human body?
(A) Heart
(B) Inner ear
(C) Kidney
(D) Nasal cavity
Answer: (B)
6. In adult athletes, muscles grow larger when exercised and are capable of regeneration after injury. This is due to proliferation and differentiation of
(A) satellite cells
(B) myelin sheath
(C) oxyntic cells
(D) choanocytes
Answer: (A)
7. The term innate behavior is a sort of animal behavior that is
(A) triggered by an environmental change
(B) learnt by hit-and-trial approach
(C) trained and taught by the parent
(D) fixed developmentally at the genetic level
Answer: (D)
Q.8 – Q.10 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).
8. A man, whose mother and father had blood groups A and O respectively, marries a woman with blood group AB. If the man has blood group A, then the number of different blood groups possible among their children will be _________ (in integer).
Answer: (3 to 3)
9. A population of snakes in an isolated island is in Hardy–Weinberg equilibrium for a gene with only two alleles (A and a). If the allelic frequency of A is 0.6, then the genetic frequency of Aa is _________ round off to 2 decimal places).
Answer: (0.48 to 0.48)
10. In the structure of a polypeptide, one α-helix (3.613 helix) contains 32 intra-chain hydrogen bonds. The number of turns in the helix will be _________(in integer).
Answer: (10 to 10)
Q.11 – Q. 16 Multiple Choice Question (MCQ), carry TWO marks each (for each wronganswer: – 2/3).
11. Match the terms in Column I with the specific descriptions in Column II.
(A) P-(iii), Q-(vi), R-(i), S-(v), T-(ii), U-(iv)
(B) P-(v), Q-(ii), R-(iii), S-(vi), T-(i), U-(iv)
(C) P-(ii), Q-(iv), R-(vi), S-(v), T-(i), U-(iii)
(D) P-(iii), Q-(vi), R-(ii), S-(v), T-(iv), U-(i)
Answer: (A)
12. Match the autoimmune diseases in Column I for the self-antigens in Column II.
(A) P-(i), Q-(ii), R-(iii), S-(iv)
(B) P-(ii), Q-(iii), R-(iv), S-(i)
(C) P-(iii), Q-(i), R-(iv), S-(ii)
(D) P-(iv), Q-(i), R-(ii), S-(iii)
Answer: (B)
13. Match the types of cell movements during gastrulation in Column I with the descriptions in Column II.
(A) P-(ii), Q-(iii), R-(iv), S-(i)
(B) P-(iv), Q-(i), R-(iii), S-(ii)
(C) P-(ii), Q-(iv), R-(i), S-(iii)
(D) P-(iii), Q-(ii), R-(iv), S-(i)
Answer: (C)
14. Match the therapeutic factors in Column I with the applications in Column II.
(A) P-(ii), Q-(iv), R-(v), S-(iii), T-(vi)
(B) P-(ii), Q-(v), R-(i), S-(iv), T-(iii)
(C) P-(v), Q-(vi), R-(iv), S-(iii), T-(i)
(D) P-(iii), Q-(iv), R-(ii), S-(v), T-(vi)
Answer: (A)
15. Match the cell organelles in Column I with the appropriate functions in Column II.
(A) P-(ii), Q-(iii), R-(v), S-(i), T-(iv)
(B) P-(iv), Q-(v), R-(i), S-(ii), T-(iii)
(C) P-(iv), Q-(v), R-(iii), S-(i), T-(ii)
(D) P-(ii), Q-(iii), R-(i), S-(v), T-(iv)
Answer: (D)
16. Cohesin and Condensin proteins of eukaryotes belong to which one of the following groups?
(A) Structural maintenance of chromosomes (SMC) proteins
(B) Histones
(C) DNA polymerases
(D) Topoisomerases
Answer: (A)
Q.17 – Q.18 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).
17. Which of the following options represent the animals as Endemic to India?
(A) Pygmy Hog
(B) Mountain Bongo
(C) Hirola
(D) Purple Frog
Answer: (A; D)
18. Which of the following amino acids contain more than one chiral center?
(A) Leucine
(B) Isoleucine
(C) Serine
(D) Threonine
Answer: (B; D)
Q.19 – Q.20 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).
19. An enzyme catalyzes the conversion of 30 μM of a substrate to product at reaction velocity of 9.0 μM s−1. When [Et] = 30 nM and Km = 10 μM, Kcat / Kmof enzyme will be n × 107 M−1s−1. The value of n is _________ (in integer).
Answer: (4 to 4)
20. A cross is made between two animals of genotypes AaBb x AaBb, where loci A and loci B assort independently. The progeny of this dihybrid cross was then allowed to self-cross. The proportion of the progeny that showed segregation for loci A (i.e., produce A- and aa progeny) in % will be_________ (in integer).
Answer: (50 to 50)
Food Technology XL (U)
Q.1 – Q.10 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. In a typical bacterial growth curve, the first order kinetics for growth rate is observed in
(A) Lag phase
(B) Log phase
(C) Stationary phase
(D) Decline phase
Answer: (B)
2. Which of the following microorganisms is NOT a causative agent for foodborne diseases?
(A) Campylobacter jejuni
(B) Clostridium perfingens
(C) Norovirus
(D) Borreliaburgdorferi
Answer: (D)
3. Which one of the followings is NOT a fermented food product?
(A) Tofu
(B) Vinegar
(C) Sauerkraut
(D) Tempeh
Answer: (A)
4. The Protein Efficiency Ratio (PER) is defined as
(A) Percentage of absorbed nitrogen retained in the body
(B) Weight gain in body mass (in gram) per gram protein intake
(C) Ratio of essential and non-essential amino acids in a protein
(D) Percent in vitro digestibility of a protein
Answer: (B)
5. Which one of the following enzymes sequentially releases maltose from starch?
(A) α−Amylase
(B) β− Amylase
(C) Glucoamylase
(D) Pullulanase
Answer: (B)
6. Highest mole % of amino acid mixture present in glutenin of wheat gluten are
(A) Glutamine and glutamic acid
(B) Serine and lysine
(C) Alanine and tryptophan
(D) Proline and glycine
Answer: (A)
7. Which one of the following compounds is present in soybean and acts asphytoesterogen?
(A) Tangeretin
(B) Lutin
(C) Quercetin
(D) Genistein
Answer: (D)
8. Which one of the followings is an oligosaccharide?
(A) Xanthan
(B) Alginate
(C) Raffinose
(D) Gellan
Answer: (C)
9. Bittering agent in grape fruit formed after juice extraction under acidic conditions is
(A) Quinine
(B) Theobromine
(C) Isohumulone
(D) Limonin
Answer: (D)
10. Difference between adsorption and desorption isotherms is known as
(A) Hysteresis
(B) Dryness
(C) Evaporation
(D) Dehydration
Answer: (A)
Q.11 – Q.13 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).
11. The conversion of pyruvate to lactic acid in homolactic fermentation iscatalyzed by
(A) Lactate dehydrogenase
(B) Pyruvate dehydrogenase
(C) Lactase
(D) Pyruvate decarboxylase
Answer: (A)
12. Which one of the following statements is INCORRECT with respect to Controlled Atmosphere Package (CAP) and Modified Atmosphere Package(MAP) of agro- produce?
(A) CAP and MAP limit microbial as well as biochemical activities.
(B) Gas composition inside a MAP during the storage is continuously monitored andregulated.
(C) CAP implies a greater degree of precision than MAP in maintaining specific levelsof the gas composition.
(D) Modification of the atmosphere inside a MAP is achieved by natural interplaybetween respiration of products and permeation of gases through the packagingfilm.
Answer: (B)
13. Match unit operation in Column I with its application in food processing in Column II.
(A) P-2, Q-4, R-2, S-I
(B) P-2, Q-3, R-4, S-1
(C) P-4, Q-1, R-2, S-3
(D) P-4, Q-2, R-1, S-3
Answer: (B)
Q.14 – Q.19 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).
14. Which of the followings are correct pair of GRAS chemical food preservative, affected organism and given food matrix?
(C) Differential scanning calorimeter – glass transition temperature – degree of caking
(D) Capillary viscometer – viscosity – sensory
Answer: (A; C)
Q.20 Numerical Answer Type (NAT), carry TWO mark (no negative marks).
20. Dry air is fed into a tray dryer. The percentage relative humidity of the air leaving the dryer is 60% at 70°C and 101.35 kPa. If, saturated vapour pressure of water at 70°C is 31.2 kPa, the humidity of the air leaving the dryer in kg water per kg dry air (round off to 3 decimal places) will be ________.
(Given : Molecular weight of water and air are 18.02 g mol-1 and 28.97 g mol-1respectively)
Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. Consider the following sentences:
(i) After his surgery, Raja hardly could walk.
(ii) After his surgery, Raja could barely walk.
(iii) After his surgery, Raja barely could walk.
(iv) After his surgery, Raja could hardly walk.
Which of the above sentences are grammatically CORRECT?
(A) (i) and (ii)
(B) (i) and (iii)
(C) (iii) and (iv)
(D) (ii) and (iv)
Answer: (D)
2. X came out of a building through its front door to find her shadow due to the morning sun falling to her right side with the building to her back. From this, it can be inferred that building is facing _________
(A) North
(B) East
(C) West
(D) South
Answer: (D)
3.
In the above figure, O is the center of the circle and, M and N lie on the circle.
The area of the right triangle MON is 50 cm2.
What is the area of the circle in cm ?
(A) 2π
(B) 50π
(C) 75π
(D) 100π
Answer: (D)
4. If
then, the value of the expression ∆ 2 ⊕ 3 ∆ ((4 ⨂ 2) ∇ 4) =
(A) −1
(B) −0.5
(C) 6
(D) 7
Answer: (D)
5. “The increased consumption of leafy vegetables in the recent months is a clear indication that the people in the state have begun to lead a healthy lifestyle”
Which of the following can be logically inferred from the information presented in the above statement?
(A) The people in the state did not consume leafy vegetables earlier.
(B) Consumption of leafy vegetables may not be the only indicator of healthy lifestyle.
(C) Leading a healthy lifestyle is related to a diet with leafy vegetables.
(D) The people in the state have increased awareness of health hazards causing by consumption of junk foods.
Answer: (C)
Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).
6. Oxpeckers and rhinos manifest a symbiotic relationship in the wild. The oxpeckers warn the rhinos about approaching poachers, thus possibly saving the lives of the rhinos. Oxpeckers also feed on the parasitic ticks found on rhinos.
In the symbiotic relationship described above, the primary benefits for oxpeckers and rhinos respectively are,
(A) Oxpeckers get a food source, rhinos have no benefit.
(B) Oxpeckers save their habitat from poachers while the rhinos have no benefit.
(C) Oxpeckers get a food source, rhinos may be saved from the poachers.
(D) Oxpeckers save the lives of poachers, rhinos save their own lives.
Answer: (C)
7.
A jigsaw puzzle has 2 pieces. One of the pieces is shown above. Which one of the given options for the missing piece when assembled will form a rectangle? The piece can be moved, rotated or flipped to assemble with the above piece.
Answer: (A)
8. The number of hens, ducks and goats in farm P are 65, 91 and 169, respectively. The total number of hens, ducks and goats in a nearby farm Q is 416. The ratio of hens:ducks:goats in farm Q is 5:14:13. All the hens, ducks and goats are sent from farm Q to farm P.
The new ratio of hens:ducks:goats in farm P is_____
(A) 5:7:13
(B) 5:14:13
(C) 10:21:26
(D) 21:10:26
Answer: (C)
9.
The distribution of employees at the rank of executives, across different companies C1, C2, …, C6 is presented in the chart given above. The ratio of executives with a management degree to those without a management degree in each of these companies is provided in the table above. The total number of executives across all companies is 10,000.
The total number of management degree holders among the executives in companies C2 and C5 together is_____.
(A) 225
(B) 600
(C) 1900
(D) 2500
Answer: (C)
10. Five persons P, Q, R, S and T are sitting in a row not necessarily in the same order. Q and R are separated by one person, and S should not be seated adjacent to Q.
The number of distinct seating arrangements possible is:
(A) 4
(B) 8
(C) 10
(D) 16
Answer: (D)
Reasoning and Comprehension (XH-B1)
Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. According to a recent article in a medical journal, consuming curcumin (from turmeric) significantly lowers the risk of COVID-19. The researchers draw this conclusion from a study that found that people who consumed one or more teaspoons of curcumin extract everyday were half as likely to be diagnosed with the disease as people who did not consume curcumin.
Which of the following, if true, most weakens the argument in the article?
(A) In another study, people who were given a zinc supplement everyday were more than four times less likely to be diagnosed with COVID-19 as those who did not.
(B) All the participants in this study were from the same state where no other spices or herbs are consumed.
(C) The participants who consumed curcumin were also more likely to exercise than those who did not.
(D) In another study, COVID-19 patients who were given curcumin were no more likely to recover than others.
Answer: (C)
2. Froot Inc. carried out an internet advertisement campaign for its new beverage CocoLoco. After the campaign, the director of the advertising company conducted a survey and found that the CocoLoco sales were higher than that of TenderJoos a competing product from Joos Inc. The agency concluded that the internet advertising campaign is more effective than advertising through other media.
Which of the following statements could strengthen the conclusion above by the agency?
(A) A Rs. 2 discount was offered on CocoLoco during the campaign period.
(B) CocoLoco sales were higher than those of TenderJoos before the internet campaign.
(C) A newspaper advertisement campaign the previous year did not increase CocoLoco sales.
(D) During the campaign for CocoLoco, Joos Inc. did not advertise TenderJoos at all.
Answer: (C)
3. An e-commerce site offered a deal last month conditional on the customer spending a minimum of Rs. 500. Any customer who buys 2 kg of fresh fruit will receive a hand mixer and any customer who buys 2 kg of fresh vegetables will receive a vegetable chopper.
Which of the following is NOT a possible outcome of the above?
(A) A customer purchased 3 kg of fresh fruit and did not receive a vegetable chopper.
(B) A customer purchased items for ₹500 which included 1 kg of vegetables and received a hand mixer.
(C) A customer purchased items for Rs. 500 which included 2 kg of vegetables and 1 kg of fruit and received a hand mixer.
(D) A customer purchased items for Rs. 300 which included 2 kg of fruit and received neither a hand mixer nor a vegetable chopper.
Answer: (C)
4. Writers of detective fiction often include an incompetent detective as a foil for the brilliant investigator-protagonist as they follow different paths in trying to solve the crime. In the individual accounts, the incompetent detective is frequently distracted by the culprit’s careful plans, while the competent investigator solves the case after a final confrontation. Analysts of such fiction believe that the authors select this story-telling technique to provide readers with more complexities in the form of misleading clues, while figuring out the crime.
Which of the following statements most logically follows from the passage above?
(A) A detective story is considered well-written if the brilliant investigator is accompanied by an incompetent detective.
(B) Writers of detective fiction use the contrast of an incompetent detective to mainly show how complex the investigation is.
(C) Writers of detective fiction never write stories where the incompetent detective solves the case.
(D) Writers of detective fiction use two investigative accounts to make it difficult for the reader to figure out the outcome.
Answer: (D)
5. The first (P1) and the last (P6) parts of a single sentence are given to you. The rest of the sentence is divided into four parts and labelled (L,M,N,O). Reorder these parts so that the sentence can be read through correctly and select one of the options given.
P1: Studies of several Sahitya Akademi award winners show that…
L: or encounter professional
M: and invariably develop a strained relationship with other literary figures
N: they often publish very little
O: after winning the prize
P6: …envy and rivalry.
The correct order is:
(A) NOLM
(B) MLON
(C) ONML
(D) MOLN
Answer: (C)
Q.6 – Q.10 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).
6. Gerrymandering refers to the targeted redrawing of election constituencies so as to benefit a particular party. This is especially important where the electoral system is “first past the post” in each constituency (i.e. one winner is selected in each constituency based on a majority of votes won) and where there is no other provision for proportional representation (as for example in the German system). For a simple illustration of gerrymandering, if a region consists of districts 1, 2, 3, …, 9 with districts 1, 2, 3, 4, 5, 6 favouring party P and 7, 8, 9 favouring party Q, then grouping of districts to constituencies as {1,2,3}, {4,5,6}, {7,8,9} will give two seats to party P and one seat to party Q, whereas the grouping {1,2,7}, {3,4,8}, {5,6,9} will give all three seats to party P, as they will secure a majority in each constituency.
Which of these statements can be deduced from the above?
(A) Gerrymandering implies that constituency boundaries can sometimes be drawn to favour one party over the other.
(B) Gerrymandering implies that proportional representation is impossible when districts are grouped to form constituencies.
(C) To counteract gerrymandering political parties should concentrate on districts where they are favoured.
(D) The grouping of districts to constituencies has very little impact on proportional representation.
Answer: (A)
7. X-ray examination of a recently discovered painting that some authorities judge to be a self-portrait by Michelangelo revealed an under-image of a woman’s face. Either Michelangelo or some other artist must have repainted over the first painting that had now been seen on the canvas. Because the woman’s face also appears on other paintings by Michelangelo, this painting is determined to indeed be an authentic painting by Michelangelo.
Which of the following assumptions must be made in reaching the conclusion above?
(A) When an already painted canvas of an artist is used, the second artist using that canvas for a new painting is usually influenced by the artistic style of the first.
(B) Several painted canvases that art historians attribute to Michelangelo contain under-images that appear on at least one other of Michelangelo’s paintings.
(C) Subject or subjects that appear in authenticated paintings of Michelangelo are rather unlikely to show up as under-images on painted canvases not attributed to Michelangelo.
(D) No painted canvas can be attributed to a particular artist with certainty without an X-ray analysis.
Answer: (C)
8. This season _______ tourists visited Ladakh than last season; however, ______ to be the biggest tourist destination in India. The tourism department explains that the number of tourists to India has ______ relative to previous years, ________ have chosen to visit Ladakh.
Select the correct sequence of phrases to fill in the blanks to complete the passage above.
(A) more / for the first time in many seasons it does not appear / increased / and it seems that most
(B) fewer / as in the past, it appears / in fact decreased / but it seems that only a small proportion
(C) fewer / for the first time in many seasons it appears / in fact decreased / but it seems that most
(D) more / this season as well, it appears / in fact decreased / but it seems that a large proportion
Answer: (C)
9. Reorder the sentences in (1) – (5) such that they form a coherent paragraph.
(1) In fact, dozens of languages today have only one native speaker still living, and that person’s death will mean the extinction of the language: It will no longer be spoken, or known, by anyone on earth.
(2) Many languages are falling out of use and are being replaced by others that are more widely used in the region or nation, such as English in Australia or Portuguese in Brazil.
(3) Many other languages are no longer being learned by new generations of children or by new adult speakers.
(4) An endangered language is one that is likely to become extinct in the near future.
(5) Unless the trends are reversed, these endangered languages will
become extinct by the end of the century.
(Adapted from What is an Endangered Language by A. Woodbury.)
(A) 2 3 1 4 5
(B) 2 3 5 4 1
(C) 4 1 5 2 3
(D) 4 2 3 1 5
Answer: (D)
10. The first (P1) and the last (P6) parts of a single sentence are given to you. The rest of the sentence is divided into four parts and labelled L,M,N,O. Reorder these parts so that the sentence can be read correctly and select one of the sequences below.
P1: For a little while…
L: it was a common belief
M: right after the treaty of Versailles
N: that Germany had caused World War I not just by her actions
O: held by analysts and politicians alike
P6: … but by also encouraging Italy in her own aggressions.
(A) LMNO
(B) MLON
(C) LNMO
(D) MOLN
Answer: (B)
Q.11 – Q.15 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).
11. After Florentino Ariza saw her for the first time, his mother knew before he told her because he lost his voice and his appetite and spent the entire night tossing and turning in his bed. But when he began to wait for the answer to his first letter, his anguish was complicated by diaorrhea and green vomit, he became disoriented and suffered from sudden fainting spells, and his mother was terrified because his condition did not resemble the turmoil of love so much as the devastation of cholera. Florentino Ariza’s godfather, an old homeopathic practitioner who had been Tránsito Ariza’s confidant ever since her days as a secret mistress, was also alarmed at first by the patient’s condition, because he had the weak pulse, the hoarse breathing, and the pale perspiration of a dying man. But his examination revealed that he had no fever, no pain anywhere, and that his only concrete feeling was an urgent desire to die. All that was needed was shrewd questioning, first of the patient and then of his mother, to conclude once again that the symptoms of love were the same as those of cholera. He prescribed infusions of linden blossoms to calm the nerves and suggested a change of air so he could find consolation in distance, but Florentino Ariza longed for just the opposite: to enjoy his martyrdom.
(Adapted from Love in a Time of Cholera by Gabriel García Márquez.)
The author of the passage is implying that:
(A) Homeopathy cures love.
(B) The doctor could not distinguish between love and cholera.
(C) The doctor could distinguish between love and cholera.
(D) The symptoms of love and cholera are similar.
Answer: (C; D)
12. Now, it is clear that the decline of a language must ultimately have political and economic causes: it is not due simply to the bad influence of this or that individual writer. But an effect can become a cause, reinforcing the original cause and producing the same effect in an intensified form, and so on indefinitely. A man may take to drink because he feels himself to be a failure, and then fail all the more completely because he drinks. It is rather the same thing that is happening to the English language. It becomes ugly and inaccurate because our thoughts are foolish, but the slovenliness of our language makes it easier for us to have foolish thoughts.
(Adapted from Politics and the English Language by George Orwell.)
The illustration of the man who takes to drink is used to underscore which of the following ideas in the passage above?
(A) Political and economic causes control deterioration of language.
(B) Foolish thoughts are enabled by inaccurate language.
(C) Effect of an action becomes the cause in a cyclic pattern.
(D) Drinking enables people to have foolish thoughts and slovenly language.
Answer: (B; C)
13. It is a pity that Caste even today has its defenders. The defences are many. It is defended on the grounds that the Caste System is but another name for division of labour, and if division of labour is a necessary feature of every civilised society, then it is argued that there is nothing wrong in the Caste System. Now the first thing to be urged against this view is that Caste System is not merely division of labour. It is also a division of labourers. Civilised society undoubtedly needs division of labour but nowhere is division of labour accompanied by this unnatural division of labourers into watertight compartments, grading them one above the other. This division of labour is not spontaneous or based on natural aptitudes. Social and individual efficiency requires us to develop the individual capacity and competency to choose and to make his own career. This principle is violated in so far as it involves an attempt to appoint tasks to individuals in advance, not on the basis of trained original capacities, but on that of birth. Industry undergoes rapid and abrupt changes and an individual must be free to change his occupation and adjust himself to changing circumstances, to gain his livelihood. (Adapted from Annihilation of Caste by Dr. B.R. Ambedkar.)
Which of the following observations substantiate the arguments found in the passage above?
(A) Newer generations are unable to change and move away from low-paying family professions, even with changed economic circumstances.
(B) Sedentary desk jobs are considered to have more value and are in greater demand than those involving manual labour.
(C) The government’s jobs guarantee programme makes low-level management jobs available across all industries to all graduates in the nation.
(D) A bus driver becomes an app creator and, in the course of one month, reaches one million downloads on Playstore with a four-star rating.
Answer: (A; B)
14. Imagine that you’re in a game show and your host shows you three doors. Behind one of them is a shiny car and behind the others are goats. You pick one of the doors and get what lies within. After making your choice, your host chooses to open one of the other two doors, which inevitably reveals a goat. He then asks you if you want to stick with your original pick, or switch to the other remaining door. What do you do? Most people think that it doesn’t make a difference and they tend to stick with their first pick. With two doors left, you should have a 50% chance of selecting the one with the car. If you agree, then you have just fallen afoul of one of the most infamous mathematical problems – the Monty Hall Problem. In reality, you should switch every time which doubles your odds of getting the car. Over the years, the problem has ensnared countless people, but not, it seems, pigeons. The humble pigeon can learn with practice the best tactic for the Monty Hall Problem, switching from their initial choice almost every time. Amazingly, humans do not!
(Adapted from an article by Ed Yong in Discover Magazine.)
Which of the following conclusions follow from the passage above?
(A) Humans calculate the probability of independent, random events such as the opening of a door by dividing the specific outcomes by the total number of possible outcomes.
(B) Humans find it very difficult to learn to account for the host’s hand in making the event non-random and, thereby, changing the outcome of the event.
(C) Calculating probabilities is difficult for humans but easy for pigeons; which is why the pigeons succeed where the humans fail.
(D) Humans are governed by reason, but pigeons are irrational and only interested in the outcome and will do whatever it takes to get food.
Answer: (A; B)
15. The truth is that, despite the recent success of car-makers P and Q, India’s automobile industry is in a state not that different from the bad old days of the license-permit quota raj when two carmakers dominated a captive domestic market with substandard vehicles and with very little, if any, research and development, and low to negligible productivity growth.High tariff barriers have certainly induced foreign automobile makers to enter the Indian market by setting up local operations, but this so-called “tariff jumping” foreign investment has produced an industry that is inefficient, operating generally at a low scale, and whose products are not globally competitive either in terms of cost or of innovation. It is noteworthy that the automobile parts industry, which has faced low tariffs (as low as 12.5%) and has been largely deregulated, has been characterised by higher productivity and much better export performance than the completely-built units’ sector in the years since liberalisation.
(Adapted from an Op-Ed in The Mint.)
Which of the following statements can be inferred from the above?
(A) Low tariff barriers increase productivity.
(B) Tariff jumping leads to increases in productivity.
(C) Deregulation has worked for the automotive parts industry and therefore should be applied to completely-built units.
(D) P and Q do not invest enough in research and development.
Answer: (A; C; D)
Economics (XH-C1)
Q.1 – Q.20 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. A firm finds that for the product that it produces, its (own) price elasticity of demand is 4. Currently, the firm is selling 2000 units per month at Rs. 5 per unit. If it wishes to increase its sales by 10%, it must
(A) lower its price by 4%
(B) lower its price by 2%
(C) lower its price by 2.5%
(D) increase its price by 2%
Answer: (C)
2. “Inflation increases the average level of prices”. Which of the following is(are) necessarily implied by this statement:
(i) The prices of commodities exceed income
(ii) Money supply grows at a higher rate than the real GDP
(A) Only (i)
(B) Only (ii)
(C) Both (i) and (ii)
(D) Neither (i) nor (ii)
Answer: (B)
3. For the production function Q = F(K, L) = √KL with PK = 4 and PL = 2, find the values of K and L that will minimize the cost of producing 2 units of output.
(A) K = 2√3 ; L = 3√2
(B) K = 2√2 ; L = √2
(C) K = √2 ; L = 2√2
(D) K = 2 ; L = 2
Answer: (C)
4. If the sum of price elasticities of imports and exports of a country exceeds unity, then a depreciation of domestic currency will ultimately result in
(A) contraction in trade deficit of the country
(B) widening of trade deficit of the country
(C) an uncertain net effect on the trade balance
(D) a huge outflow of foreign portfolio capital from that country
Answer: (A)
5. To determine the relationship between y and x1, Rohit estimated two different OLS models. In the first model, Rohit regressed y on x1 and x2 as given below
y = β0 + β1x1 + β2x2 + u (1)
In the second model, Rohit regressed y only on x1 as given below
y = δ0 + δ1x1 + v (2)
The estimated coefficients of x1 in the above two models are exactly same.
From this observation we can state conclusively that
(A) Only (i) is true
(B) Only (ii) is true
(C) Either (ii) or (iii) or both are true
(D) Neither (ii) nor (iii) is true
Answer: (C)
6. XYZ Co. Ltd. is a costless monopoly from suburban Mumbai producing and selling exotic mushrooms. The demand for mushrooms is given by
Q = 700 − 100P. Do you agree that XYZ will have a maximum possible
total revenue of Rs. 1500?
(A) Yes, the maximum possible total revenue is Rs.1500
(B) No, the maximum possible total revenue is less than Rs.1500
(C) No, the maximum possible total revenue is more than Rs.1500
(D) No, the maximum possible total revenue cannot be estimated
Answer: (B)
7. In a demand function estimation of a good X, a researcher collected data on various households’ consumption of good X (Qx) for various price levels. The researcher also collected data on household income (M) and household size (S). The estimated regression result is
where Px is price per unit of X. The values in the parentheses are the standard errors of the estimated coefficients. From the estimation one can conclude that
(A) the demand for good X is highly elastic
(B) X is an inferior good
(C) the estimated price elasticity of demand is not statistically significant
(D) the estimated price elasticity of good X is 2.345
Answer: (C)
8. Consider a duopoly market in which the market demand function is as follows: P = 40 − Q. For the two firms producing with identical marginal costs of 10, the Bertrand-Nash equilibrium price will be:
(A) 40
(B) 10
(C) 20
(D) 30
Answer: (B)
9. What would be the consequences for the OLS estimator if heteroscedasticity is present in a regression model but ignored? Assume that all the other classical assumptions are valid.
(A) It will be biased
(B) It will be inconsistent
(C) It will be unbiased but inefficient
(D) It will be unbiased but inconsistent
Answer: (C)
10. Walras’ Law implies that if there are N markets in the economy, then one only needs to find equilibrium prices in
(A) N − 2 markets
(B) N − 1 markets
(C) N + 1 markets
(D) all the N markets
Answer: (B)
11. There are many reasons why a poor country may fail to catch up with a rich neighbour. Which of the following is NOT one of these reasons?
(A) The poor country may have more rapid population growth
(B) The rich country may have more human capital
(C) The poor country may have a higher saving ratio
(D) The rich country through trade may be more integrated with the world economy
Answer: (C)
12. In a two country model, an increase in foreign country’s national income generally leads to:
(A) increased exports and increased domestic output
(B) decreased exports but increased domestic output
(C) decreased exports and decreased domestic output
(D) increased exports but decreased domestic output
Answer: (A)
13. Piku faces a lottery with outcomes of Rs. 24, Rs. 12, Rs. 48 and ₹6 given by the following probability distribution
She is indifferent between the lottery and receiving Rs. 28 with certainty. Given the information we can conclude that Piku is a
(A) risk lover
(B) risk averse
(C) risk neutral
(D) hedger
Answer: (A)
14. Consider a regression model y = β0 + βx + u where the continuous variable y is regressed on a dummy variable x, which takes the value either 1 or 0.
However, the model was estimated using the instrumental variable (IV) estimation method, wherein the indicator variable z is used as an instrument of x.
Let
be the sample averages of y when z takes the value 1 and 0, respectively
be the sample averages of x when z takes the value 1 and 0, respectively
be the sample averages of y when x takes the value 1 and 0, respectively
be the sample averages of z when x takes the value 1 and 0, respectively
Answer: (C)
15. Assuming that external economies exist, when demand increases in a perfectly competitive market, in the long-run, the price of the product
(A) rises above the initial price (before the demand increase) and quantity increases
(B) remains the same as the initial price (before the demand increase) and quantity increases
(C) falls below the initial price (before the demand increase) and quantity increases
(D) equals the initial price (before the demand increase) and quantity decreases
Answer: (C)
16. Consider an individual who maximizes her expected utility having Bernoulli utility function u(w) = α − βe−rw; w > 0 is wealth. The individual displays _________ relative risk aversion.
(A) constant
(B) increasing
(C) decreasing
(D) uncertain
Answer: (B)
17. For an open economy, the ‘twin deficits’ can be expressed by:
[where S = Savings; I = Gross Private Investment; G = Government Expenditures; TR = Transfer Payments; TX = Taxes; X = Exports; M = Imports and NFIA = Net Factor Income from Abroad]
(A) S − I = [G − TR − TX] + [X − M]
(B) I − S = [G + TX − TR] + [M − X]
(C) S − I = [G + TR − TX] + [X − M]
(D) I − S = [TX − G + TR] + [NFIA]
Answer: (C)
18. If expectations about inflation are formed as per the rational expectations hypothesis, then the short-run Philips curve will be
(A) negatively sloped
(B) parallel to the vertical axis
(C) parallel to the horizontal axis
(D) coinciding with the NAIRU
Answer: (B)
19. As economic development proceeds, income inequality tends to follow a(n) ________ curve.
(A) asymptotically convex
(B) inverted U-shaped
(C) V-shaped
(D) S-shaped
Answer: (B)
20. India has the highest amount of foreign debt in the form of
(A) Non Resident Indian (NRI) Deposits
(B) Commercial Borrowings
(C) Loans taken from the International Monetary Fund
(D) Loans taken from the Bank of England
Answer: (B)
Q.21 – Q.25 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).
21. Let A and B be two events with probabilities P(A) = 3/4 and P (B) = 1/3; then which of the following options is true?
Answer: (B)
22. If is an unbiased and consistent estimator of the population variance, then one can conclude that a(an) __________ estimator of the population standard deviation.
(A) unbiased and consistent
(B) biased and consistent
(C) unbiased and inconsistent
(D) biased and inconsistent
Answer: (B)
23. Consider the following demand−supply model, where
Demand function: P = Q2 − 12Q + 35
Supply function: 4P − 3Q = 0
The stable market equilibrium price-quantity combination will be
Answer: (A)
24. Trisha’s consumption preference on biryani (x) and pudding (y) is given by the utility function U(x, y) = x + 4y. The price per unit of biryani is Rs. 2 and the price per unit of pudding is Rs. 3. Trisha’s total income is ₹120. However, she faces an extra quantity constraint as she is not allowed to consume biryani more than 60 units and pudding more than 30 units. The optimum quantity of biryani and pudding consumed by Trisha is
(A) (x∗ y∗) = (30, 20)
(B) (x∗, y∗) = (15, 30)
(C) (x∗, y∗) = (30,15)
(D) (x∗, y∗) = (60, 0)
Answer: (B)
25. Consider a Cournot type n-firm natural spring oligopoly where the market demand for natural spring water is given by P(Q) = a − Q, a > 0. The n firms are symmetric. Each firm incurs a bottling cost of Ci = cqi, c > 0 and a > c. The equilibrium market price will be
Answer: (B)
Q.26 – Q.30 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).
26. Goods and Services Tax (GST) is
(A) a ‘destination based’ consumption tax
(B) an origin based tax assigned to the State of origin where the sale takes place
(C) an indirect tax
(D) a modified form of value added tax
Answer: (A; C; D)
27. Consider an intersection of roads without any traffic light. Two cars A and B approach an intersection and they want to proceed as indicated by respective arrows in the following diagram. If both proceed without stopping and there is an accident, then A would have a payoff of −100 and B would have a payoff of −500 (since B is responsible for the accident). If one stops, and the other proceeds then the payoff is: −5 and 10, respectively. If both of them stop, then it takes a little longer to reach their respective destinations, they have a payoff of −5 each. Find the Pure Strategy Nash Equilibrium (PSNE) of the players (Car drivers).
(A) (Car A, Car B) = (Stop, Stop)
(B) (Car A, Car B) = (Stop, Proceed)
(C) (Car A, Car B) = (Proceed, Stop)
(D) (Car A, Car B) = (Proceed, Proceed)
Answer: (B; C)
28. A Government Security (G-Sec)
(A) is a tradeable instrument issued by the Central Government
(B) is a tradeable instrument issued by State Governments
(C) can have maturity of only more than one year
(D) cannot be considered as ‘gilt-edged’ instrument
Answer: (A; B)
29. If a country has flexible exchange rate regime with perfect capital mobility, then according to the Mundell-Fleming Model, an expansionary fiscal policy will lead to
(A) no change in output
(B) reduced net exports
(C) appreciation of nominal exchange rate
(D) expansion of output
Answer: (A; B; C)
30. The basic tenets of ‘Monetarism’ are
(A) acceptance of the ‘quantity theory’ approach to macroeconomic analysis
(B) a strict rule based monetary policy
(C) a monetary approach to the balance-of-payments and exchange-rate theory
(D) an active stabilization policy through expansionary monetary/fiscal policies
Answer: (A; B; C)
Q.31 – Q.40 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).
31. Two farmers, Rohit and Harish, graze their animals on a common land. They can choose to use this common resource ‘lightly’ or ‘heavily’ and the resulting strategic interaction may be described as a simultaneous-move game. The payoff matrix is given below:
The minimum value of the discount rate (where the discount rate is less than one) under infinite repetition of the game where the threat strategy (“Graze lightly if the opponent also grazes lightly, whereas, if the opponent renege then always graze heavily in all the future periods”), is a Sub-game Perfect Nash Equilibrium (SPNE) and, both the farmers graze their animals lightly is _______ (round off to one decimal place).
Answer: (0.6 to 0.6)
32. Suppose Vijay has purchased a high-speed car worth Rs.1000000. During the purchase, an Insurance company has shared the latest available road safety survey, wherein it is mentioned that, due to heavy congestion on roads, there is 40% chance of an accident within the first year of car purchase resulting in loss of the car value by 60%. Vijay’s utility function for wealth (W) is given by U(W) = ln(W). If Vijay plans to buy an accident insurance having a premium of 30%, then he will purchase an insurance of Rs. ____________ (round off to the nearest integer).
Answer: (950000 to 999999)
33. Consider the following Table.
(All values are in Rupees Thousand Crore)
Based on the given data, the average Broad Money Multiplier for the period April – June is ________ (round off to three decimal places).
Answer: (5.300 to 5.600)
34. Consider two regression models estimated on a sample of 350 observations.
y = β0 + β1x1 + β2x2 + β3x3 + β4x4 + β5x5 + u ———(1)
y = α0 + α1x1 + α2x2 + v ———(2)
The R2 in model (1) is R12 = 0. 3521 and in model (2) is R22 = 0.2314. The value of the test statistic to test the H0: β3 = β4 = β5 = 0 is ________________(round off to three decimal places).
Answer: (21.100 to 21.800)
35. Consider a competitive market where the demand and supply functions are given by qD = 12 − 2P and qS = 4P, respectively. The tax rate per unit of output that maximizes the tax yield (revenue) is __________ (in integer).
Answer: (3 to 3)
36. Suppose the demand for a new pharmaceutical drug, on which the manufacturer has a patent monopoly, is given by: Q = (100 − P)A5 ; where Q is output, P is the price and A is advertising expenditure. Production cost of the patented drug is given by: C(Q) = 60Q. At the firm’s optimal choices, the ratio of advertising expenditure to sales revenue for the pharmaceutical product will be 1: ____ (in integer).
Answer: (8 to 8)
37. Let the rate of inflation in an economy be 4.2%, the growth rate of velocity of money be 2% and, the growth rate of real GDP be 6%. According to Milton Friedman’s ‘k’ percent rule, the rate of growth of money supply for maintaining stable prices will be __________ (round off to one decimal place).
Answer: (4.0 to 4.0)
38. The long-run cost function of all identical firms in a perfectly competitive industry is given by: C = 25q − 3q2 + 1. 5q3
The market demand function is: P = 2500 − 0. 25Q
The number of firms in the industry at equilibrium is __________(in integer).
Answer: (9904 to 9908)
39. Given below is an inter-industry transactions matrix. If final demand for the agriculture sector changes from 150 units to 300 units and for the manufacturing sector changes from 120 units to 200 units, then the output of the agriculture sector should be __________ units (in integer).
Answer: (1860 to 1880)
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40. Consider that a sample of size 3 is randomly drawn from a population that takes only two values, equally likely: − 1 and 1. Let z = max .(x1, x2, x3) where x1, x2, x3 are the sample observations. The expected value of z, E(z) is __________ (round off to two decimal places).
Answer: (0.70 to 0.80)
English (XH-C2)
Q.1 – Q.12 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. Which of the following texts is a collection of stories that a group of pilgrims tell each other?
(A) The Shepheardes Calender
(B) The Pilgrim’s Progress
(C) The Canterbury Tales
(D) Parliament of Fowls
Answer: (C)
2. Which of these is NOT an autobiography?
(A) Baby Kamble, The Prisons We Broke
(B) Bama, Karukku
(C) Mulk Raj Anand, Untouchable
(D) Om Prakash Valmiki, Joothan
Answer: (C)
3. Writers Workshop and Blaft are ___________.
(A) niche publishing houses in India that focus on particular genres
(B) little magazines that were set up by small collectives of writers
(C) digital archives of performance poetry
(D) well-known reading circles in 1950s’ Lucknow
Answer: (A)
4. The following lines capture the central trope of a well-known 18th century satirical tract.
“I have been assured by a very knowing American of my acquaintance inLondon, that a young healthy child, well nursed, is, at a year old, a mostdelicious, nourishing, and wholesome food…”
Identify the tract from the options below.
(A) John Stuart Mill, “On Liberty”
(B) Francis Bacon, “On Death”
(C) Jonathan Swift, “A Modest Proposal”
(D) Robert Graves, “Warning to Children”
Answer: (C)
5. Whose poem does Cleanth Brooks close-read to arrive at his concept of “the well-wrought urn”?
(A) William Wordsworth
(B) John Keats
(C) William Blake
(D) Alfred Tennyson
Answer: (B)
6. What is common among Charles Dickens’ A Tale of Two Cities, Mahasweta Devi’s Mother of 1084, Shobha Shakti’s Gorilla, and Chimamanda Ngozi Adichie’s Half of A Yellow Sun?
(A) These novels are set during times of political uprisings.
(B) These novels are feminist narratives.
(C) These novels have animals as central characters.
(D) These novels are picaresque novels.
Answer: (A)
7. Henry James’ essay “The Art of Fiction”, one of the earliest literary critical engagements with the form of the novel, was preceded by his book-length study of __________.
(A) William Faulkner
(B) Nathaniel Hawthorne
(C) Aphra Behn
(D) Oscar Wilde
Answer: (B)
8. Which of the following is NOT true of Bram Stoker’s Dracula?
(A) It is considered to be a gothic novel.
(B) It is narrated mostly through letters.
(C) Transylvania is an important setting in the novel.
(D) It is a bildungsroman.
Answer: (D)
9. “The name is H. Hatterr, and I am continuing . . .
Biologically, I am fifty-five of the species.”
The lines above are from an early Indian English novel. Who is the authorof this novel?
(A) G. V. Desani
(B) Allan Sealy
(C) Toru Dutt
(D) Ruth Prawer Jhabvala
Answer: (A)
10. In Areopagitica, John Milton made an impassioned appeal __________.
(A) against censorship and for freedom of expression
(B) for legal reform allowing divorce based on spousal incompatibility
(C) for freedom of the church from royal control
(D) against slavery in the New World
Answer: (A)
11. The first institution to teach English Literature in the world is – ___________.
(A) The University of Oxford, Oxford
(B) Royal Polytechnic Institution, London
(C) The College of William and Mary, Williamsburg, Virginia
(D) Fort William College, Calcutta
Answer: (MTA)
12. Which one of the following texts propounds the aesthetic theory of ‘rasa’?
(A) Natya Shastra
(B) Abhigyana Shakuntalam
(C) Manu Smriti
(D) Charaka Samhita
Answer: (A)
Q.13 – Q.20 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).
13. Which of the following novels is/are predominantly set in Bombay?
(A) Kiran Nagarkar, Ravan and Eddie
(B) Rohinton Mistry, A Fine Balance
(C) Salman Rushdie, Midnight’s Children
(D) Aravind Adiga, The White Tiger
Answer: (A; B; C)
14. Which of the following critically rewrite/s canonical English novels?
(A) J. M. Coetzee, Foe
(B) Jean Rhys, Wide Sargasso Sea
(C) Bapsi Sidhwa, Ice-Candy-Man
(D) Ben Okri, The Famished Road
Answer: (A; B)
15. Of the following, which novelist/s combine/s feminist concerns with magic realism?
(A) Virginia Woolf
(B) Toni Morrison
(C) Kamala Markandaya
(D) Svetlana Alexievich
Answer: (B)
16. In which of these Shakespearean plays do important female characters disguise themselves as men?
(A) A Midsummer Night’s Dream
(B) The Merchant of Venice
(C) As You Like It
(D) Twelfth Night
Answer: (B; C; D)
17. The following words in English are clustered according to their origin. Choose the cluster/s that contain/s words drawn from languages of the Indian subcontinent.
(A) Kedgeree, Punch, Mulligatawny, Candy
(B) Shampoo, Chintz, Calico, Juggernaut
(C) Philistine, Echo, Panic, Galaxy
(D) Anaconda, Cheroot, Bungalow, Dungaree
Answer: (A; B; D)
18. Which of the following is/are true of Charlotte Brontë’s Jane Eyre?
(A) It was published under the pen-name Currer Bell.
(B) It was published originally in three volumes.
(C) It has been read as a critique of heterosexual romance, marriage, anddomesticity.
(D) The story is told from the point of view of a “madwoman in the attic”.
Answer: (A; B; C)
19. Which of the following is an example/are examples of noir, popular both as fiction and film?
(A) The Big Sleep
(B) Murder on the Orient Express
(C) The Maltese Falcon
(D) Fargo
Answer: (A; C)
20. Which of the following use/s the device of a ‘story within a story’ withmultiple narrators?
(A) A Portrait of an Artist as a Young Man
(B) Wuthering Heights
(C) Emma
(D) Heart of Darkness
Answer: (B; D)
Q.21 – Q.30 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).
21. Match the following plays with genre or style:
(A) i-b, ii-d, iii-a, iv-c
(B) i-a, ii-c, iii-b, iv-d
(C) i-d, ii-b, iii-c, iv-a
(D) i-c, ii-d, iii-a, iv-b
Answer: (A)
22. Study the three examples below:
(i) In George Orwell’s novel 1984, the interior ministry of the totalitarian state is called the ‘Ministry of Love’.
(ii) In the genre of horror fiction, the reader knows that the killer is hiding in the closet, but the protagonist does not.
iii) “But Brutus says he was ambitious; And Brutus is an honourable man.”
(William Shakespeare, Julius Caesar)
These are instances of ____________.
(A) metaphor
(B) irony
(C) parody
(D) synecdoche
Answer: (B)
23. An “implied reader” is a ________.
(A) reader who participates in creating the meaning of a text
(B) reader who anticipates authorial intention
(C) hypothetical reader, not the actual reader, that the text addresses
(D) reader who reads critically against the grain of the text
Answer: (C)
24. Read the following:
“[…] a text is made of multiple writings, drawn from many cultures and entering into mutual relations of dialogue, parody, contestation, but there is one place where this multiplicity is focused and that place is the reader, not, as was hitherto said, the author. […] the birth of the reader must be at the cost of the death of the Author.”
Which theoretical school does the excerpt best represent?
(A) Reader-response criticism
(B) Formalism
(C) Post-structuralism
(D) New Criticism
Answer: (C)
25. Literary criticism considers which one of the following texts as offering the strongest support for mimetic theories of art?
(A) Plato, Republic
(B) Longinus, On Sublimity
(C) Horace, The Art of Poetry
(D) Aristotle, Poetics
Answer: (D)
26. The following is a passage about O. V. Vijayan’s The Legends of Khasak:
The novel is set in a remote village, in the middle of the 20th century. Thenarrative is replete with images of the vast ecosystem of the living and thenon-living, a land potent with dreams and legends.
The analysis presented in this description is congruent with which one ofthe following concepts proposed by Mikhail Bakhtin?
(A) Chronotope
(B) Dialogism
(C) Carnivalesque
(D) Polyphony
Answer: (A)
27. Which one of the following did NOT happen in 1919, the year the First World War ended?
(A) The Progressive Writers’ Association was formed in India.
(B) The radical political activist and philosopher Rosa Luxemborg was murdered.
(C) Rabindranath Tagore renounced his knighthood.
(D) James Joyce’s Ulysses was being serialised.
Answer: (A)
28. Assertion P: Dalit narratives tend to be read single-dimensionally
as evoking the reader’s pity at the protagonist’s caste humiliation,
or
as telling the story of heroic protest against discrimination, oras a description of the protagonist’s rise from misery to triumph.
Assertion Q: There is a tendency to keep the Other in the space of difference, as perpetually exotic.
In the context of the assertions above, which one of the following statements is true?
(A) P and Q are contradictory assertions.
(B) P and Q are compatible assertions.
(C) P and Q cannot be read in relation to each other.
(D) Q is the only explanation for P.
Answer: (B)
29. Some of the recent novels of the Brazilian writer Paulo Coelho were published in multiple languages simultaneously, or immediately after the Portuguese edition.
Which of the following is this phenomenon NOT an evidence of?
(A) Rebecca Walkowitz’s argument that novels are often ‘born translated’
(B) The globality of marketplace for books
(C) Paulo Coelho’s expanding popularity
(D) The ‘nation’ as the sole frame for understanding literature
Answer: (D)
30. Match the authors in the first column with their respective translators in the second column.
(A) i-d, ii-c, iii-b, iv-a
(B) i-c, ii-b, iii-d, iv-a
(C) i-c, ii-a, iii-d, iv-b
(D) i-b, ii-a, iii-d, iv-c
Answer: (C)
Q.31 – Q.40 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).
31. Which of the following is/are true about Gilles Deleuze and Felix Guattari’s conception of ‘minor literature’?
(A) The discussion focuses on the writing of Franz Kafka.
(B) Minor literature is literature that a minority produces in a major language.
(C) Minor literature is a form of popular literature.
(D) Minor literature is literature in a minor language.
Answer: (A; B)
32. Quote P:
“O wild West Wind, thou breath of Autumn’s being,
Thou, from whose unseen presence the leaves dead
Are driven, like ghosts from an enchanter fleeing,
Yellow, and black, and pale, and hectic red,
Pestilence-stricken multitudes: O thou,
Who chariotest to their dark wintry bed
[…]”
Quote Q:
“O golden-tongued Romance with serene lute!
Fair plumed Siren! Queen of far away!”
Which of the following is/are correct?
(A) Both quotes are examples of apostrophe.
(B) Both quotes use alliteration.
(C) Both quotes are examples of aporia.
(D) Both quotes are examples of personification.
Answer: (A; D)
33. Prolepsis is the representation or assumption in the present, of a future act or development.
(A) “Six decades later she would describe how at the age of thirteen she had writtenher way through a whole history of literature.” Ian McEwan, Atonement.
(B) “Horatio, I am dead.” William Shakespeare, Hamlet.
(C) “In my younger and more vulnerable years my father gave me some advice thatI’ve been turning over in my head ever since.” F. Scott Fitzgerald, The GreatGatsby.
(D) “Many years later, as he faced the firing squad, Colonel Aureliano Buendía was to remember that distant afternoon when his father took him to discover ice.”Gabriel García Márquez, One Hundred Years of Solitude.
Answer: (A; B; D)
34. Gayatri Chakravorty Spivak’s essay “Can the Subaltern Speak?” proposes which of the following?
(A) The voice of the subaltern is appropriated by ‘intellectuals’ desiring to speak for the subaltern.
(B) It is easy to confuse writing about the subaltern with the subaltern speaking for herself.
(C) All women are subaltern and therefore cannot truly speak.
(D) The ‘intellectuals’ speaking for the subaltern and the subaltern speaking for herself can be equivalent.
Answer: (A; B)
35. Which of the following is/are example/s of ‘metafiction’?
(A) Each chapter in a novel is narrated by a different character.
(B) The reader is a character in the novel who interrupts the story because herealises that he is reading an incomplete text.
(C) The narrator of the novel travels into the wild and encounters a man whoembodies the horrors of colonial power. The latter then proceeds to tell hisstory.
(D) A character in a novel encounters a shabbily dressed man. Soon, this man letsus, the readers, know that he is the author of the novel and is contemplating thefuture of this character.
Answer: (B; D)
36. Choose one or more options from below.
In contrast to traditional Historicism, New Historicism _____________.
(A) rejects the idea that history is an objective narrative of events unfolding in lineartime
(B) does not make strict distinctions between literary and non-literary texts
(C) takes a particular interest in the textualisation of the material world
(D) takes history only to be a background and context for understanding literarytexts
Answer: (A; B; C)
37. “The feminist insistence that ‘the personal is political’ has had profound effects on other genres. Feminist academics in several disciplines now insist that the subjective element must not be left out of the practice of research methods, such as the interview, or of theories of knowledge production (Skeggs 1995; Maynard and Purvis 1994; Reinharz 1992).”
From the passage above, which of the following can be correctlyconcluded?
(A) The passage argues that interviews and theories of knowledge production arenot examples of research methods.
(B) ‘The personal is political’ is a feminist argument.
(C) Skeggs, Maynard, Purvis, and Reinharz are names of feminist scholars.
(D) The passage argues that the subjective can legitimately be part of researchmethods.
Answer: (B; C; D)
38. “ARE YOU DARK? OR VERY LIGHT?” Revelation came.
“You mean—like plain or milk chocolate?”
Her assent was clinical, crushing in its light
Impersonality. Rapidly, wave-length adjusted,
I chose. “West African sepia”—and as afterthought,
“Down in my passport.” Silence for spectroscopic
Flight of fancy, till truthfulness clanged her accent
Hard on the mouthpiece. “WHAT’S THAT?” conceding
“DON’T KNOW WHAT THAT IS.” “Like brunette.”
“THAT’S DARK, ISN’T IT?” “Not altogether.
Facially, I am brunette, but, madam, you should see
The rest of me. Palm of my hand, soles of my feet
Are a peroxide blond. Friction, caused—
Foolishly, madam—by sitting down, has turned
My bottom raven black—One moment, madam!”—sensing
Her receiver rearing on the thunderclap
About my ears—“Madam,” I pleaded, “wouldn’t you rather
See for yourself?”
In Wole Soyinka’s “Telephone Conversation”, the man seeking to rent aroom responds to the white landlady’s racism by ____________.
(A) describing black as a spectrum as opposed to a single colour
(B) being the subservient Black man, who concedes to her definition of race
(C) locating race squarely in her ways of seeing
(D) fragmenting the racialised body
Answer: (A; C; D)
39. In Arthur Conan Doyle’s writings featuring Sherlock Holmes, as is the case with much of 19th century British fiction, colonialism appears as objects, events, animals, places, fears and desires. Which of the following support/s this claim?
(A) Opium dens in London, frequented by Holmes
(B) The war in which Watson served as a doctor
(C) The hound in The Hound of the Baskervilles
(D) The pet animals in “The Adventure of the Speckled Band”
Answer: (A; B; D)
40. “My Papa’s Waltz” by Theodore Roethke
The whiskey on your breath
Could make a small boy dizzy;
But I hung on like death:
Such waltzing was not easy.
We romped until the pans
Slid from the kitchen shelf;
My mother’s countenance
Could not unfrown itself.
The hand that held my wrist
Was battered on one knuckle;
At every step you missed
My right ear scraped a buckle.
You beat time on my head
With a palm caked hard by dirt,
Then waltzed me off to bed
Still clinging to your shirt.
Which of the following can be observed about this poem?
(A) The form of the poem is that of the Petrarchan sonnet.
(B) There is a simile in the first stanza.
(C) Images in the last two stanzas suggest that the father is a working-class man.
(D) The poem is in rhyming couplets.
Answer: (B; C)
Linguistics (XH-C3)
Q.1 – Q.14 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. Which of the following is NOT demonstrated by studies with Great Apes like Koko and Washoe and Sarah?
(A) The capacity to produce rule-governed, novel messages.
(B) The capacity for symbolic communication.
(C) The manual dexterity for signing.
(D) The ability to teach other members of the species.
Answer: (A)
2. The meaning relax or calm down for the word ‘chill’ is an example of what kind of semantic change?
(A) Metaphor
(B) Metonymy
(C) Synecdoche
(D) Pejoration
Answer: (A)
3. Match the following communication systems (P-T) to their type (i-vi) and select the correct sequence:
(A) P-(iii), Q-(v), R-(i), S-(ii), T-(iv)
(B) P-(v), Q-(vi), R-(ii), S-(iv), T-(iii)
(C) P-(iv), Q-(v), R-(iii), S-(ii), T-(vi)
(D) P-(ii), Q-(vi), R-(v), S-(iii), T-(i)
Answer: (A)
4. Statistical learning in language development in infants refers to __________.
(A) calculating regularities in speech to isolate words
(B) early mathematical knowledge that infants can demonstrate
(C) infant data that researchers use to understand language growth
(D) learning to differentiate phonemes as they are used in spoken words
Answer: (A)
5. If ‘Aam Aadmi’ is translated as ‘Mango Man’, which type of ambiguity does the translation demonstrate?
(A) Lexical
(B) Syntactic
(C) Morphological
(D) Morphosyntactic
Answer: (A)
6. While most of the historically known writing systems in India tend to write from left to right, identify the one which writes from right to left.
(A) Kharoṣṭhī
(B) Brāhmī
(C) Śāradā
(D) Grantha
Answer: (A)
7. Identify the pair of words with a circumfix from the list below.
(A) enlighten, embolden
(B) enquiring, inquiring
(C) transformation, transportation
(D) reduced, repeated
Answer: (A)
8. Which of the following sets illustrates sound symbolism in English?
(A) mash, splash, bash, crash
(B) flash, shine, sear, glimmer
(C) duck, suck, luck, tuck
(D) forte, piano, allegro, crescendo
Answer: (A)
9. Voice Onset Time (VOT) is an acoustic cue used by our auditory-perceptual systems. Which of the following sounds can be identified using VOT?
(i) Voiced Stops
(ii) Unvoiced Stops
(iii) Prenasalised Stops
(iv) Aspirated Stops
(v) Ejective Stops
(A) (i), (ii), (iv) but NOT (iii) and (v)
(B) (i), (ii), (iii), (iv) but NOT (v)
(C) (iv), (v) but NOT (i), (ii) and (iii)
(D) (i), (iii), (v) but NOT (ii) and (iv)
Answer: (A)
10. In syntactic terms, which of the following is the odd one out?
(A) Belle struck the Beast as incompetent.
(B) Belle regarded the Beast as incompetent.
(C) Belle identified the Beast as incompetent.
(D) Belle viewed the Beast as incompetent.
Answer: (A)
11. Which of the following speech errors is NOT expected in natural languages? The items that are swapped are indicated in capitals. The intended phrase is tight-ly pack-ed.
(A) tighKly paTed
(B) Pightly Tacked
(C) PACKly TIGHTed
(D) tightED packLY
Answer: (A)
12. Language isolates are languages that ____________.
(A) are not known to be related to any other languages
(B) are spoken in isolated parts of the world
(C) have no dialectal or sociolectal varieties
(D) are separated geographically from other members of their family
Answer: (A)
13. On the new Rs. 2000 note, how many languages can be found in the language panel displaying the denomination of the note?
(A) Fifteen
(B) Sixteen
(C) Seventeen
(D) Eighteen
Answer: (A)
14. How many unique morphemes can be isolated in this sentence?
(A) Twelve
(B) Ten
(C) Sixteen
(D) Eleven
Answer: (A)
Q.15 – Q.20 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).
15. “I look forward to visiting teachers”. What does this sentence demonstrate?
(A) Syntactic ambiguity
(B) Semantic role ambiguity
(C) Lexical ambiguity
(D) No ambiguity
Answer: (A; B)
16. Which of the following pairs of words do NOT stand in troponymous relationship?
(A) lisp-talk
(B) limp-walk
(C) dream-sleep
(D) wait-fidget
Answer: (A; B)
17. Which of the following areal/typological feature(s) may be seen in a vast majority of the languages of South Asia?
(A) Compound Verbs
(B) Retroflexed Sounds
(C) Non-nominative Subject Case
(D) Agglutinative Morphology
Answer: (A; B; C)
18. Three different ways of writing a single word in the Mayan script are given below. The glyphs (i-iii) are of a single word [ba’lam] meaning ‘jaguar’. What can we conclude about the Mayan writing system from the examples provided?
(A) The glyphs can be logograms, mean whole words.
(B) The glyphs can be syllabic.
(C) The glyphs use the rebus principle, part sound part meaning.
(D) The glyphs can be alphabetic, spelling out sounds.
Answer: (A; B; C)
19. Identify symptom(s) of phonological dyslexia.
(A) The inability to map letters to sounds.
(B) The inability to pronounce made-up or nonsense words.
(C) The inability to tell homographs apart.
(D) The inability to recognise semantic mismatches.
Answer: (A; B)
20. Creolisation and creoles are characterised by which of the following?
(A) Creolisation is the process of elaborating Pidgin languages.
(B) Creolisation happens when a Pidgin is learned by young children as a firstlanguage.
(C) Creoles have elaborated grammars but somewhat limited vocabulary.
(D) Creole vocabulary is expansive but the grammar is limited and variable.
Answer: (A; B; C)
Q.21 – Q.25 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).
21. In the following sentence, you are required to identify the type of aphasia and select the correct sequence from the options given below.
Use of jargon and words that have no meaning are typical of ___________aphasia, while the inability to differentiate between actives and passives is seen in _________ aphasia; some patients use circumlocutions for simple words and this is known as ________ aphasia; in patients with __________aphasia, production and comprehension may be reasonably preserved, butthe ability to repeat an utterance is disrupted.
(A) Wernicke’s, Broca’s, Anomic, Conduction
(B) Broca’s, Wernicke’s, Conduction, Dysphonia
(C) Anomic, Conduction, Broca’s, Wernicke’s
(D) Dysphonia, Anomic, Wernicke’s, Broca’s
Answer: (A)
22. Match the dialogues in (P-S) to the Gricean Maxim (i-v) that has been flouted to create humour.
(A) P-(iii), Q-(i), R-(ii), S-(iv)
(B) P-(i), Q-(v), R-(ii), S-(iii)
(C) P-(i), Q-(iii), R-(iv), S-(v)
(D) P-(iv), Q-(ii), R-(iii), S-(i)
Answer: (A)
23. Sign languages have long been used by the deaf communities to communicate amongst themselves. Which of the following is correct?
(A) Sign language shows duality of patterning with meaningless gestures combining to create single signs.
(B) Signs in sign languages are dominantly iconic and transparent with respect to the meaning they encode.
(C) Children who are hearing-impaired do not converge on a language without instruction in signing and/or speaking.
(D) Sign languages are pidgin like, rudimentary communication systems.
Answer: (A)
24. In the sentence “The gunman sprayed the building with bullets”, the preposition phrase (PP) ‘with bullets’ is attached to ______.
(A) ‘sprayed’, because it meets the selectional restriction of ‘sprayed’
(B) ‘sprayed’, because it serves as the adjunct of the verb ‘sprayed’
(C) ‘the gunman’, because the gunman has the gun
(D) ‘the building’, because of proximity
Answer: (A)
25. Consider the sentence “Little children marched past the church sang”. Assume the starting rule of the context free grammar describing the language to be S→NP VP, where S is the start symbol, NP is the noun phrase and VP is the verb phrase. For the given sentence, how many words does VP contain?
(A) One
(B) Two
(C) Three
(D) Four
Answer: (A)
Q.26 – Q.40 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).
26.
The above figure shows what is called a finite state machine. The machine reads one word at a time and transitions to a new state. The states are indicated by boxes and the transitions by arrows. There are three states S0,S1 and S2 and the last is the final state (indicated by two coincident boxes).The text beside each arrow means the following: DT = determiner (a, an, the), AJ = adjective, NN = noun. The machine starts at S0 and on seeing a
determiner (DT) enters the state S1. Then if it sees an adjective (AJ), i tremains in the same state. But at state S1 if it sees a noun (NN), it enters the final state. The final state is also called the “accept” state. No other states or
state transitions are defined or permitted.
Which of the following will cause the machine to enter S2, the accept state?
(A) The blue sky
(B) A vast blue sky
(C) The sky
(D) A very blue sky
Answer: (A; B; C)
27. Which of the following has/have been observed in speech perception experiments?
(A) Speech perception experiments with infants show that they are sensitive at birth to the rhythmic properties of their language, as well as the difference between stress-timed and syllable-timed languages.
(B) Infants and adults show categorical perception of consonant sounds, that is, the ability to treat what is a continuous acoustic feature as discrete.
(C) Infants are sensitive to sounds that are not part of the phonemic inventory of the language(s) to which they are exposed, but older children and adults are not.
(D) The Phoneme Restoration effect seen in speech perception experiments (where people hear phonemes that have been replaced by noise or a cough) shows that speech is perceived as linear.
Answer: (A; B; C)
28. Language games are a way to manipulate spoken words as the following examples from three languages show. Identify the correct statement(s) below about language games.
(A) The intent is to disguise or conceal conversation.
(B) Words are manipulated systematically using defined rules.
(C) The game manipulation targets varying units of the phonological form.
(D) Only children use language games.
Answer: (A; B; C)
29. What can be said about the intent and nature of prescriptive rules for languages?
(A) Provide criteria for written language.
(B) Characterise the universal grammar of languages.
(C) Characterise inter-dialectal differences.
(D) Encode changes to spoken language.
Answer: (A)
30. The use of singular they was voted ‘the word of the decade’ by linguists. Which of the following motivates the singular use?
(A) The use of they in the singular replaces the sex specific he and she pronouns.
(B) Using gendered pronouns can lead to gendered interpretations of the messages.
(C) Sometimes the gender information is not known and it is easier to use they thanhe/she.
(D) English is a sexist language.
Answer: (A; B)
31. Tok Pisin (Papua New Guinea) is an extended Pidgin/Creole language. Words borrowed from English are modified in various ways. Given the word list below, study the phonological modifications and choose the correct generalisation(s).
(A) Only single onsets permitted.
(B) Vowel epenthesis to create syllable nuclei.
(C) Fortition of fricatives to stops.
(D) Obligatory null codas.
Answer: (A; B; C)
32. Consider the following set of Phrase Structure Rules in a toy grammar:
[Note: T is tense, P is preposition, V is verb and N is noun; they project their respective phrasal units TP, PP, VP and NP]
TP → NP T VP
VP → (Adverb) V (TP) (PP)
PP → P NP
NP → (Determiner) (Adjective) N
Which of the following sentences can be generated by these rules?
(A) The golden bells are probably ringing in the church.
(B) Bells ring to let believers know that mass will begin.
(C) The golden bells in the church always ring for prayers.
(D) The silent bells say that the pastor has not visited the bell tower.
Answer: (A; B)
33. Evaluate the following according to the three principles of the Binding Theory and choose the correct statement(s).
(Note: the subscripted <i> indicates co-reference between the arguments
that bear them.)
(A) The sentence Everyone who meets Tagorei admires himi is permitted by the principles of the Binding Theory.
(B) The sentence Every one of his followers says that hei likes Tagorei is ruled out by the Binding Theory.
(C) The sentence Tagorei seems to ask himselfi about effects of education is permitted by the Binding Theory.
(D) The sentence Everyone who meets himi admires Tagorei is ruled out by the Binding Theory.
Answer: (A; B; C)
34. Given the facts (i-iv) about the World Cup, evaluate the statements using truth conditions and the truth tables of connectors to find the ‘false’ statement(s).
(i) Argentina has won the World Cup twice: 1978, 1986
(ii) Germany has won it four times: 1954, 1974, 1990, 2014
(iii) France has won it twice: 1998, 2018
(iv) Japan has never won it
(A) If [Argentina won the World Cup in 1986] then [Germany won it in 1998].
(B) [Germany didn’t win the World Cup in 1986] and [France won it in 1990].
(C) [Argentina didn’t win the World Cup in 1986] or [Japan has never won theWorld Cup].
(D) If [Argentina didn’t win the World Cup in 1978] then [France won it in 1990].
Answer: (A; B)
35. For which of the following sentence(s) can the assigned presupposition (P) hold?
(A) Who discovered the Silverback Slug in 1960?
P: Someone discovered the Silverback Slug in 1960.
(B) If she had drunk coffee this morning, she would have been more alert.
P: She had not drunk coffee.
(C) Ruchi’s parents returned to Alaska over the summer.
P: Ruchi’s parents had been to Alaska sometime before the summer.
(D) The police ordered the students to stop drinking.
P: The students were drunk.
Answer: (A; B; C)
36. Consider carefully the following data from four languages. Which deduction(s) can plausibly be made using the methods of comparative reconstruction?
(A) Languages A and D are closely related.
(B) Language A is distantly related to Language C.
(C) Language D is distantly related to Language B.
(D) Languages A,B,C and D are all unrelated languages.
Answer: (A; B)
37. Analyse the following Shakespearean sentences, and observe the differences between Early Modern English and Modern English – that is, how you would say these sentences today. What can we say in precise, grammatical terms about the syntactic changes that have occurred?
(A) The agreement forms of Early Modern English included a different form for 2ndperson, singular subjects.
(B) In wh-and yes-no questions the main verb can raise to Head, CP [Complementizer Phrase].
(C) Pronominal forms are unchanged from Early Modern into Modern English.
(D) Auxiliary verbs could raise to T [Tense] in Early Modern English but not mainverbs.
Answer: (A; B)
38. The following utterances were produced by a child aged 3 years.
(i) Put him in the bathtub.
(ii) We eated gummy bears.
(iii) Thank you for giving us these books.
(iv) I don’t know … I knowed her!
(v) He bited my finger. (After correction: He bitted my finger.)
(vi) I runned in the water.
(vii) I rided on an elephant.
Which of the following statement(s) can be deduced from the data?
(A) The child differentiates between lexical and non-lexical categories of English.
(B) The child has acquired the Spec-Head and Complement-Head orders of English.
(C) The child has acquired case marking in English.
(D) The child has not yet acquired the rule of past tense formation in English.
Answer: (A; B; C)
39. The human speech production system is characterised by which of the following?
(A) A laryngeal source
(B) A vocal tract that acts as a filter
(C) A vocal tract that acts as a resonator
(D) A laryngeal resonator
Answer: (A; B; C)
40. Which of the following kinds of evidence are offered in support of an innateness view of the human language ability?
(A) All humans, no matter how primitive their societies, have the capacity forlanguage.
(B) Children learn the language(s) in their environment without explicit instruction.
(C) Speakers of all languages are capable of producing and understanding an infinitenumber of sentences.
(D) All languages and their grammars change through time.
Answer: (A; B; C)
Philosophy (XH-C4)
Q.1 – Q.20 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. What is the mood of the following syllogistic argument?
All Professors are Academicians.
Some Academicians are Activists.
Therefore, Some Activists are Professors.
(A) A I I
(B) I I I
(C) I A I
(D) A I A
Answer: (A)
2. What is the formal fallacy committed in the following syllogistic argument?
No Students are tested Covid-positive.
Some Covid-positive cases are not Professors.
Therefore, Some Professors are not Students.
(A) Fallacy of Exclusive Premises
(B) Fallacy of Illicit Major
(C) Fallacy of Illicit Minor
(D) Fallacy of Excluded Middle
Answer: (A)
3. The Philosophy of Aurobindo may aptly be identified as
(A) Integral Non-dualism.
(B) Non-dualism.
(C) Integral Dualism.
(D) Dualism.
Answer: (A)
4. Scientists in the Institute of Virology tested Influenza-affected patients in Wuhan for all known acute respiratory diseases but could not establish the cause for their influenza from the set of known causes. Hence, they inferred for the first time that a Novel Corona Virus is the
cause of their disease.
(A) Method of Residues
(B) Method of Difference
(C) Method of Agreement
(D) Joint method of Agreement and Difference
Answer: (A)
5. In his Republic, Plato makes four-fold classification of the possible objects of knowledge. Where does he place Mathematical Objects?
(A) Dianoia [Thought]
(B) Noesis [Understanding]
(C) Pistis [Belief]
(D) Eikasia [Imagination]
Answer: (A)
6. According to Plato, which among the following is NOT a cardinal virtue?
(A) Autonomy
(B) Courage
(C) Justice
(D) Wisdom
Answer: (A)
7. In Plato’s Republic, the guardians of the ideal state reserve the right to govern because
(A) it is their duty.
(B) it is their birth-right.
(C) they are democratically elected.
(D) they have exclusive command over military power.
Answer: (A)
8. What is true of Rāmānuja’s Viśiṣṭādvaita?
(A) It accepts the conception of qualified Brahman.
(B) It accepts the conception of formless and non-qualified Brahman.
(C) It considers the individual soul/self (cit) as unreal.
(D) It considers the world (acit) as unreal.
Answer: (A)
9. In the Mīmāmsā system, apūrva stands for a link/relation between
(A) an act (action) and its fruit.
(B) the past and the present.
(C) Perception and Inference.
(D) Creator and Creation.
Answer: (A)
10. The conception of jīva in Advaita stands for:
(A) Individual self
(B) Universal Self
(C) Liberated self
(D) Living beings
Answer: (A)
11. What among the following is in conformity with Leibniz’s metaphysical assertion of Pre-established Harmony?
(A) There is a mutual coordination of mind and body.
(B) Mind and body are different kinds of substances.
(C) The mind can causally influence the body.
(D) Cause of a mental state cannot be any previous state of that mind.
Answer: (A)
12. In Edmund Husserl’s phenomenology, eidetic reduction is meant to provide access to the sphere of
(A) essential structures of pure psychic processes.
(B) accidental structures of psychic processes.
(C) inner experience as such.
(D) transcendental phenomena.
Answer: (A)
13. In Jaina classification of knowledge, Mati includes
(A) both Perception and Inference.
(B) only Perception.
(C) only Inference.
(D) Inference and Authority (śruta).
Answer: (A)
14. Among the four Brahmavihāras of Buddhism, ___________ evokes happiness at the joy and success of others.
(A) Muditā
(B) Maitrī
(C) Karuṇā
(D) Upekṣā
Answer: (A)
15. Read the following verse from Bhagavadgītā carefully.
Karmaṇyevādhikāraste mā phaleṣu kadācana;
Mā karmaphalaheturbhūrmā te sango’stvakarmaṇi.
[Your right is for action alone, never for the results. Do not become theagent of the results of action. May you not have any inclination forinaction.] (Bhagavadgītā 2: 47)
This above quoted verse is a standard reference to:
(A) Karma-yoga
(B) Bhakti-yoga
(C) Jñāna-yoga
(D) Rāja-yoga
Answer: (A)
16. Which among the following is predominantly a non-dualistic philosophical system?
(A) Kāṣmir Śaivism
(B) Śaiva-siddhānta
(C) Vīra-śaivism
(D) Vaiṣṇavism
Answer: (A)
17. Gandhi’s doctrine of Trusteeship establishes a normative relationship between labour and capital. Indicate which of the following is NOT in agreement with this doctrine?
(A) Class struggle is the key to social development and economic equality.
(B) The capitalists would function only as trustees for the poor and working class.
(C) The capitalist would keep the surplus wealth in trust in order to have economicequality and solidarity.
(D) The capitalists would be made to realise the wealth in their hands is the fruit ofthe labour of the workers.
Answer: (A)
18. Which of the following is NOT a pramāṇa in the Nyāya system?
(A) Anupalabdhi (Non-apprehension)
(B) Upamāna (Comparison)
(C) Anumāna (Inference)
(D) Pratyakṣa (Perception)
Answer: (A)
19. In the Vaiśeṣika system, which of the following is a padārtha (category)?
(A) Guṇa (Quality)
(B) Ᾱtman (Spirit/Soul)
(C) Tejas (Fire)
(D) Vāyu (Air)
Answer: (A)
20. Identify which among the following is NOT a characteristic of a simple idea according to John Locke.
(A) Varying in its appearance or conception
(B) Cannot be further divided into other simple ideas
(C) Distinctly clear
(D) Unambiguous
Answer: (A)
Q.21 – Q.40 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).
21. Which of the following are in accordance to Democritus’ cosmology?
(A) The cosmos has an underlying order.
(B) Fundamental units of the reality are atoms.
(C) Atoms are extended but indivisible and indestructible.
(D) Atoms are weightless, shapeless and always in a state of rest.
Answer: (A; B; C)
22. For Immanuel Kant, which of the following statements are appropriate examples of synthetic a priori judgment?
(A) 2 + 2 = 4
(B) The shortest distance between two points is a straight line.
(C) For every action there is an equal and opposite reaction.
(D) God is a perfect being.
Answer: (A; B; C)
23. In the Sānkhya system, which among the following are antaḥkaraṇas?
(A) Buddhi (Intellect)
(B) Ahamkāra (Ego)
(C) Jñānedriyas (Sensory Organs)
(D) Karmendriyas (Motor Organs)
Answer: (A; B)
24. Which of the following are meant by Kant’s notion of autonomy of will?
(A) A recognition of the will as duty-bound.
(B) The will is not bound by empirical laws.
(C) The will is not bound by material objects of desire.
(D) The will is only determined by the material principle of self-love.
Answer: (A; B; C)
25. On which of the following, Plato and Aristotle DISAGREE concerning the realm of the political?
(A) Women, in principle, are barred from participation in the political realm.
(B) The best form of government entails the concentration of power in a limited few.
(C) Manual labourers, traders, and businessmen are not fit for political powers.
(D) The ethical and the political are intricately connected.
Answer: (A; B; C)
26. Which among the following are part of yama in Patanjali’s Aṣṭānga-Yoga?
(A) Ahimsā (Non-violence)
(B) Satya (Truthfulness)
(C) Aparigraha (Detachment)
(D) Iśvara-praṇidhāna (Devotion to God)
Answer: (A; B; C)
27. Progress of the modern sciences and reflection on method have led to the development of new fields of analysis in Renaissance Philosophy. Which among the following correctly trace the influence of a particular science on a particular philosopher’s thought?
(A) Mathematics on Rene Descartes
(B) Mechanics on Thomas Hobbes
(C) Historical science on G.W.F. Hegel
(D) Biology and the evolutionary hypothesis on Francis Bacon
Answer: (A; B; C)
28. Gottlob Frege, in his Sense and Reference, discusses the identity relation between the statements “a=a” and “a=b”. Which of the following are his conclusions?
(A) Identity relation is between names or signs of objects.
(B) They are statements of differing cognitive value.
(C) The two ensuing judgments of the statements are different.
(D) Sense expressed in the two statements are the same.
Answer: (A; B; C)
29. If Descartes’ Meditations is credited for a modern version of mind-body dualism, which statements among the following hold true in accordance with it?
(A) Descartes is a substance dualist.
(B) Mind is essentially a thinking thing.
(C) Essential property of matter is determined by the form.
(D) Both, mind and body are indivisible.
Answer: (A; B)
30. John Stuart Mill, in his Utilitarianism, proposes the conception of Utility or Happiness as the directive rule of human conduct. Which of the following are drawn from his conception of Happiness to form the utilitarian standard?
(A) Happiness of all concerned is overriding.
(B) The agent acts as a disinterested spectator.
(C) The agent’s own happiness is paramount.
(D) Impartiality cannot be maintained in action.
Answer: (A; B)
31. Which among the following statements does W.V.O. Quine REJECT in his work, Two Dogmas of Empiricism?
(A) The distinction between analytic and synthetic truths.
(B) Every meaningful statement can be reduced to a statement about immediate experience.
(C) Truths which are grounded in meanings are dependent on truths which are grounded in fact.
(D) The verification theory of meaning is not a possible key to resolve the problem of meaning.
Answer: (A; B; C)
32. Read the following statements carefully and answer the following question.
i. Greater welfare of others is to be valued more than the individual freedom.
ii. Only when the conception of justice is on hand, the ideas of respect and human dignity can be given a more definite meaning.
iii. Principles of justice are derived from the ideas of respect and human dignity.
iv. The loss of freedom for some is not made right by a greater welfare of others.
In light of the theory of justice as fairness, as proposed by John Rawls, which of following pairs of statement DO NOT agree with Rawl’s position?
(A) i and iii
(B) iii and iv
(C) ii and iv
(D) i and ii
Answer: (A; B; C)
33. George Berkeley, in his Principles of Human Knowledge, reflects on the nature of thought and attacks abstract ideas. Which among the following hold true to his view?
(A) There cannot be an idea of anything essentially independent of mind.
(B) One cannot conceive of the unperceived.
(C) Any idea is essentially independent of mind.
(D) One can conceive of the unperceived.
Answer: (A; B)
34. In his An Enquiry Concerning Human Understanding, Hume relies on a basic distinction between two forms of perception. Which among the following are true about it?
(A) Perceptions are understood as the items of our mental world.
(B) Impressions and ideas are two categories of perceptions.
(C) Ideas are derived from impressions.
(D) Impressions include sensations, desires, and passions.
Answer: (A; B; C)
35. In Martin Heidegger’s Being and Time, which among the following correctly describe Dasein?
(A) Inquiring is one of the possibilities of Dasein’s Being.
(B) Understanding of Being is a definite characteristic of Dasein’s Being.
(C) Dasein always understands itself in terms of its existence.
(D) Dasein is closest to us but it is not we ourselves.
Answer: (A; B; C)
36. Read the passage carefully and answer the question.
“There is … a subtler domination exercised in the sphere of ideas by one culture on another, a domination all the more serious in the consequence, because it is not ordinarily felt… Slavery begins when one ceases to feel the evil and it deepens when the evil is accepted as a good. Cultural subjection is ordinarily of an unconscious character and it implies slavery from the very start. When I speak of cultural subjection, I do not mean the assimilation of an alien culture. That assimilation need not be an evil; it may be positively necessary for healthy progress and in any case it does not mean a lapse of freedom. There is cultural subjection only when one’s traditional cast of ideas and sentiments is superseded without comparison or competition by a new cast representing an alien culture which possesses one like a ghost.” (K.C.Bhattacharyya, Swaraj in Ideas, p.13)
In the light of the passage above, cultural subjection amounts to
(A) an uncritical assimilation of foreign culture.
(B) an inability to accurately distinguish the good from the evil.
(C) an uncritical discarding of one’s tradition.
(D) a complete rejection of foreign ideas.
Answer: (A; B; C)
37. Read the following statements carefully and answer the following question.
i. Rahul is not what he is and is what he is not.
ii. The book is a book and can be nothing more.
iii. Of course, a book is a book, but it can always be something more.
iv. Rahul is what he is and must always be so.
Which of the following pairs of statements given below is NOT compatible with Jean-Paul Sartre’s Existential Philosophy?
(A) iii and iv
(B) i and iii
(C) ii and iv
(D) i and ii
Answer: (A OR A; B; C)
38. Which of the following philosophical tenets are admissible in Cārvāka philosophy?
(A) The soul is nothing but the conscious body.
(B) Consciousness arises from matter.
(C) Death alone is liberation.
(D) Earth, water, fire, air, and ether are elements.
Answer: (A; B; C)
39. Read the passage carefully and answer the following question.
‘While I condemn a religion of rules, I must not be understood to hold theopinion that there is no necessity for a religion. On the contrary, I agree with Burke when he says that “True religion is the foundation of society, the basis on which all true Civil Government rests, and both their sanction.”Consequently, when I urge that these ancient rules of life be annulled, I amanxious that their place shall be taken by a religion of principles, which alone can lay claim to being a true religion.’ (B. R. Ambedkar, Annihilation of Caste,24.1)
From the above passage, which among the following accurately represents Ambedkar’s view on foundation of society?
(A) Religion of principles should provide the foundation of society.
(B) Traditional religion should provide the foundation of society.
(C) Religion of rules should provide a foundation of society.
(D) Religion is not necessary at all for the foundation of society.
Answer: (A)
40. Which among the following statements are justifiably held from Thomas Hobbes’ political theory on the social contract, in his book Leviathan?
(A) It is founded on the hypothetical State of Nature.
(B) All men are made by nature to be equals, therefore, no one has a natural right togovern others.
(C) All are to submit to the authority of an absolute sovereign power.
(D) People can live together only by submitting their individual, particular wills tothe collective will.
Answer: (A; B; C)
Psychology (XH-C5)
Q.1 – Q.19 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. According to the Path-Goal theory of leadership, a style of leadership in which the leader consults with subordinates, involving them in the decision making process is _________.
(A) participative
(B) directive
(C) supportive
(D) achievement oriented
Answer: (A)
2. A process to test reliability that involves creating a large ‘bank’ of items and then dividing it into different versions or creating two tests with items of similar difficulty is called _________.
(A) alternate and parallel form reliability
(B) measure of test homogeneity
(C) test-retest
(D) inter-rater reliability
Answer: (A)
3. Delusion of ‘reference’ is a symptom of schizophrenia in which people _______.
(A) believe that random events or comments are directed at them
(B) believe that their thoughts are being broadcasted
(C) believe they have special powers
(D) have sensory experiences in the absence of stimulus
Answer: (A)
4. A student who has prepared inadequately for an exam attributes his failing grade to an unfair test, cheating by other students or a professor whotaught badly, is expressing __________.
(A) projection
(B) reaction formation
(C) repression
(D) rationalization
Answer: (A)
5. Which of the following theories of emotion best fits with the statement that perception of an environmental situation results in emotions and both, felt emotion and bodily reactions in emotions are independent of each other, but triggered simultaneously?
(A) Cannon-Bard Theory
(B) Lazarus’s Cognitive Appraisal Theory
(C) Schachter-Singer Theory
(D) James-Lange Theory
Answer: (A)
6. The perceived fairness of the distribution of resources and rewards is described as _____.
(A) distributive justice
(B) procedural justice
(C) interactional justice
(D) informational justice
Answer: (A)
7. According to Bandura’s theory of personality, which one of the following is the most important person variables in determining personality?
(A) Self-efficacy
(B) Self-concept
(C) Self-esteem
(D) Self-determination
Answer: (A)
8. Match the events in the first column with the different categories of stress in the second column.
(A) P-(iv), Q-(i), R-(ii), S-(iii)
(B) P-(iv), Q-(iii), R-(i), S-(ii)
(C) P-(ii), Q-(i), R-(iii), S-(iv)
(D) P-(i), Q-(iv), R-(ii), S-(iii)
Answer: (A)
9. Which of the following types of colour blindness denotes blue-yellow colourdeficiency?
(A) Tritanopia
(B) Protanopia
(C) Dueteranopia
(D) Ritalin
Answer: (A)
10. Which of the following properties of sound is similar to the hue of light?
(A) Pitch
(B) Timbre
(C) Loudness
(D) Purity
Answer: (A)
11. _______ is a reinforcement schedule, where a person or animal receives the reinforcement based on varying amount of time.
(A) Variable-interval
(B) Fixed-ratio
(C) Fixed-interval
(D) Variable-ratio
Answer: (A)
12. ________ is a loss of memory of events that occurred prior to the trauma.
(A) Retrograde amnesia
(B) Anterograde amnesia
(C) Infantile amnesia
(D) Posthypnotic amnesia
Answer: (A)
13. Phobias and Obsessive Compulsive Disorder fall in the category of _________.
(A) anxiety disorders
(B) mood disorders
(C) somatoform disorders
(D) psychotic disorders
Answer: (A)
14. The smallest unit of speech perception that has meaning is _______.
(A) morpheme
(B) syntax
(C) semantics
(D) phoneme
Answer: (A)
15. In adolescence, with the development of the stage of ‘formal operations’, weare likely to see the development of ________.
(A) post-conventional morality
(B) pre-conventional morality
(C) bodily-kinesthetic intelligence
(D) transference
Answer: (A)
16. Which technique allows researchers to conduct an integrative statistical analysis of multiple independent studies addressing the same question?
(A) Meta-analysis
(B) Correlational analysis
(C) Regression analysis
(D) Bootstrapping
Answer: (A)
17. The role of culture and ‘scaffolding’ are emphasized in _________.
(A) Vygotsky’s theory of cognitive development
(B) Piaget’s theory of cognitive development
(C) Atkinson-Shiffrin’s information-processing model
(D) Kamiloff-Smith’s theory of cognitive development
Answer: (A)
18. Most people tend NOT to consider situational factors while judging others’ behaviour because _______.
(A) people are inclined to commit the fundamental attribution error
(B) of the frustration-aggression relationship
(C) people are influenced by the laws of reinforcement
(D) of the overjustification effect
Answer: (A)
19. Using archival analysis, scientists describe a culture by _______.
(A) examining documents like magazines, diaries and newspapers
(B) surveying a representative sample of members of the society
(C) observing the behaviour of members of the society
(D) comparing the direct observations of behaviour from different cultures
Answer: (A)
Q.20 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).
20. Which is/are the component(s) of Gardner’s theory of multiple intelligences?
(A) Logical-Mathematical intelligence
(B) Linguistic intelligence
(C) Spatial intelligence
(D) Insight
Answer: (A; B; C)
Q.21 – Q.23 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).
21. Match the neurotransmitter in the first column with its effect in the second column.
(A) P-(iv), Q-(i), R-(ii), S-(iii)
(B) P-(iii), Q-(i), R-(ii), S-(v)
(C) P-(i), Q-(ii), R-(iv), S-(iii)
(D) P-(iv), Q-(i), R-(v), S-(iii)
Answer: (A)
22. Match the depth cues in the first column with their description in the second column.
(A) P-(ii), Q-(iv), R-(i), S-(iii)
(B) P-(ii), Q-(iii), R-(iv), S-(i)
(C) P-(iv), Q-(i), R-(ii), S-(iii)
(D) P-(iii), Q-(iv), R-(i), S-(ii)
Answer: (A)
23. Match the concepts in the first column with the description in the second column.
(A) P-(iii), Q-(i), R-(iv), S-(ii)
(B) P-(i), Q-(ii), R-(iii), S-(iv)
(C) P-(ii), Q-(i), R-(iv), S-(iii)
(D) P-(iii), Q-(iv), R-(i), S-(ii)
Answer: (A)
Q.24 – Q.40 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).
24. Which of the following will hold true for a learning acquisition curve drawn for a classical conditioning experiment on eye blinking as conditioned response that plots the learning over a number of trials?
(A) The rate of learning on earlier trials is more than that on later trials.
(B) The learning curve is negatively accelerated.
(C) The rate of learning in later trials will be more than that on earlier trials.
(D) The rate of learning is proportionally increasing with increasing number of trials.
Answer: (A; B)
25. In the situation where ‘A teenager who hates studying science but is also not able to tell his parents fearing their reaction’, what is the conflict he is facing and which of these may be his way of dealing with this situation?
(A) Avoidance-Avoidance conflict, he will keep vacillating between telling his parents and continuing to study science.
(B) Avoidance-Avoidance conflict, he may contemplate running away from his home.
(C) Approach-Avoidance conflict, he will experience some emotional turmoil.
(D) Multiple Approach-Avoidance conflict, he will be guided by internal values.
Answer: (A; B)
26. Which of these is true about individuals high on n-achievement motivation?
(A) High n-achievement individuals like to work on situations where they have control and can get feedback.
(B) High n-achievement individuals persistently work on tasks they perceive as, either reflecting their personal characteristics like intelligence or are career-related.
(C) High n-achievement individuals prefer working on extremely challenging tasksfor bigger gains.
(D) High n-achievement individuals avoid changing their aspiration levels.
Answer: (A; B)
27. Which of the following is/are Allport’s basic assumption(s) concerning human nature?
(A) Human growth as an active process of “becoming”.
(B) Personality cannot be fully understood by examining each trait separately, though some system of conceptual schemata are essential for personality study and a trait must be related to the total pattern of personality.
(C) Personality is organized in a topographical model.
(D) All human events are determined by powerful instinctual forces.
Answer: (A; B)
28. Which of the following aspects are characteristics of the group structure in an organizational context?
(A) Task-oriented role (the activities of an individual that involve helping the group reach the goal).
(B) Socio-emotional role (the activities of an individual that involve being supportive and nurturing of other group members).
(C) Prescriptive norms (expectations within groups regarding what has to be done).
(D) Monitoring (observing work performance).
Answer: (A; B; C)
29. Which of the following needs/motives are proposed by Abraham Maslow?
(A) Deficit needs.
(B) Metaneeds.
(C) Self-actualization needs.
(D) Need-achievement.
Answer: (A; B; C)
30. A researcher is conducting a study involving two independent variables. Which of the following Analysis of Variance (ANOVA) is/are available to him/her?
(A) 2 × 2 ANOVA.
(B) 4 × 3 ANOVA.
(C) 3 × 2 × 2 ANOVA.
(D) One-way ANOVA.
Answer: (A; B)
31. Which of the following statements is true about personal space?
(A) It is silent and invisible.
(B) It is a geographic component of interpersonal relations.
(C) Invasions of personal space are a matter of degree.
(D) There are no across culture variations.
Answer: (A; B; C)
32. If a person got a score of 75 on a test, which of the following distributions allow(s) for the most favourable interpretation of that score? (assuming higher values are more favourable)
(A) Mean = 55, Standard Deviation = 4
(B) Mean = 60, Standard Deviation = 3
(C) Mean = 65, Standard Deviation = 5
(D) Mean = 50, Standard Deviation = 10
Answer: (A; B)
33. A man’s wife is dying. She is in dire need of a drug. The only place to get the drug is at the store of a pharmacist who is known to overcharge people for drugs. The man can only pay Rs. 20000 but the pharmacist wants Rs. 50000, and refuses to sell it to him for less, or to let him pay later. What will the man do
if he is at the conventional stage of morality as per Kohlberg’s theory ofmoral reasoning?
(A) He would not steal the drug, as everyone will see him as a thief, and his wife would not approve of his stealing or accept the stolen drug.
(B) No matter what, he would obey the law because stealing is a crime.
(C) The man would not steal the drug, as he may get caught and go to jail.
(D) The man would steal the drug to cure his wife and then tell the authorities what he has done. He may have to pay a penalty, but at least he would have saved ahuman life.
Answer: (A; B)
34. According to Erik Erikson, identity versus role confusion is the fifth stage of life span development. Which of the following outcomes may emerge as a result of identity crisis?
(A) Identity diffusion
(B) Identity moratorium
(C) Identity foreclosure
(D) Identity perception
Answer: (A; B)
35. Life span experts argue that biological aging begins at birth. Which of the following is/are explanation/s of aging?
(A) Cells can divide to a maximum of about 75 to 80 times and that as people age, cells become less capable of dividing.
(B) People age because when cells metabolize energy, the by-products include unstable oxygen molecules known as free radicals.
(C) Aging is due to the decay of mitochondria.
(D) Cell division increases as people age.
Answer: (A; B; C)
36. Which of the following are involved in sympathetic nervous system activation?
(A) Inhibited salivation
(B) Increased heart rate
(C) Inhibited digestion
(D) Constricted pupils
Answer: (A; B; C)
37. How is/are genetic theories of psychopathology tested?
(A) Using twin studies
(B) Using family history studies
(C) Using adoption studies
(D) Using psychodynamic studies
Answer: (A; B; C)
38. An investigator approached college students who initially believed that water should be purified and asked them to compose and recite a videotaped speech against the use of water purifiers. To do this, some were offered large
incentives and others were offered small incentives. Later their attitudes towards water purifiers were tested. Which of the following will be the expected finding(s)?
(A) The smaller the incentive, the greater will be the attitude change.
(B) All the students will change their attitudes towards water purifiers.
(C) All the students will continue to feel favourably about water purifiers.
(D) The larger the incentive, the greater will be the attitude change.
Answer: (A)
39. In which attachment style(s), do children tend to show clingy behaviour but then reject the attachment figure’s attempt to interact with them?
(A) Resistant attachment
(B) Avoidant attachment
(C) Secure attachment
(D) Disorganized attachment
Answer: (A)
40. A study is conducted to see the effectiveness of volume levels of commercials. In the graph given below, values of mean effectiveness (dependent variable) are presented on the Y axis, and three levels of volume, namely, soft, medium and loud are presented on the X axis. The graph shows the relationship between volume and mean effectiveness for males in the continuous line and for females in the dashed line. Which of the following interpretation(s) is/are correct from the graph?
(A) A linear relationship exists for males and a nonlinear relationship for females.
(B) The effect of increasing volume on effectiveness depends on whether theparticipant is a male or a female.
(C) No interaction effect is seen.
(D) A linear relationship exists for both males and females.
Answer: (A; B)
SOCIOLOGY (XH-C6)
Q.1 – Q.12 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. The term kulak refers to
(A) a type of hoe used in agriculture.
(B) a form of property right over agrarian produce.
(C) a rich farmer.
(D) the Russian word for peasant uprising.
Answer: (C)
2. M.N. Srinivas’ principal work was built around the method of
(A) conjectural history.
(B) archival research.
(C) fieldwork.
(D) content analysis.
Answer: (C)
3. In an experimental design, the dependent variable is
(A) the one that is not manipulated and in which any changes are observed.
(B) the one that is manipulated in order to observe any effects on the other.
(C) the unknown variable that emerges from the analysis of the data.
(D) the variable whose meaning depends on how informants perceive it.
Answer: (A)
4. The avunculate refers to the relationship between
(A) virilocal and neolocal families.
(B) matrilateral cross cousins.
(C) members of a matrilocal tharavad.
(D) mother’s brother and sister’s son.
Answer: (D)
5. Who among the following Indian sociologists argued against Verrier Elwin’s proposal of preserving the ‘tribal way of life’ on the grounds that the Indian tribes are not ‘aborigines’ but are “imperfectly integrated classes of Hindu society” or are ‘Backward Hindus’?
(A) Irawati Karve
(B) A.R. Desai
(C) G.S. Ghurye
(D) D.D. Kosambi
Answer: (C)
6. M. N. Srinivas called his work on Rampura ‘The Remembered Village’ because
(A) ‘collective memory’ is the concept he used to understand Rampura.
(B) his experience in Rampura was memorable.
(C) the village Headman had forbidden Srinivas from taking any notes forcing him to write this account solely from memory.
(D) he lost his field material in a fire and had to rely on his memory to write thebook.
Answer: (D)
7. “An ideal society should be mobile, should be full of channels for conveying a change taking place in one part to other parts. In an ideal society there should be many interests consciously communicated and shared. There should be varied and free points of contact with other modes of association. In other words there must be social endosmosis.”
On the basis of the above statement, which one of the following can beasserted?
(A) This is M.K. Gandhi describing his vision of Rama Rajya in ‘Hind Swaraj’.
(B) This is V.D. Savarkar describing caste equality in ‘Essentials of Hindutva’.
(C) This is Jawaharlal Nehru describing socialist society in ‘The Discovery of India’.
(D) This is B.R. Ambedkar describing fraternity in ‘The Annihilation of Caste’.
Answer: (D)
8. ‘The City and the Grassroots’ authored by _____________ is among the most important books published on urban social movements.
(A) Michel Foucault
(B) Charles Tilly
(C) Manuel Castells
(D) Veena Das
Answer: (C)
9. A fisherman in southwest Sri Lanka has received a warning that a cyclone may hit his coastal region and he has to decide whether to evacuate or stay put. He knows that the probability of the cyclone striking is 70%. He has the means to evacuate and his property is worth three times the cost of evacuation. He calculates accurately that his best chance to protect himself and his assets lies in evacuation. At a later meeting of the whole community, the village elders decide that no one will evacuate because the village shrines cannot be left unattended indefinitely. Hence in deference to the elders, the fisherman decides to stay put.
In Max Weber’s terms, his decision is closest to
(A) value rational action.
(B) instrumental rational action.
(C) traditional action.
(D) affective action.
Answer: (C)
10. The Jonestown massacre of 1978 in the United States saw the death of 900persons including children. Reverend Jones, leader of an American cult, ordered his followers ‘The Peoples Temple’ to kill a US Congressman and several journalists and then commit mass suicide by drinking fruit punchlaced with cyanide. In Durkheim’s view, this would be a case of
(A) anomic suicide.
(B) altruistic suicide.
(C) egoistic suicide.
(D) fatalistic suicide.
Answer: (B)
11. Pierre Bourdieu defined ____________ as “Systems of durable dispositions, structured structures predisposed to function as structuring structures … collectively orchestrated without being the product of the
orchestrating action of a conductor.”
Which of the following completes the above sentence?
(A) social capital
(B) culture
(C) habitus
(D) field
Answer: (C)
12. Read the following statements:
(1) Throughout the developing world, poverty rates among householdsheaded by women are higher than those headed by men.
(2) The greater ‘investment value’ associated with the survival of boys in a household in comparison with girls leads to discrimination against girl children and adult women.
(3) The unequal allocation of resources within households results in differential allotments of nutrition and healthcare that reflect the perceived inferior short-term and long-term value of females.
(4) In all transitional economies, an increase in prostitution and trafficking of women has been observed.
The above statements are all examples of
(A) the ‘feminisation of poverty’ thesis.
(B) labour market informalisation.
(C) the ‘culture of poverty’ thesis.
(D) differences in bargaining power between advanced and transitional economies.
Answer: (A)
Q.13 – Q.20 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).
13. In which of the following ways did the founding scholars usually distinguish New Social Movements (NSMs) from Old Social Movements?
(A) NSMs are devoted to changing cultural norms concerning individual dignity rather than bringing about structural transformation.
(B) NSMs are based in social class and not on social identities.
(D) NSMs are all revolutionary in their mode of action.
Answer: (A; C)
14. Which of the following option(s) correctly applies/apply to a key information sociological research?
(A) One who intentionally restricts a researcher’s access to participants.
(B) One with in-depth knowledge of the community.
(C) One who refers the researcher to those knowledgeable about the subject of theresearch.
(D) One who because of her social position provides a deeper understanding of hersociety.
Answer: (B; C; D)
15. For Karl Marx, which statement(s) below define(s) absolute surplus value?
(A) It is value extracted by using technology in the labour process.
(B) It is value saved by technology.
(C) It is value created over and above worker subsistence.
(D) It is value extracted by means of extending the working day.
Answer: (D)
16. Who among the following sociologist(s) use(s) a Marxist framework tounderstand Indian society and history?
(A) Yogendra Singh
(B) A.K. Saran
(C) Leela Dube
(D) A. R. Desai
Answer: (D)
17. Which of the following reverse(s) the process of primitive accumulation in India?
(A) NREGA
(B) The Land Acquisition Act of 1894
(C) Special Economic Zones
(D) Microfinance lending
Answer: (A; D)
18. Which of the following applies/apply to Lévi-Strauss’ fundamental unit ofkinship?
(A) It is constituted by the father and mother and their children.
(B) It is constituted by the nuclear family and the wife’s brother.
(C) It is the basis of alliance theory.
(D) It is based on the universal incest taboo.
Answer: (B; C; D)
19. Which statement(s) correctly explain(s) why feminists and women’s rights activists are uncomfortable with the term ‘honour killings’?
(A) It has been defined variously across disciplines from law to sociology to philosophy.
(B) It has become associated with the ‘uniqueness’ of Asian societies and cultures.
(C) The idea that women embody male honour makes violence against them and even their murder justifiable.
(D) It has become associated with communities that retain archaic patriarchal practices and refuse to modernise.
Answer: (B; C; D)
20. Which of the following is/are Louis Dumont’s formulation(s)?
(A) Indian sociology must lie at the confluence of Indology and anthropology.
(B) The ideological principle that religion is always superior to power is at all times found exhibited at the empirical level in India.
(C) Equality runs contrary to the general tendencies of societies.
(D) Traditional Indian ideology allows only ‘surreptitious’ entry of economic andpolitical power.
Answer: (A; C; D)
Q.21 – Q.28 Multiple Choice Question (MCQ), carry TWO mark each (for each wronganswer: – 2/3).
21. The Latin American system of compadraz go or ‘god parenthood’ is one in which, at the time of baptism of a child into the Christian church, a relationship is set up between the child’s biological mother and father and possibly unrelated persons who become the child’s spiritual parents. This may be understood as a form of
(A) fictive kinship.
(B) cognatic kinship.
(C) mystical kinship.
(D) bilateral kinship.
Answer: (A)
The Self-Employed Women’s Association (SEWA) is
(A) a trade union for self-employed women workers in the informal economy.
(B) not a trade union as its members have no employer.
(C) an association of all home-based women workers across India.
(D) a trade union for all self-employed women workers outside the agrarian sector.
Answer: (A)
23. Match statements (P), (Q), (R), (S) to names (1), (2), (3), (4):
(P) “Today, Indians no longer idealise hierarchy. What they … idealise is equality.”
(Q) “[We] do not argue that non-dalit feminists can ‘speak as’ or ‘for the’ dalit women but they can ‘reinvent themselves as dalit feminists’.”
(R) “[From] the point of view of people at the lowest end of the scale, caste has functioned (and continues to function) as a very effective system of economic exploitation.”
(S) “The pure hierarchy that Louis Dumont wrote so compellingly about a
few decades ago … now stands bereft of empirical support from practically every quarter of Hindu India.”
(1) Dipankar Gupta
(2) Sharmila Rege
(3) André Béteille
(4) Joan P. Mencher
(A) (P)-(3), (Q)-(2), (R)-(4), (S)-(1)
(B) (P)-(4), (Q)-(2), (R)-(3), (S)-(1)
(C) (P)-(3), (Q)-(1), (R)-(4), (S)-(2)
(D) (P)-(4), (Q)-(1), (R)-(2), (S)-(3)
Answer: (A)
24. Match statements (P), (Q), (R), (S) to names (1), (2), (3), (4):
(P) “The executive of the modern state is but a committee for managing the common affairs of the whole bourgeoisie.”
(Q) The state is “an institutional association of rule, which within a given territory has succeeded in gaining a monopoly of legitimate physical force as a means of ruling.”
(R) “It is only through the State that individualism is possible, although it cannot be the means of making it a reality, except in
certain precise conditions. We might say that in the State we have the prime mover. It is the State that has rescued the child from
patriarchal domination and from family tyranny; it is the State that has freed the citizen from feudal groups and later from communal
groups; it is the State that has liberated the craftsman and his master from guild tyranny.”
(S) “The family is indeed a fiction, a social arte fact, an illusion in the most ordinary sense of the word, but a ‘well-founded illusion’, because, being produced and reproduced with the guarantee of the state, it receives from the state at every moment the means to exist and persist.”
(1) Pierre Bourdieu
(2) Emile Durkheim
(3) Karl Marx and Friedrich Engels
(4) Max Weber
(A) (P)-(3), (Q)-(4), (R)-(2), (S)-(1)
(B) (P)-(3), (Q)-(4), (R)-(1), (S)-(2)
(C) (P)-(3), (Q)-(1), (R)-(2), (S)-(4)
(D) (P)-(4), (Q)-(2), (R)-(3), (S)-(1)
Answer: (A)
25. Read the abstract of the article titled ‘Taming’ Arab social movements: Exporting neoliberal governmentality” (2013).
“In the wake of the recent Arab revolutions, the European Union (EU) has sought to provide genuine and substantial support to a range of Arab social movements in the region’s emerging polities…We argue, however, that the EU’s attempts at democracy promotion in the Middle East and North Africa (MENA) region may be understood through a governmentality frame work, despite the limitations of such an approach. Specifically, theEU is actively promoting neoliberal policies in the aftermath of the Arab
Spring in order to foster a mode of subjectivity that is conducive to the EU’s own norms and interests. What we observe are not just innocent attempts at democracy promotion, but a form of politics and economics that seeks to subject the agency on the ‘Arab street’ to EU standards. We conclude by going over the radical plurality of the Arab street, and show how it was in fact earlier neoliberal reforms by their former regimes that created the conditions of possibility for the recent revolutions in Tunisia and Egypt.”
On the basis of the above statement, which of the following can be asserted?
(1) Social movements can no longer be understood as a purely intra-national phenomenon.
(2)Local social movements for democratisation have little to do with the transnationalisation of the practices of neoliberal governmentality.
(A) Both the statements are correct
(B) Both the statements are incorrect
(C) Only (1) can be asserted
(D) Only (2) can be asserted
Answer: (C)
26. According to Karl Marx, the socially necessary labour time to produce acommodity will directly vary with
(A) the particular time period and place.
(B) the annual rainfall.
(C) the average productivity of agrarian workers.
(D) the output of natural resources.
Answer: (A)
27. Imagine there is a spiritual leader from any religion who has a huge estate, organisation, publications etc. In Weberian terms, this could be considered an example of
(A) patrimonial power.
(B) bureaucratised patrimonial power.
(C) charismatic power.
(D) bureaucratised charismatic power.
Answer: (D)
28. Which of the following is a proposed explanation for a group of facts orphenomena that provides the basis for empirical testing?
(A) An ideal type
(B) A logical framework matrix
(C) A hypothesis
(D) A sampling procedure
Answer: (C)
Q.29 – Q.40 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).
29. To which of the following option(s) does C. Wright Mills’ ‘Grand Theory’ NOT apply?
(A) A theory proposed by one of classical sociological theorists.
(B) A highly abstract theory making broad generalisations about the social world.
(C) An accurate theoretical explanation of observed empirical regularities.
(D) An intellectually satisfying theory of social knowledge.
Answer: (A; C; D)
30. Which statement(s) about contemporary India is/are endorsed by recent sociological research?
(A) The skewed sex ratio at birth is enabling cross-regional marriages that may breach caste boundaries.
(B) The skewed sex ratio at birth means that women are valued more for their roles in reproduction, domestic and care work.
(C) The skewed sex ratio at birth reduces the supply of women and improves their life chances throughout society.
(D) The skewed sex ratio at birth is causing a male marriage squeeze due to the female deficit.
Answer: (A; B; D)
31. Which of the following statements is/are representation(s) of the ‘modernisation theory’ of the mid-twentieth century?
(A) All versions of this theory could be summarised as the attempt to under standhow traditional societies modernise.
(B) This theory saw the developmental efforts of all decolonised nations through the binary of communist or capitalist.
(C) Ashis Nandy termed this theory as a “secular theory of salvation”.
(D) The theory seeks to understand macro changes in terms of ‘development’ andnot how to make individuals develop modern values and sensibilities.
Answer: (A; B; C)
32. “We demanded changes that would make the law more sensitive to the cultural and economic contexts of women’s lives. Women’s groups investigating ‘dowry deaths’ demonstrated how the designation of the family as the private domain restricted women’s access to protection against domestic violence. They exposed the collusion of the law, police, medical system, and the family in classifying these deaths as suicides. Feminist scholars worked to salvage gender and women’s issues from being subsumed by class analysis, sought to extend the Marxist understanding of labour to include domestic production, and pointed out the marginality and vulnerability of women in the workforce”.
(Susie Tharu and Tejaswini Niranjana (1996), ‘Problems for a Contemporary Theory of Gender’)
Which among the following statements can be asserted from the aboveexcerpt?
(A) Women’s lives have contexts that are peculiar/unique.
(B) The division of domains into public and private allows women’s specific concerns to be fore grounded.
(C) Marxist understanding of labour is not gender-sensitive.
(D) The classification of dowry deaths as suicide lowers the institutional and social protection of women against violence.
Answer: (A; C; D)
33. “The claim, made by structuralism and dependency theory, that subordination to the world market seals the fate of nations is wrong. Inequality, poverty, low productivity and sluggish growth in the periphery, their propensity to import luxury goods and transfer profits to the centre, and the lack of coordination of economic activity in many countries, are due primarily to the social structures prevailing in the periphery, rather than their international trade relations.”
(Alfredo Saad-Filho (2005), ‘The Rise and Decline of Latin American Structuralism and Dependency Theory’)
Which among the following statements can be asserted from the above excerpt?
(A) Underdevelopment is mainly due to the balance of political forces within theperiphery.
(B) Trade patterns between core and periphery follow from “the social structures prevailing in the periphery”.
(C) Unequal exchange between core and periphery inhibits development of thelatter.
(D) There is a pathway to development through the world market.
Answer: (A; B; D)
34. There is scholarly controversy over the role of the middle peasants inpeasant movements in India. In this regard, which of the following statements is/are true?
(A) Hamza Alavi argued that the middle peasants are more likely to initiate and actively participate in peasant movements.
(B) Dhanagare argued that the middle peasants are weaker and more heterogeneous than other agrarian classes.
(C) Kathleen Gough argued that poor peasants and agricultural labourers have the potential for organising peasant movements.
(D) Gail Omvedt argued that caste is the basis of peasant mobilisation, not class.
Answer: (A; B; C)
35. In ‘The Nation and its Fragments’ (1993), Partha Chatterjee observes that“ By the 1940s, the dominant argument of nationalism against colonial rule was that the latter was impeding the…development of India….A developmental ideology…was a constituent part of the self-definition of the postcolonial state. The state was connected to the people not simply through the procedural forms of representative government; it also acquired its representativeness by directing a program of economic development on behalf of the nation.”
In what way(s) was the connection between development and the representativeness of the Indian state achieved, for Chatterjee?
(A) Colonialism had demonstrated the benefits of free trade and globalisation.
(B) Colonialism stood for economic exploitation, therefore liberty meant thereverse.
(C) The procedural forms of government would by themselves be insufficient todrive development.
(D) The procedural forms of government would inevitably fall to corruption.
Answer: (B; C)
36. Which of the following statement(s) correctly represent(s) A.M. Shah’sviews in his ‘The Household Dimension of the Family in India’?
(A) Indological conceptions of the ‘Indian joint family’ have become an obstacle tosociological investigation of the familial structure and transformation.
(B) Household and family are two different, though related, categories.
(C) The process of modernisation will break the traditional Indian joint family into nuclear families.
(D) The classification of the households into ‘simple’ and ‘complex’ resolves theexisting confusing classification of ‘elementary’ and ‘joint’ family.
Answer: (A; B)
37. See the diagram and identify which option(s) below applies/apply to it
(A) The diagram shows parallel cousin marriage which is a form of restricted exchange.
(B) The diagram shows cross cousin marriage which is a form of generalized exchange.
(C) This form of marriage creates a distinction between bride-givers and bride-takers.
(D) This form of marriage conforms to the ideal of kanyadana.
Answer: (B; C; D)
38. Which of the following statement(s) correctly applies/apply to reflexivity in sociological research?
(A) A researcher can take a bird’s eye perspective of research subjects.
(B) A researcher reflects on how her position impacts her research and findings.
(C) A researcher considers how her biases and values bear on her interpretations and analyses.
(D) A researcher reflects on how she in turn can help the community she is studying.
Answer: (B; C)
39. “If we make abstraction from its use value, we make abstraction at the same time from the material elements and shapes that make the product a use value; we see in it no longer a table, a house, yarn, or any other useful thing. Its existence as a material thing is put out of sight. Neither can it any longer be regarded as the product of the labour of the joiner, the mason, the spinner, or of any other definite kind of productive labour. Along with the useful qualities of the products themselves, we put out of sight both the useful character of the various kinds of labour embodied in them, and the concrete forms of that labour; there is nothing left but what is common to them all; all are reduced to one and the same sort of labour, human labour in the abstract.” (Karl Marx, ‘Capital’)
Which statement(s) can be asserted from the above excerpt?
(A) Abstraction refers to a material process that occurs in production.
(B) Abstraction refers to an analytical operation.
(C) Abstraction refers to the reduction of material products to their commonelement.
(D) Abstraction refers to a mathematical operation.
Answer: (B; C)
40. “The capitalistic economy of the present day is an immense cosmos into which the individual is born, and which presents itself to him, at least as an individual, as an unalterable order of things in which he must live…In order that a manner of life so well adapted to the peculiarities of capitalism could be selected at all, i.e. should come to dominate others, it had to originate somewhere, and not in isolated individuals alone, but as a way of life common to whole groups of men. This origin is what really needs explanation…The question of the motive forces in the expansion of modern capitalism is not in the first instance a question of the origin of the capital sums which were available for capitalistic uses, but, above all, of the development of the spirit of capitalism. Where it appears and is able to work itself out, it produces its own capital and monetary supplies as the means to its ends, but the reverse is not true.” (Max Weber, ‘The Protestant Ethic and the Spirit of Capitalism’)
Which among the following is/are Weber’s argument(s) in the above excerpt?
(A) The origins of capitalism cannot be explained by purely material factors.
(B) Before it is mature, capitalism does not drive individual behaviour.
(C) Before it is fully functional, capitalism needed the support of an ethic.
(D) Capitalism requires greed to be adopted by all as “a manner of life”.
Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. Gauri said that she can play the keyboard __________ her sister.
(A) as well as
(B) as better as
(C) as nicest as
(D) as worse as
Answer: (A)
2. A transparent square sheet shown above is folded along the dotted line. The folded sheet will look like ________.
Answer: (B)
3. If θ is the angle, in degrees, between the longest diagonal of the cube and any one of the edges of the cube, then, cos θ =
(A) 1/2
(B) 1/√3
(C) 1/√2
(D) √3/2
Answer: (B)
4. If then the value of x is:
(A) 2
(B) 4
(C) 6
(D) 8
Answer: (B)
5. Pen : Write :: Knife : _________
Which one of the following options maintains a similar logical relation in the above?
(A) Vegetables
(B) Sharp
(C) Cut
(D) Blunt
Answer: (C)
Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).
6. Listening to music during exercise improves exercise performance and reduces discomfort. Scientists researched whether listening to music while studying can help students learn better and the results were inconclusive. Students who needed external stimulation for studying fared worse while students who did not need any external stimulation benefited from music.
Which one of the following statements is the CORRECT inference of the above passage?
(A) Listening to music has no effect on learning and a positive effect on physical exercise.
(B) Listening to music has a clear positive effect both on physical exercise and on learning.
(C) Listening to music has a clear positive effect on physical exercise. Music has a positive effect on learning only in some students.
(D) Listening to music has a clear positive effect on learning in all students. Music has a positive effect only in some students who exercise.
Answer: (C)
7. A jigsaw puzzle has 2 pieces. One of the pieces is shown above. Which one of the given options for the missing piece when assembled will form a rectangle? The piece can be moved, rotated or flipped to assemble with the above piece.
Answer: (A)
8. The number of students in three classes is in the ratio 3:13:6. If 18 students are added to each class, the ratio changes to 15:35:21.
The total number of students in all the three classes in the beginning was:
(A) 22
(B) 66
(C) 88
(D) 110
Answer: (C)
9. The number of units of a product sold in three different years and the respective net profits are presented in the figure above. The cost/unit in Year 3 was ` 1, which was half the cost/unit in Year 2. The cost/unit in Year 3 was one-third of the cost/unit in Year 1. Taxes were paid on the selling price at 10%, 13% and 15% respectively for the three years. Net profit is calculated as the difference between the selling price and the sum of cost and taxes paid in that year.
The ratio of the selling price in Year 2 to the selling price in Year 3 is ________.
(A) 4:3
(B) 1:1
(C) 3:4
(D) 1:2
Answer: (A)
10. Six students P, Q, R, S, T and U, with distinct heights, compare their heights and make the following observations.
Observation I: S is taller than R.
Observation II: Q is the shortest of all.
Observation III: U is taller than only one student.
Observation IV: T is taller than S but is not the tallest.
The number of students that are taller than R is the same as the number of students shorter than ______.
(A) T
(B) R
(C) S
(D) P
Answer: (C)
Engineering Mathematics (XE-A)
Q.1 – Q.3 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. Let If
(A) −4
(B) −2
(C) 2
(D) 4
Answer: (D)
2. Let C be the boundary of the region R ∶ 0 ≤ x ≤ π, 0 ≤ y ≤ sin x in the xy-plane and α be the area of the region R. If C traverses once in the counter clockwise direction, then the value of the line integral ∮C(2ydx + 5xdy) is equal to
(A) α
(B) 2α
(C) 3α
(D) 4α
Answer: (C)
3. Given that i = √−1. The value of is
(A)
(B)
(C)
(D)
Answer: (B)
Q.4 – Q.7 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).
4. Let f(x) be a non-negative continuous function of real variable x. If the area under the curve y = f(x) from x = 0 to x = a is then the of f(π/2) is ________ (round off to one decimal place).
Answer: (0.5 to 0.5)
5. If the numerical approximation of the value of the integral using the Trapezoidal rule with two subintervals is 9, then the value of the real constant α is _________ (round off to one decimal place).
Answer: (0.5 to 0.5)
6. Let the transformation y(x) = exv(x) reduce the ordinary differential equation x > 0 to where α, β, γ are real constants. Then, the arithmetic mean of α, β, γ is __________ (round off to three decimal places).
Answer: (0.665 to 0.668)
7. A person, who speaks the truth 3 out of 4 times, throws a fair dice with six faces and informs that the outcome is 5. The probability that the outcome is really 5 is _________ (round off to three decimal places).
Answer: (0.375 to 0.375)
Q.8 – Q. 9 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).
8. Let f(x, y) = x4 + y4 − 2x2 + 4xy − 2y2 + α be a real valued function. Then, which one of the following statements is TRUE for all α ?
(A) (0, 0) is not a stationary point of f
(B) f has a local maxima at (0, 0)
(C) f has a local minima at (0, 0)
(D) f has a saddle point at (0, 0)
Answer: (D)
9. Let u(x, y) = (x2 − y2)v(x, y) be such that both u(x, y) and v(x, y) satisfy the Laplace equation in a domain Ω of the xy-plane. Then, which one of the following is TRUE in Ω ?
Answer: (A)
Q.10 – Q. 11 Numerical Answer Type (NAT), carry TWO marks each (no negative marks).
10. Let I denote the identity matrix of order 7, and A be a 7 × 7 real matrix having characteristic polynomial CA (λ) = λ2(λ − 1)α (λ + 2)β, where α and β are positive integers. If A is diagonalizable and rank(A) = rank(A + 2I), then rank(A − I) is ____________ (in integer).
Answer: (4 to 4)
11. Let C1 be the line segment from (0, 1) to (4/5, 3/5) and let C2 be the arc of the circle x2 + y2 = 1 from (0, 1) to (4/5, 3/5). If and where then the value of α2 + β2 is _________ (round off to two decimal places).
Answer: (0.32 to 0.32)
Fluid Mechanics (XE-B)
Q.1 – Q.8 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. The general relationship between shear stress, τ, and the velocity gradient (du/dy) for a fluid is given by where k is a constant with appropriate units. The fluid is Newtonian if
(A) n > 1
(B) n < 1
(C) n = 1
(D) n = 0
Answer: (C)
2. Which one of the following options is TRUE?
(A) Pathlines and streaklines are the same in an unsteady flow, and streamlines are tangential to the local fluid velocity at a point.
(B) Streamlines are perpendicular to the local fluid velocity at a point, and streamlines and streaklines are the same in a steady flow.
(C) Pathlines and streaklines are the same in an unsteady flow, and streamlines and streaklines are the same in a steady flow.
(D) Streamlines are tangential to the local fluid velocity at a point, and streamlines and streaklines are the same in a steady flow.
Answer: (D)
3. If Pin = 1.2 Pa and Pout = 1.0 Pa are the average pressures at inlet and outlet respectively for a fully-developed flow inside a channel having a height of 50 cm, then the absolute value of average shear stress (in Pa) acting on the walls of the channel of length 5 m is
(A) 0.005
(B) 0.02
(C) 0.01
(D) 0.05
Answer: (C)
4. Consider the fully-developed flow of a Newtonian fluid (density ρ; viscosity μ) through a smooth pipe of diameter D and length L. The average velocity of the flow is V. If the length of the pipe is doubled, keeping V, D, ρ, μ constant, the friction factor
(A) increases by two times
(B) remains the same
(C) decreases by two times
(D) increases by four times
Answer: (B)
5. The absolute value of pressure difference between the inside and outside of a spherical soap bubble of radius, R, and surface tension, γ, is :
(A) 2γ/B
(B) γ/R
(C) γ/2R
(D) 4γ/R
Answer: (D)
6. Which one of the following statements is TRUE about the continuity equation (where u, v, w are the velocity components along the x, y and z coordinates respectively):
(A) The equation is valid only for steady incompressible flows.
(B) The equation is valid for both steady and unsteady incompressible flows.
(C) The equation is valid only for steady compressible flows.
(D) The equation is valid only for unsteady compressible flows.
Answer: (B)
7. The head loss (KL) associated with the flow entry of water to an internal passage depends on the shape of the entry. The following figure shows three different types of flow entry into a pipe. Which one of the following relationships correctly represents the head loss associated with the three different flow entries?
(A) (KL)a > (KL)b > (KL)c
(B) (KL)b > (KL)a > (KL)c
(C) (KL)b ≤ (KL)a = (KL)c
(D) (KL)b < (KL)a < (KL)c
Answer: (B)
8. The form and friction drags together contribute to the total drag when flow of air occurs past any object. Two orientations of a finite flat plate are shown in the figure. In Orientation-1, the plate is placed perpendicular to the flow while in Orientation-2, the plate is placed parallel to the flow. If the velocity (V) of air in both orientations is the same, which one of the following options is TRUE?
(A) Orientation-1 has higher form drag and lower friction drag and Orientation-2 has lower form drag and higher friction drag
(B) Orientation-1 has lower form drag and lower friction drag and Orientation-2 has higher form drag and higher friction drag
(C) Orientation-1 has lower form drag and higher friction drag and Orientation-2 has higher form drag and lower friction drag
(D) Orientation-1 has higher form drag and higher friction drag and Orientation-2 has lower form drag and lower friction drag
Answer: (A)
Q.9 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).
9. A spherical ball is steadily supported against gravity by an upward air jet as shown in the figure. Take acceleration due to gravity to be g =10 m/s2. The mass flow rate of air, reaching the ball, is 0.01 kg/s and the air reaches the ball at an upward velocity of 3 m/s. Neglecting the buoyancy force, and using the principle of integral momentum balance, the mass (in grams, up to one decimal place) of the ball is ____.
Answer: (2.9 to 3.1)
Q.10 – Q. 12 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).
10. The incompressible flow of air over a curved surface having possible flow separation is schematically shown in the figure. Two zones P and Q are indicated in the figure. Which one of the following combinations is TRUE for zones P and Q?
(a) Acceleration of flow, (b) Deceleration of flow, (c) Adverse pressure gradient, (d) Favorable pressure gradient, (e) No flow separation (f) Possible flow separation.
(A) P: (a), (d), (e) and Q: (b), (c), (f)
(B) P: (a), (d), (f) and Q: (b), (d), (f)
(C) P: (a), (c), (f) and Q: (a), (d), (e)
(D) P: (a), (c), (e) and Q: (a), (d), (f)
Answer: (A)
11. A spherical metal ball (of density ρx and diameter D), attached to a string, is exposed to a crossflow (of velocity U∞) of a viscous fluid (of viscosity μ and density ρf). Due to the crossflow, the string makes an angle of inclination, θ, , with the top surface as shown in the figure. The acceleration due to gravity is denoted by g. For this flow, Reynolds number, and buoyancy force in the fluid is negligible compared to viscous force. Assuming the string to be weightless and offering negligible drag, the expression for θ is
Answer: (D)
12. In a Cartesian coordinate system, a steady, incompressible velocity field of a Newtonian fluid is given by V = μ0 (1 – ay2) i
Here, V is the velocity vector in m/s, i is the unit vector in the x-direction, u0 is a positive, real constant (in m/s), and a is a positive, real constant (in m−2). The viscosity of the fluid is μ (in Pa-s). The absolute value of the pressure gradient (in Pa/m) is
(A) aμu0
(B) 2aμu0
(C) 3aμu0
(D) 4aμu0
Answer: (B)
Q.13 – Q. 22 Numerical Answer Type (NAT), carry TWO marks each (no negative marks).
13. In a laminar, incompressible, fully-developed pipe flow of a Newtonian fluid, as shown in the figure, the velocity profile over a cross-section is given by where U is a constant. The pipe length is L and the fluid viscosity is μ. The power P required to sustain the flow is expressed as P = cμLU2, where c is a dimensionless constant. The value of the constant c (up to one decimal place) is _________.
Answer: (6.0 to 6.5)
14. The two-dimensional velocity field V of a flow in a Cartesian coordinate system is given in dimensionless form by Here, i and j are the unit vectors along the x and y directions respectively, a and b are independent of x, y and time. If the flow is incompressible, then the value of (a−b), up to one decimal place, is ______.
Answer: (0.9 to 1.1)
15. For the configuration shown in the figure, oil of density 800 kg/m3 lies above water of density 1000 kg/m3. Assuming hydrostatic conditions and acceleration due to gravity g =10 m/s2, the length L (in meters, up to one decimal place) of water in the inclined tube is _____.
Answer: (1.7 to 1.9)
16. A two-dimensional Eulerian velocity field is given (in m/s) by V = [(√5)x] i − [(√12)y] j, where x and y are the coordinates (in meters) in a Cartesian coordinate system. The magnitude of the acceleration (in m/s2, up to one decimal place) of a fluid particle at x = 1 m and y = −1 m is ______.
Answer: (12.9 to 13.1)
17. A large pump is to deliver oil at an average velocity (V) of 1.5 m/s. The pump has an impeller diameter (D) of 40 cm and the pressure rise across the pump is 400 kPa. To design this pump, a lab-scale model pump with an impeller diameter of 4 cm is to be used with water as the fluid. The viscosity (μ) of the oil is 100 times that of water, and the densities (ρ) of oil and water are identical. A complete geometric similarity is maintained between the model and prototype. If the pressure rise is a function only of V, D, ρ and μ, the pressure rise (in kPa, up to one decimal place) across the model pump is ______.
Answer: (3.9 to 4.1)
18. Water (density = 103 kg/m3) enters steadily into a horizontal pipe bend, which is part of a larger piping system, as shown in the figure. The volumetric flow rate of water is 0.1 m3/s. The gage pressure at the inlet is 500 kPa, while the exit is open to atmosphere. The x -component of the force on the support is Fx. The absolute value of Fx (in kN, up to one decimal place) is _______.
Answer: (10.5 to 12.0)
19. Air (of density 0.5 kg/m3) enters horizontally into a jet engine at a steady speed of 200 m/s through an inlet area of 1.0 m2. Upon entering the engine, the air passes through the combustion chamber and the exhaust gas exits the jet engine horizontally at a constant speed of 700 m/s. The fuel mass flow rate added in the combustion chamber is negligible compared to the air mass flow rate. Also neglect the pressure difference between the inlet air and the exhaust gas. The absolute value of the horizontal force (in kN, up to one decimal place) on the jet engine is__________.
Answer: (48.0 to 52.0)
20. Water discharges from a cylindrical tank through an orifice, as shown in the figure. The flow is considered frictionless. Initially, the water level in the tank was h1 = 2 m. The diameter of the tank is D = 1 m, while the diameter of the jet is d = 10 cm, and the acceleration due to gravity is g = 10 m/s2. The time taken (in seconds, up to one decimal place) for the water level in the tank to come down to h2 = 1 m is _______.
Answer: (17.5 to 19.5)
21. Water discharges steadily from a large reservoir through a long pipeline, as shown in the figure. The Darcy friction factor in the pipe is 0.02. The pipe diameter is 20 cm and the discharge of water is 360 m3/h. Water level in the reservoir is 10 m and acceleration due to gravity g = 10 m/s2. If minor losses are negligible, the length L (in meters, up to one decimal place) of the pipeline is ____ .
Answer: (182.0 to 192.0)
22. Water is flowing with a flow rate Q in a horizontal circular pipe. Due to the low pressure created at the venturi section (Section-1 in the figure), water from a reservoir is drawn upward using a connecting pipe as shown in the figure. Take acceleration due to gravity g = 10 m/s2. The flow rate Q = 0.1 m3/s, D1 = 8 cm, and D2 = 20 cm. The maximum height (h, in meters, up to one decimal place) of the venturi from the reservoir just sufficient to raise the liquid upto Section-1 is __________.
Answer: (18.5 to 20.0)
Materials Science (XE-C)
Q.1 – Q.7 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. Condition to be satisfied for α and β phases to be in equilibrium in a two-component (A and B) system at constant temperature and pressure is
(Given: μ is the chemical potential)
(A) entropy of the system should be maximum
(B) Gibbs energy of the system should be minimum and
(C) Gibbs energy of the system should be minimum and
(D) Helmholtz energy should be minimum
Answer: (C)
2. Amino acids react to form peptides and proteins. This process is known as
(A) addition polymerization
(B) nucleophilic substitution
(C) condensation polymerization
(D) hydration
Answer: (C)
3. The most favoured slip system in face centered cubic metal is
Answer: (D)
4. The dielectric constant of a material at ultraviolet frequencies is mainly due to
(A) dipolar polarizability
(B) ionic polarizability
(C) electronic polarizability
(D) interfacial polarizability
Answer: (C)
5. Match the different transformations/reactions in Column I with the most suitable information in Column II.
(A) P-2; Q-3; R-1
(B) P-1; Q-2; R-3
(C) P-2; Q-1; R-3
(D) P-3; Q-2; R-1
Answer: (C)
6. In scanning electron microscopy, the resolution of backscattered electron (BSE) image is poorer compared to that of secondary electron (SE) image, because
(A) energy of BSE is lower
(B) sampling volume of BSE is larger
(C) yield of BSE is lower
(D) sampling volume of SE is larger
Answer: (B)
7. Which of the following deposition conditions favour the formation of larger grains in thin film?
(A) Low deposition rate and low substrate temperature
(B) Low deposition rate and high substrate temperature
(C) High deposition rate and low substrate temperature
(D) High deposition rate and high substrate temperature
Answer: (B)
Q.8 Multiple Select Question (MSQ), Carry ONE mark each (no negative marks).
8. A metal has a melting point of 600 °C. By rapid cooling, liquid metal can be made to solidify either at 500 °C or 400 °C or 300 °C. Critical size of the solid nuclei is
(A) same for solidification at 400 °C and 500 °C
(B) smaller for solidification at 400 °C as compared to solidification at 500 °C
(C) larger for solidification at 400 °C as compared to solidification at 500 °C
(D) the smallest for solidification at 300 °C
Answer: (B; D)
Q.9 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).
9. A magnet of mass 50 g has a magnetic moment of 4.2 × 10−7 A m2. The density of the magnet is 7.2 g cm−3. The intensity of magnetization in A m−1 is _________ (round off to 3 decimal places)
Answer: (0.058 to 0.063)
Q.10 – Q. 12 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).
10. In the context of scanning electron microscopy, match the information in Column I with most appropriate information in Column II.
(A) P-3; Q-2; R-1; S-4
(B) P-2; Q-4; R-3; S-1
(C) P-1; Q-3; R-2; S-4
(D) P-4; Q-2; R-1; S-3
Answer: (B)
11. Match the heat treatment processes given in Column I with the most suitable outcomes in Column II.
(A) P-3; Q-2; R-1; S-4
(B) P-2; Q-4; R-3; S-1
(C) P-1; Q-2; R-3; S-4
(D) P-1; Q-3; R-4; S-2
Answer: (C)
12. A co-joined cross-ply laminate composite, as shown in figure, is distorted upon heating. What are the resultant shapes of edges XY and YZ ?
Answer: (C)
Q.13 Multiple Select Question (MSQ), Carry TWO marks each (no negative marks).
13. X-ray diffraction peak broadening enables the estimation of
(A) X-ray diffraction peak broadening enables the estimation of
(B) microstrain in the material
(C) precise lattice parameter
(D) residual macrostress acting on the material
Answer: (A; B)
Q.14 – Q. 22 Numerical Answer Type (NAT), carry TWO marks each (no negative marks).
14. Fe – 10 atom % C austenite (fcc), having no Fe vacancies, has a lattice parameter of 4 Å. The density of austenite in g cm−3 is _________ (round off to 2 decimal places)
(Given: atomic weight of Fe = 55.8; atomic weight of C = 12.0; Avogadro’s number = 6.023 × 1023)
Answer: (5.85 to 6.00)
15. An element transforms from α to β at 773 K and 1 atm pressure with 912 J mol−1 as enthalpy of transformation. The molar volumes of α and β phases are 7.377 cm3 and 7.317 cm3, respectively. Assume that the difference in molar volumes of α and β is independent of pressure. The pressure (in atm) required for α to β transformation to occur at 723 K is _________ (round off to nearest integer) (Given: 1 atm = 1.01325 × 105 Pa)
Answer: (9600 to 9800)
16. A binary A-B alloy has α and β phases at equilibrium. The ratio of weight percentages (wt.%) of α to β is 4. The wt.% of A in α and β phases is 70 and 20, respectively. The wt.% of B in the alloy is _________ (round off to nearest integer)
Answer: (38 to 42)
17. During heating, Ti undergoes allotropic transformation from hcp to bcc at 882 °C. The percent volume change accompanying this transformation is _________ (round off to 1 decimal place)
(Given: atomic weight of Ti = 47.9; lattice parameter of bcc Ti = 0.332 nm; density of hcp Ti = 4.51 g cm−3; Avogadro’s number = 6.023 × 1023)
Answer: (3.4 to 4.8)
18. Vickers hardness test is performed with an indenter of square-base diamond pyramid having an included angle of 136° between the opposite faces of the pyramid. If the applied load is 10 kg and the average length of diagonals of square indentation is 0.5 mm, the Vickers hardness in kg mm−2 is_______ (round off to nearest integer)
Answer: (71 to 77)
19. The drift mobility of electron in an n-type Si crystal doped with 1016 cm−3 phosphorous atoms is 1350 cm2 V−1 s−1. The electrical conductivity in Ω−1 m−1 is _________ (round off to nearest integer)
(Given: Intrinsic charge concentration of Si = 1.45 × 1010 cm−3;
Charge of an electron, e = 1.6 × 10−19 C)
Answer: (210 to 220)
20. At 1000 K, the linear thermal expansion coefficients of graphite, parallel and perpendicular to the graphite layers, are 0.8 × 10−6 K−1 and 29 × 10−6 K−1, respectively. The percentage increase in the volume of graphite when heated from 900 K to 1100 K is _________ (round off to 2 decimal places)
Answer: (0.60 to 0.62)
21. A certain ceramic has a theoretical density and sintered density of 6.76 g cm−3 and 6.60 g cm−3, respectively. The green compact has 18 volume percent porosity. For a sintered cube of side 2 cm, the required side of the cubic green compact in cm is _________ (round off to 2 decimal places)
Answer: (2.10 to 2.14)
22. When a metal (M) is immersed in de-aerated acid electrolyte, it polarizes anodically by 0.4 V. The M/Mn+ exchange current density is 10−5 A m−2 and Tafel slope is 0.1 V/decade for the anodic reaction. Assume that corrosion is uniform and, anodic and cathodic reactions are under activation control. The rate of metal dissolution in A m−2 is _________ (round off to 1 decimal place)
Answer: (0.1 to 0.1)
Solid Mechanics (XE-D)
Q.1 – Q.8 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. A force F = 40 kN is applied on the hook as shown. The equivalent force-couple system at B is
(A) 40 kN in +y direction and M = 0
(B) 40 kN in –y direction and M = 0
(C) 40 kN in +y direction and M =4000 Nm counter clockwise
(D) 40 kN in -y direction and M = 4000 Nm clockwise
Answer: (D)
2. A rigid rod OA rotates clockwise at an angular velocity of 10 rad/s. A bead B (OB = 1 m) translates outward on the rod at a speed of 5 m/s and acceleration 2.5 m/s2 (both quantities with respect to the rod). The Coriolis component of acceleration is
(A) 2.5 m/s2 in +x direction
(B) 100 m/s2 in +x direction
(C) 100 m/s2 in –y direction
(D) 25 m/s2 in + y direction
Answer: (B)
3. A two force member in equilibrium is one in which
(A) Forces act at two points and forces are collinear
(B) Forces act at two points and member is always straight
(C) Forces act at two points but the member is free to carry moment at any point
(D) Force acts at one point and moment acts at second point
Answer: (A)
4. If the yield point shear stress obtained from the torsion test of a cylindrical specimen is τy, then what is the maximum value of principal strain at yielding? (μ is Poisson’s ratio and E is Young’s modulus)
Answer: (B)
5. If the ratio of Young’s modulus to bulk modulus of a material is 3/2, then the ratio of shear modulus to the Young’s modulus of the material is
(A) 1
(B) 2/5
(C) 1/3
(D) 3/5
Answer: (B)
6. With respect to the plane of maximum shear stress, which of the following statements is INCORRECT?
(A) The normal stress on this plane is zero.
(B) The maximum shear stress is equal to the largest of the one half the difference of principal stresses
(C) The plane of maximum shear stress occurs at 45° to the principal planes.
(D) The magnitude of the maximum shear stress is equal to the largest of the radius of the Mohr’s circles.
Answer: (A)
7. A simply supported beam of length L is loaded by two symmetrically applied point loads P at L/3 from each support. Both the loads are then shifted to new points which are at a distance L/4 from each support. The bending moments at the mid-section of the beam in both the cases are same. The magnitude of P1 in terms of P is
(A) P/4
(B) 8P/3
(C) 4P/3
(D) P/3
Answer: (C)
8. A beam having rectangular cross section is subjected to transverse loading. The ratio of maximum shear stress developed in the beam to the average shear stress is
(A) 1.50
(B) 1.25
(C) 1.33
(D) 1.66
Answer: (A)
Q.9 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).
9. During an earthquake, a structure vibrates and the vibration can be assumed to be in simple harmonic motion at 5 Hz. At a measurement point, the RMS value of acceleration is 10 m/s2. The approximate amplitude of motion (in mm) at this point (rounded off to two decimal places) is ___________
Answer: (14.30 to 14.35)
Q.10–Q. 15 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).
10. For the state of plane stress shown, the components of normal and shear stresses are given in terms of stress σ and unknown constants m and n. If the normal and shear components of stress on a 45o plane are 2σ and zero, the values of m and n would be:
(A) m = 1, n = 2
(B) m = 2, n = 1
(C) m = 1, n = 1
(D) m = 2, n = 2
Answer: (C)
11. For a state of plane strain, the normal strains are given by εxx = 1000 × 10−6, εyy = 200 × 10-6 and the maximum shear strain is γmax = 1000 × 10−6. The value of shear strain γxy for this strain state is
(A) 600 × 10−6
(B) 183 × 10−6
(C) 1000 × 10−6
(D) 800 × 10−6
Answer: (A)
12. A thin cylinder (closed at its ends) of radius r and thickness t ( r ≫ t ) is subjected to internal pressure p. The maximum shear stress in the wall of the cylinder is
(A) pr/t
(B) pr/2t
(C) pr/4t
(D) 3pr/2t
Answer: (B)
13. The truss shown is subjected to a force P. All members of the truss have the same length L. The reaction at A and force in member AB are
Answer: (A)
14. The figure shows a structure with supports. The correct free body diagram when the supports are removed is
Answer: (A)
15. A hammer of mass 1 kg is used to break an almond shell. The velocity time graph of the hammer during the impact duration is shown in the figure. The shape of force time graph is also given, which can be approximated as a triangle. A force of 300 N is required for breaking the shell, while a force of 200 N will not be able to break it, but just introduce a crack. Which one of the following events will happen?
(A) The almond shell will crack but not break
(B) The almond shell will not crack.
(C) The almond shell will break
(D) Cannot be determined from the given data
Answer: (A)
16. A rigid circular disc of radius 0.2 m and mass 10 kg rolls without slip on the ground at A. The coefficient of static friction μ between ground and disc is 0.7. A torque T of 9 Nm acts on the disc as shown. Given acceleration due to gravity g = 10 m/s2. The friction force (in N) acting on the disc (in integer) is _________
Answer: (30 to 30)
17. A prismatic solid circular rod of diameter d is bent to introduce an offset s = d as shown. The rod is further subjected to an axial load P. If the maximum longitudinal stress at a section A-B in the rod (with offset) is n times the longitudinal stress in the straight rod, the value of n (in integer) would be ________
Answer: (9 to 9)
18. A naturally curved steel beam AB having Young’s modulus 208 GPa, area moment of inertia I = 26.7 cm4 and radius R = 2 m is subjected to a vertical load P = 1000 N at B. The end A at θ = 900 is rigidly fixed. The bending strain energy of the beam (in Nm, rounded off to two decimal places) is ___________
Answer: (56.50 to 56.60)
19. At room temperature of 25°C, a gap of 1 mm exists between the ends of the rods 1 and 2 as shown. Given the cross section area A of the rods is 1500 mm2, Young’s modulus E = 75 GPa and the coefficient of thermal expansion α = 23 × 10−6/° When the temperature has reached 150°C, the magnitude of normal stress in each of the rods (in MPa, rounded off to two decimal places) is _________
Answer: (90.60 to 90.65)
20. A tube of inner radius 4 cm and outer radius 5 cm can carry a maximum torque of T. This tube is now replaced by a solid circular shaft of the same material. The minimum radius of the solid circular shaft (in cm, rounded off to two decimal places) to carry the same amount of torque T is ___________
Answer: (4.17 to 4.21)
21. In System A, a rectangular block of mass M is centrally supported on a spring of stiffness K as shown. In the System B, the mass is hinged at one of its ends and is supported centrally by the spring. The ratio of natural frequency of System B to that of System A (rounded off to two decimal places) is __________
Answer: (0.80 to 0.90)
22. A coronavirus droplet of mass 1 microgram ejects from the mouth of a patient with a velocity of 0.7 m/s and travels through air. The gravitational force experienced by it can be neglected due to the buoyancy effect. However, the droplet experiences air drag force proportional to its velocity and the drag coefficient is given as 1.0 μN-s/m. The distance travelled by the droplet before its velocity drops to 10% of its initial velocity (in m, rounded off to two decimal places) is _____________.
Answer: (0.00 to 0.01)
Thermodynamics (XE-E)
Q.1 – Q.7 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. A refrigerator working on a reversed Carnot cycle has a Coefficient of Performance (COP) of 4. If it works as a heat pump and consumes work input of 1 kW, the heating effect will be:
(A) 1 kW
(B) 4 kW
(C) 5 kW
(D) 6 kW
Answer: (C)
2. The liquid phase of a pure substance is termed as _________, if its temperature is lower than the saturation temperature corresponding to its pressure P.
(A) super-heated liquid
(B) sub-cooled liquid
(C) metastable liquid
(D) flashing liquid
Answer: (B)
3. Two air streams of mass flow rates ṁ 1 and ṁ 2 enter a mixing chamber and exit after perfect mixing. The corresponding temperatures of the inlet streams are T1 and T2, respectively. Heat loss rate from the mixing chamber to the surrounding is Q̇. Assume that the process is steady, specific heat capacity is constant, and air behaves as an ideal gas. Identify the correct expression for the final exit temperature T3 after mixing. The mass specific heat capacities of the gas at constant volume and constant pressure are cv and cp, respectively. Neglect the bulk kinetic and potential energies of the streams.
Answer: (C)
4. If
h is the mass specific enthalpy,
s is the mass specific entropy,
P is the pressure,
T is the temperature,
CV is the mass specific heat at constant volume,
CP is the mass specific heat at constant pressure,
β is the coefficient of thermal expansion,
v is the mass specific volume,
κ is the isothermal compressibility,
then the partial derivative
Answer: (D)
5. If
v is the mass specific volume,
s is the mass specific entropy,
P is the pressure,
T is the temperature,
then using Maxwell relations,
Answer: (B)
6. A closed system consists of a solution of liquid water and ethanol in equilibrium with its vapours. Using the Gibbs phase rule, the degree of freedom of the system is:
(A) 0
(B) 1
(C) 2
(D) 3
Answer: (C)
7. For a real gas passing through an insulated throttling valve, the outlet temperature of the gas __________ with respect to the inlet temperature.
(A) is always higher
(B) is always lower
(C) may be higher, lower or same
(D) is always same
Answer: (C)
Q.8 Multiple Select Question (MSQ), Carry ONE mark each (no negative marks).
8. Atmospheric air with Dry Bulb Temperature (DBT) of 24°C and Relative Humidity of 35%, entering in a circular duct (assume no pressure drop in the duct) is heated by an electrical resistance arrangement inside the duct. The DBT of air measured at the outlet of the duct is equal to 30°C. Considering the flow to be steady, which of the following statement(s) is (are) correct as regards to the outlet air, with respect to the inlet air?
(A) There is no change in the Relative Humidity
(B) There is no change in the Dew Point Temperature
(C) There is no change in the Specific Humidity
(D) There is no change in the Specific Enthalpy
Answer: (B; C)
Q.9 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).
9. A cylinder of volume 1 m3 contains a mixture of CO2 (20% by mol) and O2 (80% by mol) at 100 kPa and 300 K. This cylinder is connected to a 1 MPa pressure line carrying N2 at 300 K. The cylinder is filled isothermally till the pressure of gas mixture inside it becomes 500 kPa, and then the filling is stopped. The amount of N2 gas that has entered the cylinder is _________ (in mole, 2 decimal places).
The universal gas constant is 8.3145 J/(mol K).
Answer: (159.00 to 162.00)
Q.10 – Q. 13 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).
10. The saturation pressure Psat of a pure liquid is represented by an equation of the form:
ln Psat = A – (B/T),
where, A and B are constants, and T is the absolute temperature. For this substance, which of the following expression for specific entropy difference between the saturated vapour and the saturated liquid phase (sfg) is correct?
Note: Subscripts f and g refer to saturated liquid and saturated vapour phases, respectively, and vfg is the specific volume difference between the saturated vapour and the saturated liquid phases.
Answer: (B)
11. For a refrigeration cycle, the ratio of actual COP to the COP of a reversible refrigerator operating between the same temperature limits is 0.8. The condenser and evaporator temperatures are 51°C and −30°C, respectively. If the cooling capacity of the plant is 2.4 kW, then the power input to the refrigerator is:
(COP: Coefficient of Performance)
(A) 1.00 kW
(B) 1.33 kW
(C) 1.25 kW
(D) 2.08 kW
Answer: (A)
12. Two identical pressure cookers, Cooker A and Cooker B, each having a total internal capacity of 6 litres are available. Cooker A is filled with 2 litres of liquid water at 110°C and Cooker B is filled with 4 litres of liquid water at 110°C. The remaining space in both the cookers is filled with saturated water vapour in equilibrium with the liquid water. If g represents the specific Gibbs free energy, and subscripts v and l represent the saturated vapour and the saturated liquid phases, respectively, which of the following expressions is correct?
(A) gv,A > gl,B
(B) gv,A < gl,B
(C) gv,A = gl,B
(D) gl,B = 2 gl,A
Answer: (C)
13. Four different Entropy (S) – Temperature (T) diagrams, representing liquid to vapour phase transition process of a pure substance in a closed system under constant pressure are shown. The diagram, which correctly represents the process, is:
(A) 1
(B) 2
(C) 3
(D) 4
Answer: (A)
Q.14 – Q. 22 Numerical Answer Type (NAT), carry TWO marks each (no negative marks).
14. Air having a mass flow rate of 2 kg/s enters a diffuser at 100 kPa and 30°C, with a velocity of 200 m/s. Exit area of the diffuser is 400 cm2 while the exit temperature of the air is 45°C. The rate of heat loss from the diffuser to the surrounding is 8 kJ/s. The pressure at the diffuser exit is ____________ kPa (2 decimal places).
For air, the characteristic gas constant is 287 J/(kgK) and specific heat capacity at constant pressure is 1005 J/(kgK). Assume air to be an ideal gas and the flow in the diffuser is steady.
Answer: (100.79 to 111.39)
15. For the Refrigerant R-134 (at 1 MPa and 50°C), the difference between the specific volume computed by assuming it to be an ideal gas and its actual specific volume is: videal − vactual = 4.529 × 10−3 m3/kg. If the compressibility factor associated with this state is Z = 0. 84, then vcom − vactual =_________ ×10−3 m3/kg (3 decimal places).
Here vcom is the specific volume calculated using the compressibility factor.
For Refrigerant R-134 (at 1 MPa and 50°C):
The characteristic gas constant: 0.0815 kJ/(kgK), The critical pressure and temperature are, respectively, Pcr = 4.059 MPa and Tcr = 374.2 K.
Answer: (0.300 to 0.330)
16. A mixture of air and water vapour enters a steady-flow adiabatic saturator at 50°C and 100 kPa. It leaves the saturator in a completely saturated state at temperature of 25°C and pressure of 100 kPa. Liquid water enters the saturator at 25°C. If air is considered to be an ideal gas, with constant specific heat capacity, the relative humidity of the air entering the saturator is ______ % (1 decimal place).
Specific heat capacity of air at constant pressure CP=1.005 kJ/(kgK)
Answer: (12.1 to 13.0)
17. Air at a pressure of 1 MPa and 300 K is flowing in a pipe. An insulated evacuated rigid tank is connected to this pipe through an insulated valve. The volume of the tank is 1 m3. The valve is opened and the tank is filled with air until the pressure in the tank is 1 MPa. Subsequently, the valve is closed. Consider air to be an ideal gas and neglect bulk kinetic and potential energy. The final temperature of air in the tank is _______ K (1 decimal place).
Specific heat capacity of air at constant pressure CP=1.005 kJ/(kgK) and characteristic gas constant for air = 0.287 kJ/(kgK)
Answer: (418.0 to 422.0)
18. A cylinder of volume 0.1 m3 is filled with 100 mol of propane (C3H8) at 2 MPa. If propane is assumed to obey the van der Waals equation of state, then its temperature is ______ K (1 decimal place).
The van der Waals constants for propane are: a = 939. 2 kPa (m3/kmol)2 and b = 0.0905 m3/kmol. The universal gas constant is 8.3145 J/(mol K).
Answer: (320.0 to 323.0)
19. A frictionless piston cylinder device contains 1 kg of an ideal gas. The gas is compressed according to Pv3 = constant (P is pressure and v is mass specific volume), from 100 kPa, 250 K, till it reaches a temperature of 500 K. The heat transfer from the piston cylinder device to its surroundings is __________ kJ (2 decimal places).
The characteristic gas constant is 287 J/(kgK) and the ratio of specific heat capacities is 1.4.
Answer: (56.80 to 62.78)
20. A 0.8 m3 insulated rigid tank contains 1.5 kg of an ideal gas at 100 kPa. Electric work is done on the system until the pressure in the tank rises to 135 kPa. The loss in availability (exergy) associated with the process is __________ kJ (2 decimal places).
For the ideal gas, the characteristic gas constant is 188.9 J/(kgK) and the specific heat capacity at constant volume is 680 J/(kgK). The temperature of the dead state is 298 K.
Answer: (86.66 to 95.78)
21. A rigid tank contains 1.0 kg of pure water consisting of liquid and vapour phases in equilibrium at 10 bar. If the liquid and vapour phase each occupies one half of the volume of the tank, then the net enthalpy of the contents of the tank is ________ kJ (1 decimal place).
For saturated liquid and vapour at 10 bar, the thermodynamic data table provides the following values:
vf = 1. 127 × 10−3 m3/kg, vg = 194. 3 × 10−3 m3
hf = 762. 6 kJ/kg, hg = 2776. 2 kJ/kg
/kg,
Answer: (773.0 to 775.0)
22. An air-standard Diesel cycle with a compression ratio of 16 takes air at 1 bar and 300 K. If the maximum temperature in the cycle is 2100 K, then the thermal efficiency of the cycle is _______ % (1 decimal place). The ratio of the specific heat capacities of air is 1.4.
Answer: (59.0 to 61.0)
Polymer Science and Engineering (XE-F)
Q.1 – Q.9 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. Linear low density polyethylene (LLDPE) is a copolymer of ethylene and a small fraction of _______.
(A) butadiene
(B) isoprene
(C) butene
(D) hexadiene
Answer: (C)
2. Binary polymer blends of polypropylene and polyamide 6 are immiscible. From a thermodynamic viewpoint this is due to _________.
(A) low enthalpy of mixing
(B) high entropy of mixing
(C) high enthalpy of mixing
(D) low entropy of mixing
Answer: (D)
3. Which one of the following is an elastomer?
(A) Polyamide 6,6
(B) Poly(ethylene terepthalate)
(C) Vulcanized polybutadiene
(D) High density polyethylene
Answer: (C)
4. Compression moulded isotropic polypropylene film exhibits _______ in X-ray diffraction analysis.
(A) spot pattern
(B) circular ring pattern
(C) circular ring and spot pattern
(D) arc pattern
Answer: (B)
5. Which one of the following is an example of a biodegradable polymer?
(A) Polyethylene
(B) Polyamide 6,6
(C) Polypropylene
(D) Polylactic acid
Answer: (D)
6. Polymer crystals show a range of melting points in contrast to single melting point of crystals of small molecules, because ________.
(A) there is an absence of intermolecular interactions
(B) there is an absence of long range ordering
(C) the polymer chains are not in thermodynamic equilibrium in a metastable state
(D) the melting behavior of polymer crystal is independent of sample thermal history
Answer: (C)
7. When the rate of cooling is increased during the solidification process, the glass transition temperature of a polymer ______.
(A) decreases
(B) increases
(C) stays unaltered
(D) shows a non-monotonic dependence
Answer: (B)
8. Equal and opposite forces of a constant magnitude F are applied at the two ends of a thin elastomeric rod, which is held at a temperature T1 (Tg < T1 < Tm), where Tg and Tm are the glass transition temperature and melting temperature respectively. If the temperature is increased to T2 (Tg < T2 < Tm and T2 > T1), the rod will ____________.
(A) expand along the loading direction and the transverse direction
(B) shrink along the loading direction
(C) remain dimensionally unaltered
(D) expand only along the loading direction
Answer: (B)
9. The size of a coiled polymer chain in a dilute solution is RG in a good solvent, RI in an ideal solvent and RP in a poor solvent. Select the correct ordering of sizes.
(A) RG > RI > RP
(B) RG < RI < RP
(C) RP > RG > RI
(D) RP < RG < RI
Answer: (A)
Q.10 – Q. 12 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).
10. Match the Additive to its Function.
(A) P-3, Q-2, R-1, S-4
(B) P-3, Q-1, R-4, S-2
(C) P-4, Q-1, R-3, S-2
(D) P-1, Q-2, R-4, S-3
Answer: (B)
11. Match the polymer processing operation with respect to its typical range of shear rate.
(A) P-3, Q-4, R-2, S-1
(B) P-1, Q-3, R-2, S-4
(C) P-2, Q-4, R-3, S-1
(D) P-3, Q-2, R-1, S-4
Answer: (A)
12. Shear stress (σ) and shear viscosity (η) are plotted as functions of the shear rate, γ̇, for idealized “solid-like with yielding (1)” and “liquid-like (2)” materials.
Associate the shear stress and viscosity plots with the appropriate material responses.
(A) P-2, Q-1, R-2, S-1
(B) P-1, Q-2, R-1, S-2
(C) P-1, Q-2, R-2, S-1
(D) P-2, Q-1, R-1, S-2
Answer: (B)
Q.13 – Q. 22 Numerical Answer Type (NAT), carry TWO marks each (no negative marks).
13. The plateau modulus of polystyrene has a value of 0.2 × 106 Pa at 150°C. Given, the density of polystyrene is 1.05 g/cm3, the universal gas constant, R = 8.3 J K−1 mol−1, and the monomer molecular weight is 104 g/mol. The molecular weight between entanglements (rounded off to the nearest integer) of polystyrene chains is __________ g/mol.
Answer: (18000 to 19000)
14. A unidirectional composite of epoxy and carbon fiber of 50% by volume is made. The elastic modulus of epoxy and carbon fiber are 3.5 GPa and 350 GPa, respectively. The ratio (rounded off to one decimal place) of the modulus of the composite to the matrix modulus is __________.
Answer: (50.4 to 50.6)
15. A single screw extruder is operating at a rotational speed of 2 revolutions per second for the extrusion of a Newtonian polymer under open-discharge conditions (in absence of a die, the pressure drop, ∆p = 0). The extruder has a screw diameter, D = 5 cm, a channel depth, H = 0.4 cm, distance between flights, W = 1 cm, and a helix angle, θ = 20°. Assume the value of π = 3.14. The volumetric flow rate (rounded off to 2 decimal places) is _________ cm3/s.
Answer: (5.00 to 7.00)
16. At 215°C, the viscosity of a polystyrene of molecular weight 250 × 103 g/mol is 8.0 × 103 Pa.s. The critical molecular weight of polystyrene, Mc = 35 × 103 g/mol. For a similar polystyrene of molecular weight 500 × 103 g/mol, the viscosity (rounded off to nearest integer) will be __________ × 103 s.
Answer: (62 to 99)
17. There are two different PTFE polymer specimens of the following density (ρ) and % crystallinity. For PTFE-specimen-1, ρ is 2.144 g/cm3 and % crystallinity is 50. For PTFE- specimen-2, ρ is 2.215 g/cm3 and % crystallinity is 75. Assuming the polymer is pure and defect free, the density (rounded off to 3 decimal places) of 100% amorphous PTFE specimen will be _______ g/cm3.
Answer: (1.980 to 2.040)
18. The behavior of a polymer is described by a Maxwell model consisting of a spring element of modulus 1010 Pa in series with a dashpot of viscosity 1012s. In the solid, 50 s after the sudden application of a fixed strain of 1%, the stress (rounded off to 2 decimal places) will be _________ × 107 Pa.
Answer: (6.00 to 7.00)
19. A particular free radical polymerization process yields a polymer with a number averaged degree of polymerization, The monomer concentration is doubled and the initiator concentration is increased by four times. Assuming that all rate coefficients and other parameters remain unchanged, the value of (rounded off to the nearest integer) is ________.
Answer: (100 to 100)
20. A polymer is synthesized from 2 moles of terephthalic acid (molecular weight of the repeat unit, (−OCC6H4CO−), is 132 g/mol), 1 mol of ethylene glycol (molecular weight of the repeat unit, (−OCH2CH2O−), is 60 g/mol), and 1 mol of butylene glycol (molecular weight of the repeat unit, (−O(CH2)4O−), number averaged molecular weight, (rounded off to the nearest integer) is _______ g/mol.
Answer: (10000 to 10500)
21. A sample of natural rubber (cis-1,4-polyisoprene) is vulcanized such that one of every 240 chain carbon atoms is cross-linked. The formula unit of the isoprene monomer is C5H8 (molecular weight = 68 g/mol). The average molecular weight (rounded off to the nearest integer) between cross-links is ________ g/mol.
Answer: (4000 to 4200)
22. A sample of an oriented semi-crystalline polymer is subjected to uniaxial tensile stress, σ, in an X-ray diffractometer. The wavelength of X-ray radiation (Cu Kα) is λ = 1.542 Å. The position of the (002) peak, which was found initially at a Bragg angle of 37.50° at σ = 0 MPa shifted to 37.45° at σ = 160 MPa. Assuming elastic deformation, the strain (rounded off to three decimal places) in the sample along the direction of applied stress is ________ × 10−3.
Answer: (1.000 to 1.500)
Food Technology (XE-G)
Q.1 – Q.9 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. In a typical bacterial growth curve, the first order kinetics for growth rate is observed in
(A) Lag phase
(B) Log phase
(C) Stationary phase
(D) Death phase
Answer: (B)
2. Which one of the following microorganism is NOT a causative agent for food borne diseases?
(A) Campylobacter jejuni
(B) Clostridium perfingens
(C) Norovirus
(D) Borrelia burgdorferi
Answer: (D)
3. Which of the followings is NOT a fermented food product?
(A) Tofu
(B) Vinegar
(C) Sauerkraut
(D) Tempeh
Answer: (A)
4. The Protein Efficiency Ratio (PER) is defined as
(A) Percentage of absorbed nitrogen retained in the body
(B) Weight gain in body mass (in gram) per gram protein intake
(C) Ratio of essential and non-essential amino acids in a protein
(D) Percent in vitro digestibility of a protein
Answer: (B)
5. Which one of the following enzymes sequentially releases maltose from starch?
(A) α−Amylase
(B) β−Amylase
(C) Glucoamylase
(D) Pullulanase
Answer: (B)
6. Which one of the following enzymes is involved in proteolysis of casein in cheese during aging?
(A) Myrosinase
(B) Alliinases
(C) Cathepsin
(D) Plasmin
Answer: (D)
7. Which one of the following compounds is present in soybean and acts as phytoesterogen?
(A) Tangeretin
(B) Lutin
(C) Quercetin
(D) Genistein
Answer: (D)
8. Ultra high temperature (UHT) process of pasteurization of milk is achieved by Heating at
(A) 145°F for 30 minutes
(B) 161°F for 15 seconds
(C) 280°F for 2 seconds
(D) 400°F for 15 seconds
Answer: (C)
9. Bittering agent in grape fruit formed after juice extraction under acidic conditions is
(A) Quinine
(B) Theobromine
(C) Isohumulone
(D) Limonin
Answer: (D)
Q.10–Q. 12 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).
10. The conversion of pyruvate to lactic acid in homolactic fermentation is catalyzed by
(A) Lactate dehydrogenase
(B) Pyruvate dehydrogenase
(C) Lactase
(D) Pyruvate decarboxylase
Answer: (A)
11. Which one of the following statements is INCORRECT with respect to Controlled Atmosphere Package (CAP) and Modified Atmosphere Package (MAP) of agro-produce?
(A) CAP and MAP limit microbial as well as biochemical activities.
(B) Gas composition inside a MAP during the storage is continuously monitored and regulated.
(C) CAP implies a greater degree of precision than MAP in maintaining specific levels of the gas composition.
(D) Modification of the atmosphere inside a MAP is achieved by natural interplay between respiration of products and permeation of gases through the packaging film.
Answer: (B)
12. Match unit operation in Column I with its application in food processing in Column II.
(A) P-2, Q-4, R-2, S-I
(B) P-2, Q-3, R-4, S-1
(C) P-4, Q-1, R-2, S-3
(D) P-4, Q-2, R-1, S-3
Answer: (B)
Q.13 – Q.19 Multiple Select Question (MSQ), Carry TWO marks each (no negative marks).
13. Which of the followings are correct pair of GRAS chemical food preservative, affected organism and given food matrix?
(C) Differential scanning calorimeter – glass transition temperature – degree of caking
(D) Capillary viscometer – viscosity – sensory
Answer: (A; C)
19. Choose the correct pair(s) of Governing Law and corresponding application(s)
(A) Hagen Poiseuille law – Pressure drop
(B) Rittinger’s law – Vapour pressure
(C) Stefan Boltzmann law – Radiation heat transfer
(D) Raoult’s law – Size reduction
Answer: (A; C)
Q.20 – Q. 22 Numerical Answer Type (NAT), carry TWO marks each (no negative marks).
20. An orange juice sample is concentrated from 10% to 40% (by weight) total soluble solids in a single effect evaporator with a feed rate of 3600 kg hr−1 at 25°C. The evaporator operates at sufficient vacuum to allow the product moisture to evaporate at 55°C. The specific heat of both feed and concentrated juice is 4.0 kJ kg−1 °C−1. If enthalpy of water vapour at 55°C is 2600 kJ kg−1, heat transfer rate through the heating surface area of the evaporator in kilowatt (in integer) will be________.
Answer: (1900 to 1910)
21. Dry air is fed into a tray dryer. The percentage relative humidity of the air leaving the dryer is 60% at 70°C and 101.35 kPa. If, saturated vapour pressure of water at 70°C is 31.2 kPa, the humidity of the air leaving the dryer in kg water per kg dry air (round off to 3 decimal places) will be __________.
(Given : Molecular weight of water and air are 18.02 g mol−1 and 28.97 g mol−1 respectively)
Answer: (0.135 to 0.150)
22. In a cold storage plant, 5000 kg potato having a constant specific heat capacity of 3.65 kJ kg−1 °C−1 are cooled from 28°C to 2°C in 24 hours. The heat of respiration of potato per 24 hour is 3.12 kJ kg−1 during the storage. Assuming the efficiency of the storage plant to be 70%, the capacity of the plant in ton of refrigeration (round off to 2 decimal places) is __________.
(Given: 1 ton of refrigeration = 3.517 kilowatt)
Answer: (2.20 to 2.40)
Atmospheric and Oceanic Sciences (XE-H)
Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. Western Boundary Current in the ocean is primarily due to
(A) Ekman pumping.
(B) rotation of the earth.
(C) river water forcing.
(D) ocean floor topography.
Answer: (B)
2. The relevant nondimensional number in deciding deepening of the thermocline driven by instability of ocean currents is
(A) Rossby number.
(B) Reynolds number.
(C) Richardson number.
(D) Ekman number.
Answer: (C)
3. During July-August, the highest number of monsoon low pressure systems form over
(A) Arabian Sea.
(B) Bay of Bengal.
(C) South India.
(D) Himalayan foothills.
Answer: (B)
4. CO2 concentration in the Earth’s atmosphere is increasing because 50% of the annual anthropogenic emissions are retained in the atmosphere. If nations agree to reduce annual CO2 emissions by one Giga ton every year starting from 2021, then in which year will the CO2 concentration in the atmosphere stop rising due to anthropogenic emissions?
Take the anthropogenic CO2 emissions in 2020 as 40 Giga tons.
(A) 2020
(B) 2050
(C) 2060
(D) 2100
Answer: (C)
5. The figure shows a schematic of Indian Ocean surface circulation. This pattern is representative of the circulation in which month of the year?
(A) January
(B) July
(C) May
(D) November
Answer: (C)
Q.6–Q. 7 Multiple Select Question (MSQ), Carry ONE mark each (no negative marks).
6. Over the open ocean, if the air sea temperature difference is zero, then which of the following statements is/are always true?
(A) Sensible heat flux is zero.
(B) Latent heat flux is zero.
(C) Momentum flux is zero.
(D) Net energy flux is zero.
Answer: (A)
7. The psychrometric equation, which is useful in measuring humidity, is derived assuming the following process(es).
(A) Isobaric process
(B) Isothermal process
(C) Adiabatic process
(D) Isentropic process
Answer: (A; C)
Q.8 – Q.9 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).
8. The water vapour mixing ratio of an air parcel increases from 10 g kg−1 to 20 g kg−1 at a constant pressure of 1010 hPa and temperature of 300 K. The change in virtual temperature is _____ K (to one decimal place).
Answer: (1.7 to 1.9)
9. The Ekman layer thickness, if turbulent diffusivity is 0.01 m2 s−1, is _____ m. Take Coriolis parameter to be 10−4s−1. Calculate to the nearest integer.
Answer: (0 to 11)
Q.10 – Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).
10. The figure shows vertical variation of two chemicals P and Q measured in the Pacific Ocean. Identify the correct combination showing (P, Q) pair from the list below.
(A) Oxygen, Nitrate
(B) Oxygen, Neon
(C) Nitrate, Oxygen
(D) Neon, Nitrate
Answer: (C)
Q.11 –Q. 15 Multiple Select Question (MSQ), Carry TWO marks each (no negative marks).
11. Consider tropical high-level clouds and low-level stratus clouds with bases at 12 km and 1 km above the surface of the Earth, respectively. Which of the following statement(s) is/are correct?
(A) High clouds are composed of ice crystals.
(B) High clouds have a larger albedo than low clouds.
(C) High clouds have a net warming effect on climate.
(D) Low clouds have a net warming effect on climate.
Answer: (A; C)
12. Which of the following statement(s) is/are correct in the context of Sverdrup transport?
(A) Sverdrup transport is always in the meridional direction.
(B) Sverdrup transport is always orthogonal to the wind direction.
(C) Sverdrup transport depends on the variation of the Coriolis parameter.
(D) Sverdrup transport is only due to ageostrophic currents.
Answer: (A; C)
13. Which of the following statement(s) is/are true with regard to the Hadley circulation?
(A) The ascending branch is narrower than its descending branch.
(B) Thunderstorms are more frequent in the subsiding region of the Hadley cell than in its ascending region.
(C) The lower level winds between the ascending and descending branches of the Hadley cell are north-westerly.
(D) Latent heat is transported from the subsiding to the ascending region of the Hadley cell.
Answer: (A; D)
14. Which of the following statement(s) is/are true about the ocean circulation?
(A) Large-scale ocean surface currents are driven by winds.
(B) Cold, dense and salty water forms in the North Atlantic Ocean.
(C) Upwelling currents bring warm nutrient deficient water to the surface of the ocean.
(D) Thermohaline circulation does not transport energy in the meridional direction.
Answer: (A; B)
15. Coral reefs are found primarily in tropical and subtropical shallow seawaters. Which of the following statement(s) is/are correct?
(A) Corals require plenty of sunlight for photosynthesis and sunlight is abundant in the tropical and subtropical latitudes.
(B) Corals grow optimally in seawater unsaturated in carbonate, which is found only in the tropical and subtropical oceans.
(C) Corals grow optimally in fresh low-salinity water.
(D) Corals grow optimally in water temperatures between 23°C and 29°C.
Answer: (A; D)
Q.16 – Q. 22 Numerical Answer Type (NAT), carry TWO marks each (no negative marks).
16. In an incompressible fluid, the horizontal divergence is −0.01 s−1. Then, the vertical velocity at 50 m above a flat surface is ____ m s−1. Round off to one decimal place.
Answer: (0.4 to 0.6)
17. In an atmosphere, temperature (T) decreases linearly with height above the ground (z), i.e., T(z) = To – γz, where γ is a constant. Surface pressure is 900 hPa. If the atmosphere is at rest, then the value of z at which the pressure decreases to half of that at the surface is _____ m (round off to the nearest integer).
Take acceleration due to gravity g = 10 m s−2, gas constant R = 300 J kg−1 K−1 To = 300 K and γ = 1/30 K m−1, and the atmosphere behaves as an ideal gas.
Answer: (4450 to 4550)
18. In a local Cartesian system, a zonal jet has a form u(y) = uo (1 – y2/L2), for −L ≤ y ≤ L. Here, y is the meridional distance measured from the axis of the jet and is positive northward. The vertical component of vorticity of this flow at y=L/2 is _____ s−1. Round off to 3 decimal places.
Take uo = 50 m s−1 and L = 5 km.
Answer: (0.009 to 0.011)
19. An eastward flow with a speed of 10 m s−1 goes from station M to station N, which are separated by a distance of 1 km. The temperature at station N is always higher than that at station M by 10 K. The absolute change in temperature due to advection at the mid-point between the stations in 50 s is _______ K (round off to nearest integer).
Answer: (4 to 6)
20. Suppose, because of the doubling of atmospheric CO2 concentration, an ocean water column receives an additional net energy input of 4 Wm−2. If the entire water column of depth 1 km heats up uniformly, the water temperature will increase by 1 K in ____ years (round off to the nearest integer).
Assume all the additional heat added is retained and not lost. Take density of seawater = 1000 kg m−3; specific heat capacity of seawater = 4200 J kg−1K−1.
Answer: (32 to 34)
21. Consider a layer of atmosphere between 5 and 6 km height. The downwelling longwave radiation at 5 and 6 km is 240 and 230 Wm−2, respectively. The upwelling longwave radiation at these heights is 260 and 240 Wm−2, respectively. The longwave heating rate in this layer is___ K per day. (Round off to one decimal place.)
Take the average density of air in this layer to be 0.5 kg m−3; Specific heat capacity of air at constant pressure = 1000 J kg−1 K−1.
Answer: (1.6 to 1.8)
22. A spherical asteroid, revolving around the sun in a circular orbit, is in radiative balance. Suddenly, the asteroid enters the shadow of a planet and solar radiation is cut off. Assuming that the asteroid emits as a blackbody in the longwave regime, the time taken to reduce the average temperature of the asteroid by 0.5 K is ______ seconds (round off to the nearest integer). Ignore the temporal change in radiation emitted by the asteroid during this cooling period.
The physical properties of the asteroid are: diameter = 2 m, density = 3000 kg m−3, specific heat = 2000 J kg-1 K−1 and albedo = 0.8 in shortwave radiation. Take the solar constant = 500 W m−2, Stefan-Boltzmann constant = 5.67 x 10-8 W m−2 K−4.
Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. The ratio of boys to girls in a class is 7 to 3.
Among the options below, an acceptable value for the total number of students in the class is:
(A) 21
(B) 37
(C) 50
(D) 73
Answer: (C)
2. A polygon is convex if, for every pair of points, P and Q belonging to the polygon, the line segment PQ lies completely inside or on the polygon.
Which one of the following is NOT a convex polygon?
Answer: (A)
3. Consider the following sentences:
(i) Everybody in the class is prepared for the exam.
(ii) Babu invited Danish to his home because he enjoys playing chess.
Which of the following is the CORRECT observation about the above two sentences?
(A) (i) is grammatically correct and (ii) is unambiguous
(B) (i) is grammatically incorrect and (ii) is unambiguous
(C) (i) is grammatically correct and (ii) is ambiguous
(D) (i) is grammatically incorrect and (ii) is ambiguous
Answer: (C)
4. A circular sheet of paper is folded along the lines in the directions shown. The paper, after being punched in the final folded state as shown and unfolded in the reverse order of folding, will look like _______.
Answer: (A)
5. _____ is to surgery as writer is to ________
Which one of the following options maintains a similar logical relation in the above sentence?
(A) Plan, outline
(B) Hospital, library
(C) Doctor, book
(D) Medicine, grammar
Answer: (C)
Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).
6. We have 2 rectangular sheets of paper, M and N, of dimensions 6 cm × 1 cm each. Sheet M is rolled to form an open cylinder by bringing the short edges of the sheet together. Sheet N is cut into equal square patches and assembled to form the largest possible closed cube. Assuming the ends of the cylinder are closed, the ratio of the volume of the cylinder to that of the cube is _______
(A) π/2
(B) 3/π
(C) 9/π
(D) 3π
Answer: (C)
7.
Details of prices of two items P and Q are presented in the above table. The ratio of cost of item P to cost of item Q is 3:4. Discount is calculated as the difference between the marked price and the selling price. The profit percentage is calculated as the ratio of the difference between selling price and cost, to the cost
The discount on item Q, as a percentage of its marked price, is ______
(A) 25
(B) 12.5
(C) 10
(D) 5
Answer: (C)
8. There are five bags each containing identical sets of ten distinct chocolates. One chocolate is picked from each bag.
The probability that at least two chocolates are identical is ___________
(A) 0.3024
(B) 0.4235
(C) 0.6976
(D) 0.8125
Answer: (C)
9. Given below are two statements 1 and 2, and two conclusions I and II.
Statement 1: All bacteria are microorganisms.
Statement 2: All pathogens are microorganisms.
Conclusion I: Some pathogens are bacteria.
Conclusion II: All pathogens are not bacteria.
Based on the above statements and conclusions, which one of the following options is logically CORRECT?
(A) Only conclusion I is correct
(B) Only conclusion II is correct
(C) Either conclusion I or II is correct.
(D) Neither conclusion I nor II is correct.
Answer: (C OR D)
10. Some people suggest anti-obesity measures (AOM) such as displaying calorie information in restaurant menus. Such measures sidestep addressing the core problems that cause obesity: poverty and income inequality.
Which one of the following statements summarizes the passage?
(A) The proposed AOM addresses the core problems that cause obesity.
(B) If obesity reduces, poverty will naturally reduce, since obesity causes poverty.
(C) AOM are addressing the core problems and are likely to succeed.
(D) AOM are addressing the problem superficially.
Answer: (D)
TF: Textile Engineering and Fibre Science (TF)
Q.1 – Q.13 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. Let the function f(x, y) be defined as
Then is equal to
(A) √2
(B) √3
(C) 0
(D) 1
Answer: (B)
2. If a continuous random variable X has the following probability density function then the value of k is
(A) 1
(B) 2
(C) 3
(D) 4
Answer: (C)
3. The smallest positive real number λ, for which the following problem
y′′(x) + λ y(x) = 0,
y′(0) = 0, y(1) = 0
has non-zero solution, is
(A) π2
(B) π2/2
(C) π2/4
(D) π2/8
Answer: (C)
4. The gummy substance present in raw silk fibre is
(A) Serine
(B) Fibroin
(C) Keratin
(D) Sericin
Answer: (D)
5. The technique used for producing viscose rayon is
(A) Melt spinning
(B) Wet spinning
(C) Dry spinning
(D) Dry-jet wet spinning
Answer: (B)
6. The yarn manufacturing technology that uses perforated drums for twisting is
(A) Ring spinning
(B) Rotor spinning
(C) Friction spinning
(D) Air-jet spinning
Answer: (C)
7. In roving frame, the distance between top and bottom aprons at the exit point is maintained by
(A) Spacer
(B) Trumpet
(C) Condenser
(D) Pressure-bar
Answer: (A)
8. Fabric structure related to weft knitting is
(A) Locknit
(B) Reverse locknit
(C) Double tricot
(D) 1×1 Rib
Answer: (D)
9. The nonwoven technology which uses high-pressure water jets is
(A) Needlepunching
(B) Spunlacing
(C) Spunbonding
(D) Meltblowing
Answer: (B)
10. Cotton fibre length variation can be expressed by
(A) Uniformity index
(B) Limit irregularity
(C) U%
(D) Index of irregularity
Answer: (A)
11. A high value of drape coefficient indicates
(A) Limp fabric
(B) Stiff fabric
(C) Compressible fabric
(D) Smooth fabric
Answer: (B)
12. The process for removal of protruding fibres from fabric surface is
(A) Desizing
(B) Scouring
(C) Souring
(D) Singeing
Answer: (D)
13. Dimethylol dihydroxy ethylene urea (DMDHEU) is a
(A) Crease-resist agent
(B) Flame retardant
(C) Softener
(D) Soil repellent
Answer: (A)
Q.14 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).
14. Suppose is a solution of the following initial value problem of the wave equation utt = 9 uxx, u(x, 0) = g(x), ut(x, 0) = 0. Then the value of c2 is ___________.
Answer: (9 to 9)
15. If the numerical solution of the initial value problem is obtained by the Euler’s method with step size of 0. 2, then the value of y(0. 4), (rounded off to two decimal places), is __________.
Answer: (0.98 to 1.10)
16. Assuming the atomic mass of H=1, C=12, N=14 and O=16, the molecular mass of a repeat unit of Nylon 6 fibre is ______________.
Answer: (113 to 113)
17. A textile filament records a tensile stress of 0.3 GPa at a tensile strain of 0.04. Assuming Hookean behavior, the tensile modulus (GPa) of the filament, (rounded off to one decimal place), is ___________.
Answer: (7.5 to 7.5)
18. Number of fibres, each of 40 mm length and 0.16 tex fineness, in a tuft of 24 mg mass is __________.
Answer: (3745 to 3755)
19. Twist (turns per inch) of a cotton yarn of 36 Ne count produced with a twist multiplier of 3.5 inch−1Ne−0.5 is __________.
Answer: (21 to 21)
20. In winding, if traverse speed and package surface speed are the same, the angle of wind (in degree) is ________.
Answer: (45 to 45)
21. During air-jet weft insertion, if the diameter of the yarn increases by 20 % then the percentage increase in drag force acting on the yarn would be ___________.
Answer: (20 to 20)
22. If the ratio of the linear densities (denier) of two circular fibers is 3, the corresponding ratio of their diameters, (rounded off to two decimal places), is _______.
Answer: (1.70 to 1.75)
23. If the sample size (n) is 25 and the standard deviation (σ) of population is 2, then the standard error (SE) of sample mean, (rounded off to one decimal place), is _______.
Answer: (0.4 to 0.4)
24. The wet expression for a padding mangle is set at 80 %. If the add-on of a flame retardant chemical required on the fabric is 2 % then the concentration (g/L) of the chemical in the pad bath is ________.
Answer: (25 to 25)
25. Assuming Beer-Lambert law is applicable for dilute solutions, if the molar concentration of dye in the solution is doubled then the percentage increase in absorbance would be __________.
Answer: (100 to 100)
Q.26 – Q.41 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).
26. The value of a, for which the following system of equations
2x + y + 3z = a, x + z = 2, y + z = 2
is consistent, is
(A) 6
(B) 4
(C) 3
(D) 2
Answer: (A)
27. If the function f(x, y) is defined by then
(A) Neither (0, 0) nor (1, 1) is a critical point
(B) (0, 0) is a critical point but (1, 1) is NOT a critical point
(C) (0, 0) is NOT a critical point but (1, 1) is a critical point
(D) (0, 0) and (1, 1) are both critical points
Answer: (D)
28. Determine the correctness or otherwise of the following Assertion [a] and Reason [r]
Assertion: Draw texturing of isotactic polypropylene (POY) at a relatively high speed is possible despite high crystallinity of the feeder yarn.
Reason: Isotactic polypropylene (POY) has majorly smectic mesomorphic phase.
(A) Both [a] and [r] are true and [r] is the correct reason for [a]
(B) Both [a] and [r] are true but [r] is not the correct reason for [a]
(C) Both [a] and [r] are false
(D) [a] is true but [r] is false
Answer: (A)
29. Group I gives a list of fibres and Group II contains their applications. Match the fibre with its application.
(A) P-1, Q-4, R-2, S-3
(B) P-4, Q-3, R-1, S-2
(C) P-4, Q-2, R-1, S-3
(D) P-1, Q-3, R-4, S-2
Answer: (B)
30. Techniques used for determination of orientation in fibres from amongst the followings are
P Birefringence measurement
Q Scanning electron microscopy
R X-ray diffraction
S Differential scanning calorimetry
(A) P and Q
(B) P and R
(C) Q and R
(D) Q and S
Answer: (B)
31. In a modern high performance blowroom line, the correct sequence of machines is
(A) Lower rotational speed and lower wire point density
(B) Lower rotational speed and higher wire point density
(C) Higher rotational speed and lower wire point density
(D) Higher rotational speed and higher wire point density
Answer: (A)
33. Assuming no fibre loss in draw frame, if draft is equal to doubling then the delivered sliver, as compared to fed sliver, will exhibit
(A) Decreased mass variation and higher linear density
(B) Increased mass variation and lower linear density
(C) Improved fibre orientation without change in linear density
(D) Poor fibre orientation without change in linear density
Answer: (C)
34. Group I gives a list of loom motions and Group II contains loom systems. Match the motion from Group I with the corresponding system from Group II.
(A) P-1, Q-3, R-4, S-2
(B) P-4, Q-3, R-2, S-1
(C) P-4, Q-3, R-1, S-2
(D) P-3, Q-4, R-1, S-2
Answer: (C)
35. Group I gives a list of terms related to woven fabrics and Group II contains equivalent terms related to knitted fabrics. Match the term from Group I with the equivalent term from Group II.
(A) P-3, Q-1, R-4, S-2
(B) P-3, Q-1, R-2, S-4
(C) P-1, Q-3, R-2, S-4
(D) P-1, Q-3, R-4, S-2
Answer: (B)
36. Determine the correctness or otherwise of the following Assertion [a] and Reason [r]
Assertion: In shuttle loom, late shedding is preferred for filament weaving.
Reason: In late shedding, the timing of shed dwell matches with the timing of shuttle travel through the shed, and therefore, it minimises the rubbing of warp yarns.
(A) Both [a] and [r] are true and [r] is the correct reason for [a]
(B) Both [a] and [r] are true and [r] is not the correct reason for [a]
(C) Both [a] and [r] are false
(D) [a] is true but [r] is false
Answer: (A)
37. The typical shapes of comb sorter diagram and fibrogram of polyester fibres of equal cut length will be
(A) Triangular and rectangular respectively
(B) Rectangular and triangular respectively
(C) Rectangular and S-shaped respectively
(D) S-shaped and triangular respectively
Answer: (B)
38. In Classimat system, the yarn fault H2, as compared to yarn fault C3, is
(A) Thicker and longer
(B) Thicker and shorter
(C) Thinner and longer
(D) Thinner and shorter
Answer: (C)
39. Determine the correctness or otherwise of the following Assertion [a] and Reason [r]
Assertion: Application of an optical brightening agent makes the white fabrics appear brighter.
Reason: Optical brightening agents absorb energy in the visible region and radiate back in the UV region.
(A) Both [a] and [r] are true and [r] is the correct reason for [a]
(B) Both [a] and [r] are true and [r] is not the correct reason for [a]
(C) Both [a] and [r] are false
(D) [a] is true but [r] is false
Answer: (D)
40. Determine the correctness or otherwise of the following Assertion [a] and Reason [r]
Assertion: Nylon is dyed with acid dyes in the acidic medium.
Reason: Nylon assumes positive charge in the acidic medium and thus, attracts the negatively charged acid dye molecules.
(A) Both [a] and [r] are true and [r] is the correct reason for [a]
(B) Both [a] and [r] are true and [r] is not the correct reason for [a]
(C) Both [a] and [r] are false
(D) [a] is true but [r] is false
Answer: (A)
41. Determine the correctness or otherwise of the following Assertion [a] and Reason [r]
Assertion: Discharge printing of dyed polyester fabric is not possible.
Reason: The discharging agents damage the polyester fibres significantly.
(A) Both [a] and [r] are true and [r] is the correct reason for [a]
(B) Both [a] and [r] are true and [r] is not the correct reason for [a]
(C) Both [a] and [r] are false
(D) [a] is true but [r] is false
Answer: (C)
Q.42 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).
42. If 3 and 6 are eigenvalues of the matrix then the value of μ is _______.
Answer: (5 to 5)
43. If y(x) is a solution of x2y′′ − 4 x y ′ + 6 y 0, y(−1) = 1, y ′ (−1) = 0. Then the value of y(2) is _______.
Answer: (28 to 28)
44. In melt spinning, the mass throughput rate of polymer is 210 g/min, the winding speed is 3000 m/min, and the linear density of the yarn produced is 200 denier. The effective draw ratio, (rounded off to two decimal places), is___________.
Answer: (3.00 to 3.30)
45. The molecular weight (M) of a polymer is determined from Mark-Houwink Equation by using coefficient K = 11.5×10−3 ml/g and exponent a = 0.73. If the measured intrinsic viscosity [η] of the solution is 6.0×102 ml/g then the value of M×10−6, (rounded off to two decimal places), is _________.
Answer: (2.70 to 3.10)
46. A roving of 2 Ne count is fed to a ringframe set with a mechanical draft of 30. If the length of the drafted strand delivered from the nip of the front rollers is reduced by 3 % due to twist then the count (Ne) of the yarn, (rounded off to one decimal place), is ___________.
Answer: (58.0 to 58.4)
47. In a 3 over 3 drafting arrangement, the diameter of all bottom rollers is 28 mm. The back zone draft is 1.3 and the front zone draft is 6. If the back bottom roller is eccentric then the wavelength (mm) of the resulting fault in the drawn sliver, (rounded off to two decimal places), is ___________.
Answer: (685.00 to 687.00)
48. For a given woven fabric, fractional cover is 0.5 for both warp and weft. The fractional cover of the fabric, (rounded off to two decimal places), is _________.
Answer: (0.75 to 0.75)
49. For a shuttle loom, producing plain woven fabric, if each of the dwell periods of the shedding cam corresponds to one-third of crank shaft rotation, the sum of the two dwell periods of the cam (in degree) is _______.
Answer: (120 to 120)
50. If the moisture regain (%) and moisture content (%) of a fibre are the same then the value of moisture regain (%) is _______.
Answer: (0 to 0)
51. Mass of 120 yards of cotton yarn is 3 g. The count (Ne) of yarn, (rounded off to one decimal place), is __________.
Answer: (21.0 to 22.0)
52. A woven fabric with areal density of 300 g/m2 is tested by strip tensile test method, keeping the specimen width as 5 cm and gauge length as 25 cm. If the breaking load is 900 N, the tenacity (cN/tex) of the fabric is __________.
Answer: (6 to 6)
53. A 50 tex yarn with mass CV of 12.5 % is produced from staple polyester fibres each of 4.5 denier fineness. The index of irregularity of the yarn, (rounded off to two decimal places), is ____________.
Answer: (1.25 to 1.25)
54. A counter-flow heat exchanger is attached to a stenter for waste heat recovery.
Consider the following data:
Ambient temperature : 30°C
Temperature of exhaust from stenter : 150 °C
Temperature of exhaust at exit of heat exchanger : 100°C
Specific heat of exhaust : 0.42 kcal·deg−1 ·kg−1
Specific heat of air : 0.24 kcal·deg−1 ·kg−1
At steady state, if the mass flow rates of the exhaust gas and the incoming air are the same, assuming heat loss as zero, the temperature (°C) of the air at the exit of the heat exchanger (towards the stenter), (rounded off to one decimal place), is_________.
Answer: (117.0 to 118.0)
55. Consider the following isotherms at equilibrium for two disperse dyes D1 and D2 dyed on polyester. If the partition coefficients of these are K1 and K2, respectively, the value of K2/K1 is _______.
Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. The current population of a city is 11,02,500. If it has been increasing at the rate of 5% per annum, what was its population 2 years ago?
(A) 9,92,500
(B) 9,95,006
(C) 10,00,000
(D) 12,51,506
Answer: (C)
2. p and q are positive integers and
(A) 3
(B) 7
(C) 9
(D) 11
Answer: (B)
3.
The least number of squares that must be added so that the line P-Q becomes the line of symmetry is ________
(A) 4
(B) 3
(C) 6
(D) 7
Answer: (C)
4. Nostalgia is to anticipation as _______ is to ________
Which one of the following options maintains a similar logical relation in the above sentence?
(A) Present, past
(B) Future, past
(C) Past, future
(D) Future, present
Answer: (C)
5. Consider the following sentences:
(i) I woke up from sleep.
(ii) I woked up from sleep.
(iii) I was woken up from sleep.
(iv) I was wokened up from sleep.
Which of the above sentences are grammatically CORRECT?
(A) (i) and (ii)
(B) (i) and (iii)
(C) (ii) and (iii)
(D) (i) and (iv)
Answer: (B)
Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).
6. Given below are two statements and two conclusions.
Statement 1: All purple are green.
Statement 2: All black are green.
Conclusion I: Some black are purple.
Conclusion II: No black is purple.
Based on the above statements and conclusions, which one of the following options is logically CORRECT?
(A) Only conclusion I is correct.
(B) Only conclusion II is correct.
(C) Either conclusion I or II is correct.
(D) Both conclusion I and II are correct.
Answer: (C)
7. Computers are ubiquitous. They are used to improve efficiency in almost all fields from agriculture to space exploration. Artificial intelligence (AI) is currently a hot topic. AI enables computers to learn, given enough training data. For humans, sitting in front of a computer for long hours can lead to health issues.
Which of the following can be deduced from the above passage?
(i) Nowadays, computers are present in almost all places.
(ii) Computers cannot be used for solving problems in engineering.
(iii) For humans, there are both positive and negative effects of using computers.
(iv) Artificial intelligence can be done without data.
(A) (ii) and (iii)
(B) (ii) and (iv)
(C) (i), (iii) and (iv)
(D) (i) and (iii)
Answer: (D)
8. Consider a square sheet of side 1 unit. In the first step, it is cut along the main diagonal to get two triangles. In the next step, one of the cut triangles is revolved about its short edge to form a solid cone. The volume of the resulting cone, in cubic units, is ________
(A) π/3
(B) 2π/3
(C) 3π/2
(D) 3π
Answer: (A)
9.
The number of minutes spent by two students, X and Y, exercising every day in a given week are shown in the bar chart above.
The number of days in the given week in which one of the students spent a minimum of 10% more than the other student, on a given day, is
(A) 4
(B) 5
(C) 6
(D) 7
Answer: (C)
10.
Corners are cut from an equilateral triangle to produce a regular convex hexagon as shown in the figure above.
The ratio of the area of the regular convex hexagon to the area of the original equilateral triangle is
(A) 2 : 3
(B) 3 : 4
(C) 4 : 5
(D) 5 : 6
Answer: (A)
Statistics (ST)
Q.1 – Q.9 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. Let X be a non-constant positive random variable such that E(X) = 9. Then which one of the following statements is true?
Answer: (A)
2. Let {W(t)}t≥0 be a standard Brownian motion. Then the variance of W(1)W(2) equals
(A) 1
(B) 2
(C) 3
(D) 4
Answer: (C)
3. Let X1,X2, … ,Xn be a random sample of size n (≥ 2) from a distributionhaving the probability density function
where θ ∈ (0, ∞). Then the method of moments estimator of θ equals
Answer: (A)
4. Let {x1, x2, … , xn} be a realization of a random sample of size n (≥ 2) from a N(μ,σ2) distribution, where −∞ < μ < ∞ and σ > 0. Which of the following statements is/are true?
P : 95% confidence interval of μ based on {x1, x2, … , xn} is unique when σ is known.
Q : 95% confidence interval of μ based on {x1, x2, … , xn} is NOT unique when σ is unknown.
(A) P only
(B) Q only
(C) Both P and Q
(D) Neither P nor Q
Answer: (B)
5. Let X1, X2, … , Xn be a random sample of size n (≥ 2) from a N(0, σ2) distribution. For a given σ > 0, let fσ denote the joint probability density function of (X1,X2, … ,Xn) and S = {fσ: σ > 0}. Let For any positive integer ν and any α ∈ (0, 1), let denote the (1 − α)-th quantile of the central chi-square distribution with ν degrees of freedom. Consider testing H0: σ = 1 against H1: σ > 1 at level α. Then which one of the following statements is true?
(A) S has a monotone likelihood ratio in T1 and H0 is rejected if
(B) S has a monotone likelihood ratio in T1 and H0 is rejected if
(C) S has a monotone likelihood ratio in T2 and H0 is rejected if
(D) S has a monotone likelihood ratio in T2 and H0 is rejected if
Answer: (A)
6. Let X and Y be two random variables such that p11 + p10 + p01 + p00 = 1, where pij = P(X = i, Y = j), i,j = 0, 1. Suppose that a realization of a random sample of size 60 from the joint distribution of (X, Y) gives
n11 = 10, n10 = 20, n01 = 20 and n00 = 10,
where nij denotes the frequency of (i, j) for i, j = 0, 1. If the chi-square test of independence is used to test
H0: pij = pi⋅p⋅j for i, j = 0, 1 against H1: pij ≠ pi⋅p⋅j for at least one pair
where pi⋅ = pi0 + pi1 and p⋅j = p0j + p1j, then which one of the following statements is true?
(i,j),
(A) Under H0, the test statistic follows central chi-square distribution with one degree of freedom and the observed value of the test statistic is 20/3
(B) Under H0, the test statistic follows central chi-square distribution with three degrees of freedom and the observed value of the test statistic is 20/3
(C) Under H0, the test statistic follows central chi-square distribution with one degree of freedom and the observed value of the test statistic is 16/3
(D) Under H0, the test statistic follows central chi-square distribution with three degrees of freedom and the observed value of the test statistic is 16/3
Answer: (A)
7. Let the joint distribution of (X, Y) be bivariate normal with mean vector and variance-covariance matrix where −1 < ρ < 1. Let Φρ(0, 0) = P(X ≤ 0, Y ≤ 0). Then the Kendall’s τ coefficient between X and Y equals
(A) 4Φρ(0,0) − 1
(B) 4Φρ(0,0)
(C) 4Φρ(0,0) + 1
(D) Φρ(0,0)
Answer: (A)
8. Consider the simple linear regression model
Yi = β0 + β1xi + εi, i = 1, 2, … , n (n ≥ 3),
where β0 and β1 are unknown parameters and εi’s are independent and identically distributed random variables with mean zero and finite variance σ2 > 0. Suppose that are the ordinary least squares estimators of β0 and β1, respectively. Define and , where yi 0 is the observed value of Yi, , i = 1, 2, … , n. Then for a real constant c, the variance of is
Answer: (B)
9. Let X1, X2, X3, Y1, Y2, Y3 and Y4 be independent random vectors such that Xifollows N4(0, Σ1) distribution for i = 1, 2, 3, and Yj follows N4(0, Σ2) distribution for j = 1, 2, 3, 4, where Σ1 and Σ2 are positive definite matrices. Further, let
where X = [X1X2X3] is a 4 × 3 matrix, Y = [Y1 Y2 Y3 Y4] is a 4 × 4 matrix and XT and YT denote transposes of X and Y, respectively. If Wm(n, Σ) denotes a Wishart distribution of order m with n degrees of freedom and variance-covariance matrix Σ and In denotes the n × n identity matrix, then which one of the following statements is true?
(A) Z follows W4(7,I4) distribution
(B) Z follows W4(4,I4) distribution
(C) Z follows W7 (4,I7 ) distribution
(D) Z follows W7 (7,I7) distribution
Answer: (A)
Q.10 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).
10.
Answer: (2 to 2)
11. Let
Then the value of e I1+ π equals __________ (round off to 2 decimal places).
Answer: ()
12. Let and I3 be the 3 × 3 identity matrix. Then the nullity of 5A(I3 + A 2) equals __________
Answer: (33.50 to 34.50)
13. Let A be the 2 × 2 real matrix having eigenvalues 1 and − 1, with corresponding eigenvectors respectively. If then a + b + c + d equals __________ (round off to 2 decimal places).
Answer: (2 to 2)
14. Let A and B be two events such that P(B) = 3/4 and P(A ⋃ BC) = 1/2. If A and B are independent, then P(A) equals __________ (round off to 2 decimal places).
Answer: (1.70 to 1.75)
15. A fair die is rolled twice independently. Let X and Y denote the outcomes of the first and second roll, respectively. Then E(X + Y | (X − Y)2 = 1) equals ________
Answer: (7 to 7)
16. Let X be a random variable having distribution function
where a and c are appropriate constants. Let n ≥ 1, and If P(X ≤ 1) = 1/2 and E(X) = 5/3, then P(X ∈ A) equals __________ (round off to 2 decimal places).
Answer: (0.32 to 0.35)
17. If the marginal probability density function of the kth order statistic of a random sample of size 8 from a uniform distribution on [0, 2] is then k equals __________
Answer: (7 to 7)
18. For α > 0, let be a sequence of independent random variables such that
Let S = {α > 0 ∶ Xn(a) converges to 0 almost surely as n → ∞}. Then the infimum of S equals __________ (round off to 2 decimal places).
Answer: (0.50 to 0.50)
19. Let {Xn}n≥1 be a sequence of independent and identically distributed random variables each having uniform distribution on [0, 2]. For n ≥ 1, let
Then, as n → ∞, the sequence {Zn}n≥1 converges almost surely to _______ (round off to 2 decimal places).
Answer: (0.27 to 0.35)
20. Let {Xn}n≥0 be a time-homogeneous discrete time Markov chain with state space {0, 1} and transition probability matrix If P(X0 = 0) = P(X0 = 1) = 0. 5, then equals ______
Answer: (50 to 50)
21. Let {0, 2} be a realization of a random sample of size 2 from a binomial distribution with parameters 2 and p, where p ∈ (0, 1). To test H0: p = 1/2 against H1: p ≠ 1 the observed value of the likelihood ratio test statistic equals _________ (round off to 2 decimal places).
Answer: (0.98 to 1.00)
22. Let X be a random variable having the probability density function
Then equals __________ (round off to 2 decimal places).
Answer: (8.60 to 8.75)
23. Let (Y, X1,X2) be a random vector with mean vector and variance-covariance matrix Then the value of the multiple correlation coefficient between Y and its best linear predictor on X1 and X2 equals _________ (round off to 2 decimal places).
Answer: (0.14 to 0.18)
24. Let be a random sample from a bivariate normal distribution with unknown mean vector μ and unknown variance-covariance matrix Σ, which is a positive definite matrix. The p-value corresponding to the likelihood ratio test for testing based on the realization of the random sample equals __________ (round off to 2 decimal places).
Answer: (1.00 to 1.00)
25. Let Yi = α + βxi + εi, i = 1, 2, 3, where xi’s are fixed covariates, α and β are unknown parameters and εi’s are independent and identically distributed random variables with mean zero and finite variance. Let be the ordinary least squares estimators of α and β, respectively. Given the following observations
the value of equals ________ (round off to 2 decimal places).
Answer: (6.31 to 6.35)
Q.26 – Q.43 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).
26. Let f: ℝ → ℝ be defined by
where ℝ denotes the set of all real numbers, ℤ denotes the set of all integers, ℕ denotes the set of all positive integers and gcd(p, q) denotes the greatest common divisor of p and q. Then which one of the following statements is true?
(A) f is not continuous at 0
(B) f is not differentiable at 0
(C) f is differentiable at 0 and the derivative of f at 0 equals 0
(D) f is differentiable at 0 and the derivative of f at 0 equals 1
Answer: (C)
27. Let f:[0, ∞) → ℝ be a function, where R denotes the set of all real numbers. Then which one of the following statements is true?
(A) If f is bounded and continuous, then f is uniformly continuous
(B) If f is uniformly continuous, then exists
(C) If f is uniformly continuous, then the function g(x) = f(x) sin x is also uniformly continuous
(D) If f is continuous and is finite, then f is uniformly continuous
Answer: (D)
28. Let f: ℝ → ℝ be a differentiable function such that f(0) = 0 and f′ (x) + 2f(x) > 0 for all x ∈ R, where f′ denotes the derivative of f and R denotes the set of all real numbers. Then which one of the following statements is true?
(A) f(x) > 0, for all x > 0 and f(x) < 0, for all x < 0
(B) f(x) < 0, for all x ≠ 0
(C) f(x) > 0, for all x ≠ 0
(D) f(x) < 0, for all x > 0 and f(x) > 0, for all x < 0
Answer: (A)
29. Let M be the collection of all 3 × 3 real symmetric positive definite matrices. Consider the set where 0 denotes the 3 × 3 zero matrix. Then the number of elements in S equals
(A) 0
(B) 1
(C) 8
(D) ∞
Answer: (B)
30. Let A be a 3 × 3 real matrix such that I3 + A is invertible and let B = (I3 + A)−1(I3 – A), where I3 denotes the 3 × 3 identity matrix. Then which one of the following statements is true?
(A) If B is orthogonal, then A is invertible
(B) If B is orthogonal, then all the eigenvalues of A are real
(C) If B is skew-symmetric, then A is orthogonal
(D) If B is skew-symmetric, then the determinant of A equals −1
Answer: (C)
31. Let X be a random variable having Poisson distribution such thatE(X2) = 110. Then which one of the following statements is NOT true?
(A) E(Xn) = 10 E[(X + 1)n−1], for all n = 1, 2, 3, …
(B)
(C) P(X = k) < P(X = k + 1), for k = 0, 1, … , 8
(D) P(X = k) > P(X = k + 1), for k = 10, 11, …
Answer: (B)
32. Let X be a random variable having uniform distribution on Then which one of the following statements is NOT true?
(A) Y = cot X follows standard Cauchy distribution
(B) Y = tan X follows standard Cauchy distribution
(C) has moment generating function
(D) follows central chi-square distribution with one degree of freedom
Answer: (D)
33. Let Ω = {1, 2, 3, … } represent the collection of all possible outcomes of a random experiment with probabilities P({n}) = αn for n ∈ Ω. Then which one of the following statements is NOT true?
(A)
(B)
(C) For any positive integer k, there exist k disjoint events A1, A2, … , Ak such that
(D) There exists a sequence {Ai}i≥1 of strictly increasing events such that
Answer: (B)
34. Let (X, Y) have the joint probability density function
Then which one of the following statements is NOT true?
(A) The probability density function of X + Y is
(B) P(X + Y > 4) = 3/4
(C) E(X + Y) = 4 loge 2
(D) E(Y | X = 2) = 4
Answer: (C)
35. Let X1, X2 and X3 be three uncorrelated random variables with common variance σ2 < ∞. Let Y1 = 2X1 + X2 + X3, Y2 = X1 + 2X2 + X3 and Y3 = X1 + X2 + 2X3. Then which of the following statements is/are true?
P : The sum of eigenvalues of the variance covariance matrix of (Y1, Y2, Y3) is 18σ2.
Q : The correlation coefficient between Y1 and Y2 equals that between Y2 and Y3.
(A) P only
(B) Q only
(C) Both P and Q
(D) Neither P nor Q
Answer: (C)
36. Let {Xn}n≥0 be a time-homogeneous discrete time Markov chain with either finite or countable state space S. Then which one of the following statements is true?
(A) There is at least one recurrent state
(B) If there is an absorbing state, then there exists at least one stationary distribution
(C) If all the states are positive recurrent, then there exists a unique stationary distribution
(D) If {Xn}n≥0 is irreducible, S = {1, 2} and [π1 π2] is a stationary distribution, then for i = 1, 2
Answer: (B)
37. Let customers arrive at a departmental store according to a Poisson process with rate 10. Further, suppose that each arriving customer is either a male or a female with probability 1/2 each, independent of all other arrivals. Let N(t) denote the total number of customers who have arrived by time t. Then which one of the following statements is NOT true?
(A) If S2 denotes the time of arrival of the second female customer, then
(B) If M(t) denotes the number of male customers who have arrived by time t, then
(C) E [(N(t))2] = 100t2 + 10t
(D) E[N(t)N(2t)] = 200t2 + 10t
Answer: (B)
38. Let X(1) < X(2) < X(3) < X(4) < X(5)be the order statistics corresponding to a random sample of size 5 from a uniform distribution on [0, θ], where θ ∈ (0, ∞). Then which of the following statements is/are true?
P : 3X(2) is an unbiased estimator of θ.
Q : The variance of E[2X(3) | X(5)] is less than or equal to the variance of 2X(3).
(A) P only
(B) Q only
(C) Both P and Q
(D) Neither P nor Q
Answer: (C)
39. Let X1, X2, … , Xn be a random sample of size n (≥ 2) from a distribution having the probability density function
where θ ∈ (0, ∞). Let X(1) = min{ X1, X2, … , Xn} and Then E(X(1)| T ) equals
(A) T/n2
(B) T/n
(C)
(D)
Answer: (A)
40. Let X1, X2, … , Xn be a random sample of size n (≥ 2) from a uniform distribution on [−θ, θ], where θ ∈ (0, ∞). Let X(1) = min{X1, X2, … , Xn} and X(n) = max{X1, X2, … ,Xn}. Then which of the following statements is/are true?
P : (X(1), X(n)) is a complete statistic.
Q : X(n) − X(1) is an ancillary statistic.
(A) P only
(B) Q only
(C) Both P and Q
(D) Neither P nor Q
Answer: (D)
41. Let {Xn}n≥1 be a sequence of independent and identically distributed random variables having common distribution function F(⋅). Let a < b be two real numbers such that F(x) = 0 for all x ≤ a, 0 < F(x) < 1 for all a < x < b and F(x) = 1 for all x ≥ b. Let Sn(x) be the empirical distribution function at x based on X1, X2, … ,Xn, n ≥ 1. Then which one of the following statements is NOT true?
(A)
(B) For fixed x ∈ (a, b) and t ∈ (− ∞, ∞), where Z is the standard normal random variable
(C) The covariance between Sn(x) and Sn(y) equals for all n ≥ 2 and for fixed −∞ < x, y < ∞
(D) If then {4n Yn}n≥1 converges in distribution to a central chi-square random variable with 2 degrees of freedom
Answer: (C)
42. Let the joint distribution of random variables X1,X2,X3 and X4 be where
Then which one of the following statements is true?
(A) follows a central chi-square distribution with 2 degrees of freedom
(B) follows a central chi-square distribution with 2 degrees of freedom
(C) is NOT finite
(D) is NOT finite
Answer: (D)
43. Let distribution, where I8 is the 8 × 8 identity matrix. Let be independent and follow central chi-square distributions with 3 and 4 degrees of freedom, respectively, where Σ1 and Σ2 are 8 × 8 matrices and denotes transpose of Then which of the following statements is/are true?
P : Σ1 and Σ2 are idempotent.
Q : Σ1Σ2 = 0, where 0 is the 8 × 8 zero matrix.
(A) P only
(B) Q only
(C) Both P and Q
(D) Neither P nor Q
Answer: (C)
Q.44 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).
44. Let (X, Y) have a bivariate normal distribution with the joint probability density function
Then 8 E(XY) equals ________
Answer: (3 to 3)
45. Let f: ℝ × ℝ → ℝ be defined by f(x, y) = 8x2 − 2y, where ℝ denotes the set of all real numbers. If M and m denote the maximum and minimum values of f, respectively, on the set {(x, y) ∈ ℝ × ℝ ∶ x2 + y2 = 1}, then M − m equals ________ (round off to 2 decimal places).
Answer: (10.10 to 10.15)
46. Let A = [a u1 u2 u3], B = [b u1 u2 u3] and C = [u2 u3 u1 a + b] be three 4 × 4 real matrices, where a, b, u1, u2 and u3 are 4 × 1 real column vectors. Let det(A), det(B) and det(C) denote the determinants of the matrices A, B and C, respectively. If det(A) = 6 and det(B) = 2, then det(A + B) − det(C) equals _________
Answer: (72 to 72)
47. Let X be a random variable having the moment generating function
Then P(X > 1) equals __________ (round off to 2 decimal places).
Answer: (0.60 to 0.66)
48. Let {Xn}n≥1 be a sequence of independent and identically distributed random variables each having uniform distribution on [0, 3]. Let Y be a random variable, independent of {Xn}n≥1, having probability mass function
Then P(max{X1,X2, … ,XY} ≤ 1) equals __________ (round off to 2 decimal places).
Answer: (0.20 to 0.26)
49. Let {Xn}n≥1 be a sequence of independent and identically distributed random variables each having probability density function
Let X(n) = max{X1,X2, … ,Xn} for n ≥ 1. If Z is the random variable to which {X(n) − loge n}n≥1converges in distribution, as n → ∞, then the median of Z equals __________ (round off to 2 decimal places).
Answer: (0.32 to 0.42)
50. Consider an amusement park where visitors are arriving according to a Poisson process with rate 1. Upon arrival, a visitor spends a random amount of time in the park and then departs. The time spent by the visitors are independent of one another, as well as of the arrival process, and have common probability density function
If at a given time point, there are 10 visitors in the park and p is the probability that there will be exactly two more arrivals before the next departure, then 1/p equals ________
Answer: (143 to 143)
51. Let {0. 90, 0. 50, 0. 01, 0. 95} be a realization of a random sample of size 4 from the probability density function
where 0. 5 ≤ θ < 1. Then the maximum likelihood estimate of θ based on the observed sample equals __________ (round off to 2 decimal places).
Answer: (0.50 to 0.50)
52. Let a random sample of size 100 from a normal population with unknown mean μ and variance 9 give the sample mean 5. 608. Let Φ(⋅) denote the distribution function of the standard normal random variable. If Φ(1. 96) = 0. 975, Φ(1. 64) = 0. 95 and the uniformly most powerful unbiased test based on sample mean is used to test H0: μ = 5. 02 against H1: μ ≠ 5. 02, then the p-value equals __________ (round off to 3 decimal places).
Answer: (0.045 to 0.055)
53. Let X be a discrete random variable with probability mass function p ∈ {p0, p1}, where
To test H0: p = p0 against H1: p = p1, the power of the most powerful test of size 0. 05, based on X, equals __________ (round off to 2 decimal places).
Answer: (0.20 to 0.22)
54. Let X1, X2, … , X10 be a random sample from a probability density function fθ(x) = f(x − θ), −∞ < x < ∞, where −∞ < θ < ∞ and f(−x) = f(x) for −∞ < x < ∞. For testing H0: θ = 1. 2 against H1: θ ≠ 1. 2, let T+ denote the Wilcoxson Signed-rank test statistic. If η denotes the probability of the event {T+ < 50} under H0, then 32 η equals __________ (round off to 2 decimal places).
Answer: (31.60 to 31.80)
55. Consider the multiple linear regression model Yi = β0 + β1x1,i + β2x2,i + ⋯ + β22x22,i + ϵi, i = 1, 2, … , 123, where, for j = 0, 1, 2, … , 22, βj’s are unknown parameters and ϵi’s are independent and identically distributed N(0, σ2), σ > 0, random variables.
If the sum of squares due to regression is 338. 92, the total sum of squares is 522. 30 and R2adj denotes the value of adjusted R2 then 100 R2adj, equals __________ (round off to 2 decimal places).
Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. The current population of a city is 11,02,500. If it has been increasing at the rate of 5% per annum, what was its population 2 years ago?
(A) 9,92,500
(B) 9,95,006
(C) 10,00,000
(D) 12,51,506
Answer: (C)
2. p and q are positive integers and
(A) 3
(B) 7
(C) 9
(D) 11
Answer: (B)
3.
The least number of squares that must be added so that the line P-Q becomes the line of symmetry is ________
(A) 4
(B) 3
(C) 6
(D) 7
Answer: (C)
4. Nostalgia is to anticipation as _______ is to ________
Which one of the following options maintains a similar logical relation in the above sentence?
(A) Present, past
(B) Future, past
(C) Past, future
(D) Future, present
Answer: (C)
5. Consider the following sentences:
(i) I woke up from sleep.
(ii) I woked up from sleep.
(iii) I was woken up from sleep.
(iv) I was wokened up from sleep.
Which of the above sentences are grammatically CORRECT?
(A) (i) and (ii)
(B) (i) and (iii)
(C) (ii) and (iii)
(D) (i) and (iv)
Answer: (B)
Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).
6. Given below are two statements and two conclusions.
Statement 1: All purple are green.
Statement 2: All black are green.
Conclusion I: Some black are purple.
Conclusion II: No black is purple.
Based on the above statements and conclusions, which one of the following options is logically CORRECT?
(A) Only conclusion I is correct.
(B) Only conclusion II is correct.
(C) Either conclusion I or II is correct.
(D) Both conclusion I and II are correct.
Answer: (C)
7. Computers are ubiquitous. They are used to improve efficiency in almost all fields from agriculture to space exploration. Artificial intelligence (AI) is currently a hot topic. AI enables computers to learn, given enough training data. For humans, sitting in front of a computer for long hours can lead to health issues.
Which of the following can be deduced from the above passage?
(i) Nowadays, computers are present in almost all places.
(ii) Computers cannot be used for solving problems in engineering.
(iii) For humans, there are both positive and negative effects of using computers.
(iv) Artificial intelligence can be done without data.
(A) (ii) and (iii)
(B) (ii) and (iv)
(C) (i), (iii) and (iv)
(D) (i) and (iii)
Answer: (D)
8. Consider a square sheet of side 1 unit. In the first step, it is cut along the main diagonal to get two triangles. In the next step, one of the cut triangles is revolved about its short edge to form a solid cone. The volume of the resulting cone, in cubic units, is ________
(A) π/3
(B) 2π/3
(C) 3π/2
(D) 3π
Answer: (A)
9.
The number of minutes spent by two students, X and Y, exercising every day in a given week are shown in the bar chart above.
The number of days in the given week in which one of the students spent a minimum of 10% more than the other student, on a given day, is
(A) 4
(B) 5
(C) 6
(D) 7
Answer: (C)
10.
Corners are cut from an equilateral triangle to produce a regular convex hexagon as shown in the figure above.
The ratio of the area of the regular convex hexagon to the area of the original equilateral triangle is
(A) 2 : 3
(B) 3 : 4
(C) 4 : 5
(D) 5 : 6
Answer: (A)
Production & Industrial Engineering (PI)
Q.1 – Q.17 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. A product has an exponential time-to-failure distribution with a constant failure rate of 0.00006 per hour. The reliability of the product after 4000 hours of operation is
(A) 0.5866
(B) 0.6866
(C) 0.7866
(D) 0.8866
Answer: (C)
2. In a typical product development process under concurrent engineering approach, all elements of product life cycle from conception to disposal are considered at
(A) Product design stage
(B) Process design stage
(C) Manufacturing stage
(D) Disposal stage
Answer: (A)
3. When acceptance number of a single sampling plan under attribute category is zero with sample size less than or equal to 10, the Operating Characteristic (OC) curve is
(A) A horizontal line
(B) A vertical line
(C) A convex function
(D) An inverted S-shaped curve
Answer: (C)
4. Which one of the following is an improvement type heuristic algorithm for computerized layout design technique?
(A) Systematic layout planning (SLP)
(B) Computerized relative allocation of facilities technique (CRAFT)
(D) Plant layout analysis and evaluation technique (PLANET)
Answer: (B)
5. Which one of the following is NOT a measure of forecast error?
(A) Mean absolute deviation (MAD)
(B) Mean squared error (MSE)
(C) Mean absolute percent error (MAPE)
(D) Mean sum product error (MSPE)
Answer: (D)
6. Pearlite microstructure in an eutectoid steel consists of alternating layers of two phases, namely α ferrite and
(A) Martensite
(B) Austenite
(C) Cementite
(D) Bainite
Answer: (C)
7. Which one of the following defects is NOT associated with welding processes?
(A) Angular distortion
(B) Hot tear
(C) Hydrogen embrittlement
(D) Earring
Answer: (D)
8. Match the component with the corresponding manufacturing process in the table below.
(A) P-3, Q-2, R-1, S-4
(B) P-3, Q-4, R-2, S-1
(C) P-2, Q-3, R-4, S-1
(D) P-1, Q-3, R-2, S-4
Answer: (B)
9. In a turning operation, doubling the cutting speed (V) reduces the tool life (T) to 1/8th of the original tool life. The exponent n in the Taylor’s tool life equation, VTn = C is
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/8
Answer: (B)
10. Which one among the following mechanisms is NOT used for transforming rotation to translation in machine tools?
(A) Screw-nut system
(B) 4-bevel gear type differential mechanism
(C) Cam and cam follower system
(D) Whitworth mechanism
Answer: (B)
11. Match the measuring feature with the corresponding measuring instrument in the table below.
(A) P-4, Q-1, R-2, S-3
(B) P-1, Q-3, R-4, S-2
(C) P-2, Q-4, R-3, S-1
(D) P-4, Q-3, R-1, S-2
Answer: (B OR D)
12. The frequency of pulsing in a die-sinking electric discharge machine (EDM) is 10 kHz. The pulse off-time is set at 40 micro-seconds. The duty factor at this setting is
(A) 0.40
(B) 0.60
(C) 0.67
(D) 2.50
Answer: (B)
13. A cantilever beam of length 0.3 m is subjected to a uniformly distributed load C = 10 kN/m, as shown in the figure. The bending (flexural) rigidity of the beam is 5000 Nm2. Neglecting the self-weight of the beam, the magnitude of beam curvature in m−1 at the fixed end is
(A) 1.10
(B) 0.02
(C) 0.09
(D) 0.05
Answer: (C)
14. A circular rod of length l = 2 m is subjected to a compressive load P, as shown in the figure. The bending (flexural) rigidity of the rod is 2000 Nm2. If both ends are pinned, then the critical load Pcr in N (rounded to the nearest integer) at which the rod buckles elastically is
(A) 4935
(B) 2000
(C) 5167
(D) 1238
Answer: (A)
15. Two cylindrical parts of equal length l, as shown in the figure, made of steel having Young’s modulus E = 200 GPa and Poisson’s ratio v = 0.33 are press fitted upon one another. If radial interference δ = 0.05 mm, and radii R = 25 mm and R0 = 40 mm, then the contact pressure P in MPa at the interface upon press fit is
(A) 10.7
(B) 60.9
(C) 121.9
(D) 1005.3
Answer: (C)
16. The dimensionless number defined by the ratio of inertial force to viscous force is called
(A) Mach number
(B) Froude number
(C) Weber number
(D) Reynolds number
Answer: (D)
17. A small capillary tube of 3 mm inner diameter is inserted into a fluid having density 900 kg/m3, surface tension 0.1 N/m, and contact angle 300. The rise in the height of fluid in the capillary tube due to surface tension is
(A) 111.4 mm
(B) 128.3 mm
(C) 89.1 mm
(D) 154.1 mm
Answer: (MTA)
Q.18 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).
18. A given steel has identical yield strength of 700 MPa in uni-axial tension and uni-axial compression. If the steel is subjected to pure shear stress such that the three principal stresses are σ1 = σ, σ2 = 0, σ3 = − σ with σ1 ≥ σ2 ≥ σ3, then the stress σ in MPa for the initiation of plastic yielding in the steel as per von Mises yield criterion is ________. [round off to 2 decimal places]
Answer: (404.00 to 405.00)
19. A cylindrical mild steel tensile test specimen of gauge length 50 mm and diameter 10 mm is extended in two stages at a deformation speed of 4 mm/min. The specimen is extended from 50 mm to 55 mm in the first stage, and from 55 mm to 60 mm in the second stage. Neglecting elastic deformation, the total longitudinal true strain is _________. [round off to2 decimal places]
Answer: (0.17 to 0.19)
20. A M30 bolt needs to be subjected to pretension Fi = 350 kN. If the torque coefficient K of the bolt is 0.2, then the torque in Nm needed to achieve this pretension is _________. [in integer]
Answer: (2100 to 2100)
21. A 150 mm wide polyamide flat belt is transmitting 15 kW power through a belt-pulley system. The driving pulley of 150 mm pitch diameter is rotating at 200 RPM. If F1 is the belt tension on high tension side, and F2 is the belt tension on low tension side, then the difference in belt tensions ∆F = F1 – F2 in N is _________. [round off to one decimal place]
Answer: (9545.0 to 9555.0)
22. Heat is being removed from a refrigerator at a rate of 300 kJ/min to maintain its inside temperature at 2° If the input power to the refrigerator is 2 kW, the coefficient of performance of the refrigerator is ________. [round off to one decimal place]
Answer: (2.4 to 2.6)
23. In an ideal Otto cycle, 800 kJ/kg is transferred to air during the constant volume heat addition process and 381 kJ/kg is removed during the constant volume heat rejection process. The thermal efficiency in % of the cycle is __________. [round off to one decimal place]
Answer: (52.2 to 52.5)
24. If (3i +1)x + (4i + 4)y + 5 = 0 with x, y being real and i = √−1, then x = ________. [correct up to one decimal place]
Answer: (2.4 to 2.6)
25. The minimum value of function f defined by f(x, y, z) = x2 + 5y2 + 5z2 − 4x + 40y − 40z + 300 is ____________. [in integer]
Answer: (136 to 136)
Q.26 – Q.36 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).
26. For a given process control chart, there are four rules for determining out-of-control state of the process which are being used simultaneously. The probability of Type-I error for the four rules are 0.005, 0.02, 0.03, and 0.05. Assuming independence of the rules, the probability of overall Type-I error when all the four rules are used simultaneously is
(A) 0.101
(B) 0.201
(C) 0.001
(D) 0301
Answer: (A)
27. An in-control process has an estimated standard deviation of 2 mm. The specification limits of the component being processed are 120 ± 8 mm. When the process mean shifts to 118 mm, the values of the process capability indices, Cp and Cpk, respectively are,
(A) 1.000, 1.667
(B) 1.333, 1.667
(C) 1.333, 1.000
(D) 1.000, 1.000
Answer: (C)
28. There are a number of identical components in a parallel system. When the system reliability is 0.97 and the reliability of each individual component is 0.68, the number of identical components in the system is (if actual value is a fraction, it may be rounded up to the next higher integer).
(A) 2
(B) 4
(C) 6
(D) 8
Answer: (B)
29. A retail chain company has identified four sites A, B, C and D to open a new retail store. The company has selected four factors as the basis for evaluation of these sites. The factors, their weights, and the score for each site are given in the following table.
The site that should be selected to open the new retail store is
(A) Site A
(B) Site B
(C) Site C
(D) Site D
Answer: (C)
30. In the classical economic order quantity (EOQ) model, let Q and C denote the optimal order quantity and the corresponding minimum total annual cost (the sum of the inventory holding and ordering costs). If the order quantity is estimated incorrectly as Q′ = 2Q, then the corresponding total annual cost C′ is
(A) C′ = 1.25C
(B) C′ = 1.5C
(C) C′ = 1.75C
(D) C′ = 2C
Answer: (A)
31. The eigenvalues of matrix are 5 and 10. For matrix B = A + α I, where α is a constant and I is 2×2 identity matrix, its eigenvalues are
(A) 5, 10
(B) 5 + α, 10 + α
(C) 5 – α, 10 – α
(D) 5α, 10α
Answer: (B)
32. A company manufactures two products P and Q with unit profit of 4 and 5, respectively. The production requires manpower and two kinds of raw materials R1 and R2. The following table summarizes the requirement and availability of resources.
The maximum profit the company can make is
(A) 45
(B) 48
(C) 42
(D) 54
Answer: (B)
33. A tool of an NC machine has to move along a circular arc from (20,20) to (10,10), while performing an operation. The center of the arc is at (20,10). Which one of the following NC tool commands performs the above mentioned operation?
(A) N020 G03 X20 Y20 X10 Y10 R10
(B) N020 G02 X20 Y20 X10 Y10 R10
(C) N020 G02 X10 Y10 X20 Y20 R10
(D) N020 G01 X20 Y20 X10 Y10 R10
Answer: (A)
34. In a shaft-hole assembly, the hole is specified as The mating shaft has a clearance fit with minimum clearance of 0.01 mm. The tolerance on the shaft is 0.03 mm. The maximum clearance in mm between the hole and the shaft is
(A) 0.04
(B) 0.05
(C) 0.08
(D) 0.10
Answer: (C)
35. ‘GO’ and ‘NO GO’ snap gauges are to be designed for a shaft Gauge tolerance can be taken as 5% of the hole tolerance. Following the ISO system of gauge design, the respective sizes of ‘GO’ and ‘NO GO’ gauges are
(A) 36.013 mm and 36.067 mm
(B) 36.015 mm and 36.065 mm
(C) 36.018 mm and 36.062 mm
(D) 36.020 mm and 36.060 mm
Answer: (A)
36. A circular tank of 4 m diameter is filled up to a height of 3 m. Assuming almost steady flow and neglecting losses, the time taken in seconds to empty the tank through a 5 cm diameter hole located at the center of the tank bottom (take acceleration due to gravity g = 9.81 m/s2) is [round off to the nearest integer]
(A) 5005
(B) 1807
(C) 8097
(D) 3154
Answer: (A)
Q.37 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).
37. The probability mass function P(x) of a discrete random variable X is given by where x = 1, 2, ⋯ , ∞. The expected value of X is _______. [in integer]
Answer: (2 to 2)
38. The time to pass through a security screening at an airport follows an exponential distribution. The mean time to pass through the security screening is 15 minutes. To catch the flight, a passenger must clear the security screening within 15 minutes. The probability that the passenger will miss the flight is __________. [round off to 3 decimal places]
Answer: (0.365 to 0.370)
39. A machine shop has received four jobs A, B, C and D for processing on a single CNC machine. All jobs are available for processing on the first day of the production schedule calendar, and processing times and due dates as applicable on the first day are given below. Using earliest due date rule, the average tardiness (in days) is ________. [in integer]
Answer: (4 to 4)
40. A time study is carried out for a spot welding operation which is being performed by an operator. The time taken (in seconds) for five observations are recorded as 40, 35, 45, 37 and 43, respectively. If the standard time and the allowance for this operation are 45 seconds and 9 seconds, respectively, then the performance rating (in percentage) of the operator is ________. [in integer]
Answer: (90 to 90)
41. The initial cost of a machine is INR 10,00,000 and its salvage value after 10 years of use is INR 50,000. Using the straight line depreciation method, the book value in INR of the machine at the end of 7th year is ________. [in integer]
Answer: (335000 to 335000)
42. A project consists of eight activities. The time required for each activity and its immediate predecessor(s) are given in the table below.
If the project completion time using critical path method (CPM) is 15 days, then the value of X (in days) is ________. [in integer]
Answer: (5 to 5)
43. A wire of 5 mm diameter is drawn into a wire of 4 mm diameter through a conical die at a constant pulling speed of 5 m/s. Neglecting the coefficient of friction and redundant work, the drawing stress (σd) in MPa for the above process is given by where is the mean flow strength of wire material in MPa, and r is the ratio of decrease in area of cross-section to initial area of cross-section of the wire. If the mean flow strength of wire material is 600 MPa, then the power required in kW in the above wire drawing process is ________.
[round off to 2 decimal places]
Answer: (16.80 to 16.84)
44. In an arc welding process, the DC power source characteristic is linear with an open circuit voltage of 60 V and short circuit current of 600 A. The heat required for melting a metal during the welding is 10 J/mm3, and the heat transfer and melting efficiencies are 80% and 25%, respectively. If the weld cross-sectional area of 20 mm2 is made using the maximum arc power, then the required welding speed in mm/s is ________. [round off to one decimal place]
Answer: (8.8 to 9.2)
45. A company is producing a disc-shaped product of 50 mm thickness and 1.0 m diameter using sand casting process. The solidification time of the above casting process is estimated by Chvorinov’s equation where B is the mold constant, and V and A are the volume and surface area of the casting, respectively. It is decided to modify both the thickness and diameter of the disc to 25 mm and 0.5 m, respectively, maintaining the same casting condition. The percentage reduction in solidification time of the modified disc as compared to that of the bigger disc is _________.[round off to one decimal place]
Answer: (74.5 to 75.5)
46. A single point cutting tool with 150 orthogonal rake angle is used to machine a mild steel plate under orthogonal machining condition. The depth of cut (uncut thickness) is set at 0.9 mm. If the chip thickness is 1.8 mm, then the shear angle in degree is ________. [round off to one decimal place]
Answer: (28.0 to 30.0)
47. The top layer of a flat 750 mm × 300 mm rectangular mild steel plate is to be machined with a single depth of cut using a shaping machine. The plate hasbeen fixed by keeping 750 mm side along the tool travel direction. If the approach and the over-travel are 25 mm each, average cutting speed is 10 m/min, feed rate is 0.4 mm/stroke, and the ratio of return time to cutting time of the tool is 1:2, the time (in minutes) required to complete the machining operation is _______. [round off to one decimal place]
Answer: (89.0 to 91.0)
48. A 3 mm thick steel sheet, kept at room temperature of 30 °C, is cut by a fiber laser beam. The laser spot diameter on the top surface of the sheet is 0.2 mm. The laser absorptivity of the sheet is 50%. The properties of steel are density = 8000 kg/m3, specific heat = 500 J/kg.°C, melting temperature = 1530 °C, and latent heat of fusion = 3 × 105 J/kg. Assume that melting efficiency is 100% and that the kerf width is equal to the laser spot diameter. The maximum speed (in m/s) at which the sheet can be fully cut at 2 kW laser power is ________.
[round off to 3 decimal places]
Answer: (0.193 to 0.203)
49. In a point-to-point open-loop NC drive, a stepper motor with 1.80 step angle is coupled to a leadscrew through a gear reduction of 4:1 (4 rotations of the motor enables 1 rotation of leadscrew). The single-start leadscrew has a pitch of 4 mm. The worktable of the system is driven by the leadscrew. If the table moves at a uniform speed of 10 mm/s, the pulse frequency (in Hz) required to drive the stepper motor is ________. [round off to one decimal place]
Answer: (1999.0 to 2001.0)
50. A 30 kg smooth, solid sphere rests on two frictionless inclines as shown in the figure. The magnitude of contact force in N acting at the point A is (take acceleration due to gravity g = 9.81 m/s2 and consider both sphere and inclines to be rigid) _________. [round off to 2 decimal places]
Answer: (147.00 to 147.30)
51. Consider the truss shown in the figure. The members AB, BC, and CA are all rigid and form an equilateral triangle. The contact between roller and ground at C is frictionless. If the self-weight of members is neglected, the force in member BC in N is (negative sign should be used if the force is compressive and positive if the force in the member is tensile) _________. [round off to one decimal place]
Answer: (-5773.7 to -5773.4)
52. A fluid with dynamic viscosity μ = 1 Pa.s is flowing through a circular pipe with diameter 1 cm. If the flow rate (discharge) in the pipe is 0.2 liter/s, the maximum velocity in m/s of the fluid in the pipe is (assume fully developed flow and take fluid density ρ = 1000 kg/m3) ________. [round off to one decimal place]
Answer: (5.0 to 5.2)
53. Values of function y(x) at discrete values of x for 0 ≤ x ≤ 10 are given in table. Using trapezoidal rule,
[round off to one decimal place]
Answer: (33.4 to 33.6)
54. Temperature field inside a sphere of radius R = 1 m with origin at its center is T(x, y, z) = 100 – 70x + 51y – 80z – 10x2 – 20y2 – 20z2. If thermal conductivity of the sphere material is K = 50 W/m.K and Fourier law of heat conduction is valid, net heat leaving the sphere per unit time in W is _________. [round off to one decimal place]
Answer: (20.943.8 to 20944.1)
55. A 3.5 mm thick sheet is rolled using a two high rolling mill to reduce the thickness under plane strain condition. Both rolls have a diameter of 500 mm and are rotating at 200 RPM. The coefficient of friction at the sheet and roll interface is 0.08, and the elastic deflection of the rolls is negligible. If the mean flow strength of the sheet material is 400 MPa, then the minimum possible thickness (in mm) of sheet that can be produced in a single pass is _________. [round off to 2 decimal places]
Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. (i) Arun and Aparna are here.
(ii) Arun and Aparna is here.
(iii) Arun’s families is here.
(iv) Arun’s family is here.
Which of the above sentences are grammatically CORRECT?
(A) (i) and (ii)
(B) (i) and (iv)
(C) (ii) and (iv)
(D) (iii) and (iv)
Answer: (B)
2.
Answer: (B)
3. Two identical cube shaped dice each with faces numbered 1 to 6 are rolled simultaneously. The probability that an even number is rolled out on each dice is:
(A) 1/36
(B) 1/12
(C) 1/8
(D) 1/4
Answer: (D)
4. ⊕ and ⊙ are two operators on numbers p and q such that p ⊙ q = p – q, and p ⊕ q – p × q
Then, (9 ⊙ (6 ⊕ 7)) ⨀ (7 ⊕ (6 ⊙ 5) =
(A) 40
(B) -26
(C) -33
(D) -40
Answer: (D)
5. Four persons P, Q, R and S are to the seated in a row, R should not be seated at the second position from the left end of the row. The number of distinct seating arrangement possible is:
(A) 6
(B) 9
(C) 18
(D) 24
Answer: (C)
Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).
6. On a planar field, you travelled 3 units East from a point O. Next you travelled 4 units South to arrive at point P. Then you travelled from P in the North-East direction such that you arrive at a point that is 6 units East of point O. Next, you travelled in the North-West direction, so that you arrive at point Q that is 18 units North of Point P.
The distance of point Q to point O, in the same units, should be_____
(A) 3
(B) 4
(C) 5
(D) 6
Answer: (C)
7. The author said, “Musicians rehearse before their concerts. Actors rehearse their roles before the opening of a new play, On the other hand, I find it strange that many public speakers think key can just walk on to the stage and start speaking. In my opinion, it is no less important for public speakers to rehearse their talks.”
Based on the above passage, which one of the following is TRUE?
(A) The author is of the opinion that rehearsing is important for musicians, actors and public speakers.
(B) The author is of the opinion that rehearsing is less important for public speakers than for musicians and actors.
(C) The author is of the opinion that rehearsing is more important only for musicians than public speakers.
(D) The author is of the opinion that rehearsal is more important for actors than musicians.
Answer: (A)
8. (1) Some football players play cricket.
(2) All cricket players play hockey.
Among the options given below, the statement that logically follows from the two statements 1 and 2 above, is:
(A) No football player plays hockey.
(B) Some football players play hockey.
(C) All football players play hockey.
(D) All hockey players play football.
Answer: (B)
9. In the figure shown above, PQRS is a square. The shaded portion is formed by the intersection of sectors of circles with radius equal to the side of the square and centers at S and Q.
The probability that any point picked randomly within the square falls in the shaded area is______
(A)
(B) 1/2
(C) π/2
(D) π/4
Answer: (C)
10. In an equilateral triangle PQR, side PQ is divided into four equal parts, side QR is divided into six equal parts and side PR is divided into eight equal parts. The length of each subdivided part in cm is an integer.
The minimum area of the triangle PQR possible, in cm2, is
(A) 18
(B) 24
(C) 48√3
(D) 144√3
Answer: (D)
Physics (PH)
Q.1 – Q.9 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. Choose the graph that best describes the variation of dielectric constant (ϵr) with temperature (T) in a ferroelectric material.
(TC is the Curie temperature)
Answer: (A)
2. A matter wave is represented by the wave function
Ψ(x, y, z, t) = Aei(4x+3y+5z−10πt)
where A is a constant. The unit vector representing the direction of propagation of this matter wave is
Answer: (A)
3. As shown in the figure, X-ray diffraction pattern is obtained from a diatomic chain of atoms P and Q. The diffraction condition is given by a cos θ = nλ, where n is the order of the diffraction peak. Here, a is the lattice constant and λ is the wavelength of the X-rays. Assume that atomic form factors and resolution of the instrument do not depend on θ. Then, the intensity of the diffraction peaks is
(A) lower for even values of n, when compared to odd values of n
(B) lower for odd values of n, when compared to even values of n
(C) zero for odd values of n
(D) zero for even values of n
Answer: (B)
4. As shown in the figure, two metal-semiconductor junctions are formed between an n-type semiconductor S and metal M. The work functions of S and M are φS and φM, respectively with φM > φS.
The I − V characteristics (on linear scale) of the junctions is best represented by
Answer: (A)
5. Consider a tiny current loop driven by a sinusoidal alternating current. If the surface integral of its time-averaged Poynting ector is constant, then the magnitude of the time-averaged magnetic field intensity, at any arbitrary position is proportional to
(A) 1/r3
(B) 1/r2
(C) 1/r
(D) r
Answer: (C)
6. Consider a solenoid of length L and radius R, where R ≪ A steady-current flows through the solenoid. The magnetic field is uniform inside the solenoid and zero outside.
Among the given options, choose the one that best represents the variation in the magnitude of the vector potential, (0,Aφ, 0) at z = L/2, as a function
of the radial distance (r) in cylindrical coordinates.
Useful information: The curl of a vector in cylindrical coordinates is
Answer: (C)
7. Assume that 13N (Z = 7) undergoes first forbidden β+ decay from its ground state with spin-parity Jπi, to a final state Jπf. The possible values for Jπi and Jπf, respectively, are
Answer: (A)
8. In an experiment, it is seen that an electric-dipole (E1) transition can connect an initial nuclear state of spin-parity Jπi = 2+ to a final state Jπf. All possible values of Jπf are
(A) 1+, 2+
(B) 1+, 2+, 3+
(C) 1−, 2−
(D) 1−, 2−, 3−
Answer: (D)
9. Choose the correct statement from the following.
(A) Silicon is a direct band gap semiconductor.
(B) Conductivity of metals decreases with increase in temperature.
(C) Conductivity of semiconductors decreases with increase in temperature.
(D) Gallium Arsenide is an indirect band gap semiconductor.
Answer: (B)
Q.10 – Q.16 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).
10. A two-dimensional square lattice has lattice constant a.
k represents the wavevector in reciprocal space. The coordinates (kx, ky) of reciprocal space where band gap(s) can occur, are
Answer: (B; C; D)
11. As shown in the figure, an electromagnetic wave with intensity II is incident at the interface of two media having refractive indices n1 = 1 and n2 = √3. The wave is reflected with intensity IR and transmitted with intensity IT. Permeability of each medium is the same. (Reflection coefficient R = IR/II and Transmission coefficient T = IT/II).
Choose the correct statement(s).
(A) R = 0 if θI = 0° and polarization of incident light is parallel to the plane of incidence.
(B) T = 1 if θI = 60° and polarization of incident light is parallel to the plane of incidence.
(C) R = 0 if θI = 60° and polarization of incident light is perpendicular to the plane of incidence.
(D) T = 1 if θI = 60° and polarization of incident light is perpendicular to the plane of incidence.
Answer: (B)
12. A material is placed in a magnetic field intensity H. As a result, bound current density Jb is induced and magnetization of the material is M. The magnetic flux density is B. Choose the correct option(s) valid at the surface of the material.
(A) ∇. M = 0
(B) ∇. B = 0
(C) ∇. H = 0
(D) ∇. Jb = 0
Answer: (B; D)
13. For a finite system of Fermions where the density of states increases with energy, the chemical potential
(A) decreases with temperature
(B) increases with temperature
(C) does not vary with temperature
(D) corresponds to the energy where the occupation probability is 0.5
Answer: (A; D)
14. Among the term symbols
4S1, 2D7/2, 3S1 and 2D5/2
choose the option(s) possible in the LS coupling notation.
(A) 4S1
(B) 2D7/2
(C) 3S1
(D) 2D5/2
Answer: (C; D)
15. To sustain lasing action in a three-level laser as shown in the figure, necessary condition(s) is(are)
(A) lifetime of the energy level 1 should be greater than that of energy level 2
(B) population of the particles in level 1 should be greater than that of level 0
(C) lifetime of the energy level 2 should be greater than that of energy level 0
(D) population of the particles in level 2 should be greater than that of level 1
Answer: (A; B)
16. If yn(x) is a solution of the differential equation
y′′ − 2xy′ + 2ny = 0
where n is an integer and the prime ( ′ ) denotes differentiation with respect to x, then acceptable plot(s) of is (are)
Answer: (B; C)
Q.17 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).
17. The donor concentration in a sample of n-type silicon is increased by a factor of 100. Assuming the sample to be non-degenerate, the shift in the Fermi level (in meV) at 300 K (rounded off to the nearest integer) is ______.
(Given: kBT= 25 meV at 300 K)
Answer: (115 to 116)
18. Two observers O and Oʹ observe two events P and Q. The observers have a constant relative speed of 0.5c. In the units, where the speed of light, c, is taken as unity, the observer O obtained the following coordinates:
Event P: x = 5, y = 3, z = 5, t = 3
Event Q: x = 5, y = 1, z = 3, t = 5
The length of the space-time interval between these two events, as measured by Oʹ, is L. The value of |L| (in integer) is ______.
Answer: (2 to 2)
19. A light source having its intensity peak at the wavelength 289.8 nm is calibrated as 10,000 K which is the temperature of an equivalent black body radiation. Considering the same calibration, the temperature of light source (in K) having its intensity peak at the wavelength 579.6 nm (rounded off to the nearest integer) is ______.
Answer: (5000 to 5000)
20. A hoop of mass M and radius R rolls without slipping along a straight line on a horizontal surface as shown in the figure. A point mass m slides without friction along the inner surface of the hoop, performing small oscillations about the mean position. The number of degrees of freedom of the system (in integer) is ______.
Answer: (2 to 2)
21. Three non-interacting bosonic particles of mass m each, are in a one-dimensional infinite potential well of width a. The energy of the third excited state of the system is The value of x (in integer) is ______.
Answer: (5 to 6)
22. The spacing between two consecutive S-branch lines of the rotational Raman spectra of hydrogen gas is 243. 2 cm−1. After excitation with a laser of wavelength 514. 5 nm, the Stoke’s line appeared at 17611. 4 cm−1 for a particular energy level. The wavenumber (rounded off to the nearest integer), in cm−1, at which Stoke’s line will appear for the next higher energy level is ______.
Answer: (17367 to 17371)
23. The transition line, as shown in the figure, arises between 2D3/2 and 2P1/2 states without any external magnetic field. The number of lines that will appear in the presence of a weak magnetic field (in integer) is _______.
Answer: (6 to 6)
24. Consider the atomic system as shown in the figure, where the Einstein A coefficients for spontaneous emission for the levels are A2→1 = 2 × 107s–1 and A1→0 = 108s–1. If 1014 atoms/cm3 are excited from level 0 to level 2 and a steady state population in level 2 is achieved, then the steady state population at level 1 will be x × 1013 cm–3. The value of x (in integer) is ______.
Answer: (2 to 2)
25. If are constant vectors, are generalized positions and conjugate meomenta, respectively, then for the transformation to be canonical, the value of (in integer) is ______.
Answer: (-1 to -1)
Q.26 – Q.41 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).
26.
The above combination of logic gates represents the operation
(A) OR
(B) NAND
(C) AND
(D) NOR
Answer: (B)
27. In a semiconductor, the ratio of the effective mass of hole to electron is 2:11 and the ratio of average relaxation time for hole to electron is 1:2. The ratio of the mobility of the hole to electron is
(A) 4:9
(B) 4:11
(C) 9:4
(D) 11:4
Answer: (D)
28. Consider a spin S = ħ⁄2 particle in the state The probability that a measurement finds the state with Sx = +ħ⁄2 is
(A) 5/18
(B) 11/18
(C) 15/18
(D) 17/18
Answer: (D)
29. An electromagnetic wave having electric field E = 8 cos(kz − ωt) ŷ V cm−1 is incident at 90°(normal incidence) on a square slab from vacuum (with refractive index n0 = 1. 0) as shown in the figure. The slab is composed of two different materials with refractive indices n1and n2. Assume that the permeability of each medium is the same. After passing through the slab for the first time, the electric field amplitude, in V cm−1, of the electromagnetic wave, which emerges from the slab in region 2, is closest to
(A) 11/1.6
(B) 11/3.2
(C) 11/13.8
(D) 11/25.6
Answer: (A)
30. Consider a point charge +Q of mass m suspended by a massless, inextensible string of length l in free space (permittivity ε0) as shown in the figure. It is placed at a height d (d > l) over an infinitely large, grounded conducting plane. The gravitational potential energy is assumed to be zero at the position of the conducting plane and is positive above the plane.
If θ represents the angular position and pθ its corresponding canonical momentum, then the correct Hamiltonian of the system is
Answer: (D)
31. Consider two concentric conducting spherical shells as shown in the figure. The inner shell has a radius a and carries a charge +Q. The outer shell has a radius b and carries a charge −Q. The empty space between them is half-filled by a hemispherical shell of a dielectric having permittivity ε1. The remaining space between the shells is filled with air having the permittivity ε0.
The electric field at a radial distance r from the center and between the shells (a < r < b) is
Answer: (A)
32.
For the given sets of energy levels of nuclei X and Y whose mass numbers are odd and even, respectively, choose the best suited interpretation.
(A) Set I: Rotational band of X
Set II: Vibrational band of Y
(B) Set I: Rotational band of Y
Set II: Vibrational band of X
(C) Set I: Vibrational band of X
Set II: Rotational band of Y
(D) Set I: Vibrational band of Y
Set II: Rotational band of X
Answer: (D)
33. Consider a system of three distinguishable particles, each having spin S = 1/2 such that Sz = ±1/2 with corresponding magnetic moments μz = ±μ. When the system is placed in an external magnetic field H pointing along the z-axis, the total energy of the system is μH. Let x be the state where the first spin has Sz = 1/2. The probability of having the state x and the mean magnetic moment (in the +z direction) of the system in state x are
Answer: (A)
34. Consider a particle in a one-dimensional infinite potential well with its walls at x = 0 and x = L. The system is perturbed as shown in the figure.
The first order correction to the energy eigenvalue is
(A) V0/4
(B) V0/3
(C) V0/2
(D) V0/5
Answer: (C)
35. Consider a state described by ψ(x, t) = ψ2(x, t) + ψ4(x, t), where ψ2(x, t) and ψ4(x, t) are respectively the second and fourth normalized harmonic oscillator wave functions and ω is the angular frequency of the harmonic oscillator. The wave function ψ(x, t = 0) will be orthogonal to ψ(x, t) at time t equal to
(A) π/2ω
(B) π/ω
(C) π/4ω
(D) π/6ω
Answer: (A)
36. Consider a single one-dimensional harmonic oscillator of angular frequency ω, in equilibrium at temperature T = (kBβ)−1. The states of the harmonic oscillator are all non-degenerate having energy with equal probability, where n is the quantum number. The Helmholtz free energy of the oscillator is
Answer: (B)
37. A system of two atoms can be in three quantum states having energies 0, ε and 2ε. The system is in equilibrium at temperature T = (kBβ)−1. Match the following Statistics with the Partition function.
(A) CD:Z1, CI:Z2, FD:Z3, BE:Z4
(B) CD:Z2, CI:Z3, FD:Z4, BE:Z1
(C) CD:Z3, CI:Z4, FD:Z1, BE:Z2
(D) CD:Z4, CI:Z1, FD:Z2, BE:Z3
Answer: (C)
38. The free energy of a ferromagnet is given by F = F0 + a0(T − TC)M2 + bM4, where F0, a0, and b are positive constants, M is the magnetization, T is the temperature, and TC is the Curie temperature. The relation between M2 and T is best depicted by
Answer: (B)
39. Consider a spherical galaxy of total mass M and radius R, having a uniform matter distribution. In this idealized situation, the orbital speed v of a star of mass m (m ≪ M) as a function of the distance r from the galactic centre is best described by
(G is the universal gravitational constant)
Answer: (A)
40. Consider the potential U(r) defined as where α and U0 are real constants of appropriate dimensions. According to the first Born approximation, the elastic scattering amplitude calculated with U(r) for a (wave-vector) momentum transfer q and α → 0, is proportional to
((Useful integral:
(A) q−2
(B) q−1
(C) q
(D) q2
Answer: (A)
41. As shown in the figure, inverse magnetic susceptibility (1/χ) is plotted as a function of temperature (T) for three different materials in paramagnetic states.
(Curie temperature of ferromagnetic material =TC
Néel temperature of antiferromagnetic material= TN)
Choose the correct statement from the following
(A) Material 1 is antiferromagnetic (T < TN), 2 is paramagnetic, and 3 is ferromagnetic (T < TC).
(B) Material 1 is paramagnetic, 2 is antiferromagnetic (T < TN), and 3 is ferromagnetic (T < TC).
(C) Material 1 ferromagnetic (T < TC), 2 is antiferromagnetic (T < TN), and 3 is paramagnetic.
(D) Material 1 is ferromagnetic (T < TC), 2 is paramagnetic, and 3 is antiferromagnetic (T < TN).
Answer: (A)
Q.42 – Q.46 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).
42. A function f(t) is defined only for t ≥ 0. The Laplace transform of f(t) is
whereas the Fourier transform of f(t) is
The correct statement(s) is(are)
(A) The variable s is always real.
(B) The variable s can be complex.
(C) L(f; s) and can never be made connected.
(D) L(f; s) and can be made connected.
Answer: (B; D)
43. P and Q are two Hermitian matrices and there exists a matrix R, which diagonalizes both of them, such that RPR−1 = S1 and RQR−1 = S2 , where S1 and S2 are diagonal matrices. The correct statement(s) is(are)
(A) All the elements of both matrices S1 and S2 are real.
(B) The matrix PQ can have complex eigenvalues.
(C) The matrix QP can have complex eigenvalues.
(D) The matrices P and Q commute.
Answer: (A; D)
44. A uniform block of mass M slides on a smooth horizontal bar. Another mass m is connected to it by an inextensible string of length l of negligible mass, and is constrained to oscillate in the X-Y plane only. Neglect the sizes of the masses. The number of degrees of freedom of the system is two and the generalized coordinates are chosen as x and θ, as shown in the figure.
If px and pθ are the generalized momenta corresponding to x and θ, respectively, then the correct option(s) is(are)
(A)
(B)
(C) px is conserved
(D) pθ is conserved
Answer: (A; C)
45. The Gell-Mann – Okuba mass formula defines the mass of baryons as where M0, a and b are constants, I represents the isospin and Y represents the hypercharge. If the mass of Σ hyperons is same as that of Λ hyperons, then the correct option(s) is(are)
(A) M ∝ I(I + 1)
(B) M ∝ Y
(C) M does not depend on I
(D) M does not depend on Y
Answer: (B; C)
46. The time derivative of a differentiable function g(qi, t) is added to a Lagrangian L(qi, qi̇ , t) such that where qi, q̇i, t are the generalized coordinates, generalized velocities and time, respectively. Let pi be the generalized momentum and H the Hamiltonian associated with L(qi, q̇i, t). If p’i and H’ are those associated with L′, then the correct option(s) is(are)
(A) Both L and L′ satisfy the Euler-Lagrange’s equations of motion
(B)
(C) If pi is conserved, then p’i is necessarily conserved
(D)
Answer: (A; B)
Q.47 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).
47. A linear charged particle accelerator is driven by an alternating voltage source operating at 10 MHz. Assume that it is used to accelerate electrons. After a few drift-tubes, the electrons attain a velocity 2. 9 × 108 m s–1. The minimum length of each drift-tube, in m, to accelerate the electrons further (rounded off to one decimal place) is______.
Answer: (14.0 to 15.0)
48. The Coulomb energy component in the binding energy of a nucleus is 18.432 MeV. If the radius of the uniform and spherical charge distribution in the nucleus is 3 fm, the corresponding atomic number (rounded off to the nearest integer) is _______.
Answer: (8 to 8 OR 9 to 9)
49. For a two-nucleon system in spin singlet state, the spin is represented through the Pauli matrices σ1, σ2 for particles 1 and 2, respectively.
The value of (σ1 ⋅ σ2) (in integer) is ________.
Answer: (-3 to -3)
50. A contour integral is defined as where n is a positive integer and C is the closed contour, as shown in the figure, consisting of the line from −100 to 100 and the semicircle traversed in the counter-clockwise sense.
The value of (in integer) is ______.
Answer: (5 to 5)
51. The normalized radial wave function of the second excited state of hydrogen atom is
where a is the Bohr radius and r is the distance from the center of the atom. The distance at which the electron is most likely to be found is y × a. The
value of y (in integer) is ______.
Answer: (4 to 4)
52. Consider an atomic gas with number density n = 1020 m−3, in the ground state at 300 K. The valence electronic configuration of atoms is f7. The paramagnetic susceptibility of the gas χ = m × 10−11. The value of m (rounded off to two decimal places) is ______.
(Given: Magnetic permeability of free space μ0 = 4π × 10−7 H m−1
Bohr magneton μB = 9. 274 × 10−24A m2
Boltzmann constant kB = 1. 3807 × 10−23 J K−1)
Answer: (5.40 to 5.50)
53. Consider a cross-section of an electromagnet having an air-gap of 5 cm as shown in the figure. It consists of a magnetic material (μ = 20000μ0) and is driven by a coil having NI = 104A, where N is the number of turns and I is the current in Ampere.
Ignoring the fringe fields, the magnitude of the magnetic field (in Tesla, rounded off to two decimal places) in the air-gap between the magnetic poles is ______.
Answer: (0.24 to 0.26)
54. The spin and orbital angular momentum total angular momentum. precesses about an axis fixed by a magnetic field where B0 is a constant. Now the magnetic field is changed to Given the orbital angular momentum quantum number l = 2 and spin quantum number s = 1⁄2, θ is the angle between for the largest possible values of total angular quantum number j and its z-component jz. The value of θ (in degree, rounded off to the nearest integer) is______.
Answer: (27 to 93)
55. The spin-orbit effect splits the 2P → 2S transition (wavelength, λ = 6521 Å) in Lithium into two lines with separation of ∆λ = 0. 14 Å. The corresponding positive value of energy difference between the above two lines, in eV, is m × 10−5. The value of m (rounded off to the nearest integer) is ______.
Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. The current population of a city is 11,02,500. If it has been increasing at the rate of 5% per annum, what was its population 2 years ago?
(A) 9,92,500
(B) 9,95,006
(C) 10,00,000
(D) 12,51,506
Answer: (C)
2. p and q are positive integers and
(A) 3
(B) 7
(C) 9
(D) 11
Answer: (B)
3.
The least number of squares that must be added so that the line P-Q becomes the line of symmetry is ________
(A) 4
(B) 3
(C) 6
(D) 7
Answer: (C)
4. Nostalgia is to anticipation as _______ is to ________
Which one of the following options maintains a similar logical relation in the above sentence?
(A) Present, past
(B) Future, past
(C) Past, future
(D) Future, present
Answer: (C)
5. Consider the following sentences:
(i) I woke up from sleep.
(ii) I woked up from sleep.
(iii) I was woken up from sleep.
(iv) I was wokened up from sleep.
Which of the above sentences are grammatically CORRECT?
(A) (i) and (ii)
(B) (i) and (iii)
(C) (ii) and (iii)
(D) (i) and (iv)
Answer: (B)
Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).
6. Given below are two statements and two conclusions.
Statement 1: All purple are green.
Statement 2: All black are green.
Conclusion I: Some black are purple.
Conclusion II: No black is purple.
Based on the above statements and conclusions, which one of the following options is logically CORRECT?
(A) Only conclusion I is correct.
(B) Only conclusion II is correct.
(C) Either conclusion I or II is correct.
(D) Both conclusion I and II are correct.
Answer: (C)
7. Computers are ubiquitous. They are used to improve efficiency in almost all fields from agriculture to space exploration. Artificial intelligence (AI) is currently a hot topic. AI enables computers to learn, given enough training data. For humans, sitting in front of a computer for long hours can lead to health issues.
Which of the following can be deduced from the above passage?
(i) Nowadays, computers are present in almost all places.
(ii) Computers cannot be used for solving problems in engineering.
(iii) For humans, there are both positive and negative effects of using computers.
(iv) Artificial intelligence can be done without data.
(A) (ii) and (iii)
(B) (ii) and (iv)
(C) (i), (iii) and (iv)
(D) (i) and (iii)
Answer: (D)
8. Consider a square sheet of side 1 unit. In the first step, it is cut along the main diagonal to get two triangles. In the next step, one of the cut triangles is revolved about its short edge to form a solid cone. The volume of the resulting cone, in cubic units, is ________
(A) π/3
(B) 2π/3
(C) 3π/2
(D) 3π
Answer: (A)
9.
The number of minutes spent by two students, X and Y, exercising every day in a given week are shown in the bar chart above.
The number of days in the given week in which one of the students spent a minimum of 10% more than the other student, on a given day, is
(A) 4
(B) 5
(C) 6
(D) 7
Answer: (C)
10.
Corners are cut from an equilateral triangle to produce a regular convex hexagon as shown in the figure above.
The ratio of the area of the regular convex hexagon to the area of the original equilateral triangle is
(A) 2 : 3
(B) 3 : 4
(C) 4 : 5
(D) 5 : 6
Answer: (A)
Petroleum Engineering (PE)
Q.1 – Q.13 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. MOPU (in the context of offshore drilling and production systems) stands for
(A) Mobile Offshore Process Unit
(B) Mobile Offshore Piping Unit
(C) Mobile Offshore Production Unit
(D) Mobile Oil Production Unit
Answer: (C)
2. Which ONE of the following statements is INCORRECT?
(A) Conductor is the outer casing of a well
(B) Riser is used for transporting fluid
(C) Conductor and riser have the same functions
(D) Conductor is used for shielding the well flow lines from external forces
Answer: (C)
3. Which ONE of the following offshore installations uses Dynamic Positioning System (DPS) for station keeping?
(A) Jacket
(B) Jack-up
(C) Semi-submersible
(D) Tension Leg Platform
Answer: (C)
4. Which ONE of the following is NOT a primary safety system for offshore installations?
(A) Emergency Shut Down
(B) Isolation
(C) Fire Protection
(D) Blowdown
Answer: (C)
5. The primary function of the thruster in the Dynamic Positioning System (DPS) of an offshore installation is
(A) To apply thrust in the direction opposite to the resultant environmental force
(B) To apply thrust in the same direction as the resultant environmental force
(C) To apply thrust in the direction opposite to the motion
(D) To apply thrust in the same direction as the motion
Answer: (A OR C)
6. Select the CORRECT firefighting system for electrical switchgear room in an offshore facility.
(A) Wet chemical
(B) Halon system
(C) Foam
(D) Water sprinklers
Answer: (B)
7. Which ONE of the following options can be used to quantify secondary porosity?
(A) Sonic and Gamma Ray Logs
(B) Sonic and Neutron Logs
(C) Sonic and Caliper Logs
(D) Density and Neutron Logs
Answer: (B)
8. Among the options given below, what is the typical temperature range for significant oil generation in a source rock associated with conventional crude-oil reservoirs?
(A) 10 °C – 40 °C
(B) 60 °C – 175 °C
(C) 225 °C – 325 °C
(D) 350 °C – 425 °C
Answer: (B)
9. In the original Darcy’s law as proposed by Henry Darcy, which of the following drives the fluid flow through a fully saturated sand column?
(A) Pressure-gradient or hydraulic-gradient
(B) Viscous force per unit volume
(C) Capillary force per unit volume
(D) Inertial force per unit volume
Answer: (A)
10. At which ONE of the following scales is Darcy’s law for fluid flow through a porous medium applicable?
(A) Nano-scale
(B) Molecular-scale
(C) Microscopic-scale
(D) Macroscopic-scale
Answer: (D)
11. Pressure – Temperature phase diagram of CO2 is shown below. Identify the correct phases from the given options.
(A) I = Solid Phase, II = Liquid Phase, III = Gas Phase, IV = Supercritical Phase
(B) I = Gas Phase, II = Supercritical Phase, III = Solid Phase, IV = Liquid Phase
(C) I = Supercritical Phase, II = Liquid Phase, III = Solid Phase, IV = Gas Phase
(D) I = Gas Phase, II = Solid Phase, III = Liquid Phase, IV = Supercritical Phase
Answer: (D)
12. A measure of the potential of crude oil to form surfactants for Enhanced Oil Recovery (EOR) is given by the Total Acid Number (TAN). TAN is the mass of _________ (in milligrams) that is required to neutralize one gram of crude oil.
(A) Ca(OH)2
(B) NaCl
(C) KOH
(D) NaOH
Answer: (C)
13. In Water-Alternating-Gas (WAG) injection, the purpose of the injection is to _____I_____ the “relative permeability” of gas and to ____II_____ the “mobility” of the gas.
(A) I = reduce, II = enhance
(B) I = reduce, II = reduce
(C) I = enhance, II = reduce
(D) I = enhance, II = enhance
Answer: (B)
Q.14 – Q.19 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).
14. Solids that may possibly form in the offshore pipelines during the production of oil and gas from deep-water reservoirs are
(A) Wax
(B) Char
(C) Hydrates
(D) Asphaltenes
Answer: (A; C; D)
15. Oil and gas pipelines, which are at an elevated pressure (about 3 MPa) and sub-ambient temperature (below 298 K), may get blocked by the formation of solid hydrates. One of the strategies adopted to inhibit the formation of hydrates is the injection of Thermodynamic Hydrate Inhibitors (THIs) into the reservoir fluid.
Identify all suitable chemicals that are commonly used as THIs.
(A) Sodium Chloride
(B) Methanol
(C) Polyvinylpyrrolidone
(D) Sodium Dodecyl Sulphate
Answer: (A; B)
16. When CO2 and liquid water are brought in contact with each other, they may form solid hydrates. The three-phase hydrate boundary is shown in the Pressure -Temperature plot given below.
Identify the correct statements.
G = Gas Phase, H = Hydrate Phase, L = Liquid Phase
(A) Hydrates are stable in region I
(B) Hydrates are stable in region II
(C) Hydrates are stable in region III
(D) Hydrates are stable in region IV
Answer: (B; D)
17. Heavy oil recovered from reservoirs can be represented by CXH5X. Suitable processes to reduce the density of heavy oil are
(A) Carbon Rejection
(B) Pyrolysis
(C) Hydrogenation
(D) Filtration
Answer: (A; C OR A; B; C)
18. Identify the CORRECT statements for a n × n matrix.
(A) Under elementary row operations, the rank of the matrix remains invariant
(B) Under elementary row operations, the eigenvalues of the matrix remain the same
(C) If the elements in a row can be written as a linear combination of two or more rows, then the matrix is singular.
(D) The rank of the matrix is equal to n if the determinant of the matrix is zero.
Answer: (A; C)
19. During a drilling operation, kick occurs if
(A) the shear ram in the Blow Out Preventer (BOP) does not work.
(B) the formation pressure is equal to the drilling fluid pressure.
(C) the volume of the mud used to fill the hole is less than that of the pipe being pulled out.
(D) the formation pressure is more than the drilling fluid pressure.
Answer: (C; D OR D)
Q.20 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).
20. The value of is __________ (correct up to one decimal place).
Answer: (0.5 to 0.5)
21. Given two complex numbers, z1 = 4 + 3i and z2 = 2 − 5i, the real part of is _____.
Answer: (-7 to -7)
22. The number of ‘three-digit numbers’ that can be formed using the digits from 1 to 9 without the repetition of each digit is ________.
Answer: (504 to 504)
23. The estimate for the root of the function f(x) = e2x + 2x after one iteration with an initial guess of x0 = 0, using the Newton-Raphson method is________ (correct up to two decimal places).
Answer: (-0.25 to -0.25)
24. A saturated oil reservoir has an average reservoir pressure of 3000 psia tested for flowing bottom-hole pressure (BHP) of 2000 psia and production rate of 500 STB/day. The maximum reservoir deliverability based on Vogel’s equation for two-phase flow is ________ STB/day.
Answer: (960 to 990)
25. If the specific heat ratio of natural gas is 1.28, the critical pressure ratio (ratio of outlet pressure to upstream pressure) through a choke is ________ (round off to two decimal places).
Answer: (0.52 to 0.57)
Q.26 – Q.37 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).
26. Match the suitable artificial lift methods (GROUP I) to meet the requirements (GROUP II) given in the table.
(A) P – I, Q – II, R – IV, S – III
(B) P – II, Q – I, R – IV, S – III
(C) P – I, Q – II, R – III, S – IV
(D) P – II, Q – I, R – III, S – IV
Answer: (D)
27. Match the Enhanced Oil Recovery (EOR) methods (GROUP I) with the corresponding laboratory tests (GROUP II).
(A) P – III, Q – II, R – I, S – IV
(B) P – II, Q – IV, R – I, S – III
(C) P – III, Q – IV, R – II, S – I
(D) P – III, Q – II, R – IV, S – I
Answer: (C)
28. Identify the following well test methods corresponding to the transient pressure profiles in the figures given below. (BHP: Bottom-hole pressure, BOPD: Barrels of oil per day)
(P) Flow-after-flow test
(Q) Interference test
(R) Fall-off test
(S) Modified isochronal test
(A) P – IV, Q – II, R – I, S – III
(B) P – II, Q – III, R – IV, S – I
(C) P – II, Q – III, R – I, S – IV
(D) P – IV, Q – I, R – III, S – II
Answer: (C)
29. Match the following wire-line logging methods (GROUP I) based on the physical principles of measurements (GROUP II).
(A) P – II, Q – I, R – IV, S – III
(B) P – II, Q – I, R – IV, S – III
(C) P – III, Q – II, R – IV, S – I
(D) P – II, Q – I, R – III, S – IV
Answer: (B)
30. Match the following rock types (GROUP I) with their respective chemical compositions (GROUP II) from the given options.
(A) P – III, Q – II, R – IV, S – I
(B) P – II, Q – III, R – I, S – IV
(C) P – III, Q – I, R – IV, S – II
(D) P – III, Q – I, R – II, S – IV
Answer: (C)
31. The following equations describe the transient fluid flow in a typical petroleum reservoir system. Here, p is pressure, x and r are the spatial coordinates in rectangular and cylindrical systems respectively, and t is time. Also, ϕ (porosity), μ (viscosity), cf (formation compressibility), ct (total compressibility) and k(permeability) are constant coefficients.
Match the equations (GROUP I) with their corresponding descriptions (GROUP II).
(A) P – IV, Q – I, R – II, S – III
(B) P – IV, Q – III, R – II, S – I
(C) P – III, Q – IV, R – II, S – I
(D) P – III, Q – IV, R – I, S – II
Answer: (A)
32. Select the INCORRECT statement related to Enhanced Oil Recovery (EOR) techniques from the following options.
(A) Alkaline flooding recovers crude oil by reduction of interfacial tension (IFT) and reversal of wettability of rocks.
(B) In-situ combustion recovers crude oil by the application of heat, thus lowering the viscosity of the crude oil.
(C) Nitrogen flue gas flooding recovers crude oil by vaporizing the lighter components of the crude oil.
(D) Polymer flooding recovers crude oil by reducing the viscosity and increasing the mobility of water.
Answer: (D)
33. Match the petroleum reservoir forming traps (GROUP I) with their general classifications (GROUP II).
(A) P – III, Q – II, R – IV, S – I
(B) P – II, Q – III, R – IV, S – I
(C) P – III, Q – I, R – II, S – IV
(D) P – II, Q – III, R – I, S – IV
Answer: (B)
34. An Ideal Pressure Buildup Test yields a single straight line for all times, when shut-in Bottom-Hole Pressure (Pws) is plotted against . Here tp is the well production time and Δt is the time elapsed since shut-in. However, in an actual Pressure Buildup Test, a non-linear curve is obtained which can be logically divided into distinct regions.
Choose the INCORRECT option from the following.
(A) A late-time region, in which the radius of investigation has reached the well’s drainage boundaries.
(B) A middle-time region during which the pressure transient has moved away from the wellbore and into the bulk formation.
(C) An early-time region during which a pressure transient is moving through the formation nearest the wellbore.
(D) An early-time region during which a pressure transient is moving away from the drainage boundary.
Answer: (D)
35. When two immiscible fluid phases are placed in contact with a solid surface, one phase usually is attracted to solid more strongly than the other phase. The more strongly attracted phase is called the ‘wetting phase’.
The inter-molecular interaction of the non-wetting phase with the solid is ___I___ than its intra-molecular interaction. Due to this, the non-wetting phase tends to occupy the ____II_____ of the reservoir.
(A) I = stronger, II = smaller pores
(B) I = stronger, II = larger pores
(C) I = weaker, II = smaller pores
(D) I = weaker, II = larger pores
Answer: (D)
36. Coal bed methane is methane gas adsorbed in coal seams. To desorb the methane from the coal seam it should be exposed to CO2 and (or) N2. Which ONE of the following is an appropriate reason to enhance the desorption process?
(A) N2 is used because it has low kinetic energy compared to CH4
(B) CO2 is used as it has high kinetic energy compared to CH4
(C) CO2 is used as it strongly binds with coal compared to CH4
(D) N2 is used as it strongly binds with coal compared to CH4
Answer: (C)
37. Match the platforms (GROUP I) with appropriate support systems (GROUP II).
(A) P – IV, Q – III, R – I, S – II
(B) P – II, Q – III, R – I, S – IV
(C) P – III, Q – I, R – IV, S – II
(D) P – I, Q – IV, R – II, S – III
Answer: (A)
Q.38 – Q.39 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).
38. Select the CORRECT statements from the following.
Well testing operations on a typical crude oil reservoir
(A) do not measure rock and fluid properties of the reservoir when the well is flowing or shut-in.
(B) measure variation in pressure response of the reservoir with time when the well is flowing or shut-in.
(C) measure productivity index and partial well completion.
(D) do not measure length and conductivity of hydraulic fractures.
Answer: (B; C; OR A; B; C)
39. Crude oil from oil sands contains bitumen and asphaltene and this crude is heavy and viscous at room temperature. Assume that one such crude oil is represented by CXH2XOY. For easier transportation through pipelines it should be processed further. Identify the processes which help in transportation of this crude oil.
(A) Drying
(B) Vis-breaking
(C) Coking process
(D) Hydro-treating
Answer: (B; C; D)
Q.40 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).
40. Given matrix The eigenvalue corresponding to the eigenvector is ________.
Answer: (3 to 3)
41. The maximum value of the function f(x) = x4 − 8x2 + 2 for −2 ≤ x ≤ 2 is ________.
Answer: (2 to 2)
42. Given the second order ordinary differential equation: y′′ + 3y′ − 4y = 0with the initial conditions y(0) = 3, and y′(0) = −7, the value of y(1) is ________ (round off to two decimal places).
Answer: (2.71 to 2.79)
43. The directional derivative of f(x, y, z) = x2 + 3y2 + z2, at point (2, 1, 0) along the unit vector in x-direction, î, is _________.
Answer: (4 to 4)
44. A productivity test conducted on a crude oil well indicates a stabilized flow rate of 150 STB/day (water-free oil production) at a bottom-hole flowing pressure of 935 psig. After shutting the well for 24 hours, the bottom-hole pressure reached a static value of 1250 psig.
The Absolute Open Flow (AOF) potential of the well is __________STB/day.
Answer: (580 to 610)
45. A porous medium (shown schematically in the figure) has the following properties.
Length L = 600 m, Width W = 8 m, Height h = 0.5 m,
Permeability k = 100 mD, Porosity ϕ = 15%.
An incompressible fluid having a viscosity of 2 cP is flowing through a porous medium at the inlet and exit pressures of 7 × 106 Pa and 6 × 106 Pa, respectively.
The actual fluid velocity through the porous medium is _______× 10−7 m/s.
(1 Darcy = 10−12 m2)
Answer: (5 to 6)
46. A tubing with an inner diameter of 2.259 inch delivers oil from a well at the rate of 1000 bbl/day. The API gravity and viscosity of the oil are 40o and 1.2 cP, respectively. The tubing makes an angle of 15o with the vertical. Assuming a fanning friction factor of 0.006, the pressure-drop over a length of 1000 ft tubing is _________ psi (round off to nearest integer).
[1 bbl = 5.615 ft3]
Answer: (340 to 360)
47. A cylindrical crude oil reservoir with a radius of 3000 ft is under water influx from a cylindrical aquifer with an estimated radius of 9000 ft. The reservoir has the following properties.
Aquifer thickness, h = 40 ft
Porosity, ϕ = 15%
Formation compressibility, Cf = 4.5 × 10−6 psi−1
Water compressibility, Cw = 4.0 × 10-6 psi−1
Assuming a pot reservoir model with fractional encroachment angle as unity, the water influx into the reservoir for a pressure drop of 700 psi is ________ MMbbl (million barrels) (round off to two decimal places).
(π = 3.14, 1 bbl = 5.615 ft3)
Answer: (1.36 to 1.50)
48. A heavy oil reservoir with an initial oil recovery of 10% has the following properties.
Confined area A = 1.5 acres, thickness of the reservoir h = 15 ft,
An in-situ combustion test was conducted in the above reservoir. Oil recovery due to the combustion process at the well is observed to be 12000 bbl.
The total (overall) oil recovery at the end of the in-situ combustion process is __________% (round off to nearest integer) of the original oil in place.
(1 acre = 43560 ft2, 1 bbl = 5.615 ft3)
Answer: (68 to 78)
49. A double acting duplex pump with a rod diameter of 2.5 inch and a stroke of 20 inch is to be operated at 60 strokes per minute for drilling down to 10000 ft. The flow rate is 600 gpm. If the volumetric efficiency of the pump is 80%, the liner size is_________ inch (round off to one decimal place).
[1 gallon = 231 inch3]
Answer: (6.5 to 7.5)
50. The fluid flow through an under-saturated oil reservoir is driven by solution gas drive mechanism. The reservoir parameters are as given below.
Compressibility of water, cw = 1 × 10−6 psi−1
Compressibility of formation, cf = 1 × 10−5 psi−1
Connate water saturation, Swc = 0. 2
Initial reservoir pressure, pi = 4000 psi
Reservoir pressure at bubble-point, pb = 3000 psi
Oil formation volume factor, Boi = 1. 24 rb/STB
Formation volume factor at bubble point pressure, Bob = 1. 26 rb/STB.
The percentage of oil recovered as a fraction of the Original Oil in Place (OOIP) is ________% (round off to one decimal place).
Answer: (2.6 to 3.0)
51. During drilling, a well is damaged out to a radial distance of 5 ft from the periphery of the wellbore so that the permeability within the damaged zone is reduced to 1/50th of the undamaged effective permeability. After completion, the well is stimulated so that the permeability out to a radial distance of 15 ft from the periphery of the wellbore is increased to twenty times the permeability of the undamaged zone.
The radial inflow equation for stabilized flow conditions under semi-steady state conditions is given by
where pe is effective pressure, pwf is flowing bottom-hole pressure, q is flow-rate, μ is viscosity, ke is average effective permeability, h is reservoir thickness, re is drainage radius, rw is wellbore radius and S is skin factor.
If rw = 0. 5 ft and re = 500 ft, then the increase in Productivity Index ratio is ___________ (round off to one decimal place).
Answer: (32 to 42)
52. A depleted and shut-in oil reservoir originally contained 25 × 106 STB of oil with a formation volume factor of 1.35 res bbl/STB and a connate water saturation of 0.25. Cumulative oil production to date has been 2. 5 × 106 STB of oil. The oil formation volume factor is now 1.25 res bbl/STB. Assuming no water influx, the gas saturation in the reservoir is ___________ %(round off to one decimal place).
Answer: (11 to 14)
53. Surface tension of liquid A in a capillary is being measured in the laboratory using capillary rise (refer the figure given below). The capillary radius (r) is 100 μm, the height of liquid column (h) is 10 cm and Ө = 38°. Density of air can be neglected. Assume liquid A to have the same density as water.
Surface tension of liquid A at room temperature is ___________dynes/cm (round off to one decimal place).
Answer: (61 to 65)
54. Miscible displacement process is one of the EOR techniques. The performance of this process depends on fluid physical properties that affect flow behavior in a reservoir. Two of the important properties are density and viscosity. Consider the use of CO2 for one such process. The density of CO2 at the reservoir condition is ____________ lb/ft3 (round off to one decimal place).
Relevant data for this calculation are given below.
Reservoir temperature = 300 °F (422 K)
Reservoir pressure = 1470 psig (100 atm)
Compressibility factor (z) at the reservoir condition = 0.5
Values of Universal Gas Constant (R) in different units are listed below.
Universal Gas Constant (R) = 8.314 m3.Pa.K−1mol−1
= 10.731 psi. ft3.lb. mol−1 °R−1
= 0.082 L. atm. K−1 mol−1
Answer: (15.7 to 16.1)
55. In a counter current heat exchanger, the hot fluid enters at 175 °F and exits at 100 ° The cold fluid enters at 75 °F and exits at 85 °F. For the calculation of heat transfer rate, consider the tube surface area (per unit length) to be 0.26 ft2/ft and a tube length of 40 ft. The overall heat transfer coefficient of the exchanger is 100 BTU/hr-ft2. The minimum number of tubes required in the exchanger for a heat duty of 15 × 105 BTU/hr is____________ (round off to nearest integer).
Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. Five persons P, Q, R, S and T are to be seated in a row, all facing the same direction, but not necessarily in the same order. P and T cannot be seated at either end of the row. P should not be seated adjacent to S. R is to be seated at the second position from the left end of the row. The number of distinct seating arrangements possible is:
(A) 2
(B) 3
(C) 4
(D) 5
Answer: (B)
2. Consider the following sentences:
(i) The number of candidates who appear for the GATE examination is staggering.
(ii) A number of candidates from my class are appearing for the GATE examination.
(iii) The number of candidates who appear for the GATE examination are staggering.
(iv) A number of candidates from my class is appearing for the GATE examination.
Which of the above sentences are grammatically CORRECT?
(A) (i) and (ii)
(B) (i) and (iii)
(C) (ii) and (iii)
(D) (ii) and (iv)
Answer: (A)
3. A digital watch X beeps every 30 seconds while watch Y beeps every 32 seconds. They beeped together at 10 AM.
(A) 10.08 AM
(B) 10.42 AM
(C) 11.00 AM
(D) 10.00 PM
Answer: (A)
4. If ⊕÷⊙= 2 ; ⊕÷ Δ = 3; ⊙ +Δ = 5; Δ ×⊗ =10,
Then, the value of (⊗ − ⊕)2, is:
(A) 0
(B) 1
(C) 4
(D) 16
Answer: (B)
5. The front door of Mr. X’s house faces East. Mr. X leaves the house, walking 50 m straight from the back door that is situated directly opposite to the front door. He then turns to his right, walks for another 50 m and stops. The direction of the point Mr. X is now located at with respect to the starting point is ______
(A) South-East
(B) North-East
(C) West
(D) North-West
Answer: (D)
Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).
6. Given below are two statements 1 and 2, and two conclusions I and II.
Statement 1: All entrepreneurs are wealthy.
Statement 2: All wealthy are risk seekers.
Conclusion I: All risk seekers are wealthy.
Conclusion II: Only some entrepreneurs are risk seekers.
Based on the above statements and conclusions, which one of the following options is CORRECT?
(A) Only conclusion I is correct
(B) Only conclusion II is correct
(C) Neither conclusion I nor II is correct
(D) Both conclusions I and II are correct
Answer: (C)
7. A box contains 15 blue balls and 45 black balls. If 2 balls are selected randomly, without replacement, the probability of an outcome in which the first selected is a blue ball and the second selected is a black ball, is _____
(A) 3/16
(B) 45/236
(C) 1/4
(D) 3/4
Answer: (B)
8.
The ratio of the area of the inscribed circle to the area of the circumscribed circle of an equilateral triangle is____
(A) 1/8
(B) 1/6
(C) 1/4
(D) 1/2
Answer: (C)
9. Consider a square sheet of side 1 unit. The sheet is first folded along the main diagonal. This is followed by a fold along its line of symmetry. The resulting folded shape is again folded along its line of symmetry. The area of each face of the final folded shape, in square units, equal to _______
(A) 1/4
(B) 1/8
(C) 1/16
(D) 1/32
Answer: (B)
10. The world is going through the worst pandemic in the past hundred years. The air travel industry is facing a crisis, as the resulting quarantine requirement for travelers led to weak demand.
In relation to the first sentence above, what does the second sentence do?
(A) Restates an idea from the first sentence.
(B) Second sentence entirely contradicts the first sentence.
(C) The two statements are unrelated.
(D) States an effect of the first sentence.
Answer: (D)
Metallurgical Engineering (MT)
Q.1 – Q.13 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).
1. For the matrix given below, the eigenvalues are:
(A) 0, 2, 2
(B) 1, 1, 2
(C) 0, 1, 2
(D) 0, 1, 3
Answer: (C)
2. Which one of the following is a homogeneous function of degree three?
(A) x3 + 2x2y2
(B) y2x + 2yx2
(C) y3 + 2x2
(D) xy2 + 3xy
Answer: (B)
3. The divergence of a vector field where its three components (Vx, Vy, Vz) are functions of x, y, z, is:
Answer: (A)
4. Which one of the following is ‘center split’ defect in rolling operation?
Answer: (D)
5. Single crystal turbine blades of nickel-based superalloys for aero-engines are manufactured using:
(A) Investment casting
(B) Die casting
(C) Squeeze casting
(D) Directional solidification
Answer: (D)
6. Elements A and B have the same crystal structure. For a dilute solution of B in A, which one of the following is true?
(Given: ∆Hmix – Mixing enthalpy, aB – Activity of B and XB – Mole fraction of B)
(A) If ∆Hmix = 0, then aB < XB
(B) If ∆Hmix = 0, then aB > XB
(C) If ∆Hmix > 0, then aB < XB
(D) If ∆Hmix < 0, then aB < XB
Answer: (D)
7. For uniaxial tensile stress-strain behaviour of polycrystalline aluminium, which one of the following statements is FALSE?
(A) True stress is always higher than the engineering stress.
(B) At the ultimate tensile stress point on the true stress – strain curve,
(C) Resilience is the area under the elastic region of the engineering stress – strain curve.
(D) Maximum true stress does not correspond to the maximum load.
Answer: (B)
8. Which one of the following is FALSE for creep deformation?
(A) The minimum creep rate is obtained in the primary stage (stage I).
(B) Creep resistance decreases with decrease in grain size.
(C) Coble creep occurs via grain boundary diffusion.
(D) Nabarro-Herring creep occurs via lattice diffusion.
Answer: (A)
9. Which one of the following elements alloyed with iron is a ferrite stabilizer?
(A) Nickel
(B) Manganese
(C) Carbon
(D) Silicon
Answer: (D)
10. Which one of the following is the correct decreasing sequence of Quenching Power for quenchants used in heat treatment of steels?
(A) Oil > Water > Brine > Air
(B) Brine > Oil > Water > Air
(C) Brine > Water > Oil > Air
(D) Water > Brine > Oil > Air
Answer: (C)
11. For a zeroth order chemical reaction, which one of the following is FALSE?
(A) Concentration versus time plot is a straight line.
(B) Increase in concentration of reacting species increases the rate of reaction.
(C) Half-life depends on the initial concentration and zero-order rate constant.
(D) Rate of reaction depends on temperature.
Answer: (B)
12. Which one of the following elements oxidizes first in basic oxygen steel making process?
(A) Silicon
(B) Carbon
(C) Manganese
(D) Phosphorus
Answer: (A)
13. Which one of the following is a hydrometallurgical operation?
(A) Roasting
(B) Leaching
(C) Zone refining
(D) Smelting
Answer: (B)
Q.14 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).
14. The value of is: ____________ (round off to nearest integer).
Answer: (25 to 25)
15. The grain size (X) of annealed specimens follows a symmetric distribution with a mean (μ) of 5 μm and a standard deviation (σ) of 0.5 μm. The percentage of specimens with grain size in the range 5 to 6 μm is expected to be: __________ (round off to nearest integer).
Given: For the symmetric distribution: Probability P(X ≤ μ + 2σ) = 0. 98
Answer: (48 to 48)
16. If the value of (in J mol−1) at 298 K is: ________ (round off to nearest integer).
Given: F = 96500 C mol−1
Answer: (-48251 to -48240)
17. Melting point of Cu is 1358 K and its enthalpy of melting is 13400 J mol−1The value of free energy change (in J mol−1) for liquid to solid transformation at 1058 K is: _____________ (round off to nearest integer).
Answer: (-2962 to -2958)
18. A body is subjected to a state of stress given by the following stress tensor:
If yielding is predicted by the Tresca Criterion, the uniaxial tensile yield stress (in MPa) of the body should be less than or equal to: ___________ (round off to nearest integer).
Answer: (150 to 150)
19. Consider homogeneous nucleation of a spherical solid in liquid. For a given undercooling, if surface energy of a nucleus increases by 20 %, the corresponding increase (in percent) in the critical radius of the nucleus is: ________ (round off to nearest integer).
Answer: (20 to 20)
20. If saturation magnetization of iron at room temperature is 1700 kA m-1, the magnetic moment (in A m2) per iron atom in the crystal is: _______ × 10−23 (round off to 1 decimal place).
(Given: Lattice parameter of iron at room temperature = 0.287 nm)
Answer: (1.7 to 2.3)
21. In the X-ray diffraction pattern of a FCC crystal, the first reflection occurs at a Bragg angle (θ) of 30°. The Bragg angle (in degree) for the second reflection will be: __________ (round off to 1 decimal place).
Answer: (34.8 to 36.1)
22. A 0.6 wt.% C steel sample is slowly cooled from 900°C to room temperature. The fraction of proeutectoid ferrite in the microstructure is: ___________ (round off to 2 decimal places).
Given: Eutectoid composition: 0.8 wt.% C
Maximum solubility of carbon in α-Fe: 0.025 wt.% C
Answer: (0.22 to 0.30)
23. If the degree of polymerization of polyethylene is 30000, the average molecular weight (in g mol−1) is: _____________ (round off to nearest integer).
(Given: Atomic weights of carbon and hydrogen are 12 and 1, respectively)
Answer: (840000 to 840000)
24. Water flows over a plate of finite length. At x = x1 from the leading edge, the velocity of the flow is Vx = 0. 5y – 0. 5y3. The thickness, δ (in meter) of the boundary layer at x = x1 is: _________ (round off to 2 decimal places).
Given: V∞ is the free stream velocity.
Answer: (0.53 to 0.59)
25. The vacancy concentration in a crystal doubles upon increasing the temperature from 27 °C to 127 ° The enthalpy (in kJ mol−1) of vacancy formation is: ________ (round off to 2 decimal places).
Given: R = 8.314 J mol−1 K−1
Answer: (6.85 to 7.00)
Q.26 – Q.36 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).
26. The minimum value of y for the equation y = x2 − 2x + 4 is ______.
(A) 3
(B) 1
(C) 4
(D) 6
Answer: (A)
27. Match the forming process (in Column I) with its name (in Column II):
(A) P−1, Q−2, R−3, S−4
(B) P−3, Q−1, R−4, S−2
(C) P−3, Q−4, R−1, S−2
(D) P−1, Q−4, R−3, S−2
Answer: (B)
28. Match the nondestructive technique (in Column I) with its underlying phenomenon (in Column II):
(A) P−4, Q−3, R−2, S−1
(B) P−2, Q−1, R−3, S−4
(C) P−2, Q−1, R−4, S−3
(D) P−3, Q−2, R−1, S−4
Answer: (C)
29. Number of degrees of freedom for the following reacting system is: M (s) + CO2 (g) = MO (s) + CO (g)
(A) 0
(B) 1
(C) 2
(D) 3
Answer: (C)
30. The condition for getting the binary phase diagram of A-B (shown below) is:
Answer: (B)
31. In the absence of any external stress, which one of the following statements related to the interaction of point defect and a dislocation is FALSE:
(A) An oversized solute atom would preferentially migrate below the slip plane of an edge dislocation.
(B) A spherically symmetric point defect can interact with both the hydrostatic and shear stress fields of a dislocation.
(C) A point defect can locally modify the elastic modulus and thereby can change the interaction energy.
(D) Vacancies are attracted towards the compressive region of dislocation.
Answer: (B)
32. A single crystal aluminium sample is subjected to uniaxial tension along [112] direction. If the applied tensile stress is 100 MPa and the critical resolved shear stress (CRSS) is 25 MPa, which one of the following slip systems will be activated?
Answer: (A)
33. One-dimensional steady-state temperature distribution in two adjacent refractory blocks (with thermal conductivities, k1 and k2) of unit cross-sectional area are shown below. The temperature T1 and thermal contact resistance of the interface, respectively, are:
(A) 200 K, 0.5 K W−1
(B) 400 K, 1.0 K W−1
(C) 200 K, 0.25 K W−1
(D) 500 K, 0.5 K W−1
Answer: (A)
34. For a fully developed 1-D flow of a Newtonian fluid through a horizontal pipe of radius R (see figure), the axial velocity (vz) is given by:
where, ∆P is the pressure difference (P1 –P2), μ is the viscosity, r is the radial distance from the axis and L is the length of the tube. The shear stress exerted by the fluid on the tube wall is:
(A) ∆PR/2L
(B) ∆PR/L
(C) 3∆PR/2L
(D) 2∆PR/L
Answer: (A)
35. Match the terms (in Column I) with the unit process (in Column II)
(A) P−2, Q−1, R−4, S−3
(B) P−4, Q−1, R−2, S−3
(C) P−4, Q−3, R−1, S−2
(D) P−2, Q−3, R−4, S−1
Answer: (A)
36. A blast furnace uses hematite ore with 80% Fe2O3 and 20% gangue materials. It uses 600 kg coke per ton of hot metal. The coke contains 85% C and 15% ash. The composition of hot metal is 95.5% Fe and 4.5% C.
The weight of iron ore used and slag produced per ton of hot metal respectively, are:
Given: Atomic weight: O = 16, C = 12, N = 14, Fe = 56
All the compositions are in wt.%.
1 ton = 1000 kg
Assume that the gangue materials of the ore and ash content of coke form slag while Fe2O3 in the ore is consumed in making hot metal.
(A) 1705 kg, 431 kg
(B) 2131 kg, 546 kg
(C) 1705 kg, 331 kg
(D) 1500 kg, 431 kg
Answer: (A)
Q.37 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).
37. Consider the function f(x) = x − cos x. Using Newton-Raphson method, the estimated root of f(x) after the first iteration is: ______ (round off to 3 decimal places).
Assume: Initial guess of the root = 0.5 radians.
Answer: (0.745 to 0.770)
38. The work done by a force along a straight line from point (0, 0) to (1, 2) is: ____________ (round off to nearest integer).
Answer: (7 to 7)
39. A coin is tossed three times. Given that there are more heads than tails, the probability of getting exactly one tail is: ___________ (round off to 2 decimal places).
Answer: (0.75 to 0.75)
40. A continuous fillet weld is made using a 3000 W welding machine. At a travel speed of 6 mm s−1, the cross-sectional area (in mm2) of the weld is: _________ (round off to nearest integer).
Given: The unit energy required to melt the metal is 6 J mm−3
Heat transfer factor = 0.6
Melting factor = 0.5
Answer: (25 to 25)
41. Liquid iron is cast into a spherical sand mold (6 cm radius) and a cubical sand mold (12 cm edge length). If solidification time is 60 minutes in the spherical casting, the time (in minutes) required to solidify in the cubical casting is: ____________ (round off to nearest integer).
Answer: (58 to 62)
42. True strain for 60% height reduction of a sample subjected to hot forging is: ___________ (round off to 2 decimal places).
Answer: (0.90 to 0.94 OR -0.94 to -0.90)
43. For the equilibrium reaction: 2Cu (s) + SO2(g) = Cu2S (s) + O2 (g), the value of ln at 973 K is: ________ (round off to 2 decimal places).
Given: 2Cu (s) + 0. 5S2(g) = Cu2S (s) ΔG° at 973 K = −100 kJ
SO2(g) = 0. 5S2(g) + O2(g) ΔG° at 973 K = 292 kJ
R = 8.314 J mol−1 K−1
Assume: Cu and Cu2S are pure solids.
Answer: (-24.00 to -23.50)
44. One mole of an ideal gas at 10 atm. and 300 K undergoes reversible adiabatic expansion to a pressure of one atm. The work done (in Joule) by the gas is: ________ (round off to nearest integer).
45. The figure shows the entropy versus temperature (S-T) plot of a reversible cycle of an engine. If T1 = 200 K and T2 = 600 K, the efficiency of the engine (in percent) is: ___________ (round off to 2 decimal places).
Answer: (63.00 to 71.00)
46. Two dislocation lines parallel to z-axis lying in the x-z plane are shown in the figure. The glide force (in Newton) exerted by the edge dislocation on the screw dislocation is: __________ (round off to nearest integer)
For the edge, the shear stress component is given by:
Given:Shear modulus, G = 28 GPa
Poisson’s ratio, v = 0.3
Burgers vector, b = 0.29 nm
Distance between the two dislocations = 0.5 nm
Answer: (0 to 0)
47. In a material, a shear stress of 100 MPa is required to bow a dislocation line between precipitates with a spacing of 0.2 μm. If the spacing between the precipitates is increased to 0.5 μm, the shear stress (in MPa) to bow the dislocation would be: _________ (round off to nearest integer).
Answer: (40 to 40)
48. A metal plate is in a state of plane strain (εzz = 0) with σxx = σyy ≠ 0 and τxy = τxz = τyz = 0. If the Poisson’s ratio is 0.3, the ratio, σzz/ σxx is ___________ (round off to 1 decimal place).
Answer: (0.6 to 0.6)
49. An infinite metal plate has a central through-thickness crack of length 80/π The maximum applied stress (in MPa) that the plate can sustain in mode I is: _________ (round off to nearest integer).
Assume: Linear elastic fracture mechanics is valid
Given: Fracture toughness, KIC= 20 MPa m1/2
Answer: (98 to 102)
50. A hypothetical binary eutectic phase diagram of A – B is shown below. An alloy with 5 wt.% B solidifies with no convection. Assuming steady state, the critical temperature gradient (in K mm−1) required to maintain planar solidification front is: ___________ (round off to nearest integer).
Given: Diffusivity of B in liquid = 10−9 m2s−1
Velocity of solidification front = 4 μm s−1
Answer: (298 to 302)
51. A thick steel plate containing 0.1 wt.% C is carburized at 950 ° The plate’s surface carbon concentration is maintained at 1.1 wt.% C. After 9 hours, the depth (in mm) below the surface at which the carbon concentration is 0.6 wt.% C will be: _________ (round off to 2 decimal places).
Given: Diffusivity of carbon in γ-Fe at 950 °C = 1.6 x 10−11 m2s−1
Error function table:
Answer: (0.65 to 0.75)
52. At 25 °C, iron corrodes in a deaerated acid of pH 3 with a corrosion current density of 4 μA cm−2 . The corrosion potential (V) is: ________ (round off to 2 decimal places).
Given: βc = 0.1 V per decade of current density
Exchange current density of hydrogen on iron surface = 10−9 A cm−2
R = 8.314 J mol-1 K−1, F = 96500 C mol−1
All potentials are with reference to standard hydrogen electrode.
Answer: (-0.60 to -0.50)
53. The radius of an interstitial atom which just fits (without distorting the structure) inside an octahedral void of a bcc-iron crystal (in nm) is: ________ (round off to 3 decimal places).
Assume the radius of Fe atom to be 0.124 nm.
Answer: (0.017 to 0.023)
54. Nickel undergoes isothermal oxidation at 800 K for a duration of 400 s resulting in a weight gain of 2 mg cm−2. The weight gain (mg cm−2) after a duration of 1600 s is: __________ (round off to nearest integer).
Assume: Weight gain is proportional to square root of time.
Answer: (4 to 4)
55. A solid sphere (0.5 m radius) is enclosed within a larger hollow sphere (1 m radius), as shown in figure. The radiation exchange takes place between the outer surface (surface 1) of the small sphere and the inner surface (surface 2) of the bigger sphere. The value of the view factor, F22 is: _________ (round off to 2 decimal places).
Given: View factor (Fij) is the fraction of the radiation leaving surface i that is intercepted by surface j.