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)
3. Both the numerator and the denominator of 3/4 are increased by a positive integer, x, and those of 15/17 are decreased by the same integer. This operation results in the same value for both the fractions.
What is the value of x ?
(A) 1
(B) 2
(C) 3
(D) 4
Answer: (C)
4. A survey of 450 students about their subjects of interest resulted in the following outcome.
• 150 students are interested in Mathematics.
• 200 students are interested in Physics.
•175 students are interested in Chemistry.
• 50 students are interested in Mathematics and Physics.
• 60 students are interested in Physics and Chemistry.
• 40 students are interested in Mathematics and Chemistry.
• 30 students are interested in Mathematics, Physics and Chemistry.
• Remaining students are interested in Humanities.
Based on the above information, the number of students interested in Humanities is
(A) 10
(B) 30
(C) 40
(D) 45
Answer: (D)
5.
For the picture shown above, which one of the following is the correct picture representing reflection with respect to the mirror shown as the dotted line?
Answer: (A)
Q.6 – Q.10 Carry TWO marks each.
6. In the last few years, several new shopping malls were opened in the city. The total number of visitors in the malls is impressive. However, the total revenue generated through sales in the shops in these malls is generally low.
Which one of the following is the CORRECT logical inference based on the information in the above passage?
(A) Fewer people are visiting the malls but spending more
(B) More people are visiting the malls but not spending enough
(C) More people are visiting the malls and spending more
(D) Fewer people are visiting the malls and not spending enough
Answer: (B)
7. In a partnership business the monthly investment by three friends for the first six months is in the ratio 3: 4: 5. After six months, they had to increase their monthly investments by 10%, 15% and 20%, respectively, of their initial monthly investment. The new investment ratio was kept constant for the next six months.
What is the ratio of their shares in the total profit (in the same order) at the end of the year such that the share is proportional to their individual total investment over the year?
(A) 22 : 23 : 24
(B) 22 : 33 : 50
(C) 33 : 46 : 60
(D) 63 : 86 : 110
Answer: (D)
8. Consider the following equations of straight lines:
Line L1: 2x– 3y = 5
Line L2: 3x + 2y = 8
Line L3: 4x– 6y = 5
Line L4: 6x– 9y = 6
Which one among the following is the correct statement?
(A) L1 is parallel to L2 and L1 is perpendicular to L3
(B) L2 is parallel to L4 and L2 is perpendicular to L1
(C) L3 is perpendicular to L4 and L3 is parallel to L2
(D) L4 is perpendicular to L2 and L4 is parallel to L3
Answer: (D)
9. Given below are two statements and four conclusions drawn based on the statements.
Statement 1: Some soaps are clean.
Statement 2: All clean objects are wet.
Conclusion I: Some clean objects are soaps.
Conclusion II: No clean object is a soap.
Conclusion III: Some wet objects are soaps.
Conclusion IV: All wet objects are soaps.
Which one of the following options can be logically inferred?
(A) Only conclusion I is correct
(B) Either conclusion I or conclusion II is correct
(C) Either conclusion III or conclusion IV is correct
(D) Only conclusion I and conclusion III are correct
Answer: (D)
10. An ant walks in a straight line on a plane leaving behind a trace of its movement. The initial position of the ant is at point P facing east.
The ant first turns 72° anticlockwise at P, and then does the following two steps in sequence exactly FIVE times before halting.
(1) moves forward for 10 cm.
(2) turns 144o clockwise.
The pattern made by the trace left behind by the ant is
Answer: (C)
Chemistry (XL-P)
Q.11 – Q.19 Carry ONE mark Each
11. Consider a second order reaction, 2A ⟶ Product
The concentration of A is represented as [A].
Which of the following is the CORRECT plot for determining the rate constant for the above reaction?
Answer: (C)
12. Which among the following has the least second ionization energy?
(A) Al
(B) Si
(C) P
(D) S
Answer: (B)
13. Which among the following metal ions has the highest enthalpy of hydration?
(Assume the given metal ions have the same counter ion.)
Given: Atomic numbers of Ti, V, Cr and Mn are 22, 23, 24 and 25, respectively.
(A) Ti2+
(B) V2+
(C) Cr2+
(D) Mn2+
Answer: (B)
14. Among the following, the one having smallest bond angle is
(A) PH3
(B) PF3
(C) NF3
(D) NH3
Answer: (A)
15. Which of the following is the CORRECT statement about hexoses?
(A) D-mannose is C- 4 epimer of D-glucose
(B) D-galactose is C- 2 epimer of D-glucose
(C) D-glucose and L-glucose are diastereomers
(D) D-glucose and D-galactose are diastereomers
Answer: (D)
16. The bases present in DNA are
(A) adenine, cytosine, guanine and thymine
(B) adenine, guanine, thymine and uracil
(C) adenine, cytosine, thymine and uracil
(D) cytosine, guanine, thymine and uracil
Answer: (A)
17. The CORRECT order of basicity for the following compounds is
(A) I > II > III
(B) II > III > I
(C) II > I > III
(D) III > I > II
Answer: (C)
18. Molar conductance of monobromoacetic acid at infinite dilution is calculated to be x × 10−4 S m2 mol−1 at 25°
The value of x is (round off to the nearest integer)
Given:
(A) 164
(B) 195
(C) 389
(D) 467
Answer: (C)
19. A sample of benzene, contaminated with a non-volatile and non-ionic solute, boils at 0.31°C higher than that of pure benzene. The molality of the solute in the contaminated solution is ______ (round off to two decimal places).
Given: Gas constant = 8.314 J K−1 mol−1
Molecular weight of benzene is 78.11 g mol−1
Normal boiling point of benzene is 80.1°C
Enthalpy of vaporization of benzene is 30.76 kJ mol−1
Answer: (0.11 to 0.13)
Q.20 – Q.27 Carry TWO marks Each
20. Among the following statements about cobalt complexes, which is/are CORRECT?
Given: Atomic number of Co is 27
(A) [Co(NH3)4]2+ exhibits square planar geometry
(B) [Co(en)3]3+ does not show optical isomerism (en = ethylenediamine)
(C) [Co(H2O)6]3+ is paramagnetic in nature
(D) [Co(NH3)5Cl)]2+ shows ligand-to-metal charge transfer
Answer: (D)
21. Consider the following reaction:
The CORRECT statement(s) related to mono-chlorination at carbon-2 position is/are
(A) The reaction proceeds through alkyl radical intermediate
(B) Complete inversion of configuration at carbon-2 takes place
(C) Complete retention of configuration at carbon-2 takes place
(D) A mixture of enantiomers is formed
Answer: (A, D)
22. Consider the following enzyme catalyzed reaction:
where E is enzyme, S is substrate, ES is enzyme-substrate complex and P is product.
The CORRECT statement(s) for the above reaction is/are
(A) Maximum possible rate of product formation is dependent on k2 and initial concentration of enzyme.
(B) For a low substrate concentration, the rate of product formation is first order with respect to enzyme and also first order with respect to the substrate.
(C) The rate of product formation is independent of the concentration of enzyme substrate complex.
(D) For a very high substrate concentration, initial rate of product formation is zero order with respect to the substrate.
Answer: (A, B, D)
23. Consider the following reaction:
The CORRECT pathway(s) involved in the reaction is/are
(A) E2 followed by isomerization
(B) E1 followed by isomerization
(C) SN1 followed by isomerization
(D) Isomerization through carbocation
Answer: (B, D)
24. An aqueous solution of aspirin (HA) is prepared at pH 7.4. The ratio of concentration of A− and HA at equilibrium is ______ (round off to the nearest integer).
Given: Ka of aspirin is 3.98 × 10–4
Answer: (9700 to 10000)
25. The total number of 3-centre-2-electron bonds in B4H10 is ______ (in integer).
Answer: (4 to 4)
26. The equilibrium constant for isomerization of 1-butene to trans-2-butene at 27°C is ______ (round off to one decimal place).
Given: Gas constant = 8.314 J K−1 mol−1
∆fG° of 1-butene = +71.39 kJ mol−1
∆fG° of trans-2-butene = + 63.06 kJ mol−1
Answer: (28.2 to 28.3)
27. A 16 mW monochromatic light emits 4×1016 photons in 1 second. When this light incidents on a metal strip, photoelectrons are emitted. The wavelength of the emitted photoelectrons (in Å) is ______ (round off to one decimal place).
Given: Work function of the metal = 2.0 eV
Charge of an electron = 1.6 × 10−19 C
Mass of an electron = 9.1 × 10−31 kg
Planck’s constant = 6.626 × 10−34J s
Answer: (17.3 to 17.5)
Biochemistry XL (Q)
Q.28 – Q.35 Carry ONE mark Each
28. Which of the immune cells listed below are agranular?
(P) Eosinophils
(Q) Mast cells
(R) Monocytes
(S) T-cells
(A) P and Q only
(B) Q and R only
(C) R and S only
(D) S and P only
Answer: (C)
29. Which one of the following enzymes is located in the outer mitochondrial membrane?
(A) Citrate synthase
(B) Fumarase
(C) Monoamine oxidase
(D) Succinate dehydrogenase
Answer: (C)
30. Which one of the following statements about the DNA polymerase III of E. coli is NOT correct?
(A) It catalyzes nick translation.
(B) Its absence is lethal to E. coli.
(C) It synthesizes a complementary DNA strand using a single-stranded template.
(D) It possesses 3′ → 5′ exonuclease activity.
Answer: (A)
31. Which one of the following compounds is NOT a translation inhibitor?
(A) Chloramphenicol
(B) Cycloheximide
(C) Puromycin
(D) Rifampicin
Answer: (D)
32. A dye was allowed to undergo migration on a chromatographic paper using a solvent. The dye, and the solvent-front migrated 5 and 20 cm, respectively, from the point of origin. The retention factor (rounded off to two places of decimals) for the dye is _____.
Answer: (0.25 to 0.25)
33. The pKa values of the carboxylic and amino groups of an amino acid with a non-ionizable side chain are 2.17 and 9.13, respectively. The isoelectric point (rounded off to two places of decimals) of this amino acid is _____.
Answer: (5.65 to 5.65)
34. The number of ATP molecules required for the complete assimilation of one molecule of CO2 in Calvin cycle is _____.
Answer: (3 to 3)
35. The absorbance of a 5 × 10−4 M solution of tyrosine at 280 nm wavelength is 0.75. The path length of the cuvette is 1 cm. The molar absorption coefficient at the given wavelength in M−1 cm−1, correct to the nearest integer, is _____.
Answer: (1500 to 1500)
Q.36 – Q.46 Carry TWO marks Each
36. Filamentous photosynthetic algae were placed on a microscopic slide and illuminated with light of different colors as illustrated.
The bacteria that are known to migrate towards the region of high O2 were also added uniformly on the slide. Which one of the following options illustrates the distribution of bacteria along the length of the microscopic slide after illumination?
Answer: (A)
37. Two RNAs shown below were used separately as templates in an in vitro translation system, which can generate proteins in all possible reading frames.
RNA1 : 5′ − (AG)n − 3′
RNA2: 5′ − (AAG)n − 3′
The RNA1 translated product contained Arg and Glu.
The RNA2 translated product contained Arg, Glu, and Lys.
Which one of the following codons directs the incorporation of Arg?
(A) AAG
(B) AGA
(C) GAA
(D) GAG
Answer: (B)
38. Which of the following statements about endogenous synthesis of insulin are correct?
(P) Insulin is synthesized as preproinsulin.
(Q) Preproinsulin is converted to proinsulin.
(R) Single-site cleavage of proinsulin eliminates C chain.
(S) Mature insulin consists of disulphide-linked A and B chains.
(A) P, Q, and R
(B) P, Q, and S
(C) P, R, and S
(D) Q, R, and S
Answer: (B)
39. Which one of the following enzymes converts testosterone to estradiol?
(A) Aromatase
(B) 3β-hydroxysteroid dehydrogenase
(C) 5α-reductase
(D) 17β-hydroxysteroid dehydrogenase
Answer: (A)
40. Purification of 6×His-tagged protein using Ni-NTA column is an example of ________
(A) affinity chromatography
(B) hydrophobic-interaction chromatography
(C) ion-exchange chromatography
(D) size-exclusion chromatography
Answer: (A)
41. Which of the following carbohydrates has/have a β1 → 4 glycosidic linkage?
(A) Cellulose
(B) Chitin
(C) Lactose
(D) Maltose
Answer: (A, B, C)
42. Which of the following statements about IgA is/are correct?
(A) It is secreted into colostrum.
(B) It is transported across the cell by transcytosis.
(C) Its secretion is facilitated by poly-Ig receptor.
(D) It primarily exists as a dimer in serum.
Answer: (A, B, C)
43. The standard free energy changes for conversion of phosphoenol pyruvate (PEP) to pyruvate, and ATP synthesis are shown below.
PEP + H2O ⇌ pyruvate + Pi ∆G′° = −61.9 kJ ∙ mol−1
ADP + Pi⇌ ATP + H2O ∆G′° = 30.5 kJ ∙ mol−1
The starting concentrations of PEP, ADP, pyruvate, and ATP are 25, 25, 50,
and 50 mM, respectively. The value of universal gas constant (R) is 8.314 J ∙ mol−1 K−1. The actual free energy change in kJ ∙ mol−1 for the reaction
PEP + ADP ⟶ pyruvate + ATP
carried out at 37°C will be ______ (rounded off to one place of decimal).
Answer: (-28.1 to -27.8)
44. The dissociation constant for a receptor-ligand pair is 0.25 × 10−7The ligand was added to a solution of the receptor such that the receptor was 50% saturated at equilibrium. Assume that the receptor has one ligand binding site. The concentration of the free ligand at equilibrium in nM, correct to the nearest integer, should be _____
Answer: (25 to 25)
45. The half-maximal velocity of an enzyme catalyzed reaction was found at a substrate concentration of 0.5 × 10−6 This enzyme follows Michaelis-Menten kinetics. In the presence of a competitive inhibitor, the half-maximal velocity was found at a substrate concentration of 1.5 × 10−6 M. Given that the enzyme-inhibitor pair has a dissociation constant of 2 × 10−7 M, the concentration of the competitive inhibitor in μM, rounded off to one place of decimal, was_____.
Answer: (0.4 to 0.4)
46. A forty-times diluted sample of ssRNA gave an A260 of 0.01. The concentration of the ssRNA before the dilution in μg/mL was _____ (correct to the nearest integer).
Answer: (16 to 16)
Botany XL (R)
Q.47 – Q.54 Carry ONE mark Each
47. In Angiosperms, normally ‘Exarch Xylem’ occurs in
(A) dicot stem
(B) monocot stem
(C) dicot root
(D) dicot leaf
Answer: (C)
48. ‘Quiescent Center’ is present in
(A) leaf meristem
(B) root apical meristem
(C) shoot apical meristem
(D) floral meristem
Answer: (B)
49. With reference to virulence (vir) region of nopaline type Ti plasmid of Agrobacterium tumefaciens, match Group-I (vir gene) and Group-II (coded protein) in CORRECT combination.
(A) P-IV, Q-III, R-II, S-I
(B) P-IV, Q-III, R-I, S-II
(C) P-IV, Q-II, R-I, S-III
(D) P-I, Q-III, R-II, S-IV
Answer: (B)
50. Anomalous secondary growth is observed in
(A) Triticum
(B) Oryza
(C) Zea
(D) Dracaena
Answer: (D)
51. Which of the following plant diseases is/are caused by bacteria?
(A) Angular leaf spot of cotton
(B) Citrus canker
(C) Apple scab
(D) Leaf curl of papaya
Answer: (A, B)
52. Phylogenetic system of classification is/are proposed by
(A) Carolus Linnaeus
(B) John Hutchinson
(C) Engler and Prantl
(D) Bentham and Hooker
Answer: (B, C)
53. Which of the following is/are part of marine ecosystem?
(A) Open ocean
(B) Chaparral
(C) Deep sea
(D) Estuaries
Answer: (A, C, D)
54. In NADP+-malic enzyme type C4 photosynthesis cycle, n molecule(s) of ATP is/are required for the assimilation of one molecule of CO2. The value of n is ________ (in integer).
Answer: (5 to 5)
Q.55 – Q.65 Carry TWO marks Each
55. An Arabidopsis thaliana mutant plant developed defective flowers with altered floral organ identity and patterning. In this mutant, the four floral whorls contain Sepal-Sepal-Carpel-Carpel, from the periphery to the center of the flower.
Based on the typical ABC model of floral organ patterning, which among thefollowing are mutated in this plant?
(A) Class A gene(s)
(B) Class B gene(s)
(C) Class C gene(s)
(D) Double mutant for Class A and Class C genes
Answer: (B)
56. Match the secondary metabolites in Group-I with types of secondary metabolites in Group-II in CORRECT order.
(A) P-I, Q-V, R-II, S-IV, T-III
(B) P-V, Q-II, R-IV, S-I, T-III
(C) P-II, Q-III, R-IV, S-V, T-I
(D) P-V, Q-I, R-II, S-IV, T-III
Answer: (D)
57. Match Group-I (enzyme), Group-II (reaction catalyzed by the enzyme), and Group-III (subcellular localization of the enzyme and the associated metabolic process) in CORRECT combination.
(A)P-III-a, Q-IV-d, R-I-b, S-II-c
(B)P-II-a, Q-III-d, R-I-b, S-IV-c
(C) P-IV-a, Q-II-b, R-I-d, S-III-c
(D) P-IV-a, Q-II-d, R-I-b, S-III-c
Answer: (A)
58. Match Group-I (selection agent) and Group-II (gene) in CORRECT combination.
(A)P-III, Q-VI, R-II, S-I
(B) P-IV, Q-III, R-II, S-I
(C) P-I, Q-VI, R-III, S-II
(D) P-II, Q-I, R-V, S-VI
Answer: (A)
59. Match Group I (plant natural product), Group II (class) and Group III (source plant) in CORRECT combination.
(A) P-I-d, Q-II-c, R-IV-a, S-III-b
(B) P-III-d, Q-IV-b, R-I-c, S-II-a
(C) P-II-a, Q-III-b, R-I-d, S-IV-c
(D) P-III-d, Q-I-c, R-IV-b, S-II-a
Answer: (D)
60. Match Group I (plant disease), Group II (causal organism) and Group III (affected plant) in CORRECT combination.
(A) P-II-a, Q-V-b, R-III-d, S-I-e
(B) P-III-d, Q-V-c, R-II-e, S-IV-f
(C) P-III-d, Q-V-c, R-I-b, S-II-e
(D) P-V-c, Q-I-d, R-VI-b, S-II-e
Answer: (C)
61. Make CORRECT match between Group-I and Group-II, in relation to interaction between two species.
(A) P-I, Q-II, R-III, S-IV
(B) P-III, Q-II, R-IV, S-I
(C) P-IV, Q-III, R-II, S-I
(D) P-III, Q-IV, R-II, S-I
Answer: (C)
62. Which of the following matches is/are CORRECT?
(D) Non-drying oil – Castor oil – Ricinus communis
Answer: (A, D)
63. Which of the following is/are phanerogamic parasite(s)?
(A) Cuscuta reflexa
(B) Orobanche cernua
(C) Ocimum sanctum
(D) Santalum album
Answer: (A, B, D)
64. When a true breeding tall plant containing red flowers was crossed with the true breeding dwarf plant containing white flowers, all F1 plants were tall with red flowers. When the F1 plant was self-pollinated, considering independent assortment of plant height and flower colour traits, the calculated percentage probability of dwarf plants bearing red flowers in the F2 generation is ________ per cent (round off to 2 decimal places).
Answer: (18.75 to 18.75)
65. A hypothetical plant gene ADSH22 is encoded by the nuclear genome. The length of the mature mRNA for ADSH22 is 2150 nucleotides (nts). This mRNA has a 270 nts long 5′ UTR and 200 nts long 3′ UTR. Taking average molecular weight of an amino acid as 115 Dalton (Da), the calculated molecular weight of ADSH22 protein is ________ kDa (round off to 1 decimal place).
Answer: (64.2 to 64.3)
Microbiology XL (S)
Q.66 – Q.73 Carry ONE mark Each
66. The terminal acceptor of electron during anaerobic respiration in Methanococcus is ______________.
(A) Nitrate ion
(B) Sulfate ion
(C) Carbon dioxide
(D) Oxygen
Answer: (C)
67. Which one of the following mutagens convert DNA’s adenine to hypoxanthine?
(A) Ultraviolet light
(B) Mitomycin C
(C) Methyl methanesulfonate
(D) Nitrous acid
Answer: (D)
68. Which one of the following leukocytes are present in the largest proportion in healthy human blood?
(A) Neutrophils
(B) Eosinophils
(C) Basophiles
(D) Monocytes
Answer: (A)
69. The site of photosynthesis in cyanobacteria is ____________.
(A) Chloroplast
(B) Chromatophores
(C) Thylakoids
(D) Chlorosomes
Answer: (C)
70. The antimicrobial activity of vancomycin is due to the _________.
(A) inhibition of nucleic acid synthesis
(B) damage to the cytoplasmic membrane
(C) inhibition of cell wall synthesis
(D) regulation of DNA supercoiling
Answer: (C)
71. Phenolics act as disinfectant by ____________.
(A) rupturing plasma membrane followed by leakage of cellular contents
(B) bond formation between adjacent pyrimidine bases
(C) forming adduct with amino acid and unsaturated fatty acids
(D) alkylation of proteins
Answer: (A)
72. Which of the following methods are used for the identification of microorganisms?
(A) Nucleic acid hybridization
(B) Southern blotting
(C) 16s rRNA sequencing
(D) Percentage G-C content
Answer: (A, B, C)
73. Which of the following are present in Gram-negative bacteria?
(A) Lipopolysaccharide
(B) Teichoic acid
(C) Periplasm
(D) Endotoxin
Answer: (A, C, D)
Q.74 – Q.84 Carry TWO marks Each
74. Nonsense suppressor mutation is found in _________.
(A) rRNA
(B) tRNA
(C) start codon of mRNA
(D) stop codon of mRNA
Answer: (B)
75. Choose the correct match for structural components of bacteria to their function.
(A) (P)-(ii), (Q)-(iii), (R)-(i), (S)-(iv)
(B) (P)-(ii), (Q)-(i), (R)-(iii), (S)-(iv)
(C) (P)-(ii), (Q)-(i), (R)-(iv), (S)-(iii)
(D) (P)-(i), (Q)-(iv), (R)-(iii), (S)-(ii)
Answer: (B)
76. Match the pathogen with the appropriate disease.
(A) (P)-(ii), (Q)-(iii), (R)-(i), (S)-(iv)
(B) (P)-(ii), (Q)-(i), (R)-(iii), (S)-(iv)
(C) (P)-(i), (Q)-(iv), (R)-(ii), (S)-(iii)
(D) (P)-(i), (Q)-(iv), (R)-(iii), (S)-(ii)
Answer: (C)
77. Match the correct mode of cell division with respective bacteria.
Bacteria
(P) Streptomyces species
(Q) Rhodopseudomonas acidophila
(R) Bacillus subtilis
(S) Nocardia species
(A) (P)-(ii), (Q)-(iii), (R)-(i), (S)-(iv)
(B) (P)-(ii), (Q)-(i), (R)-(iii), (S)-(iv)
(C) (P)-(iv), (Q)-(ii), (R)-(i), (S)-(iii)
(D) (P)-(i), (Q)-(iv), (R)-(iii), (S)-(ii)
Answer: (C)
78. The correct sequence of overall biochemical reaction which expresses the process of denitrification is ____
Answer: (B)
79. Which of the following diseases are caused by family of DNA viruses?
(A) Hepatitis B
(B) Smallpox
(C) Influenza
(D) Rabies
Answer: (A, B)
80. Which of the following Gram-positive cocci are found in biofilm of dental plaque?
(A) Gonococcus
(B) Streptococcus mutans
(C) Streptococcus sobrinus
(D) Fusobacterium species
Answer: (B, C)
81. Which of the following statements are TRUE for archaea?
(A) Cell wall in archaea contains muramic acid and D-amino acid
(B) N-Formylmethionine is the first amino acid to initiate new polypeptide chainsynthesis in archaea
(C) Methionine is the first amino acid used during protein synthesis in archaea
(D) Membrane of archaea contains phytanyl rather than fatty acids
Answer: (C, D)
82. If the plasmid given below is digested with restriction enzymes HindIII and EcoRI, considering complete digestion, how many DNA fragments will be released?
Answer: (4 to 4)
83. Escherichia coli growing under favorable conditions doubles in every 20 minutes. If the initial number of Escherichia coli cells is 100, what will be the logarithmic number of cells at 17th generation? (Answer up to 1 decimal place)
Answer: (7.1 to 7.2)
84. What will be value of the Numerical Aperture (NA), if half aperture angle is 58° and oil immersed objective is used for the process of light microscopy? (Answer up to 1 decimal place)
Consider Sin 58° = 0.85 and refractive index of immersion oil used is = 1.50.
Answer: (1.2 to 1.3)
Zoology (XL-T)
Q.85 – Q.92 Carry ONE mark each
85. Which one of the following organic compounds is composed of only (i) a nitrogen containing base, (ii) a single five-carbon sugar, and (iii) a triphosphate?
(A) Nucleoside
(B) Nucleotide
(C) Base
(D) Nucleic acid
Answer: (B)
86. Which one of the following animals develops adaptive predator avoidance morphology because of the presence of high predator number in its habitat?
(A) Daphnia sp.
(B) Scaphiopus sp.
(C) Wolbachia sp.
(D) Rhodnius sp.
Answer: (A)
87. To which class of Drosophila developmental genes does fushi tarazu (ftz) belong?
(A) Gap genes
(B) Segment polarity genes
(C) Pair rule genes
(D) Maternal effect genes
Answer: (C)
88. The action of which class of enzyme inhibitors can be reversed by adding an excess of substrate?
(A) Uncompetitive inhibitors
(B) Competitive inhibitors
(C) Non-specific inhibitors
(D) Allosteric inhibitors
Answer: (B)
89. Mendel deduced the genetic principle of inheritance by experimenting on sweet pea plants. One of the experiments involved crossing plants with two contrasting characters, tall (dominant) and dwarf (recessive), which yielded all tall plants in the first generation. When the same genetic cross was independently repeated by a researcher, only short plants were obtained. Which one of the following can possibly explain the altered outcome?
(A) Tall plants were heterozygous
(B) An enhancer for the tall allele is present in the dwarf plant
(C) A suppressor for the tall allele is present in the dwarf plant
(D) Dwarf plants are homozygous
Answer: (C)
Q.90 – Q.92 Multiple Select Question (MSQ) carry ONE mark each (no negative marks)
90. Which of the following is/are responsible for reversible receptor-ligand interaction?
(A) Ionic interactions
(B) Hydrogen bonding
(C) Peptide bonding
(D) Hydrophobic interactions
Answer: (A, B, D)
91. In the human body, which of the following is/are involved in processing of a foreign antigen?
(A) B-cells
(B) Macrophages
(C) Red blood cells
(D) Platelets
Answer: (A, B)
92. Animals can be classified as ‘specialists’ or ‘generalists’ with respect to diet and habitat selection. Which of the following organism/s belong/s to the specialist category?
(A) Raccoon
(B) Panda
(C) Polar Bear
(D) Koala Bear
Answer: (B, C, D)
Q.93 – Q.103 Multiple Choice Questions (MCQ) carry TWO marks each (for each wrong answer: – 2/3)
93. Match the drug/chemicals listed in Column I with the developmental/physiological defects listed in Column II.
(A) P-(iii); Q-(iv); R-(ii); S-(i)
(B) P-(i); Q-(iv), R-(iii), S-(ii)
(C) P-(ii), Q-(iv), R-(iii), S-(i)
(D) P-(ii), Q-(iii), R-(iv), S-(i)
Answer: (A)
94. Match the animals listed in Column I with primary tissue or organ of residence in the host listed in Column II.
(A) P-(iii), Q-(iv), R-(ii), S-(i)
(B) P-(i), Q-(iv), R-(iii), S-(ii)
(C) P-(ii), Q-(iii), R-(iv), S-(i)
(D) P-(iii), Q-(i), R-(iv), S-(ii)
Answer: (D)
95. Match the cell types listed in Column I with their sources in Column II and the primary functional roles listed in Column III.
(A) P-(iii)-b, Q-(iv)-c, R-(ii)-a, S-(i)-d
(B) P-(ii)-c, Q-(iv)-d, R-(i)-a, S-(iii)-b
(C) P-(i)-a, Q-(iv)-b, R-(ii)-c, S-(iii)-d
(D) P-(iii)-c, Q-(iv)-b, R-(ii)-a, S-(i)-d
Answer: (D)
96. Match the ecological concepts listed in Column I with their definitions listed in Column II.
(A) P-(ii), Q-(iv), R-(i), S-(iii)
(B) P-(iv), Q-(iii), R-(i), S-(ii)
(C) P-(iii), Q-(iv), R-(i), S-(ii)
(D) P-(i), Q-(iv), R-(iii), S-(ii)
Answer: (B)
97. Match the hormones listed in Column I with their primary source tissues in Column II and the primary target tissues listed in Column III.
(A) P-(iii)-b, Q-(iv)-c, R-(ii)-a, S-(i)-d
(B) P-(iv)-c, Q-(iii)-b, R-(ii)-a, S-(i)-d
(C) P-(iv)-b, Q-(iii)-d, R-(ii)-c, S-(i)-a
(D) P-(iii)-b, Q-(iv)-c, R-(ii)-d, S-(i)-a
Answer: (C)
Q.98 – Q.100 Multiple Select Questions (MSQ) carry TWO marks each (no negative marks)
98. 2-Deoxyglucose (2-DG) inhibits the proliferation of cells and hence finds use as an anti-cancer agent. It is also used in COVID therapy, where it blocks hyperproliferation of virus-infected cells. Mechanistically, 2-DG blocks glycolysis by inhibiting the activities of which of the following enzyme/s?
(A) Hexokinase
(B) Glucose 6-phosphate isomerase
(C) Glucose-6 phosphate dehydrogenase
(D) Phosphofructokinase
Answer: (A, B)
99. According to Abbe’s equation on microscopy, the ability to resolve two entities inside a cell by light microscopy depends on which of the following factor/s?
(A) Magnification of the objective lens
(B) Intensity of incident light
(C) Wavelength
(D) Numerical aperture of the objective lens
Answer: (C, D)
100. Match the animal inactivity behaviors listed in Column I with representative animals in Column II and their definitions listed in Column III.
(A) P-(ii)-c, Q-(iv)-b, R-(i)-a, S-(iii)-d
(B) P-(iv)-c, Q-(iii)-d, R-(ii)-a, S-(i)-b
(C) P-(iv)-c, Q-(ii)-b, R-(i)-a, S-(iii)-d
(D) P-(iv)-b, Q-(i)-c, R-(ii)-d, S-(iii)-a
Answer: (B)
Q.101 – Q.103 Numerical Answer Type (NAT), carry TWO marks each (no negative marks).
101. If the vital capacity (VC) of an individual is 4900 ml, the tidal volume (TV) is 500 ml, and the inspiratory reserve volume (IRV) is 3300 ml, the expiratory reserve volume (ERV) of the individual is ________ml. (in integer).
Answer: (1100 to 1100)
102. A typical food chain involves producers, herbivores, primary carnivores and secondary carnivores. Based on Lindeman’s law of trophic efficiency, if producers have 40 kJ of energy, the energy that will be stored in secondary carnivores is _____ kJ. (round off to two decimal places)
Answer: (0.04 to 0.04)
103. The average body length of Drosophila nasuta collected from Andaman and Nicobar Islands is 2 mm. From this population, a few males and females having a body length of 3 mm were selected and interbred. The average body length of the resultant progeny was 2.5 mm. The heritability (h2) of the body length in this population is ______. (round off to one decimal place)
Answer: (0.5 to 0.5)
Food Technology XL (U)
Q.104 – Q.111 Carry ONE mark Each
104. Which among the given options truly depict the lines 1 and 2 in the figure below with respect to the effect of heat processing on food?
(A) 1-Safety, 2-Quality
(B) 1-Yield, 2-Safety
(C) 1-Yield, 2-Quality
(D) 1-Quality, 2-Safety
Answer: (A)
105. Homogenization of milk leads to disintegration of fat globules by
(A) Turbulence and pasteurization
(B) Pasteurization and cavitation
(C) Pasteurization and pressurization
(D) Turbulence and cavitation
Answer: (D)
106. The lowest water activity (aw) supporting the growth of Staphylococcusaureus in food under aerobic condition is
(A) 0.98
(B) 0.91
(C) 0.89
(D) 0.86
Answer: (D)
107. Cultures used in industrial production of yogurt are
(A) Lactococcus lactis subsp. lactis
(B) Streptococcus thermophilus
(C) Leuconostoc mesenteroides subsp. cremoris
(D) Lactobacillus delbrueckii subsp. bulgaricus
Answer: (B, D)
108. In a dairy plant, spray drying technology is used to produce whey powder. The rate of spray drying depends on
(A) Temperature of the incoming air
(B) Shape of the cyclone separator
(C) Diameter of the whey droplet
(D) Heat transfer coefficient of hot air
Answer: (A, C, D)
109. The parboiling of paddy results into
(A) Increase in the milling losses
(B) Increase in the nutritional value of rice
(C) Increase in the head rice recovery
(D) Increase in the broken rice percentage
Answer: (B, C)
110. One hundred kg paddy is dried from 18% wet basis to 13% wet basis moisture content. The amount of water removed (in kg) from the paddy is _______ (round off to one decimal place).
Answer: (5.5 to 6.0)
111. In a canning industry, the total process time (F0) was calculated as 3 min. If each can contains 20 spores having decimal reduction time of 1.6 min, the probability of spoilage would be ______ in 100 cans (round off to the nearest integer).
Answer: (25 to 28)
Q.112 – Q.122 Carry TWO marks Each
112. Match the edible oil refining stages given in Column I with their respective functions in Column II.
(A) P-3, Q-2, R-1, S-4
(B) P-2, Q-1, R-3, S-4
(C) P-3, Q-4, R-2, S-1
(D) P-3, Q-1, R-2, S-4
Answer: (C)
113. Make the correct pair of food packaging technology given in Column I with operating principle or description in Column II.
(A) P-3, Q-4, R-1, S-2
(B) P-3, Q-2, R-1, S-4
(C) P-1, Q-4, R-3, S-2
(D) P-3, Q-1, R-4, S-2
Answer: (A)
114. Which of the following is not a caramel flavour producing compound?
(A) 3-Hydroxy-2-methylpyran-4-one
(B) 2H-4-Hydroxy-5-methylfuran-3-one
(C) 3-Hydroxy-2-acetylfuran
(D) p-Amino benzoicacid
Answer: (D)
115. Match the size reduction equipment in Column I with the method of operation in Column II.
(A) P-2, Q-4, R-1, S-3
(B) P-3, Q-1, R-2, S-4
(C) P-4, Q-1, R-2, S-3
(D) P-3, Q-4, R-2, S-1
Answer: (A)
116. Most commonly used refrigerant in direct immersion freezing of food is
(A) Monochlorodifluoromethane
(B) Dichlorodifluoromethane
(C) Liquid nitrogen
(D) Freon
Answer: (C)
117. Which among the following are -6 poly unsaturated essential fatty acids?
(A) 18:2 Linoleic acid
(B) 18:3 α-Linolenic acid
(C) 18:3 γ-Linolenic acid
(D) 20:4 Arachidonic acid
Answer: (A, C, D)
118. Which among the following statements are true with respect to protein denaturation?
(A) There may be an increase in α-helix and β-sheet structure
(B) It is an irreversible process
(C) When fully denatured, globular proteins resemble a random coil
(D) The peptide bonds are broken
Answer: (A, C)
119. Identify the correct pair(s) of milling equipment and the grain for which it is used.
(A) Mist polisher–Rice
(B) Break roll–Wheat
(C) Rubber roll–Pigeon pea
(D) Beall degermer–Maize
Answer: (A, B, D)
120. Which among the following expression(s) is/are correct?
Answer: (A, C)
121. In a dairy processing plant, milk enters a 30 m long and 2 cm diameter tube at 60°C and leaves at 57° The total heat loss over the tube length is 381.15 W. The specific heat capacity, density, and viscosity of milk are 3.85 kJ kg−1 K−1 1020 kg m−3, and 1.20 cP, respectively. The Reynolds number for the flow is ______ (round off to the nearest integer).
Given: π = 3.14
Answer: (1700 to 1800)
122. The dry bulb temperature and relative humidity of air inside a storage chamber are 37°C and 50%, respectively. The saturation pressure of water vapour at 37°C andbarometric pressure are 6.28 kPa and 101.32 kPa, respectively. The humidity ratioof air inside the chamber is ______ kg water (kg dry air)−1 (round off to threedecimal places).
Given: Molecular weight of water vapour and dry air are 18.02 g mol−1 and28.97 g mol−1, respectively.
1. Inhaling the smoke from a burning _________ could _________ you quickly.
(A) tire / tier
(B) tire / tyre
(C) tyre / tire
(D) tyre / tier
Answer: (C)
2. A sphere of radius r cm is packed in a box of cubical shape.
What should be the minimum volume (in cm3) of the box that can enclose the sphere?
(A) r3/8
(B) r3
(C) 2r3
(D) 8r3
Answer: (D)
3. Pipes P and Q can fill a storage tank in full with water in 10 and 6 minutes, respectively. Pipe R draws the water out from the storage tank at a rate of 34 litres per minute. P, Q and R operate at a constant rate.
If it takes one hour to completely empty a full storage tank with all the pipes operating simultaneously, what is the capacity of the storage tank (in litres)?
(A) 26.8
(B) 60.0
(C) 120.0
(D) 127.5
Answer: (C)
4. Six persons P, Q, R, S, T and U are sitting around a circular table facing the center not necessarily in the same order. Consider the following statements:
• P sits next to S and T.
• Q sits diametrically opposite to P.
• The shortest distance between S and R is equal to the shortest distance between T and U.
Based on the above statements, Q is a neighbor of
(A) U and S
(B) R and T
(C) R and U
(D) P and S
Answer: (C)
5. A building has several rooms and doors as shown in the top view of the building given below. The doors are closed initially.
What is the minimum number of doors that need to be opened in order to go from the point P to the point Q?
(A) 4
(B) 3
(C) 2
(D) 1
Answer: (C)
Q.6 – Q. 10 Carry TWO marks each.
6. Rice, a versatile and inexpensive source of carbohydrate, is a critical component of diet worldwide. Climate change, causing extreme weather, poses a threat to sustained availability of rice. Scientists are working on developing Green Super Rice (GSR), which is resilient under extreme weather conditions yet gives higher yields sustainably.
Which one of the following is the CORRECT logical inference based on the information given in the above passage?
(A) GSR is an alternative to regular rice, but it grows only in an extreme weather
(B) GSR may be used in future in response to adverse effects of climate change
(C) GSR grows in an extreme weather, but the quantity of produce is lesser than regular rice
(D) Regular rice will continue to provide good yields even in extreme weather
Answer: (B)
7. A game consists of spinning an arrow around a stationary disk as shown below. When the arrow comes to rest, there are eight equally likely outcomes. It could come to rest in any one of the sectors numbered 1, 2, 3, 4, 5, 6, 7 or 8 as shown. Two such disks are used in a game where their arrows are independently spun. What is the probability that the sum of the numbers on the resulting sectors upon spinning the two disks is equal to 8 after the arrows come to rest?
(A) 1/16
(B) 5/64
(C) 3/32
(D) 7/64
Answer: (D)
8. Consider the following inequalities.
(i) 3p − q< 4
(ii) 3q − p< 12
Which one of the following expressions below satisfies the above two inequalities?
(A) p + q < 8
(B) p + q = 8
(C) 8 ≤ p + q < 16
(D) p + q ≥ 16
Answer: (A)
9. Given below are three statements and four conclusions drawn based on the statements.
Statement 1: Some engineers are writers.
Statement 2: No writer is an actor.
Statement 3: All actors are engineers.
Conclusion I: Some writers are engineers.
Conclusion II: All engineers are actors.
Conclusion III: No actor is a writer.
Conclusion IV: Some actors are writers.
Which one of the following options can be logically inferred?
(A) Only conclusion I is correct
(B) Only conclusion II and conclusion III are correct
(C) Only conclusion I and conclusion III are correct
(D) Either conclusion III or conclusion IV is correct
Answer: (C)
10. Which one of the following sets of pieces can be assembled to form a square with a single round hole near the center? Pieces cannot overlap.
Answer: (C)
XH-B1
Q.11 – Q.17 Carry ONE mark Each
11. A relationship is expressed as Iodine : Goitre.
The pair(s) of words showing SIMILAR relationship is/are
Space for Figure/Equation, if any:
(A) Mango : Anaemia
(B) Insulin : Diabetes
(C) Fat : Obesity
(D) Hormones : Heredity
Answer: (B)
12. Three individuals are named P, Q, and R. Together they have a total of fifteen children of which nine are boys. P has three girls and Q has same number of boys. Q has one more child than P, who has four children. R has four more boys than the number of girls. The number of girls of R is equal to the number of boys of P. How many boys do R and P have?
Space for Figure/Equation, if any:
(A) R = 3, P = 3
(B) R = 4, P = 2
(C) R = 5, P = 1
(D) R = 2, P = 4
Answer: (C)
13. A sentence has been given below.
The train will leave at 8:30 PM, we have been ready by 7:30 PM, so that we can reach the station on time.
To make the above sentence grammatically correct, the phrase marked in bold is tobe replaced by
Space for Figure/Equation, if any:
(A) were
(B) are
(C) must be
(D) should have
Answer: (C)
14. Complete the sentence correctly using the options given below.
Hastings____(p)_____ developed as a holiday resort after ___(q)____ .
Space for Figure/Equation, if any:
(A) (p) = a seaside town, (q) = the first world war
(B) (p) = , a seaside town, (q) = the First World War
(C) (p) = , a Seaside Town, (q) = World War I
(D) (p) = A seaside town (q) = World War I
Answer: (B)
15. The Arecibo telescope does not resemble what most of us think of when we hear the word telescope. Its reflective surface covers an area of 20 acres, which is quite remarkable. Dangling above it are towers and cables, sub-reflectors and antennas, all of which can be positioned using 26 motors to transmit radio waves and receive echoes with astonishing precision.
From the passage, it can be inferred that most telescopes
Space for Figure/Equation, if any:
(A) are not as large as Arecibo
(B) do not have reflective surface
(C) cannot be re-positioned
(D) strictly have 26 motors
Answer: (A)
16. Tailgating another vehicle is unsafe and illegal. Many rear-end collisions are caused by drivers following too close to the vehicle in front of them. The rules state that a driver must keep significant distance from the vehicle in front in order to stop safely and avoid a collision. Drivers should allow a minimum two seconds gap between their vehicle and the one ahead. At 60 km per hour, this equates to a gap of 33 meters; at 100 km per hour, it equates to a gap of 55 meters. More distance is needed to safely stop in rain or poor visibility, as during rain slippery roads reduce the effectiveness of braking.
Which of the following statement(s) can be inferred from the above passage?
Space for Figure/Equation, if any:
(A) People drive faster in rain and under poor visibility.
(B) Braking may not be as effective during rain as in the dry conditions.
(C) Tailgating is against the road rules.
(D) Collision has no relationship with tailgating.
Answer: (B, C)
17. There are three separate, but equal-sized boxes. Inside each box, there are two separate small boxes. Inside each of the small boxes, there are four even smaller boxes. The total number of boxes will be _______ .
Space for Figure/Equation, if any:
Answer: (33 to 33)
Q.18 – Q.26 Carry TWO marks Each
18. In a specific language, xer dan means “big horse”, liro cas means “red tomato” and dum cas dan means “big red barn”.
The equivalent word for barn in this language is
Space for Figure/Equation, if any:
(A) dum
(B) liro
(C) dan
(D) cas
Answer: (A)
19. Park street is parallel to Rock street. Garden street is perpendicular (90o) to Lake
street. Lake street is parallel to Rock street.
For the situation described above, the TRUE statement is
Space for Figure/Equation, if any:
(A) Park street is perpendicular to Lake street
(B) Rock street is parallel to Garden street
(C) Park street is parallel to Garden street
(D) Garden street is perpendicular to Park street
Answer: (D)
20. Six examinations are required to be conducted in a week starting from Sunday to Saturday. Hindi is not scheduled on the first day and English is not scheduled before Hindi. Mathematics is scheduled one day after Physics. Biology is scheduled two days after Hindi. One day prior to Chemistry, there is no examination. Only one examination can be scheduled on a single day and Sunday is not an off day. What are the subjects scheduled on first and the last days?
Space for Figure/Equation, if any:
(A) First day Physics, Last day Biology
(B) First day Physics, Last day Chemistry
(C) First day Physics, Last day English
(D) First day English, Last day Biology
Answer: (B)
21. A passage consists of 6 sentences. The first and sixth sentences of the passage are at their correct positions, while the middle four sentences (represented by P, Q, R, and S) are jumbled up.
First sentence: Smoke oozed up between the planks.
P: Passengers were told to be ready to quit the ship.
Q: The rising gale fanned the smouldering fire.
R: Everyone now knew there was fire onboard.
S: Flames broke out here and there.
Sixth sentence: Most people bore the shock bravely.
The most logically CORRECT order for the given jumbled up sentences is
Space for Figure/Equation, if any:
(A) QSRP
(B) QPSR
(C) RSPQ
(D) PQRS
Answer: (A)
22. For a painting to succeed, it is essential that the painter and his public agree about what is significant. The subject of the painting may have a personal meaning for the painter or a common person; but there can also be the possibility of their agreement on its general meaning. It is at this point that the culture of the society and the period in question precedes the artists and her/his art. Renaissance art would have meant nothing to the Aztecs, and vice versa. If, to some extent, a few intellectuals can appreciate them both today, it is because their culture is a historical one. Its inspiration is history and all known developments to date.
According to the passage, which of the following is/are NOT necessarily among the attributes needed for a painter to succeed?
Space for Figure/Equation, if any:
(A) The subject must have a personal meaning for the painter.
(B) The painter is able to communicate and justify the significance of its subject selection.
(C) The painter and the public agree on what is significant.
(D) The painting of the subjects is driven by public demand.
Answer: (A OR D)
23. Vinod has a pre-determined route. Each morning he delivers 37 newspapers to customers in his neighbourhood. It takes Vinod 50 minutes to deliver all the papers. When Vinod was sick or had other engagements, his friend Tarun, who lives on the
same street delivered the papers on his behalf.
Find the statement(s) that must be TRUE according to the given information.
Space for Figure/Equation, if any:
(A) Vinod and Tarun lived in the same locality.
(B) It was dark outside when Vinod began his delivery.
(C) It took Tarun more than 50 minutes to deliver the papers.
(D) Tarun delivered 37 newspapers to customers.
Answer: (A, D)
24. Cholera, typhoid, diphtheria and tuberculosis cause huge number of deaths. Poor quality drinking water has always been the world’s greatest single carrier of sickness. Disease is transmitted when sewage and drinking water come into contact. Children are particularly vulnerable. In some of the poorest countries the infant mortality rate is high. The separation of sewage and the supply of clean drinking water are the domain of civil engineers, and their work makes a significant contribution to public health. That contribution was recognized when public sanitation was voted the greatest medical breakthrough, beating the discoveries including antibiotics and vaccines in a poll organized by the British Medical Journal.
Identify the statement(s), which is/are NOT TRUE according to the passage.
Space for Figure/Equation, if any:
(A) Children are less prone to water borne diseases.
(B) The infant mortality rate was high in economically weaker countries.
(C) The provision of sewage and drinking water should be adequately separated from each other.
(D) The literature states that the public health and sanitation was never given its due importance.
Answer: (A, D OR A, B, D)
25. Shark’s teeth have evolved to correspond to the diet of each particular species of shark. Consequently, the teeth of the great white shark bear little resemblance to those of the bull shark or nurse shark. There were essentially four different shark diets and thus four varieties of shark teeth. Sharks that feed on fish have needle like teeth, perfect for spearing and ripping. Sharks that eat mammals such as seals and sea lions have heavy, serrated teeth, typically triangular on the upper jaw and pointed on the lower jaw. Shark that feed in the benthic zone of the ocean have flattened teeth for crushing the shell of the creatures they find scuttling in the sand or clinging to rocks. Sharks that bask have teeth that are largely non-functional; these sharks filter food from the water by passing it through their gills.
Which of the following is/are the CORRECT inference(s) as per the passage?
Space for Figure/Equation, if any:
(A) Shark’s teeth are not specially designed for slaughter.
(B) The shape of the shark’s teeth relates to its prey.
(C) Some species of sharks filter food through their gills.
(D) Shark’s teeth relate to its diet.
Answer: (B, C, D)
26. A particular school management wants to contact all parents, all businessmen and all engineers. The following statistics are available with the school.
Businessmen = 50
Engineers = 25
Parents = 2500
Businessmen who are engineers = 0
Businessmen who are parents = 25
Engineers who are parents = 15
The number of people needs to be contacted are _______ .Space for Figure/Equation, if any:
Answer: (2535 to 2535)
Economics (C1)
XH-C1: Q.27 – Q.35 Carry ONE mark Each
27. Suppose that a firm has a technology represented by the following production function:
Y(K, L) = KxLy
where K denotes capital, L denotes labour, Y denotes the maximum output that is possible to produce using capital K and labour L. x and y are two positive real numbers. It is also known that the production function satisfies constant returns to scale. Then which of the following is true?
(A) x + y = 0.5
(B) x + y = 1
(C) x + y = 1.5
(D) x + y = 2
Answer: (B)
28. The Human Development Index (HDI), as reported by the United Nations Development Program, is based on three components. Two of these components are per-capita income and a measure of educational attainment of society. The third component is
(A) Gini coefficient
(B) percentage of population who have access to safe drinking water
(C) percentage of population who work in non-agricultural sector
(D) life expectancy at birth
Answer: (D)
29. Suppose we estimate the following regression equation:
ln(xt) = α0 + α1ln (yt) + εt, α0α1> 0
where xt and yt are some variables. α0 and α1 are the intercept and the slope, respectively. εt is the residual term. What is the interpretation of the coefficient α1?
(A) A 1% increase in yt causes a α1% increase in xt
(B) A 1% increase in yt causes a α1 × 0.01 unit increase in xt
(C) A one unit increase in yt causes a 100 × α1% increase in xt
(D) A one unit increase in yt causes a α1 unit increase in xt
Answer: (A)
30. Consider the following system of equations in three variables x, y, z:
−x − y − z = 3
x + y + z = 10
2x– 3y = 6
This system of equations has
(A) no combination of values of (x, y, z) that satisfy this system simultaneously
(B) only one combination of values of (x, y, z) that satisfy this system simultaneously
(C) only two combinations of values of (x, y, z) that satisfy this system simultaneously
(D) infinitely many combinations of values of (x, y, z) that satisfy this system simultaneously
Answer: (A)
31. Which of the following models appropriately explains the fluctuations in potential output and long-run aggregate supply by understanding the shocks to productivity or the willingness of the worker?
(A) Solow growth model
(B) Real business cycle model
(C) IS-LM model
(D) Harrod-Domar Model
Answer: (B)
32. The change in equilibrium output for an equal amount of change in government expenditure and tax revenue is linked to which one of the following multipliers?
(A) Expenditure multiplier
(B) Balanced Budget multiplier
(C) Lum-sum tax multiplier
(D) Trade multiplier
Answer: (B)
33. Solaris is a firm that can install solar panels at an airport to generate electricity for the airport’s usage. The company claims that in 70 percent of all airports where its solar panels are installed, an airport’s electricity bill is reduced by at least 40 percent. The probability that an airport’s electricity bill is reduced by at least 40 percent, in seven out of ten airports where the company’s solar panels are installed, equals approximately:
(A) 0.082
(B) 0.002
(C) 0.490
(D) 0.267
Answer: (D)
34. IndiaSMart is a retail shop that accepts either a Rupay credit card, or a Visa credit card. 31 percent of IndiaSMart’s customers carry a Rupay credit card, 44 percent of its customers carry a Visa credit card, while 18 percent of its customers carry a Rupay credit card as well as a Visa credit card. What is the probability that a customer carries at least one of the two, i.e. either a Rupay or a Visa credit card?
(A) 0.75
(B) 0.93
(C) 0.57
(D) 0.49
Answer: (C)
35. What is the user cost of capital for a firm when the rate of depreciation of machine is 20% and the cost of financial capital is 15%?
(A) 37%
(B) 50%
(C) 35%
(D) 31%
Answer: (C)
36. Which among the following Gini coefficients exhibits the highest equality?
(A) 0.1
(B) 0.2
(C) 0.5
(D) 0.6
Answer: (A)
37. Let f(x, y) be a continuously differentiable homogenous function of degree 4. Which of the following is necessarily true?
Answer: (C)
38. Which of the following committees was set-up to address issues related to capital account convertibility in India?
(A) Tandon Committee
(B) AbidHussain Committee
(C) Tarapore Committee
(D) Percy Mistry Committee
Answer: (C)
39. The demand curve for tea in Borduria is given by
D(P) = 40 – 2P
and the domestic supply curve of tea in Borduria is given by
Here D(P) denotes quantity demanded when price is P and S(P) is quantity supplied by domestic producers at price P. Tea is traded in a competitive world market and imported into Borduria at a price of 9 per unit. Initially there was no restriction on trade. However, as a result of lobbying by the domestic suppliers, the Bordurian government imposes a tariff of 3 per unit on each unit imported. As a result of the tariff, import of tea decreased by how many units?
(A) 2
(B) 3
(C) 8
(D) 9
Answer: (C)
40. Bretton Woods agreement gave birth to the following organization:
(A) GATT
(B) RBI
(C) NAFTA
(D) ASEAN
Answer: (A)
41. Which one of the following is a test of heteroscedastity?
(A) White test
(B) Jarque-Bera test
(C) Breusch-Godfrey test
(D) Ljung-box test
Answer: (A)
42. The law that explains the relationship between income growth and the size of government expenditure is appropriately linked to:
(A) Wagner’s law
(B) Okun’s law
(C) Walras law
(D) Ricardian equivalence
Answer: (A)
43. As per recent Economic Survey, how many states and Union Territories (UTs) are driven by services sector in India?
(A) 15
(B) 19
(C) 25
(D) 21
Answer: (A)
44. An economy is characterized by the following production function:
Y = AK0.25L0.75
where K denotes capital, L denotes labour, A denotes the total factor productivity
and Y denotes output produced. All capital and labour are fully employed.
Suppose that the growth rate of labour is 1%, the growth rate of capital is 4%, andthe growth rate of output is 4%. The growth rate of total factor productivity A is
(A) 1.5 %
(B) 1.75%
(C) 2.25%
(D) 2.5%
Answer: (C)
Q.45 – Q.65 Carry TWO marks Each
45. Suppose a firm has the following production function:
f(x1, x2, x3, x4) = min{x1, x2} + min{x3, x4}
The per unit cost of input xi is given by wi, where i = 1, 2, 3, 4. Suppose that w1 = 1, w2 = 5, w3 = 3, and w4 = 6.If the firm is minimizing cost, which of the following input choices by the firm can be observed?
(A) x1> 0, x2 = 0, x3> 0, x4 = 0
(B) x1> 0, x2> 0, x3 = 0, x4 = 0
(C) x1> 0, x2 = 0, x3 = 0, x4> 0
(D) x1 = 0, x2 = 0, x3> 0, x4> 0
Answer: (B)
46. Suppose an econometrician had specified the following regression:
yt = β1 + β2z2t + β3z3t + β4z4t + εt
but a researcher estimated the following regression:
yt = β1 + β2z2t + β3z3t + β4z4t +β5z5t+εt
What will be the consequence of including the irrelevant variable on the estimated coefficients?
(A) Coefficient estimates will be unbiased, consistent but inefficient
(B) Coefficient estimates will be consistent, asymptotically efficient but biased
(C) Coefficient estimates will be inconsistent and efficient
(D) Coefficient estimates will be biased, consistent and efficient
Answer: (A)
47. Okun’s law says that a 1% increase in unemployment for one year is associated with a 2% decrease in GDP growth. Suppose an economy has the following expectations augmented Phillips curve:
π = πe – β(U – UN), β > 0
where π and πe are the inflation and expected inflation rates, respectively. U and UN are the unemployment and natural rate of unemployment, respectively. β measures sensitivity of inflation to unemployment gap. When β = 2, by what percentage does output fall short of full-employment given that the inflation rate, expected inflation rate and natural rate of unemployment are 8%, 10% and 6%,respectively?
(A) 2
(B) 4
(C) 6
(D) 8
Answer: (A)
48. Let f(x) be the probability distribution function of a random variable X, where
f(x) = (5x4/64) if −2 < x < 2
= 0 otherwise
Let │∙│ denote the modulus function. Then, P (│X│ < 1) and P (X2< 3) are given
by (respectively):
(A) (1/32) and 9(√3/32)
(B) (5/64) and 5(√3/32)
(C) (1/64) and (√3/32)
(D) 2(√3/32) and (1/32)
Answer: (A)
49. Liquidity Adjustment Facility (LAF) uses the following instruments:
(A) Call Money Rate and Mumbai Inter-bank Offered Rate
(B) Repo Rate and Reverse Repo Rate
(C) Bank Rate and Statutory Liquidity Ratio
(D) Cash Reserve Ratio and Prime Lending Rate
Answer: (B)
50. What is the weight age of manufacturing sector in the Index of Industrial
Production (IIP) during 2020-2021?
Note: numbers are in approximate values
(A) 78%
(B) 81%
(C) 65%
(D) 71%
Answer: (A)
51. The curve that explains the relationship between tax rate and tax revenue is known as:
(A) Laffer curve
(B) Engle curve
(C) Beveridge curve
(D) Phillips curve
Answer: (A)
52. Suppose the estimated consumption equation of an economy is:
C = 40 + βYd
where Yd is the personal disposable income, β is the marginal propensity to consume (MPC). Government expenditure (G) is given as 90. Total tax (Tx) received is δY, where Y is aggregate output or real income and δ is tax to real income proportionality factor. Autonomous investment (IA) is given as 80. What are the tax revenue and budget surplus of the government when β = 0.75 and δ =0.20? All units are measured in constant rupees.
(A) Tax revenue = Rs. 105 and surplus = Rs. 15
(B) Tax revenue = Rs. 118 and surplus = Rs. 28
(C) Tax revenue = Rs. 110 and surplus = Rs. 20
(D) Tax revenue = Rs. 125 and surplus = Rs. 35
Answer: (A)
53. Consider a two-period consumption model in which a representative house hold lives for two periods only. In period 1, he earns income y1 and consumes c1. In period 2, he earns y2 and consumes c2. He can borrow and lend at the same rate of interest (r). His lifetime utility function is as follows:
U(c1, c2) = ln(c1) + βln(c2)
where β > 0 measures the sensitivity of future period’s consumption. What will be the marginal propensity to consume of current consumption, i.e.∂c1/∂y1?
Answer: (A)
54. Suppose an investigator has specified the following simultaneous equation model:
y1,t = α1,0 + α1,2y2,t + α2Mt + α3Kt + ut (1)
y2,t = α2,0 + α2,1y1,t + α3It + vt (2)
where y1,t and y2,tare endogenous variables. Mt, Kt and It are predetermined
variables. ut and vt are residual terms. Based on the order condition of identification, which one of the following statements are correct?
(A) Equations (1) and (2) are exactly identified
(B) Equation (1) is exactly identified and equation (2) is over-identified
(C) Equation (1) is over-identified and equation (2) is exactly identified
(D) Both the equations are under-identified
Answer: (B)
55. There are two regions in a country. The demand for chocolates in region 1 is given by
Q1(P) = 100 − P
and the demand for chocolates in region 2 is given by
Q2(P) = 200 –P
where Q1(P) and Q2(P) denote the demand for chocolates in region 1 and 2respectively at a price P. There is only one seller who is licensed to sell chocolates in the country. Suppose the seller sets a price of P = 125. The total demand for chocolates in the country at this price is
(A) 50
(B) 75
(C) 100
(D) 125
Answer: (B)
56. A producer manufactures batteries by using techniques I and II. The capacities (in ampere hours) of 12 randomly selected batteries manufactured by using technique I are: 140, 132, 136, 142, 138, 150, 154, 150, 152, 136, 144 and 142. Moreover, the capacities (in ampere hours) of 14 randomly selected batteries manufactured by using technique II are: 144, 134, 132, 130, 136, 146, 140, 128, 131, 128, 150,137, 130 and 135.
Suppose that battery capacities manufactured by using techniques I and II are normally distributed, with unknown means, μI and μII respectively, and an unknown common varianceσ2.Consider the null hypothesis H0 : (μI – μII) = γ ampere hours.
For which of the following values of γ should the null hypothesis H0 be accepted, against the alternative hypothesis H1 :(μI – μII) ≠ γ ampere hours, at 10% level of
significance?
Note that if Z is a standard normal variate, then: P(Z ≤ 1.282) = 0.900,
Further, if a random variable T follows the Student’s t-distribution, with degrees of freedom r, then the α-percentile values tα,r for various values of α and r are given by (where P(T ≤ tα,r) = α):
57. Tom and Jerry both arrive at a petrol pump. Without worrying about price, Tom says, “I want 10 liters of petrol.” Also, without worrying about price, Jerry says, “Iwant petrol worth 1000 rupees.” The own price elasticities of demand for Tom (denoted by εT) and Jerry (denoted by εJ) are:
(A) εT = 0, εJ = −∞
(B) εT = 0, εJ = −1
(C) εT = −∞, εJ = 0
(D) εT = −1, εJ = 0
Answer: (B)
58. Which of the following variables are pushed upwards by ‘Seigniorage’?
(A) Money supply
(B) Inflation
(C) Tax rate
(D) Interest rate
Answer: (A, B)
59. Suppose Raju enters the job market at age 25 and earns annual income of Rs.6000. He retires at age 65 and his life expectancy is 75 years. He does not own any assets. Assume that Raju consumes annual income uniformly over his lifetime. What will be his average propensity to consume during employment years?
(A) 0.90
(B) 0.80
(C) 0.50
(D) 0.40
Answer: (B)
60. A monopolist faces the following inverse demand function:
P = 40 – Q
where P denotes price and Q denotes quantity. The monopolist has zero fixed cost and a marginal cost of 5 per unit of output produced. The monopolist aims to maximize profit. Suppose the government imposes a tax of 5 per unit of output on the monopolist. As a result, the price charged by the profit-maximizing monopolist to the consumer increases by:
(A) 0
(B) 2.5
(C) 5
(D) 10
Answer: (B)
61. In the flexible exchange rate environment with perfect capital mobility, a fiscal stimulus will be linked to which of the following statements?
(A) Fiscal policy increases the domestic outcome
(B) Fiscal policy does not increase the domestic output
(C) Fiscal policy leads domestic exports to fall
(D) Fiscal policy appreciates the domestic currency
Answer: (B, C, D)
62. Consider a lottery with two possible outcomes:
• Rupees 100 with probability 0.6
• Rupees 50 with probability 0.4
The maximum amount that a risk-neutral person would be willing to pay to play the above lottery equals Rupees (in integer).
Answer: (80 to 80)
63. Sharma’s consumption preference for tea (denoted by x) and sugar (denoted by y) is given by the utility function
U(x, y) = min{x, 2y)
The price per unit of tea is 10 and the price per unit of sugar is 10. Mr. Sharma’s total income is 900.
The optimum quantity of tea purchased by Mr. Sharma equals (in ________ integer).
Answer: (60 to 60)
64. Suppose α is a real number between 0 and 1. Rohit is choosing x and y to maximize the following utility function:
U(x, y) x2 + 2xy + y2 + 4α2 + 8α + 10
subject to the following constraints:
2x + y = 10,
x, y ≥ 0
Then the optimal value of 𝑦 chosen by Rohit is (in ______ integer).
Answer: (10 to 10)
65. In a competitive market for dry-cleaning, the inverse market demand function is given by
P = 100 – Q
where P denotes price and Q denotes quantity. The (private) marginal cost (MC)of production for all the dry-cleaning firms together is given by
MC = 20 + 2Q
The market pollution generated by the dry-cleaning processes of all firms creates external damages given by the marginal external cost (MEC):
MEC = 2Q
The socially efficient output of dry-cleaning is (in ______ integer).
Answer: (16 to 16)
English (C2)
XH-C2: Q.27 – Q.44 Carry ONE mark each
27. “He who is unable to live in society, or who has no need because he is sufficient for himself, must be either a beast or a god.”
Who has given the above statement?
(A) Aristotle
(B) Plato
(C) Socrates
(D) Rousseau
Answer: (A)
28. “History is not made only in statecraft; its lasting results are produced in the ranks of learned men.”
Name the play from which the above excerpt has been taken.
(A) Mahesh Dattani’s Thirty Days in September
(B) Vijay Tendulkar’s Silence! The Court is in Session
(C) Girish Karnad’s Tughlaq
(D) Rabindranath Tagore’s Mukta-Dhara
Answer: (C)
29. Who amongst the following popularised the term ‘objective correlative’, which is often used in formalist criticism?
(A) Virginia Woolf
(B) C. S. Lewis
(C) Matthew Arnold
(D) T. S. Eliot
Answer: (D)
30. Which of the following critics preferred Shakespeare’s comedies to his tragedies?
(A) Samuel Johnson
(B) Alexander Pope
(C) John Dryden
(D) Thomas De Quincey
Answer: (A)
31. Who among the following has been credited with laying the foundation of comparative literature by Russian Formalists?
(A) Viktor Shklovsky
(B) Alexander Veselovsky
(C) Vladimir Propp
(D) Roman Jakobson
Answer: (B)
32. Lyrical Ballads, considered to be the manifesto of Romantic Poetry, was first published in the year ________.
(A) 1795
(B) 1797
(C) 1789
(D) 1798
Answer: (D)
33. Identify the work from which the following excerpt has been taken:
“In a universe that is suddenly deprived of illusions and of light, man feels a stranger. He is an irremediable exile …. This divorce between man and his life, the actor and his setting, truly constitutes the feeling of Absurdity.”
(A) Frantz Kafka’s The Trial
(B) Samuel Beckett’s Waiting for Godot
(C) Albert Camus’ The Myth of Sisyphus
(D) Harold Pinter’s The Homecoming
Answer: (C)
34. What does gynocriticism recommend as an approach to literature?
(A) Considering women’s literature from men’s point of view
(B) Examining women’s literature confirming gender stereotypes only
(C) Becoming more familiar with the history of women and women’s writing
(D) Becoming more familiar with gerontology
Answer: (C)
35. Identify the novel which opens with the following lines:
“It was the best of times, it was the worst of times, it was the age of wisdom, it was the age of foolishness, it was the epoch of belief, it was the epoch of incredulity, it was the season of light, it was the season of darkness, it was the spring of hope, it was the winter of despair.”
(A) Jane Austen’s Emma
(B) Emily Brontë’s Wuthering Heights
(C) Charles Dickens’ A Tale of Two Cities
(D) H. G. Wells’ The Time Machine
Answer: (C)
36. Which of the following terms does not form a part of seven types of ambiguities propounded by William Empson?
(A) Simulacra
(B) Metaphor
(C) Pun
(D) Simile
Answer: (A)
37. Which of the following poem(s) has/have been influenced by Hindu philosophy?
(A) The Solitary Reaper
(B) Brahma
(C) The Curse of Kehama
(D) Kubla Khan
Answer: (B, C)
38. Which of the following human behaviour(s) is/are important to a Freudian psychoanalytical study of William Shakespeare’s Hamlet?
(A) Art of speaking
(B) Changes in emotional states
(C) Neurotic behaviour
(D) Merry-making
Answer: (B, C)
39. Which of the following novel-author combination(s) is/are correct?
(A) Where Shall We Go This Summer-Jane Austen
(B) A Passage to England- Nirad C Chaudhuri
(C) The Mayor of Casterbridge-Thomas Hardy
(D) Pride and Prejudice- Anita Desai
Answer: (B, C)
40. Which of the following statements is/are correct about Phenomenology?
(A) It is a form of methodological idealism, seeking to explore an abstraction called ‘human consciousness’.
(B) It is a philosophical method associated with Edmund Husserl.
(C) It believes that the act of thinking and the object of thought are internally related, mutually dependent.
(D) Heidegger’s Being and Time is an important phenomenological treatise supporting the stand of Husserl.
Answer: (A, B, C)
41. Chitra Divakaruni’s The Mistress of Spices is ________.
(A) an experiment in magic realism
(B) about immigrant experience
(C) a science fiction
(D) an epistolary novel
Answer: (A, B)
42. Which of the following is/are correct about postmodernist critics?
(A) They foreground fiction and exemplify ‘disappearance of the real’.
(B) They foreground irony.
(C) They tend towards reflexivity.
(D) They challenge the distinction between high and low cultures.
Answer: (A, B, D)
43. The literary theory of Deconstruction argues that ________.
(A) texts are always heterogeneous
(B) the meaning of a text never relies on context
(C) any system for the production of meaning may be bound by context, yet also limitless
(D) texts are always rigid in meaning
Answer: (A, C)
44. In the context of the Reader-Response Theory, Louise M Rosenblatt in her essay “The Poem as Event”, considers that the reader should ________.
(A) participate in a transaction with the text
(B) act against a text
(C) be acted upon by the text
(D) reject the text
Answer: (A, C)
Q.45 – Q.65 Carry TWO marks each.
45. Roland Barthes in his famous essay, “The Death of the Author” ________.
(A) believes that the text is to be interpreted in the biographical context of the author
(B) challenges the author’s claim as “cogito”, or origin of all knowledge
(C) believes that the author has sole claim to his work
(D) concludes that an author is an atypical product of his social milieu
Answer: (B)
46. What is common among the following novels?
Cormac McCarthy’s The Road
George Orwell’s Nineteen Eighty Four
Margaret Atwood’s The Handmaid’s Tale
(A) These are examples of Utopian fiction.
(B) These are examples of Dystopian fiction.
(C) They present an idealistic picture of the world.
(D) They abound in pleasant descriptions of landscapes, peoples and places.
Answer: (B)
47. Match the following authors with their pseudonyms:
(A) i-d, ii-b, iii-a, iv-c
(B) i-b, ii-a, iii-c, iv-d
(C) i-a, ii-d, iii-b, iv-c
(D) i-c, ii-a, iii-d, iv-b
Answer: (D)
48. “This literary mode parallels the flouting of authority and inversion of social hierarchies that, in many cultures, are permitted in a season of …. It does so by introducing a mingling of voices from diverse social levels that are free to mock and subvert authority, to flout social norms by ribaldry, and to exhibit various ways of profaning what is ordinarily regarded as sacrosanct.”
The above description explains the concept of ________.
(A) Magic Realism
(B) Intertextuality
(C) Carnivalesque
(D) Heteroglossia
Answer: (C)
49. “Postcolonial perspectives emerge from the colonial testimony of Third World countries and the discourses of ‘minorities’ within the geopolitical divisions of East and West, North and South. They intervene in those ideological discourses of modernity that attempt to give a hegemonic ‘normality’ to the uneven development and the differential, often disadvantaged, histories of nations, races, communities, people.”
The above commentary on the postcolonial perspective has been extracted from which of the following?
(A) Edward Said’s Orientalism
(B) Homi K Bhabha’s The Location of Culture
(C) Leela Gandhi’s Postcolonial Theory
(D) Bill Ashcroft et al., eds. The Post-colonial Studies Reader
Answer: (B)
50. Match the following excerpts with their authors:
(A) i-a, ii-c, iii-b, iv-d
(B) i-b, ii-d, iii-a, iv-c
(C) i-c, ii-a, iii-d, iv-b
(D) i-d, ii-c, iii-b, iv-a
Answer: (C)
51. Which of the following statements is the most appropriate in the context of Francoise d’ Eaubonne’s concept of Eco-feminism?
(A) It is a revolution by women against men to protect Nature.
(B) It is a philosophical idea to counter the oppression of women by men, as similar to the oppression and destruction of Nature by men.
(C) It is a term used to describe how the human race could be saved by men initiating an ecological revolution.
(D) It is a term used to describe the interface between women and technology.
Answer: (B)
52. Which of the following books is considered as one of the sources behind T. S. Eliot’s poem, The Waste Land?
(A) William James’ Principles of Psychology
(B) Jessie Weston’s From Ritual to Romance
(C) Franz Kafka’s The Metamorphosis
(D) Sigmund Freud’s Interpretation of Dreams
Answer: (B)
53. “The people who believe most that our greatness and welfare are proved by our being very rich, and who most give their lives and thoughts to becoming rich, are just the very people whom we call Philistines.”
What can be inferred from the above statement of Matthew Arnold?
(A) Greatness of people lies in their being rich and prosperous.
(B) Material prosperity is not the true criterion of a nation’s achievement.
(C) Philistines are great people.
(D) Arnold thinks very highly of himself.
Answer: (B)
54. ‘Anagnorisis’, as used by Aristotle in his theory of Tragedy, stands for ________.
(A) the hero’s recognition of his tragic flaw
(B) the hero’s ignorance about his tragic flaw
(C) the hero’s recognition of his adversary
(D) the hero’s rejection of his tragic end
Answer: (A)
55. Which of the following thinkers does not belong to the school of Existentialism?
(A) Jean Paul Sartre
(B) Albert Camus
(C) Roland Barthes
(D) Søren Kierkegaard
Answer: (C)
56. Which of the following statement(s) is/are closely associated with the term Fetishism?
(A) It is generally defined as an act of paying excessive attention or attributing mystical ability, to an inanimate thing.
(B) It is related to Western theories of aesthetics, economics and psychology.
(C) It is used in reference to religious objects believed to have magical or spiritual powers.
(D) It is generally used to describe Gothic expressionism.
Answer: (A, B, C)
57. Why does the thin grey strand
Floating up from the forgotten
Cigarette between my fingers,
Why does it trouble me?
Ah, you will understand;
When I carried my mother downstairs,
A few times only, at the beginning
Of her soft-foot malady,
I should find, for a reprimand
To my gaiety, a few long grey hairs
On the breast of my coat; and one by one
I watched them float up the dark chimney.
Which of the following can be considered as correct about the above poem?
(A) It is written in the process of grieving for the poet’s mother.
(B) It is an autobiographical poem.
(C) It is a symbolic poem.
(D) It is a poem of youthful celebration.
Answer: (A, B, C)
58. Which of the given examples of rhetorical/figurative devices is/are correctly paired?
(A) ‘What is man, that thou art mindful of him?’ : Paradox
(B) ‘Truth makes the greatest libel.’ : Personification
(C) ‘Reading furnishes the mind only with material of knowledge; it is thinking makes what we read ours.’ : Antithesis
(D) ‘It is a truth universally acknowledged that a single man in possession of a good fortune must be in want of a wife.’ : Irony
Answer: (C, D)
59. As per the distinctions made by Toril Moi, regarding the terms ‘feminist’, ‘female’ and ‘feminine’, which of the following is/are correct?
(A) The first is ‘a matter of economic manumission’.
(B) The second is a ‘matter of psychology’.
(C) The first is ‘a political position’.
(D) The third is a set of ‘culturally defined characteristics’.
Answer: (C, D)
60. Which of the following author(s) has/have won the Booker Prize twice?
(A) Nadine Gordimer
(B) J. G. Farrell
(C) William Golding
(D) Peter Carey
Answer: (B, D)
61. “Nothing feels normal to Ashima, it’s not so much the pain which she will survive. Its consequence: motherhood in a foreign land … unmonitored by those she loves … she is terrified to raise a child in a country where she knows so little, where life seems so tentative and spare.”
In the above passage of The Namesake, the writer tries to say that Ashima ________.
(A) feels isolated in the new world
(B) should have been surrounded by her own people
(C) is facing a cultural shock
(D) is able to adapt herself to an alien culture
Answer: (A, B, C)
62. Jean Baudrillard, a post-modern thinker, has suggested that a sign refers to other signs. He has given four stages/phases to support his proposition. Which of the following do(es) not constitute a part of these stages/phases?
(A) The sign disguises the fact that there is no corresponding reality underneath.
(B) The sign is always peripheral.
(C) The sign bears no relation to any reality at all.
(D) The sign misrepresents or distorts the reality behind it.
Answer: (B)
63. Which of the following apply/applies to the term ‘parapraxis’?
(A) It is used in connection with Marxist interpretation of literature.
(B) It refers to an error in speech, memory, or physical action that occurs because of the interference of an unconscious subdued wish.
(C) The term is generally associated with Jung.
(D) The original German word referring to the term is ‘Fehlleistung’.
Answer: (B, D)
64. The epilogue to William Congreve’s The Way of the World, given below, signals some warning(s). What is/are it/they?
“Other there are whose malice we’d prevent,
Such, who watch plays, with scurrilous intent
To mark out who by characters are meant.
These, with false glosses feed their own ill nature,
And turn to libel, what was meant a satire.”
(A) Critics should always be supportive of the author.
(B) Critics should not look for portrait of real people in the play’s characters and remember that the play is a social satire.
(C) Critics should avoid writing malicious reviews, lest they are accused of libel.
(D) Critics should try to identify the real life equivalent for each character.
Answer: (B, C)
65. Read the following lines and mark your correct observation(s):
Take my shirt off
and go in there to do the puja
No thanks.
Not me.
But you go right ahead
if that’s what you want to do.
Give me the match box
before you go,
will you?
I will be out in the courtyard
where no one will mind it
if I smoke.
(A) The poem is written in the form of an ode.
(B) The poem is skeptic in nature.
(C) The poet uses surreal and astonishing images.
(D) The poem expresses a rebellious attitude.
Answer: (B, D)
Linguistics (C3)
XH-C3: Q.27 – Q.44 Carry ONE mark each
27. Linguistic determinism is best captured in __________.
(A) Generative grammar
(B) Sound symbolism
(C) Critical-age hypothesis
(D) Sapir-Whorf hypothesis
Answer: (D)
28. Match the phonological processes in column Y to their names in column X.
(A) P – ii, Q – iv, R – iii, S – i
(B) P – iv, Q – ii, R – iii, S – i
(C) P – ii, Q – iv, R – i, S – iii
(D) P – iv, Q – ii, R – i, S – iii
Answer: (MTA)
29. ‘Bilingual language acquisition’ refers to the __________.
(A) Simultaneous acquisition of two languages at a very early age
(B) Learning of a second language after 18 years of age
(C) Ability to acquire a second language during the first 12 months
(D) Sequential acquisition of two languages in adulthood
Answer: (A)
30. Which of the following is the sequence of derivation as per Minimalist Program?
(A) Numeration → Spell-Out → Merge → Move
(B) Numeration → Merge → Move → Spell-Out
(C) Numeration → Move → Merge → Spell-Out
(D) Merge → Move → Numeration → Spell-Out
Answer: (B)
31. Linguistic determinism is the strongest form of the __________.
(A) P – (ii), Q – (iv), R – (i), S – (iii)
(B) P – (iv), Q – (ii), R – (i), S – (iii)
(C) P – (ii), Q – (iv), R – (iii), S – (i)
(D) P – (iv), Q – (ii), R – (iii), S – (i)
Answer: (D)
32. Which of the given statements is TRUE?
Statement (I): Every spoken language includes discrete sound segments that can all be defined by a finite set of sound properties or features.
Statement (II): Speakers of all languages are capable of producing and comprehending an infinite set of sentences.
(A) Both statement (I) and statement (II) are correct
(B) Both statement (I) and statement (II) are incorrect
(C) Statement (I) is correct but statement (II) is incorrect
(D) Statement (I) is incorrect but statement (II) is correct
Answer: (A)
33. The sound change of Proto-Indo-Aryan /p/ to Germanic /f/, deduced by comparing cognates like Latin pater, Sanskrit pita and English father, is an example of _____.
(A) Grassman’s Law
(B) Lyman’s Law
(C) Grimm’s Law
(D) Verner’s Law
Answer: (C)
34. Which of the following diagrams depict(s) the violation of a principle of autosegmental phonology?
(A) Representation (i)
(B) Representation (ii)
(C) Both (i) and (ii)
(D) Neither (i) nor (ii)
Answer: (B)
35. In the given sentences, the semantic relationship of hyponymy can be found in between _______.
(i) The thing in the grass is a small snake.
(ii) The thing in the grass is a small reptile.
(A) reptile : grass
(B) grass : snake
(C) snake : reptile
(D) small : snake
Answer: (C)
36. Bill walked into a store in New York, looking for a restroom. He asked a storekeeper which floor the men’s restroom is and he replied, /ðə fɔθ flɔ/ for the fourth floor. What kind of store Bill must have walked into?
(A) A high class store
(B) A middle class store
(C) A lower class store
(D) A Latino owned store
Answer: (C)
37. Which of the followings occurred due to the Great Vowel Shift of the English language?
(A) [a:] became [u:]
(B) All the front vowels shifted to back
(C) [ɡe:s] became [ɡi:s]
(D) The high, long vowels became diphthongized
Answer: (C, D)
38. Which of the following statements are true for the pulmonic consonant table in an IPA chart?
(A) Voiceless consonants aligned to the left of the cell
(B) Places of articulation are arranged in rows
(C) Manners of articulation are arranged in columns
(D) The most constricted consonants to the least are arranged from the top to bottom
Answer: (A, D)
39. Identify the compounds in the given data.
repeat blackboard toy factory underestimate
deform backward bystander sky-high
(A) repeat and backward
(B) blackboard and toy factory
(C) sky-high and underestimate
(D) bystander and deform
Answer: (B, C)
40. In the production of the /z/ sound which of the following will take place?
(A) Vocal cords will vibrate
(B) Velum will be raised
(C) The two lips will be in contact
(D) Air will pass without any turbulence
Answer: (A, B)
41. The phrase “the first person in space” refers to Yuri Gagarin. Which of the following could be used to determine reference?
(A) Russell’s Theory of Description
(B) Prototype Theory
(C) Speech Act Theory
(D) Gricean Maxims
Answer: (A)
42. Which of the following statement(s) apply to pidgins?
(A) Pidgins have complex grammatical rules
(B) Pidgins do NOT have grammatical rules
(C) Pidgin phonology is rule based
(D) Pidgins are passed on from one generation to the other
Answer: (C, D)
43. In the given tree-structure NP1 C-commands NP2 but not vice versa because:
(A) C-command cannot be a reciprocal relationship
(B) No node dominates both NP2 and NP1
(C) VP1 dominates NP2 and C-commands NP1
(D) VP1 dominates NP2 but not NP1
Answer: (C, D)
44. Which of the given pronunciations DO NOT conform to the phonological rule?
(A) [dud]
(B) [kut]
(C) [mutab]
(D) [pum]
Answer: (A, C)
Q.45 – Q.65 Carry TWO marks Each
45. Determine the correct nature of the following two utterances from the choices given below.
P: Hasnain said ki woh kal aayegaa
(COMP he tomorrow come.will)
“Hasnain said that he will come tomorrow”
Q: Rohan will get some desi vegetables.
(local)
“Rohan will get some local vegetables”
(A) Code switching in P and Q
(B) Borrowing in P and Q
(C) Code switching in P and borrowing in Q
(D) Borrowing in P and code switching in Q
Answer: (C)
46. Consider the given script showing a sequence of 11 graphemes. It represents the sentence: /apa pal talip tani mil/. Each grapheme in the script contains a _________.
(A) Rhyme
(B) Syllable
(C) Consonant
(D) Mora
Answer: (D)
47. In the given examples, column Y are examples of __________ sentences.
(A) Topicalization
(B) Cleft
(C) Pseudo-cleft
(D) Gapping
Answer: (B)
48. A second language speaker uses the word [phonetic] as a singular noun because she interprets the word [phonetics] as a plural noun. In doing so, she is deducing a new word by the process of ___________.
(A) Blocking
(B) Back formation
(C) Bracketing
(D) Back tracking
Answer: (B)
49. Given the rules P and Q, what is the name of the rule ordering in dialect X and Y?
(A) X has counter-feeding and Y has counter bleeding order
(B) X has bleeding and Y has counter-bleeding order
(C) X has counter-bleeding and Y has counter-feeding order
(D) X has counter bleeding and Y has bleeding order
Answer: (B)
50. Which of the given statements is/are TRUE?
Statement (I): Diglossia and dialect continuum are synonymous.
Statement (II): Bilingual speakers are also bidialectal.
(A) Both statement (I) and statement (II) are correct
(B) Both statement (I) and statement (II) are incorrect
(C) Statement (I) is correct but statement (II) is incorrect
(D) Statement (I) is incorrect but statement (II) is correct
Answer: (B)
51. Look into the data from Micaocan Aztec and match the words (P-S) to their meaning (i-iv) and select the correct sequence.
(A) P-(ii), Q-(iv), R-(i), S-(iii)
(B) P-(iv), Q-(ii), R-(i), S-(iii)
(C) P-(ii), Q-(iv), R-(iii), S-(i)
(D) P-(iv), Q-(ii), R-(iii), S-(i)
Answer: (D)
52. Match the languages (P – U) to the language families (i – iv) and select the correct sequence.
(A) P – (ii), Q – (i), R – (iv), S – (i), T – (iii), U – (iv)
(B) P – (i), Q – (i), R – (iii), S – (iii), T – (iv), U – (i)
(C) P – (ii), Q – (i), R – (iii), S – (i), T – (iii), U – (iv)
(D) P – (i), Q – (i), R – (iv), S – (iii), T – (iii), U – (ii)
Answer: (A)
53. Which of the given statements is/are TRUE?
Statement (I): The International Phonetic Alphabet (IPA) is a transcription system for describing human speech sounds from all languages.
Statement (II): The voiceless pharyngeal plosive sound is missing in the IPA chart because it is physiologically impossible to articulate.
(A) Both statement (I) and statement (II) are correct
(B) Both statement (I) and statement (II) are incorrect
(C) Statement (I) is correct but statement (II) is incorrect
(D) Statement (I) is incorrect but statement (II) is correct
Answer: (C)
54. Match the terms in column X (P – S) to their descriptions in column Y (i – iv) and select the correct sequence.
(A) P – ii, Q – iv, R – iii, S – i
(B) P – iv, Q – ii, R – iii, S – i
(C) P – ii, Q – iv, R – i, S – iii
(D) P – iv, Q – ii, R – i, S – iii
Answer: (D)
55. Match the following morphological changes (P-S) to their type (i-iv) and select the correct sequence.
(A) P – (ii), Q – (iv), R – (i), S – (iii)
(B) P – (iv), Q – (ii), R – (i), S – (iii)
(C) P – (ii), Q – (iv), R – (iii), S – (i)
(D) P – (iv), Q – (ii), R – (iii), S – (i)
Answer: (D)
56. Which of the given statements is/are TRUE?
(A) Bangla is similar to Hindi and Sambalpuri but not Telugu.
(B) Bangla is similar to Hindi but not Sambalpuri.
(C) Sambalpuri is similar to Telugu but not Bangla.
(D) Sambalpuri is similar to Hindi but not Bangla.
Answer: (B, C)
57. Lesions in different areas of the left hemisphere lead to qualitatively distinct aphasia syndromes. Which of the given statements is/are TRUE?
(A) The brain lesions associated with classical anomia involves the dominant angular gyrus.
(B) Conduction aphasia follows from a lesion in the posterior part of the inferior frontal gyrus.
(C) Wernicke’s aphasia is the consequence of a lesion in the auditory association cortex of the temporal lobe.
(D) Broca’s aphasia follows from localized lesions in the temporoparietal regions.
Answer: (A, C)
58. Consider the following data from English. Which linguistic change(s) is/are associated with the addition of the suffix ‘-able’?
This book is readable.
(A) sociolinguistic change
(B) grammatical category change
(C) semantic change
(D) typological change
Answer: (B, C)
59. Children are biologically equipped to acquire all aspects of grammar. Which of the given statements is/are TRUE?
(A) ‘Telegraphic speech’ occurs during the holophrastic stage.
(B) Children generally go through three phases in the acquisition of an irregular form (overgeneralization).
(C) Children learn approximately 100 words a day up to 12 months.
(D) Mean length of utterances is used to measure a child’s language development.
Answer: (B, D)
60. Wolof speakers use a secret language called Kall. Words in Wolof are changed to Kall in a systematic manner, as shown in the data. In the change from Wolof to Kall, which of the given constraints cannot be violated?
(A) MAX-IO
(B) DEP-IO
(C) FOOT-BINARITY
(D) LINEARITY-IO
Answer: (A, C)
61. The given sentence is ungrammatical because:
*Tailan believes that himself is smarter than Po
(A) Principle A of Binding Theory is not satisfied.
(B) Principle B of Binding Theory is not satisfied.
(C) Principle C of Binding Theory is not satisfied.
(D) Both Po and Tailan are possible antecedents for himself.
Answer: (A)
62. Which of the given statements support the Design Features proposed by Hockett?
(A) Humans produce as many sentences as they have acquired.
(B) Sentences cannot be broken into smaller units as they have specific meaning.
(C) Humans can talk about things that are not in their immediate vicinity.
(D) Linguistic units do not bear any direct resemblance to the things they represent.
Answer: (C, D)
63. Which of the given logical forms correspond to the following sentence where x ϵ student, y ϵ teacher and A=admires?
Every student admires a teacher.
(A) ∀x∃y A(x,y)
(B) ∀y∃x A(y,x)
(C) ∃x∀y A(y,x)
(D) ∃y∀x A(x,y)
Answer: (A, D)
64. Identify the possible set(s) of stops that correlate with the corresponding VOT values.
(A) /p/ = 10, /ph/ = 78, /b/ =−110
(B) /t/ = 120, /th/ = −110, /b/ =67
(C) /k/ = −121, /kh/ = 121, /g/ =−108
(D) /ph/ = 89, /th/ = 92, /kh/ =98
Answer: (A, D)
65. The estimated fundamental frequency of the given sine wave is (in integer) _________Hz.
Answer: (50 to 50)
PHILOSOPHY (C4)
XH-C4: Q.27 – Q.44 Carry ONE mark Each
27. Let us consider the cases of Shweta and Rani. While Shweta has access to, and can afford to buy good quality dairy products, she and her spouse decide to pursue a vegan lifestyle. Therefore, she no longer buys milk or dairy-based products for her family. Rani’s family on the other hand, has a meagre income. Although Rani’s children like milk and kheer, Rani refrains from buying milk and instead spends on rice.
In light of the concepts of functioning and capability as defined by Martha Nussbaum, which one of the following options holds for the above cases?
(A) They differ on the basis of capability
(B) They differ on the basis of functioning
(C) They differ on the basis of both functioning and capability
(D) They do not differ since the end-result is the same in both
Answer: (A)
28. In the opposition of propositions, which one among the following is the contradictory of A proposition?
(A) Only O
(B) Only E
(C) Only I
(D) E and O
Answer: (A)
29. A study in Europe concluded that whenever there is an increase in the circulation of fake news in social media, the ruling party gains political mileage. Conversely, a proportionate decrease in the circulation of fake news, corresponds to the decline in its popularity.
Which one of Mill’s methods is entailed in the above reasoning?
(A) Method of Concomitant Variation
(B) Joint Method of Agreement and Difference
(C) Method of Residues
(D) Method of Difference
Answer: (A)
30. Which one among the following Greek philosophers upholds the ontology of things by stating that ‘all things are flowing’ and ‘nothing ever is, everything is becoming?’
(A) Heraclitus
(B) Pythagoras
(C) Thales
(D) Anaxagoras
Answer: (A)
31. Which one among the following will be in agreement with Rene Descartes’ confirmation of the cogito, in his Discourse on Method?
(A) Self exists as an imperfect thing
(B) Self exists as a perfect thing
(C) Only the world exists
(D) Only the self exists
Answer: (A)
32. According to Immanuel Kant, duty as rationally conceived is determined by:
(A) The will as an a priori principle
(B) The self-interest of the will
(C) The divine will
(D) The desire as the will
Answer: (A)
33. Which one among the following is NOT a pramāṇa in Sānkhya epistemology?
(A) Comparison (upamāna)
(B) Perception (dṛṣta/pratyakṣa)
(C) Inference (anumāna)
(D) Valid testimony (āptavacana)
Answer: (A)
34. ‘Hare’s horn (śaśa-viṣāṇa)’, according to the Philosophy of Yoga, is a valid example of which kind of citta-vṛtti?
(A) Constructive Imagination (vikalpa)
(B) Wrong cognition or false knowledge (viparyaya)
(C) Absence of cognition or sleep (nidra)
(D) Memory (smṛti)
Answer: (A)
35. According to Jaimini, in Mīmāmsā, which one among the following is a command or injunction that impels humans to perform action?
(A) Dharma
(B) Apūrva
(C) Adṛṣṭa
(D) Niṣkāmakarma
Answer: (A)
36. According to Vaiśeṣika theory of atomism, which one of the following is NOT atomic?
(A) Ether (ākāśa)
(B) Earth (pṛthvi)
(C) Fire (tejas)
(D) Air (vāyu)
Answer: (A)
37. The Cārvāka system rejects inference (anumāna) as a pramāṇa because it does not accept:
(A) Invariable concomitance (vyāpti)
(B) Comparison (upamāna) as a pramāṇa
(C) The theory of pramāṇa altogether
(D) Śabda as a pramāṇa
Answer: (A)
38. The Muṇḍakopaniṣad distinguishes between ‘higher knowledge’ (parā vidyā) and ‘lower knowledge’ (aparā vidyā). What does the higher knowledge (parā vidyā) imply?
(A) Knowledge of the Ātman
(B) Knowledge of the World
(C) Knowledge of Karma
(D) Knowledge of God
Answer: (A)
39. In the Bhagavadgītā, the conception of ‘lokasamgraha’ denotes that the perfect person:
(A) Purely acts for the wellbeing and welfare of humanity.
(B) Purely concentrates on the Absolute by negating the world.
(C) Fully detaches herself/himself from worldly affairs.
(D) Fully devotes herself/himself to speak about God to people.
Answer: (A)
40. Radhakrishnan, in his An Idealistic View of Life, delineates the nature of ultimate reality as “pure consciousness, pure freedom and infinite possibility.” Which school of Indian Philosophy influenced him most?
(A) Advaita Vedānta
(B) Sānkhya
(C) Cārvāka
(D) Mīmāmsā
Answer: (A)
41. Karl Marx in his Economic and Philosophic Manuscripts discusses various forms of alienation within capitalist society. Which of the following appear(s) in Marx’s list of alienation?
(A) From the product of one’s labour
(B) From one’s species-being
(C) From one another
(D) From one’s natural rights
Answer: (A, B, C)
42. Which among the following option(s) define(s) the nature of Forms according to Plato?
(A) Non-mental
(B) Independent of particulars
(C) Temporal
(D) Residing in God
Answer: (A, B)
43. Jīva and Ajīva are the Categories (padārtha) in Jainism. Which of the following are included in Ajīva?
(A) Matter (pudgala)
(B) Space (ākāśa)
(C) Motion (dharma)
(D) Cause (hetu)
Answer: (A, B, C)
44. In the Śaivasiddhānta, the Supreme Reality is called Pati, the individual self/soul is called Paśu, and the fetters which bind the souls are called Pāśa. Which of the following are included in Pāśa?
(A) Karma
(B) Māyā
(C) Kāma
(D) Moha
Answer: (A, B)
Q.45 – Q.65 Carry TWO marks Each
45. Read the passage carefully and answer the question:
“Only, unlike Kant, we do not see man as being essentially a positive will. On the contrary, he is first defined as a negativity. He is first at a distance from himself. He can coincide with himself only by agreeing never to rejoin himself. There is within him a perpetual playing with the negative, and he thereby escapes himself, he escapes his freedom. And it is precisely because an evil will is here possible that the words “to will oneself free” have a meaning. Therefore, not only do we assert that the existentialist doctrine permits the elaboration of an ethics, but it even appears to us as the only philosophy in which an ethics has its place. For, in a metaphysics of transcendence, in the classical sense of the term, evil is reduced to error; and in humanistic philosophies it is impossible to account for it, man being defined as complete in a complete world. Existentialism alone gives – like religions – a real role to evil, and it is this, perhaps, which make its judgments so gloomy. Men do not like to feel themselves in danger.”
– Simone de Beauvoir, The Ethics of Ambiguity
Which one of the following claim is made in the passage regarding Existentialism?
(A) Its emphasis on negativity means that it can account for evil.
(B) It cannot give rise to an ethic since it rejects the idea of evil.
(C) It believes that evil is a kind of error.
(D) It must withhold judgments about evil.
Answer: (A)
46. Keeping in mind the central commitments of John Dewey’s Pragmatism, which one of the following applies to his concept of experience?
(A) It involves transaction between the individual and her environment.
(B) It is an inferior source of knowledge.
(C) It is shaped by the environment but cannot modify the environment.
(D) It is overridden by reason in validating knowledge.
Answer: (A)
47. All Covid-19 patients are fighters
No Covid-19 patients are children
Therefore, no children are fighters
Which one among the following options determines the mood, figure, and fallacy of the above argument?
(A) AEE, III Figure, Illicit Major
(B) AEE, II Figure, Undistributed Middle
(C) AEE, III Figure, Illicit Minor
(D) AEE, II Figure, Existential Fallacy
Answer: (A)
48. In the theory of causation, the effect (kārya) is non-existent (asat) before its creation; it is a new beginning (ārambha). Which one of the following schools of thought in Indian philosophy upholds this theory?
(A) Nyāya
(B) Vedānta
(C) Yoga
(D) Sānkhya
Answer: (A)
49. Read the passage carefully and answer the question:
“Passive resistance is a method of securing rights by personal suffering; it is the reverse of resistance by arms. When I refuse to do a thing that is repugnant to my conscience, I use soul-force. For instance, the Government of the day has passed a law which is applicable to me. I do not like it. If by using violence I force the Government to repeal the law, I am employing what may be termed body-force. If I do not obey the law and accept the penalty for its breach, I use soul-force. It involves sacrifice of self.”
– M. K. Gandhi, Hind Swaraj or Indian Home Rule
Which one among the following is NOT in conformity with the above passage?
(A) Soul-force is brute force
(B) Passive resistance involves sacrifice
(C) Conscience is the soul-force
(D) Active resistance is body-force
Answer: (A)
50. In light of Merleau-Ponty’s concepts of the body and perception in his Phenomenology of Perception, which of the following claim(s) is/are true about my body?
(A) It is the vantage-point of my perception.
(B) It is the subject of perception.
(C) It can appear in my perception just like other objects.
(D) It is not embedded in my field of perception.
Answer: (A, B)
51. Plato’s theory of recollection sheds light on the origins of knowledge. Which among the following option(s) does it intend to explain?
(A) Philosophical and mathematical discoveries
(B) Our linguistic capacities
(C) Innateness of knowledge
(D) Only higher learning but not the ordinary learning
Answer: (A, B, C)
52. Which among the following is/are correct statement(s) about Aristotle’s approach to the study of logic and its contribution to science (episteme)?
(A) Logic is a mere tool and not an end in itself.
(B) Logic makes an important but incomplete contribution to science.
(C) The mind-independent nature of things is not accessible only through Logic.
(D) Science employs only Deductive Logic.
Answer: (A, B, C)
53. Which among the following statement(s) is/are in accordance with John Locke’s epistemological concern in his An essay concerning human understanding?
(A) All our knowledge ultimately derives from experience.
(B) Experience immediately provides us with ideas, not knowledge as such.
(C) Reason has no role to play in our acquisition of knowledge.
(D) Our knowledge has no limits.
Answer: (A, B)
54. Which among the following fundamental rationalist beliefs concerning the cause and effect relation does David Hume reject?
(A) Causes contain their effects.
(B) Causes entail their effects.
(C) There is necessary connection between cause and effect.
(D) Causal reasoning is not like demonstrative reasoning.
Answer: (A, B, C)
55. If Immanuel Kant is said to have brought about a Copernican revolution in philosophy, it is because of the following reasons:
(A) For bringing foundational change in metaphysics.
(B) For showing that objects conform to perception and not perception to objects.
(C) For placing mind at the center of epistemology.
(D) For bringing foundational change in the theory of morality.
Answer: (A, B, C)
56. What differentiates Logical Positivism of the Vienna Circle from the earlier forms of Empiricism and Positivism of Hume, Mach, Comte and Mill?
(A) In holding that the ultimate basis of knowledge rests upon public experimental verification rather than personal experience.
(B) In holding that metaphysical doctrines are not false but meaningless.
(C) In holding that all genuine knowledge about nature can be expressed in a single language common to all the sciences.
(D) In confirming the possibility of synthetic a priori.
Answer: (A, B, C)
57. Bertrand Russell’s philosophy of Logical Atomism intends to establish his methodological and metaphysical standpoints. Which among the following is/are in accordance with his doctrine?
(A) Everything we experience can be analyzed into logical atoms.
(B) Logical atoms are particulars, qualities, and relations.
(C) Logical atoms are universals, and not about qualities and relations.
(D) We can apprehend the reality as it is in itself, unaffected by the medium of thought.
Answer: (A, B)
58. Using the theories of punishment to argue for or against capital punishment, which among the following is/are true?
(A) A combination of Utilitarian and Deterrent theories will argue for capital punishment.
(B) A combination of Utilitarian and Retributive theories will argue for capital punishment.
(C) A combination of Utilitarian and Reformative theories will argue against capital punishment.
(D) A combination of Reformative and Retributive theories will argue against capital punishment.
Answer: (A, B OR A, B, C)
59. Gilbert Ryle believed that Descartes’ mind-body dualism commits a category mistake. Which of the following motive(s) of Descartes lead(s) to this category mistake?
(A) Endorsement of the claims of mechanics but not the Hobbesian kind
(B) Belief in religion and morality
(C) The mental cannot be a variety of the mechanical
(D) Complete endorsement of Hobbesian mechanics
Answer: (A, B, C)
60. Ludwig Wittgenstein, in his Tractatus Logico-Philosophicus, writes, “A picture can depict any reality whose form it has.” Which of the following proposition(s) will be in line with this?
(A) A picture can always display a pictorial form.
(B) A picture has logical form.
(C) A logical picture can depict the world.
(D) A picture can depict its pictorial form.
Answer: (A, B, C)
61. Select the CORRECT combinations of the Vedanta schools (Group-I) and their propounders (Group-II) from the table.
(A) (a) and (iii)
(B) (d) and (ii)
(C) (b) and (i)
(D) (c) and (iv)
Answer: (A, B)
62. Which of the following is/are part of the six pāramitās (ṣaḍpāramitā) in Buddhism?
(A) Charity or giving (dāna)
(B) Virtuous conduct (śīla)
(C) Forbearance or patience (kṣānti)
(D) Non-violence (ahimsā)
Answer: (A, B, C)
63. Read the passage carefully and answer the question:
“Habits of the constitutional morality may be essential for the maintenance of a constitutional form of government. But the maintenance of a constitutional form of Government is not the same thing as a self-government by the people. Similarly, it may be granted that adult suffrage can produce government of the people in the logical sense of the phrase, i.e., in contrast to the government of a king. But it cannot by itself be said to bring about a democratic government, in the sense of the government by the people and for the people.”
– B. R. Ambedkar, “Democracy”, The Essential Writings of B. R. Ambedkar
Which of the following statements is/are NOT in conformity with the above passage?
(A) The maintenance of self-governance is always maintenance of constitutional government.
(B) Constitutional morality may not be essential for preservation of constitutional form of government.
(C) Adult suffrage itself is sufficient to bring about a democratic government.
(D) Elected government is logically in contrast to the government of a king.
Answer: (A, B, C)
64. Read the passage carefully and answer the question:
“What do I mean by the ideal of universal religion? I do not mean any one universal philosophy, or any one universal mythology, or any one universal ritual held by all; for I know that this world must go on working, wheel within wheel, this intricate mass of machinery, most complex, most wonderful. What can we do then? We can make it run smoothly, we can lessen the friction; we can grease the wheels, as it were. How? By recognizing natural necessity of variation. Just as we have recognized unity by our very nature, so we must also recognize variation. We must learn that truth may be expressed in a hundred thousand ways, and that each of these ways is true as far as it goes. We must learn that same thing can be viewed from a hundred different standpoints, and yet be the same thing.”
– Swami Vivekananda, “The Ideal of a Universal Religion”, The Complete Works of Swami Vivekananda, Vol.II
Which of the following is/are characteristics of Vivekananda’s ideal of universal religion?
(A) No adherence to any particular religion
(B) Celebration of differences
(C) Recognition of multiple truths
(D) Reduction of all religions into a single religion
Answer: (A, B)
65. Read the song carefully and answer the question:
Deliverance is not for me in renunciation. I feel the embrace of freedom in a thousand bonds of delight.
Thou ever pourest for me the fresh draught of thy wine of various colours and fragrance, filling this earthern vessel to the brim.
My world will light its hundred different lamps with thy flame and place them before the altar of thy temple.
No, I will never shut the doors of my senses. The delights of sight and hearing and touch will bear thy delight.
Yes, all my illusions will burn into illumination of joy, and all my desires ripen into fruits of love.
– Rabindranath Tagore, Gitanjali, Song 73
The above song voices Tagore’s philosophy of life. Which among the following is/are in conformity with the message of the song?
(A) Denial of asceticism.
(B) Worldliness and divinity are not at odds with each other.
(C) Appreciation and enjoyment of the world.
(D) Denial of sensuous indulgence in the world.
Answer: (A, B, C)
PSYCHOLOGY (C5)
XH-C5: Q.27 – Q.44 Carry ONE mark Each
27. The construct validity of a test is assessed through ________.
(A) Convergent and Discriminant validity
(B) Concurrent and Predictive validity
(C) Convergent and Predictive validity
(D) Discriminant and Predictive validity
Answer: (A)
28. Memory involves three stages. Find out the correct sequence from the following:
(A) Storage, Encoding, Retrieval
(B) Retrieval, Encoding, Storage
(C) Encoding, Storage, Retrieval
(D) Decoding, Encoding, Storage
Answer: (C)
29. Erickson’s fifth stage of psychosocial development is
(A) Identity vs role confusion
(B) Intimacy vs isolation
(C) Generative vs stagnation
(D) Integrity vs despair
Answer: (A)
30. Test developers use reverse coding of certain items in a scale to offset the effects of
(A) Social desirability
(B) Acquiescence
(C) Faking
(D) Random responding
Answer: (B)
31. According to Kohlberg’s theory of Moral development, at which level individuals judge morality in terms of abstract principles?
(A) Pre-conventional
(B) Post-conventional
(C) Conventional
(D) Transcendental
Answer: (B)
32. You had been driving a car with manual-gear for 5 years. Recently, you started driving a new car with an auto- gear. If you are having any trouble, it is most likely due to _________.
(A) Proactive interference
(B) Retroactive interference
(C) Anterograde interference
(D) Learning Difficulties
Answer: (A)
33. Which of the following is not a behaviour therapy technique?
(A) Flooding
(B) Countertransference
(C) Counterconditioning
(D) Systematic desensitization
Answer: (B)
34. According to Robert Sternberg, “Street Smarts” refers to –
(A) Analytical intelligence
(B) Creative intelligence
(C) Emotional intelligence
(D) Practical intelligence
Answer: (D)
35. Research design in which several age groups of participants are studied at one particular point of time is called:
(A) Cross-sequential design
(B) Functional design
(C) Cross-sectional design
(D) Longitudinal design
Answer: (C)
36. Proximo-distal direction of development explains the nature of the development from _____.
(A) Top to bottom
(B) Internal organs to external organs
(C) Centre to periphery
(D) Sensory organ to motor organs
Answer: (C)
37. A cricket player who could not play an easy ball and gets out without scoring any run and blames the pitch, is an expression of _______.
(A) Sublimation
(B) Regression
(C) Projection
(D) Rationalization
Answer: (C)
38. The process through which we seek to identify the causes of other’s behaviour and gain knowledge of their stable traits and dispositions is known as _______.
(A) Distribution
(B) Dissemination
(C) Retribution
(D) Attribution
Answer: (D)
39. Which of the following techniques is used to measure the variations in the activity of Ascending Reticular Activating System (ARAS)?
(A) ECG
(B) PET
(C) fMRI
(D) EEG
Answer: (D)
40. The statement “I can do no wrong, but, you can do no right”, refers to ______.
(A) The self-serving bias
(B) The self-other bias
(C) The other-self bias
(D) The other- serving bias
Answer: (A)
41. Which of the following is a qualitative research design where learned experiences of individuals are examined in their life world?
(A) Phenomenology
(B) Ethnography
(C) Focused-group discussion
(D) Grounded-theory
Answer: (A)
42. Which part of the brain is responsible for transferring information from STM to LTM?
(A) Amygdala
(B) Hypothalamus
(C) Hippocampus
(D) Cerebellum
Answer: (C)
43. The mean of a distribution is 14 and standard deviation is 5. What would be the value of coefficient of variation? (round off to two decimal places)
Answer: (35.71 to 35.72)
44. Swami gets a test score of 190, the mean is 150 and SD is 25. Assuming normal distribution, the Z score would be _________.
(round off to one decimal place)
Answer: (1.6 to 1.6)
Q.45 – Q.65 Carry TWO marks Each
45. Which of the following statement(s) is/are correct regarding Multiple Analysis of Variance (MANOVA)?
(A) Tests the mean difference of more than two groups on one dependent variable.
(B) Tests the mean difference of more than two groups across several dependent variables.
(C) The independent variable is measured on a nominal scale and dependent variable on an interval or ratio scale.
(D) The dependent variable is measured on nominal scale and independent variable on an interval or ratio scale.
Answer: (B, C)
46. Which of the following statements is/are related to observational learning?
(A) Remembering the steps to perform a task
(B) A person in a dinner wants to know how to use the utensils by watching others
(C) A person uses chocolate to motivate his son to perform the task
(D) A person is capable of reproducing the action after viewing it
Answer: (A, B, D)
47. Find out the statements which are related to different types of reliability?
(A) The same test is administered to the same people at two points in time
(B) Give the test once and have it scored by two scorers or by two methods
(C) Give the test in one administration and then split the test into two halves for scoring
(D) The extent to which people score on a measure are correlated with other variables
Answer: (A, B, C)
48. Which of the following statement(s) regarding test scores and their interpretations is/are correct?
(A) Frequency distribution are graphs to help us understand the distribution of test scores
(B) Normal probability distribution is a theoretical distribution to help us understand the distribution of test scores
(C) Central tendency measures are numerical tools to help us locate the middle of a distribution of a test score
(D) Measurement of variability are numerical tools to help us understand the spread of a distribution of a test score
Answer: (B, C, D)
49. Which of the following statement(s) is/are correct regarding the negative symptoms of schizophrenia?
(A) Auditory hallucination, persecution, and disorganized thinking
(B) Lack of effect in situation, poor motivation, and social withdrawal
(C) Loss of interest in day-to-day activities, lack of will, and difficulty in expressing emotions
(D) Visual hallucination, delusions of grandeur, and delusion of control
Answer: (B, C)
50. Which of the following statement(s) is/are correct about children with ADHD (Attention Deficit Hyperactivity Disorder)?
(A) They have deficit in brain related executive function
(B) They have difficulty to control voluntary movements, verbal expression and problem solving due to frontal lobes
(C) Cerebellum (an area of the brain) does not work properly, which coordinates muscular activity
(D) It is also known as hypokinetic disorder
Answer: (A, B, C)
51. Which of the following assumptions are correct about equity theory?
(A) Focusses on procedural justice
(B) Motivation is influenced by relative and absolute rewards
(C) Referent is the other-inside
(D) Achieving balance between input-output
Answer: (B, C, D)
52. Which of the following statement(s) are related to Bem’s theory of self-perception?
(A) It starts with development of one’s basic self-concept
(B) Behaviour is a source of knowledge
(C) It is related to attitude formation
(D) It suggests that people change their attitude because of their behaviour
Answer: (B, C, D)
53. Which of the following statements are related to social cognition?
(A) How individuals interpret, analyze, remember and use information about the social world
(B) How people create mental structure to organise knowledge about the social world
(C) How people think about themselves and the social world
(D) It does not allow interaction between people and the environment
Answer: (A, B, C)
54. Which of the following theory(ies) is/are related to work motivation?
(A) Motivation-Hygiene Theory
(B) Expectancy Theory
(C) Trait Theory
(D) ERG Theory
Answer: (A, B, D)
55. Which of the following are not part of Thurstone’s theory of primary mental abilities?
(A) Numerical Ability
(B) Word Fluency
(C) Analytical Ability
(D) Short-Term Memory
Answer: (C, D)
56. Which of the following are the competencies of a Bystander?
(A) Deciding how to help a person in need
(B) Deciding how to avoid a person at the time of his/her distress
(C) Deciding to standby with a person at the time of his/her emergency
(D) Too busy to help
Answer: (A, C)
57. Which of the following functions are related to pancreas?
(A) Release of hormones
(B) Converts food we eat into fuel for the body cells
(C) It regulates the level of glucose in the blood
(D) It damages digestive system
Answer: (A, B, C)
58. Which of the following psychologists do not belong to behaviourism?
(A) Sigmund Freud
(B) B. F. Skinner
(C) William James
(D) J. B. Watson
Answer: (A, C)
59. Which of the following theories of emotion explains that arousal must occur before experience of emotion?
(A) Schachter & Singer’s Theory
(B) Hertzberg’s Theory
(C) Cannon-Bard’s Theory
(D) Maslow’s Theory
Answer: (A OR A, C)
60. Who among the following psychologists do not belong to the domain of emotional intelligence?
(A) David Mayer
(B) Sigmund Freud
(C) William James
(D) Robert R. Baron
Answer: (B, C, D)
61. Which of the followings are the projective tests of personality?
(A) Rorschach Inkblot Test
(B) 16 PF
(C) TAT
(D) WAT
Answer: (A, C, D)
62. Which of the followings are not learning disorders?
(A) Dyslexia
(B) Dystopia
(C) Dysgraphia
(D) Dystonia
Answer: (B, D)
63. Which of the following concepts are not related to Piaget’s theory of cognitive development?
(A) Imprinting
(B) Attachment
(C) Schemas
(D) Zone of Proximal Development
Answer: (A, B, D)
64. Which of the following statement(s) is/are correct regarding exploratory factor analysis (EFA) technique?
(A) It helps to reduce large number of variables into few numbers of factors.
(B) It helps researchers to investigate concepts that cannot easily be measured directly.
(C) It extracts maximum common variance from all variables and put them into a common score.
(D) A technique used to verify the factor structure of a set of observed variables.
Answer: (A, B, C)
65. If you want to examine the difference between the work values of employees in public and private sector and the relationship of work values with employee engagement, what would be the appropriate statistics to test the hypotheses?
(A) F-test
(B) t-test
(C) Pearson Product moment correlation
(D) Chi-square
Answer: (A, B, C)
SOCIOLOGY (C6)
XH-C6: Q. 27 – Q. 44 Multiple Choice Questions (MCQ), carry ONE mark each
27. In a questionnaire based survey, the following item was asked to a respondent:
“I found the course interesting and structured.”
Yes No
Which one of the given options clearly describes the item?
(A) This is a double barreled item.
(B) This is a leading item.
(C) This is negatively worded item.
(D) This item is correctly constructed.
Answer: (A)
28. Which one of the following is used in causal analysis?
(A) Pearson correlation
(B) Linear regression
(C) Frequency distribution
(D) Standard deviation
Answer: (B)
29. Which one of the given options reflects Karl Popper’s falsification principle?
(A) Any theory is scientific only if it allows empirical facts to disprove it
(B) Manipulation of observational data will help the researchers to give new results
(C) Scientists should not report false data
(D) Lab based scientific experiments cannot be falsified
Answer: (A)
30. Resource mobilization theory of social movements analyses social movements as _______.
(A) the rational undertakings by activists in a movement as they build a collective project
(B) the emotional dynamics of the activists in a movement
(C) the pre-existing solidarities of movement entrepreneurs that bring people together
(D) the revolutionary potential of ordinary people
Answer: (A)
31. Which one of the following methods uses a control group while validating the impact of intervention programmes?
(A) Qualitative interviews
(B) Quantitative survey
(C) Experimental designs
(D) National sample survey
Answer: (C)
32. Which is not a trait of a sociological theory?
(A) It is logically interconnected propositions.
(B) It has no relationship with the data.
(C) It can be speculative.
(D) It may predict facts.
Answer: (B)
33. According to Pierre Bourdieu, the way one speaks or having an accent is ______ form of cultural capital.
(A) an objectified
(B) an embodied
(C) an institutionalized
(D) an unusual
Answer: (B)
34. Which one of the given options is not a latent function of attending a university?
(A) To receive a certificate or a degree
(B) To find a suitable spouse
(C) To establish startups
(D) To improve physical fitness
Answer: (A)
35. Who among the following highlighted the concept of ‘Swaraj’ in the reconstruction of traditional village life?
(A) Jawaharlal Nehru
(B) Mahatma Gandhi
(C) B.R. Ambedkar
(D) Ram Mohan Roy
Answer: (B)
36. In the 1960s, India adopted a heavy usage of high yielding varieties of seed, chemical fertilizers, pesticides, and new machines to raise the productivity of agricultural land. This process was described as ___________.
(A) White Revolution
(B) Land Revolution
(C) Green Revolution
(D) Technology Revolution
Answer: (C)
37. Among the Toda of South India, property is inherited patrilineally and ritualistic privileges are inherited matrilineally. This is an example of _______.
(A) unilateral descent
(B) matrilineal descent
(C) pragmatic descent
(D) bilateral descent
Answer: (D)
38. Which of the following scholars described India’s villages as a ‘den of ignorance, narrow-mindedness and communalism’?
(A) B.R. Ambedkar
(B) M.K. Gandhi
(C) Jawaharlal Nehru
(D) S.S. Jodhka
Answer: (A)
39. Who among the following gave the concept of ‘global village’?
(A) Marshall McLuhan
(B) Anthony Giddens
(C) Roland Robertson
(D) T.H. Marshall
Answer: (A)
40. Commodity chain is defined as __________.
(A) a series of production stages, or network of labour inputs, distributed globally among production sites
(B) importing commodities to meet the domestic needs
(C) outsourcing the marketing of commodities to private agencies
(D) import substituted industrialization
Answer: (A)
41. Which of the following is a process wherein socialist states guide economic growth through the planned allocation of public and human resources, as an alternative to allocation through the market?
(A) Social capitalism
(B) Centralized planning
(C) Corporatism
(D) Developmentalism
Answer: (B)
42. An approach that reformulates development emphasizing essential human needs over and above rising incomes is referred to as _________.
(A) integrated development approach
(B) endogenous development approach
(C) basic needs approach
(D) community development approach
Answer: (C)
43. Which of the following scholars emphasized the subaltern perspective in social movements involving peasants?
(A) Veena Das
(B) Geeta Chakraborty-Spivak
(C) Jan Breman
(D) Ranajit Guha
Answer: (D)
44. Which of the following institutions provides the structural link between caste and gender in kinship in India?
(A) Panchayat
(B) Class
(C) Household
(D) Marriage
Answer: (D)
Q.45 – Q. 65 Multiple Choice Question (MCQ), carry TWO marks each
45. A researcher is conducting a survey about internet use among the students. She was asked to follow a probability sampling technique. Which one of the given options is most suitable?
(A) Stand in front of the library located in her college and hand over the survey questionnaires.
(B) Collect the email ids of the students and send the questionnaire.
(C) Collect the roster of students from the college administration and give the questionnaire to those selected through a lottery.
(D) Give the questionnaires to a data collection agency.
Answer: (C)
46. According to Talcott Parsons, the dichotomies of pattern variables or alternatives an actor can choose in society are: ascription vs _________; affectivity vs _________; and diffuseness vs _________.
(A) achievement, neutrality, specificity
(B) attribution, emotion, distraction
(C) achievement, hatred, specificity
(D) attribution, neutrality, distraction
Answer: (A)
47. According to Peter Blau, there is ________ price in social exchange but only _____ exchange ratio between two social benefits, because personal considerations and social norms influence the process of _______.
(A) an exact equilibrium, an approximate, social exchange
(B) no exact equilibrium, an equal, social exchange
(C) no exact equilibrium, an approximate, social exchange
(D) no exact equilibrium, an approximate, social relationships
Answer: (C)
48. ANOVA means ______.
(A) analysis of variance
(B) analysis of variable average
(C) another variable average
(D) a non-parametric variable
Answer: (A)
49. A researcher got excited on seeing a celebrity tweeting about COVID19. She downloaded one million tweets using a software application. Then she analyzed the data to find out whether celebrities have a social conscience. What is this research approach called?
(A) Abductive approach
(B) Inductive approach
(C) Deductive approach
(D) Operations approach
Answer: (B)
50. According to Robert Merton, innovation is a mode of adaptation when cultural goals are ______ and institutionalized means are _________.
(A) accepted, rejected
(B) rejected, accepted
(C) accepted, accepted
(D) rejected, rejected
Answer: (A)
51. According to Erving Goffman, __________ refers to an institution where all aspects of a person’s life are regulated by a single authority. Through a process of __________ceremony, the person shall become secondary and invisible in the overbearing social environment.
(A) university, graduation
(B) total institution, degradation
(C) university, degradation
(D) total institution, graduation
Answer: (B)
52. Match the following:
(A) A-III, B-II, C-V, D-I
(B) A-III, B-IV, C-II, D-I
(C) A-V, B-III, C-II, D-I
(D) A-IV, B-III, C-II, D-V
Answer: (B)
53. According to Walt W. Rostow, all nations pass through ________ stages of economic development and _________ stage marks the interval when the old blocks and resistances to steady growth are finally overcome.
(A) five, the take-off
(B) four, the drive to maturity
(C) five, the preconditions for take-off
(D) four, the age of high consumption
Answer: (A)
54. Which of the following statements are correct?
[i] Gustavo Esteva argues that the 1949 address of the US President Harry S. Truman marks the opening of the era of development.
[ii] According to Escobar, ‘development can best be described as an apparatus that links forms of knowledge about the Third World with the deployment of forms of power and intervention, resulting in the mapping and production of Third World societies’.
(A) [i] only
(B) [ii] only
(C) Both [i] and [ii]
(D) Neither [i] nor [ii]
Answer: (C)
Q. 55 – Q. 65 Multiple Select Question (MSQ), carry TWO marks each
55. Which among the listed options most closely replicate(s) Jurgen Habermas’ idea of the public sphere?
(A) PayTM App
(B) Facebook
(C) IRCTC Portal
(D) YouTube
Answer: (B, D)
56. In the light of given information, which pairs are correct?
M1: Anthony Giddens M2: Robert Merton M3: George Ritzer
X1: Macdonaldization of society X2: Mathew Effect X3: The Third Way
(A) M1X3
(B) M2X2
(C) M1X1
(D) M2X3
Answer: (A, B)
57. What concepts were studied in the famous Milgram social experiment where teachers did not hesitate to give electric shocks to learners?
(A) Conformity
(B) Obedience
(C) Deviance
(D) Consciousness
Answer: (A, B)
58. According to Max Weber, in addition to power what are the other TWO distinct components of stratification?
(A) Status
(B) Class
(C) Counter Culture
(D) Social Control
Answer: (A, B)
59. While writing on the diversity of rural settlements, Bernard Cohn has identified which of the following village patterns?
(A) Nucleated Village
(B) Hamleted Village
(C) Dispersed Village
(D) Joint Village
Answer: (A, B, C)
60. According to Andre Gunder Frank, which of the following factors are responsible for the development of underdevelopment in Latin America?
(A) The survival of archaic institutions
(B) The relationship between the satellite and the metropolis
(C) The existence of capital shortage in developed regions
(D) Participation in the process of world capitalist development
Answer: (B, D)
61. Which of the following statements describe the concept of sustainable development?
(A) Shrinking role of the government in favour of the market forces
(B) Meeting the needs of the present without compromising the needs of the future generations
(C) Conserving natural resources and adopting appropriate technologies
(D) Privileging of the urban classes and manufacturing sector over rural society
Answer: (B, C)
62. The categories of caste and tribe have been understood as colonial constructions. Which statements instantiate the above?
(A) British anthropologists used the categories of caste and tribe to further knowledge and understanding of Indian society.
(B) The character of these categories were solidified through processes of enumeration and classification undertaken during British rule.
(C) These categories had no existence prior to British rule.
(D) Census operations and administrative practices of the colonial regime made these categories what they are today.
Answer: (A, B, D)
63. Which statements express the ideas of A. M. Shah with regard to family and household in India?
(A) Households are task-oriented residence units while families are kinship groupings that need not be localized.
(B) Households imply the entire biradari (kin network) while families are neo-local units.
(C) Households are operational units that function with a family and kinship ideology.
(D) The family provides the larger ideological set-up within which the household operates.
Answer: (A, C, D)
64. According to Celestin Bougle, the spirit of the caste system is determined by the mutual repulsion that exists between castes. Identify TWO different aspects in which such mutual repulsion is manifested:
(A) Upward mobility
(B) Endogamy
(C) Westernization
(D) Commensal restrictions
Answer: (B, D)
65. Which of the following statements explain and illustrate the term ‘tragedy of commons’?
(A) Wasteland development and the ensuing privatization of commons
(B) Transference of rights and control from the community to development agencies
(C) Regeneration of ecologically appropriate tree cover
(D) Socially appropriate community control over a regenerated resource base
3. Both the numerator and the denominator of 3/4 are increased by a positive integer, x, and those of 15/17 are decreased by the same integer. This operation
results in the same value for both the fractions.
What is the value of x?
(A) 1
(B) 2
(C) 3
(D) 4
Answer: (C)
4. A survey of 450 students about their subjects of interest resulted in the following outcome.
• 150 students are interested in Mathematics.
• 200 students are interested in Physics.
• 175 students are interested in Chemistry.
• 50 students are interested in Mathematics and Physics.
• 60 students are interested in Physics and Chemistry.
• 40 students are interested in Mathematics and Chemistry.
• 30 students are interested in Mathematics, Physics and Chemistry.
• Remaining students are interested in Humanities.
Based on the above information, the number of students interested in Humanities is
(A) 10
(B) 30
(C) 40
(D) 45
Answer: (D)
5.
For the picture shown above, which one of the following is the correct picturerepresenting reflection with respect to the mirror shown as the dotted line?
Answer: (A)
Q.6 – Q.10 Carry TWO marks each.
6. In the last few years, several new shopping malls were opened in the city. The total number of visitors in the malls is impressive. However, the total revenue generated through sales in the shops in these malls is generally low.
Which one of the following is the CORRECT logical inference based on the information in the above passage?
(A) Fewer people are visiting the malls but spending more
(B) More people are visiting the malls but not spending enough
(C) More people are visiting the malls and spending more
(D) Fewer people are visiting the malls and not spending enough
Answer: (B)
7. In a partnership business the monthly investment by three friends for the first six months is in the ratio 3: 4: 5. After six months, they had to increase their monthly investments by 10%, 15% and 20%, respectively, of their initial monthly investment. The new investment ratio was kept constant for the next six months.
What is the ratio of their shares in the total profit (in the same order) at the end of the year such that the share is proportional to their individual total investment over the year?
(A) 22 : 23 : 24
(B) 22 : 33 : 50
(C) 33 : 46 : 60
(D) 63 : 86 : 110
Answer: (D)
8. Consider the following equations of straight lines:
Line L1: 2x− 3y= 5
Line L2: 3x+ 2y= 8
Line L3: 4x− 6y= 5
Line L4: 6x− 9y= 6
Which one among the following is the correct statement?
(A) L1 is parallel to L2 and L1 is perpendicular to L3
(B) L2 is parallel to L4 and L2 is perpendicular to L1
(C) L3 is perpendicular to L4 and L3 is parallel to L2
(D) L4 is perpendicular to L2 and L4 is parallel to L3
Answer: (D)
9. Given below are two statements and four conclusions drawn based on the statements.
Statement 1: Some soaps are clean.
Statement 2: All clean objects are wet.
Conclusion I: Some clean objects are soaps.
Conclusion II: No clean object is a soap.
Conclusion III: Some wet objects are soaps.
Conclusion IV: All wet objects are soaps.
Which one of the following options can be logically inferred?
(A) Only conclusion I is correct
(B) Either conclusion I or conclusion II is correct
(C) Either conclusion III or conclusion IV is correct
(D) Only conclusion I and conclusion III are correct
Answer: (D)
10. An ant walks in a straight line on a plane leaving behind a trace of its movement. The initial position of the ant is at point P facing east.
The ant first turns 72° anticlockwise at P, and then does the following twosteps in sequence exactly FIVE times before halting.
(1)moves forward for 10 cm.
(2) turns 144° clockwise.
The pattern made by the trace left behind by the ant is
Answer: (C)
Engineering Sciences
XE-A
Q.11 – Q.17 Carry ONE mark Each
11. The value of is
(A) 0
(B) 4
(C) 5
(D) 6
Answer: (C)
12. Let ℂ = {z = x + iy : x and y are real numbers, i = √−1} be the set of complex numbers. Let the function f(z) = u(x, y) + iv(x, y) for z = x + iy ∈ℂ be analytic in ℂ, where
u(x, y) = xy3 – yx3 and
If f′(z) denotes the derivative of f(z), then
(A) |f′ (−1 + i)|2 = 1
(B) |f′(−1 + i)|2 = 7
(C) |f′(−1 + i)|2 = 8
(D) |f′(−1 + i)|2 = 10
Answer: (C)
13. If the partial differential equation
is parabolic on the circle (x – a)2 + (y – b)2 = r2, then the values of a, b and r are given by
(A) a = 1, b = 2, r = 1
(B) a = −1, b = 2, r = 1
(C) a = 1, b = −2, r = 1
(D) a = −1, b = −2, r = 1
Answer: (B)
14. Let Γ be the positively oriented circle x2 + y2 = 9 in the xy-plane. If
whereα is a real constant, then α is equal to ________.
Answer: (36 to 36)
15. Let y1 (x) and y2(x) be two linearly independent solutions of
Let W(y1, y2) (x) denote the Wronskian of y1(x) and y2(x) at x.
If W(y1, y2) (1) = 1 then W(y1, y2) (2) is equal to______.
Answer: (4 to 4)
16. Let Then the sum of the geometric multiplicities of the distinct eigenvalues of A is equal to ________.
Answer: (2 to 2)
17. In a cosmopolitan city, the population comprises of 30% female and 70% male. Suppose that 5% of female and 30% of male in the population are foreigners. A person is selected at random from this population. Given that the selected person is a foreigner, the probability that the person is a female is ________ (round off to three decimal places).
Answer: (0.066 to 0.068)
Q.18 – Q.21 Carry TWO marks Each
18. Let f: (0, ∞) →ℝ be the continuous function such that x > 0, where for all x > 0. Then f(2) is equal to
(A) 2 + loge 2
(B) 2 – loge 2
(C) 2 + loge 4
(D) 2 – loge 4
Answer: (C)
19. Let A and B be n × n matrices with real entries.
Consider the following statements:
P: If A is symmetric then rank(A) = Number of nonzero eigenvalues (counting multiplicity) of A.
Q: If AB = 0 then rank(A) +rank (B)≤ n.
Then
(A) both P and Q are TRUE
(B) P is TRUE and Q is FALSE
(C) P is FALSE and Q is TRUE
(D) both P and Q are FALSE
Answer: (A)
20. Let f :ℝ2→ℝ be given by f(x, y) = 4xy – 2x2 – y4 + 1. The number of critical points where f has local maximum is equal to ________.
Answer: (2 to 2)
21. If the quadrature rule where α, β, γ are real constants, is exact for all polynomials of degree ≤ 3, then γ + 3(α2 + β2) + (α3 + β3) is equal to _______.
Answer: (3 to 3)
Fluid Mechanics: XE-B
(Q.22 – Q.30 Carry ONE mark Each)
22. A heavy horizontal cylinder of diameter D supports a mass of liquid having density ρ as shown in the figure. Find out the vertical component of force exerted by the liquid per unit length of the cylinder if g is the acceleration due to gravity.
Answer: (B)
23. The figure shows the developing zone and the fully developed region in a pipe flow where the steady flow takes place from left to right. The wall shear stress in the sections A, B, C, and D are given byτA, τB, τC, and τD, respectively. Select the correct statement.
(A) τA>τB
(B) τB>τA
(C) τC>τB
(D) τC>τD
Answer: (A)
24. The left hand column lists some non-dimensional numbers and the right hand column lists some physical phenomena. Indicate the correct combination
(A) 1-iii, 2-i, 3-ii, 4-iv
(B) 1-i, 2-ii, 3-iv, 4-iii
(C) 1-iv, 2-iii, 3-iv, 4-iii
(D) 2-iv, 1-iii, 3-ii, 4-i
Answer: (A)
25. As temperature increases
(A) the dynamic viscosity of a gas increases.
(B) the dynamic viscosity of a liquid decreases.
(C) the dynamic viscosity of a liquid does not change.
(D) the dynamic viscosity of a gas decreases.
Answer: (A, B)
26. Which of the following statement(s) regarding a venturimeter is/are correct?
(A) In the direction of flow, it consists of a converging section, a throat, and adiverging section.
(B) In the direction of flow, it consists of a diverging section, a throat, and aconverging section.
(C) It is used for flow measurement at a very low Reynolds number.
(D) Pressure tappings are provided just upstream of the venturimeter and at the throat.
Answer: (A, D)
27. Which of the following statement(s) is/are true for streamlines in a steady incompressible flow?
(A) Two streamlines cannot intersect each other.
(B) Flow rate increases between two diverging streamlines.
(C) Flow rate decreases between two diverging streamlines.
(D) Stream function has a constant value along a streamline.
Answer: (A, D)
28. A flow has a velocity potential given by ϕ = Ax3 where ‘A’ is a non-zero constant. Which of the following statement(s) is/are true about the flow?
(A) The flow is incompressible.
(B) The flow is irrotational.
(C) The flow has local acceleration.
(D) The flow has convective acceleration.
Answer: (B, D)
29. A boundary layer develops due to a two-dimensional steady flow over a horizontal flat plate. Consider a vertical line away from the leading edge which extends from the wall to the edge of the boundary layer. Which of the following quantity/quantities is/are not constant along the vertical line? u and v represent the components of velocity in the direction along the plate and normal to it, respectively and x is taken along the length of the plate while p is the pressure. Neglect body forces.
(A) u
(B) ∂u/∂x
(C) v
(D) p
Answer: (A, B, C)
30. A 10 kg mass placed on an infinitely long horizontal massless flat platform is to be supported by a steady vertical water jet as shown in the figure. The diameter of the jet is 5 cm. What minimum average velocity is required to hold the mass in place?
Assume ρwater = 1000 kg/m3, and π = 3.14. Neglect friction. (Round off to two decimal places)
Answer: (6.95 to 7.20)
Q.31 – Q.43 Carry TWO marks Each
31. Consider an inviscid flow through a smooth pipe which has a pitot-static tube arrangement as shown. Find the centre-line velocity in the pipe. Consider that the density of the fluid is 1000 kg/m3, acceleration due to gravity is 10 m/s2, and the specific gravity of the manometric fluid is 11.
(A) 2 m/s
(B) 3m/s
(C) 5m/s
(D) 7m/s
Answer: (A)
32. The speed of propagation, c, of a capillary wave depends on the density of the fluid, ρ, the wavelength of the wave, λ, and the surface tension, σ. If the density and wavelength remain constant, halving the surface tension would lead to a new velocity, c’, given by
(A) c’ = 2c
(B) c’ = √2c
(C) c’ = c/√2
(D) c’ = c
Answer: (C)
33. A two-dimensional flow field is described by a combination of a source of strength m at the origin and a uniform flow, U, in the positive x-direction such that the velocity potential is given by
The stagnation streamline is shown in the figure. Find the distance aa’.
(A) m/U
(B) 2m/U
(C) 8m/U
(D) m/2U
Answer: (D)
34. A typical boundary layer over a flat plate has a linear velocity profile with zero velocity at the wall and free stream velocity, U∞, at the outer edge of the boundary layer. What is the ratio of the momentum thickness to the thickness of the boundary layer?
(A) 1/2
(B) 1/4
(C) 1/6
(D) 1/3
Answer: (C)
35. Identify the configuration(s) in which steady two-dimensional internal flow may show boundary layer separation if the flow direction is left to right.
Answer: (C, D)
36. Consider steady fully developed flow of a liquid through two large horizontal flat parallel plates separated by a distance of 2 mm. One of the plate is fixed and the other plate moves at a speed of 0.5 m/s. What is the magnitude of the pressure gradient (in Pa/m) in the direction of the flow required to ensure that the net flow through the plates is zero?
Dynamic viscosity of the liquid is 5× 10−4 Ns/m2
(Round off to the nearest integer)
Answer: (374 to 376)
37. Consider two-dimensional turbulent flow of air over a horizontal flat plate of length 1 m. Skin friction coefficient at a length x from the leading edge of the plate is obtained as:
where, Rex is the local Reynolds number.
Find out the drag force per unit width (in N/m2) on the plate if the free stream air velocity is 10 m/s.
Density and dynamic viscosity of air are given as 1.2 kg/m3 and 1.83 × 10−5 N-s/m2,respectively.
(Round off to three decimal places)
Answer: (MTA)
38. For an inviscid fluid with density 1 kg/m3, the Cartesian velocity field is given as:
u = (−2x + y)ti + (2x + y) tj m/s
Neglecting the body forces, find the magnitude of pressure gradient in (Pa/m) at (x, y) = (1 m, 1 m) at t = 1s.
(Round off to two decimal places)
Answer: (5.60 to 5.70)
39. Consider a lawn sprinkler with horizontal arms of radius, a = 10 cm which has water introduced vertically through the centre, as shown in the figure. The exit area of the jet is 25 cm2 and the jet velocity is 1 m/s. The water is ejected orthogonal to the sprinkler arm and the jet makes an angle of 60° with the horizontal plane. Find the torque (in N-m) required to hold the sprinkler stationary.
Consider water density 1000 kg/m3. Neglect the effects of friction and gravity.
(Round off to two decimal places)
Answer: (0.24 to 0.26)
40. A wooden cylinder (specific gravity = 0.6) of length L and diameter D floats in water (density 1000 kg/m3). Find out the minimum value of D/L for which the cylinder floats with its axis vertical.
(Round off to three decimal places)
Answer: (1.380 to 1.390)
41. Consider a cart of mass 10 kg placed on an inclined plane (angle of inclination 60° with horizontal) as shown in the figure. A turning vane of negligible weight is mounted on the cart. A horizontal steady water jet is issued from a stationary nozzle of area 0.1 m2 and strikes the turning vane as shown in the figure. The vane turns the jet downward parallel to the inclined plane. Find out the minimum jet velocity (in m/s) which will not allow the cart to come down. Neglect friction, consider density of water = 1000 kg/m3 and acceleration due to gravity = 10 m/s2. (Round off to two decimal places)
Answer: (0.74 to 0.78)
42. A siphon is used to drain out water (density 1000 kg/m3) from a tank as shown in the figure. What can be the maximum height z (in meter) of the point C?
Consider acceleration due to gravity = 10 m/s2, pressure at point A = 101 kPa, vapour pressure of water = 29.5 kPa and neglect friction.
(Round off to two decimal places)
Answer: (5.1 to 5.2)
43. The horizontal belt of negligible weight shown in the figure moves with a steady velocity (V) of 2.5 m/s and skims over the top surface of an oil-film of depth h = 3 cm. The length (L) and width (b) of the belt are, respectively, 2 m and 60 cm. Find the viscosity of the oil (in Pa-s), given that the minimum power required to move the belt is 100 W. Neglect the end effects. (Round off to two decimal places)
Answer: (0.39 to 0.41)
Materials Science XE-C
Q.44 – Q.52 Carry ONE mark Each
44. Number of atoms per unit area of the (110) plane of a body centered cubic crystal, with lattice parameter ‘a’, is
(A) 1/a2
(B) √2/a2
(C) 1/√3a2
(D) 1/√2a2
Answer: (B)
45. Match the following materials with their corresponding bonding types.
(A) P – 4; Q – 2; R – 3; S – 1
(B) P – 3; Q – 4; R – 2; S – 1
(C) P – 3; Q – 2; R – 1; S – 4
(D) P – 3; Q – 1; R – 4; S – 2
Answer: (C)
46. In an ideal rubber, the primary factor responsible for elasticity up to small strains is
(A) Change in both enthalpy and entropy
(B) Change in enthalpy, but no change in the entropy
(C) No change in enthalpy, but change in the entropy
(D) Neither a change in enthalpy, nor a change in the entropy
Answer: (C)
47. Which one of the following statements is true for an intrinsic semiconductor?
(A) Electrical conductivity increases with increasing temperature and pressure
(B) Electrical conductivity increases with increasing temperature and decreasing pressure
(C) Electrical conductivity increases with decreasing temperature and increasing pressure
(D) Electrical conductivity increases with decreasing temperature and pressure
Answer: (A)
48. A differential scanning calorimetry (DSC) experiment tracks the heat flow into or out of a system as a function of temperature. If the experiments given in the options below are performed at 1 atmospheric pressure, then in which case will the DSC thermogram exhibit a spike, either upward or downward?
(A) Heating 10 mg of pure Cu from 323 K to 673 K
(B) Cooling pure water from 323 K to 278 K
(C) Heating pure ice from 263 K to 284 K
(D) Cooling a Pb-Sn alloy at the eutectic composition from 323 K to 273 K
Answer: (C)
49. Which one of the following solvent environments will likely result in swelling of solid polystyrene?
(A) 0.1 M NaOH in H2O
(B) HCl (aq.) of pH = 6
(C) Distilled water
(D) Benzene
Answer: (D)
50. Vickers microhardness (HV) of a ductile material A is higher than another ductile material B. Which of the following is/are true?
(A) Young’s modulus of A is greater than B
(B) Yield strength of A is greater than B
(C) Scratch resistance of A is greater than B
(D) Ductility of A is greater than B
Answer: (B, C)
51. The enthalpy required to create an oxygen vacancy in CeO2 is 4 eV. The number
of oxygen vacancies present per mole of CeO2 at 1000 K is _________.
(Round off to the nearest integer)
Given:
NA :Avogadro’s number = 6.02 × 1023 mole−1
kB : Boltzmann’s constant = 8.62 × 10−5 eV/K
Answer: (4232 to 4249)
52. An electrochemical reaction is known to occur at +4.50 V against a Li+/Li reference electrode. The potential of the same reaction against a Zn2+/Zn reference electrode is __________ V. (Round off to two decimal places).
Given:
E0 (Li+/Li) = −3.04 V versus Standard Hydrogen Electrode
E0 (Zn2+/Zn) = −0.77 V versus Standard Hydrogen Electrode
Answer: (2.20 to 2.30)
Q.53 – Q.65 Carry TWO marks Each
53. For a binary system at constant pressure, there are two types of invariant reactions:
(i) α ↔ β + γ
(ii) α + β ↔ γ
Analogously, how many different types of invariant reactions may exist under
variable temperature and pressure, for a binary system?
(A) 1
(B) 2
(C) 3
(D) 4
Answer: (C)
54. For a glass marginally below its glass transition temperature, which one of the following statements is true?
(A) Glass has higher enthalpy than both the corresponding crystalline and liquid phases
(B) Glass has lower enthalpy than both the corresponding crystalline and liquid phases
(C) Glass has higher entropy than the corresponding crystalline phase and lower entropy than the corresponding liquid phase
(D) Glass has lower entropy than the corresponding crystalline phase and higher entropy than the corresponding liquid phase
Answer: (C)
55. Which one of the following samples of high-purity aluminium (Al) single crystal will plastically yield at the lowest applied load under ambient conditions? Loading axis is along the direction shown in the schematic.
(A) (i)
(B) (ii)
(C) (iii)
(D) (iv)
Answer: (D)
56. Refer to the schematic shown. Two dog-bone samples, labelled 1 and 2, of a Cualloy are tested under tension at room temperature to points “E” and “P”, respectively. Subsequently, they are unloaded completely and metallographically polished. Brinell hardness testing was performed in the gauge section of the samples. Which one of the following can be inferred about the measured Brinell hardness number (BHN)?
(A) BHN of 1 > BHN of 2
(B) BHN of 1 = BHN of 2
(C) BHN of 1 < BHN of 2
(D) A conclusion about BHN of samples 1 and 2 cannot be made, with the provided information
Answer: (C)
57. During the ageing of a homogenized Al-Cu alloy (1 to 4 wt.% Cu) below the GP zone solvus, hardness of the alloy:
(A) increases monotonically
(B) decreases monotonically
(C) first increases and then decreases
(D) first decreases and then increases
Answer: (C)
58. A student aims to deposit a thin metallic film on SiO2 substrate, with an adhesion layer between the metal film and substrate, in a contiguous planar fashion. Island type of growth must be avoided. The student performs an extensive optimization exercise. Which one of the following steps is in the right direction?
(A) Choose a metallic adhesion layer with very low interfacial energy with the deposited thin film
(B) Choose a metallic adhesion layer with very low interfacial energy with SiO2,irrespective of its interaction with metal film to be deposited
(C) Increase the substrate temperature and decrease the deposition rate
(D) Use intermittent stages of deposition followed by annealing
Answer: (A)
59. For a diffusional transformation (i.e., growth of β precipitates in an α matrix), which of the following is/are true with increasing degree of undercooling?
(A) Rate of transformation first increases and then decreases
(B) Rate of transformation first decreases and then increases
(C) Thermodynamic driving force increases monotonically
(D) Mobility of atoms in α matrix remains unchanged
Answer: (A, C)
60. A two-phase (α + β) mixture of an A-B binary system has the following properties:
(i) Phase α has equal weight percentages of A and B.
(ii) Phase β has twice the mole fraction of A compared to B.
(iii) The two-phase mixture has equal amounts of α and β.
(iv) Atomic mass of A is twice that of B.
The mole fraction of A in the resultant two-phase mixture is _________.(Round off to one decimal)
Answer: (0.5 to 0.5)
61. It is known that component A diffuses into a solid to a depth of 10 μm in 1 hour at 300 K. Treat diffusion in one dimension. The time taken for A to diffuse to the same depth at 600 K is ________ seconds. (Round off to 1 decimal).
Diffusivity of A in the solid is given by
DA0 : Diffusivity coefficient
Ea : Activation energy = 0.3 eV
kB : Boltzmann’s constant = 8.62 × 10−5 eV/K
T : Absolute temperature
Answer: (9.7 to 11.2)
62. A spherical β particle nucleates from the α matrix on a non-deformable substrate δ, forming a contact angle of θ as shown in the schematic.
The value of is _________. (Round off to three decimal places)
∆G*hom = Gibbs free energy change at the critical radius for homogeneous nucleation
∆G*het = Gibbs free energy change at the critical radius for heterogeneous nucleation
α-β interfacial energy = 0.4 J/m2
α-δ interfacial energy = 0.3 J/m2
β-δ interfacial energy = 0.02 J/m2
Answer: (0.057 to 0.062)
63. The resistivity of a pure semiconductor at 298 K is 3000 Ωm. Assume that the number of electrons excited (ne) across the band gap is given by the relation
NA :Avogadro’s number = 6.02×1023 mole−1
kB :Boltzmann’s constant = 8.62× 10−5 eV/K
T: Absolute temperature
Mobility of electrons in the semiconductor = 0.14 m2/(V s)
Mobility of holes in the semiconductor = 0.06 m2/(V s)
Absolute charge of an electron = 1.60×10−19 C
The band gap (Eg) of the semiconductor is ________ eV.(Round off to two decimals)
Answer: (0.45 to 0.47)
64. A new glass material is developed to minimize the transmission of the light through the window with glass panel of thickness 5 mm. The refractive index of the glass material is 1.5 and the absorption coefficient can be changed from 0.3 cm-1 to 1 cm-1. In the given range of absorption coefficients, the ratio of the maximum to the minimum fraction of the light coming out of the other side of the glass panel is ________. (Round off to two decimal places)
Answer: (1.40 to 1.43)
65. The third peak in the X-ray diffraction pattern of a face-centered cubic crystal is at 2θ value of 45°, where 2θ is the angle between the incident and reflected rays. The wavelength of the monochromatic X-ray beam is 1.54 Å. Considering first-order reflection, the lattice parameter of the crystal is _________ Å. (Round off to two decimal places)
Answer: (5.64 to 5.73)
Solid Mechanics XE-D
Q.66 – Q.74 Carry ONE mark Each
66. A force F is applied at an angle θ = 30° on an elastic column as shown in the figure. E and I are respectively the Young’s modulus and area moment of inertia. The smallest magnitude of 𝐹 needed to cause buckling is
Answer: (A)
67. The shear stress due to a transverse shear force in a linear elastic isotropic beam of rectangular cross-section
(A) varies linearly along the depth in the transverse direction of the beam
(B) is zero at the neutral axis
(C) is maximum at the neutral axis
(D) remains constant along the depth in the transverse direction of the beam
Answer: (C)
68. A massless semicircular rod held fixed at end A is in the xy-plane, as shown in the figure. A force P along the negative z direction is acting at point B on the rod. The unit vectors along x, y and z directions are denoted respectively as i, j and k. Due to the applied force P, the cross-section of the rod at point D will be subjected to
(A) a twisting moment PR(1 – cos θ), a bending moment PR sin θ j, and a shear force –P k
(B) a twisting moment PR(1 – sin θ) i, a bending moment PR cos θ j, and a shear force P k
(C) a twisting moment PR(cos θ – 1) i, a bending moment –PR sin θ j, and a shear force –P k
(D) a twisting moment PR sin θ i, a bending moment PR(1 – cos) θ j, and a shear force P k
Answer: (A)
69. In the truss shown in the figure, all the members are pin jointed to each other. The members AB, BD, DE and DC have the same length. For the given loading, which of the following is the correct statement?
(A) BD is a zero-force member, and AB and ED are in compression
(B) AB is in tension, ED is in compression, and BD is a zero-force member
(C) AB and DC are in tension, and BC is in compression
(D) ED is in tension, and DC and BC are in compression
Answer: (B)
70. End B of the 2 m long rigid rod AB is constrained to move horizontally in the slot as shown in the figure and has a velocity of 1.0 i m/s. The angular velocity of the rod at the instant shown is 2 rad/s. The unit vectors along x and y directions are denoted respectively as i and j. The velocity of point A in m/s is then given by
(A) (1 – 2√3)i + 2j
(B) (1 + 2√3)i − 2j
(C) −2√3i + 2j
(D) 2√3i − 2j
Answer: (A)
71. The assembly of four masses connected by rigid mass-less rods is kept on a smooth horizontal floor as shown in the figure. Under the applied force 2F, the magnitude of angular acceleration of the assembly at the instant shown is
(A) F/mc
(B) F/2mc
(C) 2F/3mc
(D) F/3mc
Answer: (B)
72. A particle is constrained to move at a constant speed on an inclined plane (ABCD) along the curved path shown in the figure. Edges AD and BC are parallel to the y axis. The inclined plane makes an angle θ with the xy-plane. The velocity vector of the particle makes an angle ϕ with the dotted line which is parallel to edge AB. If the speed of the particle is 2 m/s, ϕ = 30°, and θ = 40°, then the z-component of the velocity of the particle in m/s is _________
(A) −132
(B) −1.00
(C) −1.11
(D) −1.50
Answer: (C)
73. A uniform elastic rod of constant cross-section is fixed at its left end as shown in the figure. An axial force P is acting as shown. Assume that plane sections remain plane during deformation. The ratio of axial displacements at point A(x = 4L) to that at point B (x = L) is ______ (rounded off to one decimal place)
Answer: (1.9 to 2.1)
74. A thin-walled spherical pressure vessel has a mean radius of 500 mm and wall thickness of 10 mm. The yield strength of the material is 500 MPa. The internal pressure in MPa at which the spherical pressure vessel will yield according to the Tresca criterion is ____________ (rounded off to one decimal place)
Answer: (19 to 21)
Q.75 – Q.87 Carry TWO marks Each
75. The beam in the figure is subjected to a moment M0 at mid span as shown. Which of the following is the vertical reaction at B?
Answer: (A)
76. A spring-mass system having a mass m and spring constant k, placed horizontally on a foundation, is connected to a vertically hanging mass m with the help of an inextensible string. Ignore the friction in the pulleys and also the inertia of pulleys, string and spring. Gravity is acting vertically downward as shown. The natural frequency of the system in rad/s is
Answer: (D)
77. One end of a uniform rigid rod OA of length L and mass m is attached to a frictionless hinge at O. The other end of the rod is connected to the roof at B with a mass-less inextensible thread AB. Initially the rod is horizontal and at rest. The gravity is acting vertically downward as shown. Immediately after the thread AB is cut, the reaction on the rod at O is
(A) mg/4 in the positive y-direction
(B) mg/2 in the negative y-direction
(C) 3mg/4 in the negative y-direction
(D) mgin the positive y-direction
Answer: (A)
78. A circular shaft is rigidly connected to a wall at one end. The shaft has a solid portion and a hollow portion as shown in the figure. The length of each portion is L and the shear modulus of the material is G. The polar moment of inertia of the hollow portion is J and that of the solid portion is 50 J. A torque T is applied at the right most end as shown. The rotation of the section PQ is
(A) 27TL/100JG
(B) TL/40JG
(C) 5TL/4JG
(D) 3TL/4JG
Answer: (A)
79. A rectangular plate of uniform thickness having initial length a and width b is placed between two rigid immovable walls. The temperature of the plate is increased by ∆ The plate is free to expand along the y and z directions. The mid-surface of the plate remains in the xy-plane. The Poisson’s ratio is v and the coefficient of thermal expansion is α. Assuming that the plate is initially free of stresses, the change in length of the plate after the increase in temperature is given by
(A) a(1 – v)α∆T
(B) a(1 + v)α∆T
(C) aα∆T
(D) 2aα∆T
Answer: (B)
80. A mass m = 10 kg is attached to a spring as shown in the figure. The coefficient of friction between the mass and the inclined plane is 0.25. Assume that the acceleration due to gravity is 10 m/s2 and that static and kinematic friction coefficients are the same. Equilibrium of the mass is impossible if the spring force is
(A) 30 N
(B) 45 N
(C) 60 N
(D) 75 N
Answer: (A)
81. The frame shown in the figure is subjected to a uniformly distributed load of 1000 N/m over a distance of 0.6 m. Neglecting the weight of the frame, the maximum shear force (in N) in the region between the supports A and B of the frame is ________.
Answer: (295 to 305)
82. A slider moving in a frictionless slot is connected with a linear spring OA as shown in the figure. The following is known: stiffness of the spring = 2 kN/m, mass of the slider = 10 kg, and the unstretched length of the spring = 1 m. If the slider is released from rest at A the magnitude of its velocity (in m/s) when it passes through point B is ________ (rounded off to the nearest integer)
Answer: (39 to 41)
83. A sphere A of mass 𝑚 is thrown into the air at 50 m/s along a direction tan−1 (3/4) up from the horizontal. At the topmost point of its trajectory, it has a central (nonoblique) collision with another sphere B which is at rest on top of a vertical pole. Sphere B has a mass of 3m. Acceleration due to gravity is 10 m/s2. Neglect contact friction and air-resistance. If the coefficient of restitution is 0.3, then the speed (in m/s) of sphere A immediately after the collision is _______ (rounded off to one decimal place)
Answer: (0.9 to 1.1)
84. The truck shown in the figure is moving on a horizontal road at a speed of 20 m/s. It is carrying a box of mass 1000 kg, which is simply placed on the truck platform. The coefficient of friction between the truck platform and the box is 0.25. Take acceleration due to gravity as 10 m/s2. Assume uniform deceleration during braking, and the coefficients of static and kinetic friction to be the same. The shortest distance in meters in which the truck can be brought to rest without the box slipping is _______(round off to the nearest integer)
Answer: (79 to 81)
85. The stepped rod of length 2 m, shown in the figure, is fixed at both ends (A and C). The area of cross-section of portion AB is 200 mm2 and that of portion BC is 100 mm2. Force F is applied at section B such that the section is displaced by 0.1 mm in the direction of the force. Young’s modulus of the rod is 200 GPa. The applied force F in N is _______ (round off to the nearest integer)
Answer: (5990 to 6010)
86. A cantilever beam has a span of 1 m and carries a uniformly distributed load of q = 1250 N/m over a portion as shown. A force F =1000 N acts at a distance L from the fixed end. The distance L is such that the bending moment at the fixed end is zero. The beam has a rectangular cross-section of depth 20 mm and width 24 mm. For this loading, the magnitude of the maximum bending stress in the beam in MPa is _________(round off to the nearest integer)
Answer: (123 to 127)
87. The figure shows two identical mass-less beams AB and CD, each clamped at one of their ends. The left end of beam CD rests on the right end of beam AB such that the ends of the beams are just in contact. The beams are unstressed before the application of load. Assume no friction at the contact. Now, if a uniformly distributed load of 800 N/m is applied on beam CD, the bending moment at the end B of beam AB in N.m is ________ (rounded off to the nearest integer)
Answer: (148 to 152)
Thermodynamics XE (E)
Q.88 – Q.96 Carry ONE mark each
88. The energy equation for a reversible non-flow process can be expressed as δq = du + pdv, where q is the heat transfer per unit mass, u is the internal energy per unit mass, p is the pressure, and v is the mass specific volume. This energy equation is not in exact differential form. It can be made exact differential by multiplying with the following integrating factor:
(T is the absolute temperature)
(A) 1/p
(B) 1/v
(C) 1/T
(D) 1/uT
Answer: (C)
89. An air standard Diesel cycle consists of four processes: 1-2 (isentropic compression), 2-3 (constant pressure heat addition), 3-4 (isentropic expansion) and4-1 (constant volume heat rejection). T4 is the temperature (in K) attained at the end of isentropic expansion (3-4) before constant volume heat rejection. The constant volume heat rejection process (4-1) is replaced by a constant pressure heat rejection process (4a-1) such that T4a is the temperature (in K) reached at the end of isentropic expansion (3-4a), and the state point 1 remains the same. Then
(A) T4a< T4
(B) T4a> T4
(C) T4a = T4
(D) T4a = 2T4
Answer: (A)
90. Gas in a cylinder-piston device expands from state 1 ( p1,V1,T1) to state (p2,V2, T2). The expansion process is polytropic, i.e., pVn = constant, n ≠ Assuming the ideal gas behaviour, the expression for the work done, W by the system is given by
Answer: (B)
91. The temperature of the working fluid in a real heat engine cycle changes during heat addition and heat rejection processes. The maximum and minimum temperatures of the cycle are Tmax and Tmin, respectively. If ηC is the thermal efficiency of a Carnot engine operating between these temperature limits, then the thermal efficiency, η of the real heat engine satisfies the relation
(A) η > ηC
(B) η < ηC
(C) η = ηC
(D) η = 1 + ηC
Answer: (B)
92. A 1.2 m3 rigid vessel contains 8 kg of saturated liquid-vapor mixture at 150 kPa. The specific enthalpy of this mixture is ______ kJ/kg (round off to 2 decimal places).
93. Air in a closed system undergoes a thermodynamic process from an initial temperature of 300 K to the final temperature of 400 K. The specific heat of air at constant volume, cv varies linearly with the temperature, T (in K) as
cv = (0.7 + 0.27 × 10−3T) kJ/(kg K).
Change in the specific internal energy of the air in the system is _______ kJ/kg
(round off to 2 decimal places).
Answer: (79.00 to 80.00)
94. A vertical cylinder-piston device contains a fixed mass of gas in equilibrium. The cross-sectional area of the piston is 0.05 m2. For 150 kPa pressure of the gas in the cylinder, the mass of the piston is _______ kg (round off to 2 decimal places). Assume that the atmospheric pressure is 100 kPa and the acceleration due to gravity is 9.81 m/s2.
Answer: (254.00 to 255.00)
95. A steam power plant operates on Rankine cycle. At certain operating condition of the plant, there is a reduction of 20% net work output (kJ/kg) as compared to 100% capacity. This reduction will cause the specific steam consumption (kg/kJ) to increase by _______% (in integer).
Answer: (25 to 25)
96. A Carnot heat pump extracts heat from the environment at 250 K, and supplies 6 kW of heat to a room which is maintained at a constant temperature TH. The heat pump requires a power input of 1 kW for its operation. Then, the temperature of the room TH is _______ K (round off to nearest integer).
Answer: (300 to 300)
Q.97 – Q.109 Carry TWO marks each
97. One of the Maxwell equations is expressed as where s is the entropy per unit mass, v is the mass specific volume, p is the pressure, and T is the temperature. In this expression, s is a continuous function of T and v. The derivatives of s are also continuous. Let cv be specific heat capacity at constant volume for a gas. Then, can be written as
Answer: (C)
98. The general relation among the properties x , y and z at any state point can be expressed as If p, T and h are continuous functions and μ is the Joule-Thomson coefficient, then is
(A) −μcp
(B) cpT
(C) –cp/T
(D) μcp
Answer: (A)
99. An air-conditioning system consists of an insulated rigid mixing chamber designed to supply air at 24°C to a building. The mixing chamber mixes two air streams: (i) a cold air stream at 10°C and mass flow rate and (ii) a stream of fresh ambient air at 30°C and mass flow rate Assume air to be an ideal gas with constant specific heat (cp = 1.005 kJ/(kg K), γ = cp/cv = 1.4). Neglect change in kinetic and potential energies as compared to change in enthalpy. Under the steady state condition, the ratio of the mass flow rates of the two streams is
(A) 7/3
(B) 3/7
(C) 2/7
(D) 4/7
Answer: (B)
100. An ideal gas mixture consists of 80% N2 and 20% O2 on mass basis. If the total pressure is 300 kPa, then the partial pressure of N2 (in kPa) is
(Molecular weights of N2 = 28 kg/kmol and O2 = 32 kg/kmol)
(A) 246.15
(B) 230.34
(C) 254.78
(D) 213.54
Answer: (A)
101. On the basis of the ideal gas equation and van der Waals equation, the temperatures of a gas at pressure 10 MPa and specific volume 0.005 m3/kg would be, respectively
(Assume gas constant R = 0.3 kJ/(kg K), a = 0.18 m6 kPa/kg2 and b = 0.0014 m3/kg)
(A) 166.67 K and 235.89 K
(B) 166.67 K and 206.40 K
(C) 166.67 K and 267.21 K
(D) 166.67 K and 240.90 K
Answer: (B)
102. An ideal Brayton cycle operates between maximum and minimum temperatures of T3 and T1, respectively. For constant values of T3 and T1, the pressure ratio (rp) for maximum work output is (γ is the specific heat ratio of air)
Answer: (C)
103. An insulated rigid tank of volume 10 m3 contains air initially at 1 MPa and 600 K. A valve connected to the tank is opened, and air is allowed to escape until the temperature inside the tank drops to 400 K. The temperature of the discharged air can be approximated as the average of the initial and final temperatures of the air in the tank. Neglect kinetic and potential energies of the discharged air. Assume that air behaves as an ideal gas with constant specific heat so that internal energy u = cvT and enthalpy h = cp Then, the final pressure of the air in the tank is _______ MPa (round off to 2 decimal places).
Assume cp = 1.005 kJ/(kg K), γ = cp/cv = 1.4
Answer: (0.20 to 0.24)
104. Steam enters a steam turbine at 5 MPa and 600°C, and exits as saturated vapor at 50 kPa. Under steady state condition, the turbine loses heat to the surroundings at the rate of 50 kJ per kilogram of steam flowing through the turbine. The ambient temperature is 300 K, and the heat transfer to the surroundings takes place at the outer surface of the turbine at a temperature of 450 K. The irreversibility per unit mass of steam flowing through the turbine is _______ kJ/kg (round off to 2 decimal places).
Neglect the change in kinetic and potential energies of the steam, and use the
following property values:
Super heated steam at 5 MPa, 600°C
v = 0.07870 m3/kg, u = 3273.3 kJ/kg, h = 3666.9 kJ/kg, s = 7.2605 kJ/(kg K)
105. A heat engine receives heat at 1000 K and rejects heat to the environment at 300 K. The efficiency of the heat engine is half of the efficiency of a Carnot engine operating between the above mentioned temperature limits. The work output from the heat engine is completely used to drive a refrigerator that steadily removes heat from a cold space at 260 K at a rate of 5.2 kW, and rejects the heat to the same environment at 300 K. The COP (coefficient of performance) of the refrigerator is half of the COP of the Carnot refrigerator operating between the same temperature limits as that of the refrigerator. Then, rate of heat supplied to the heat engine is _______ kW (round off to 2 decimal places).
Answer: (4.50 to 4.65)
106. A room contains air at 25°C, 100 kPa and 80% relative humidity. If the saturation pressure of water vapor at 25°C is 3.1698 kPa, then the specific humidity of air is _______ kg of water vapor/kg of dry air (round off to 4 decimal places).
Answer: (0.0160 to 0.0165)
107. An insulated rigid container is divided into two parts by a thin partition. One part of the container contains 6 kg of saturated liquid-vapor mixture with a dryness fraction of 0.7 at 0.3 MPa. The other part contains 12 kg of saturated liquid at 0.6 MPa of the same substance. When the partition is removed and the system attains equilibrium, the final specific volume of the mixture is _______ m3/kg (round off to 2 decimal places).
108. During a steady state air-conditioning process, air enters a heating section at 15°C with 40% relative humidity and leaves at 30° Assuming the heating process takes place at 100 kPa, the relative humidity of the air at exit is ______ % (round off to nearest integer).
Saturation pressures of water vapor at 15°C and 30°C are 1.7057 kPa and 4.2469kPa respectively.
Answer: (15 to 17)
109. Steam enters a steam turbine at 10 MPa and 600°C with a mass flow rate of 16 kg/s. The steam exits the turbine as saturated vapor at 10 kPa. Under steady state condition, the turbine generates 16.2 MW power. If the ambient temperature is 25°C, the rate of entropy generation in the turbine is _______ kW/K (round off to 2 decimal places).
Neglect the change in kinetic and potential energies of the steam, and use the
following property values:
Super heated steam at 10 MPa, 600°C
v = 0.03837 m3/kg, u = 3241.68 kJ/kg, h = 3625.34 kJ/kg, s = 6.9028 kJ/kg(kg K)
110. Interfacial polymerization can be used to prepare
(A) Nylon 6
(B) Nylon 66
(C) Polyacrylonitrile
(D) Poly(butyl acrylate)
Answer: (B)
111. In a rubber sample with a Mooney viscosity of 60 ML(1 + 4) 100°C, the number 4 signifies
(A) Applied shear rate in s−1
(B) Number of samples tested
(C) Time in minutes after starting the motor when the measurement is taken
(D) Preheating time in minutes
Answer: (C)
112. The initiator system which can be used for free radical polymerization at 5°C is
(A) FeSO4 + t-butyl hydroperoxide
(B) Azobisisobutyronitrile
(C) Potassium persulfate
(D) Benzoyl peroxide
Answer: (A)
113. Weather resistance of high impact polystyrene can be improved by blending polystyrene with
(A) Styrene butadiene rubber
(B) Natural rubber
(C) Ethylene propylene rubber
(D) Nitrile rubber
Answer: (C)
114. Which of the following is a discontinuous polymer processing operation?
(A) Calendering
(B) Extrusion
(C) Film blowing
(D) Thermoforming
Answer: (D)
115. The blend of polyethylene and polypropylene is
(A) Immiscible due to enthalpic constraints
(B) Immiscible due to entropic constraints
(C) Miscible as they are polyolefins
(D) Miscible due to comparable solubility parameters
Answer: (B)
116. Toughness in a polymer can be inferred from
(A) Izod impact strength
(B) Depth of indentation
(C) Area under the stress-strain curve
(D) Charpy impact strength
Answer: (A, C, D)
117. Which of the following polymers are polyesters?
(A) Poly(acrylic acid)
(B) Poly(lactic acid)
(C) Polyhydroxybutyrate
(D) Poly(ε-caprolactone)
Answer: (B, C, D)
118. The functionality of adipic acid for condensation reaction with glycerol is ________ (in integer).
Answer: (2 to 2)
Q.119 – Q.131 Carry TWO marks Each
119. From the dynamic mechanical analysis of a polymer sample with a phase angle of 30°, the relationship between storage modulus (E’) and loss modulus (E”) can be expressed as
(A) E’ = √3 E”
(B) 2E’ = √3 E”
(C) E” = √3 E′
(D) 2E” = √3 E′
Answer: (A)
120. Match the properties in Column A with their respective unit in Column B
(A) P-1; Q-3; R-4; S-2
(B) P-2; Q-3; R-1; S-4
(C) P-3; Q-1; R-4; S-2
(D) P-3; Q-1; R-2; S-4
Answer: (C)
121. Match the following polymer product with its most appropriate processing technique
(A) P-3; Q-4; R-1; S-2
(B) P-3; Q-4; R-2; S-1
(C) P-4; Q-3; R-2; S-1
(D) P-3; Q-2; R-4; S-1
Answer: (B)
122. Match the following additives to their respective functions
(A) P-4; Q-2; R-1; S-3
(B) P-3; Q-1; R-2; S-4
(C) P-4; Q-1; R-3; S-2
(D) P-4; Q-1; R-2; S-3
Answer: (D)
123. Match the polymers with their characteristic infrared (IR) stretching frequency
(A) P-4; Q-3; R-2; S-1
(B) P-3; Q-4; R-2; S-1
(C) P-3; Q-4; R-1; S-2
(D) P-3; Q-2; R-4; S-1
Answer: (B)
124. Match the following polymers to the most appropriate product
(A) P-2; Q-1; R-4; S-3
(B) P-2; Q-4; R-1; S-3
(C) P-3; Q-1; R-2; S-4
(D) P-3; Q-1; R-4; S-2
Answer: (D)
125. Match the polymers to the polymerization method used for their synthesis
(A) P-2; Q-1; R-4; S-3
(B) P-2; Q-1; R-3; S-4
(C) P-2; Q-3; R-4; S-1
(D) P-2; Q-4; R-1; S-3
Answer: (A)
126. If 5 g of a monodisperse polystyrene sample of molecular weight 10,000 g mol−1 is mixed with 15 g of another monodisperse polystyrene sample of molecular weight 20,000 g mol−1, then the polydispersity of the resulting mixture is ________ (rounded off to two decimal places).
Answer: (1.04 to 1.14)
127. For a polymer sample with a viscosity of 6 × 1011 poise, if the apparent plateau modulus of 3 × 106 dyne cm−2 drops to zero above a certain temperature, the relaxation time of the polymer is _________ days (rounded off to one decimal place).
Answer: (2.1 to 2.5)
128. The thermal conductivity values of glass fiber and epoxy resin are 1.05 W m−1 K−1 and 0.25 W m−1 K−1, respectively. The thermal conductivity of a glass fiber reinforced epoxy composite with a fiber content of 60% by volume along the fiber direction is ________ W m−1 K−1 (rounded off to two decimal places).
Answer: (0.71 to 0.75)
129. The tensile modulus of a thermosetting polyester resin and glass fiber are 3 GPa and 80 GPa, respectively. If a tensile stress of 110 MPa is applied along the fiber direction on a continuous uniaxially aligned glass fiber reinforced thermosetting polyester composite with a fiber content of 60% by volume, the resulting strain will be ________ × 10−3 (rounded off to one decimal place).
Answer: (2.1 to 2.4)
130. The amount of low molecular weight plasticizer with a Tg of −60°C that must be added to nylon 6 to reduce its Tg from 50°C to 30°C is __________ % (rounded off to nearest integer).
Answer: (12 to 14)
131. The enthalpy of fusion for a polymer is found to decrease from 135.6 J g−1 to 120 J g−1 after five years of use. If the enthalpy of fusion of the same polymer with 100% crystallinity is 290 J g−1, then the loss in crystallinity after five years is _______ % (rounded off to one decimal place).
Answer: (5.2 to 5.6)
Food Technology XE-G
Q.132 – Q.140 Carry ONE mark Each
132. Which among the given options truly depict the lines 1 and 2 in the figure below with respect to the effect of heat processing on food?
(A) 1-Safety, 2-Quality
(B) 1-Yield, 2-Safety
(C) 1-Yield, 2-Quality
(D) 1-Quality, 2-Safety
Answer: (A)
133. Homogenization of milk leads to disintegration of fat globules by
(A) Turbulence and pasteurization
(B) Pasteurization and cavitation
(C) Pasteurization and pressurization
(D) Turbulence and cavitation
Answer: (D)
134. The lowest water activity (aw) supporting the growth of Staphylococcus aureus in food under aerobic condition is
(A) 0.98
(B) 0.91
(C) 0.89
(D) 0.86
Answer: (D)
135. Cultures used in industrial production of yogurt are
(A) Lactococcus lactis subsp. lactis
(B) Streptococcus thermophilus
(C) Leuconostoc mesenteroides subsp. cremoris
(D) Lactobacillus delbrueckii subsp. bulgaricus
Answer: (B, D)
136. In a dairy plant, spray drying technology is used to produce whey powder. The rate of spray drying depends on
(A) Temperature of the incoming air
(B) Shape of the cyclone separator
(C) Diameter of the whey droplet
(D) Heat transfer coefficient of hot air
Answer: (A, C, D)
137. The parboiling of paddy results into
(A) Increase in the milling losses
(B) Increase in the nutritional value of rice
(C) Increase in the head rice recovery
(D) Increase in the broken rice percentage
Answer: (B, C)
138. One hundred kg paddy is dried from 18% wet basis to 13% wet basis moisture
content. The amount of water removed (in kg) from the paddy is _______ (round off to one decimal place).
Answer: (5.5 to 6.0)
139. The radius of a centrifuge bowl is 0.1 m and is rotating at 850 revolutions per minute. The centrifugal force developed in terms of gravity force (g-force) is ________(round off to two decimal places).
Given: Acceleration of gravity (g) = 9.81 m s−2 and π = 3.14
Answer: (79.50 to 81.50)
140. In a canning industry, the total process time (F0) was calculated as 3 min. If each can contains 20 spores having decimal reduction time of 1.6 min, the probability of spoilage would be ______ in 100 cans (round off to the nearest integer).
Answer: (25 to 28)
Q.141 – Q.153 Carry TWO marks Each
141. Match the edible oil refining stages given in Column I with their respective functions in Column II
(A) P-3, Q-2, R-1, S-4
(B) P-2, Q-1, R-3, S-4
(C) P-3, Q-4, R-2, S-1
(D) P-3, Q-1, R-2, S-4
Answer: (C)
142. Make the correct pair of food packaging technology given in Column I with operating principle or description in Column II.
(A) P-3, Q-4, R-1, S-2
(B) P-3, Q-2, R-1, S-4
(C) P-1, Q-4, R-3, S-2
(D) P-3, Q-1, R-4, S-2
Answer: (A)
143. Which of the following is not a caramel flavour producing compound?
(A) 3-Hydroxy-2-methylpyran-4-one
(B) 2H-4-Hydroxy-5-methylfuran-3-one
(C) 3-Hydroxy-2-acetylfuran
(D) p-Amino benzoicacid
Answer: (D)
144. Match the size reduction equipment in Column I with the method of operation in Column II.
(A) P-2, Q-4, R-1, S-3
(B) P-3, Q-1, R-2, S-4
(C) P-4, Q-1, R-2, S-3
(D) P-3, Q-4, R-2, S-1
Answer: (A)
145. Most commonly used refrigerant in direct immersion freezing of food is
(A) Monochlorodifluoromethane
(B) Dichlorodifluoromethane
(C) Liquid nitrogen
(D) Freon
Answer: (C)
146. Which among the following are ω-6 poly unsaturated essential fatty acids?
(A) 18:2 Linoleic acid
(B) 18:3 α-Linolenic acid
(C) 18:3 γ-Linolenic acid
(D) 20:4 Arachidonic acid
Answer: (A, C, D)
147. Which among the following statements are true with respect to protein denaturation?
(A) There may be an increase in α-helix and β-sheet structure
(B) It is an irreversible process
(C) When fully denatured, globular proteins resemble a random coil
(D) The peptide bonds are broken
Answer: (A, C)
148. Identify the correct pair(s) of milling equipment and the grain for which it is used.
(A) Mist polisher–Rice
(B) Break roll–Wheat
(C) Rubber roll–Pigeon pea
(D) Beall degermer–Maize
Answer: (A, B, D)
149. Which among the following expression(s) is/are correct?
Answer: (A, C)
150. In sieve analysis of coffee powder, the particle size distribution is given below
The Sauter mean diameter (in μm) of the coffee powder is ______(round off to one decimal place).
Answer: (19.0 to 20.5)
151. In a dairy processing plant, milk enters a 30 m long and 2 cm diameter tube at
60°C and leaves at 57°C. The total heat loss over the tube length is 381.15 W. The specific heat capacity, density, and viscosity of milk are 3.85 kJ kg−1 K−1, 1020 kg m−3, and 1.20 cP, respectively. The Reynolds number for the flow is ______(round off to the nearest integer).
Given :π = 3.14
Answer: (1700 to 1800)
152. Apple juice flows through a steel pipe having thermal conductivity of 50 W m−1 K−1. The outer surface of pipe is exposed to ambient environment. The inside diameter and thickness of the pipe are 3 cm and 1.5 cm, respectively. The overall heat transfer coefficient based on inside area is 25 W m−2 K−1. If the internal convective heat transfer coefficient is 30 W m−2 K−1, the external convective heat transfer coefficient (in W m−2 K−1) will be __________ (round off to two decimal places).
Answer: (73.00 to 84.00)
153. The dry bulb temperature and relative humidity of air inside a storage chamber are 37°C and 50%, respectively. The saturation pressure of water vapour at 37°C and barometric pressure are 6.28 kPa and 101.32 kPa, respectively. The humidity ratio of air inside the chamber is ______ kg water (kg dry air)−1 (round off to three decimal places).
Given: Molecular weight of water vapour and dry air are 18.02 g mol−1 and 28.97 g mol−1, respectively.
Answer: (0.017 to 0.021)
Atmospheric and Oceanic Sciences XE-H
Q.154 – Q.162 Carry ONE mark Each
154. The figure shows a schematic of vertical profiles of concentrations of two gases P and Q in the atmosphere near a coastal station. The correct pair representing P and Q, respectively, is
(A) water vapor and CO2
(B) O3 and water vapor
(C) CO2 and O3
(D) N2 and O2
Answer: (A)
155. A form of momentum equation for an incompressible fluid is
where ρ is density, V is velocity, t is time, p is pressure, μ is viscosity and
B represents body force per unit volume. The dimension of term (iii) is
(M, L and T stand for mass, length and time, respectively).
(A) [L]1 [T]−2
(B) [M]1 [L]−2 [T]−2
(C) [M]1 [L]1 [T]−2
(D) [M]1 [L]1 [T] −1
Answer: (B)
156. Tropical cyclones usually do not form close to the Equator primarily because
(A) sea surface temperature at the Equator is too cold.
(B) beta effect dissipates clouds.
(C) Coriolis force is too weak.
(D) vertical shear of the zonal wind is weak.
Answer: (C)
157. Which one of the following statements regarding equatorial under current (EUC) in the Pacific Ocean is correct?
(A) EUC flows from west to east.
(B) EUC flows from east to west.
(C) EUC flows from north to south.
(D) EUC flows from south to north.
Answer: (A)
158. Which one of the following statements is correct regarding the dominant energy balance in the troposphere in a tropical convergence zone?
159. Which one of the following processes is primarily responsible for the poleward transport of energy in the midlatitude troposphere?
(A) atmospheric tides
(B) baroclinic waves
(C) gravity waves
(D) turbulence in the boundary layer
Answer: (B)
160. Which of the following feature(s) characterize the seasonal mean flow in the upper troposphere near 200 hPa level over the Tibetan Plateau during the boreal summer?
(A) cyclonic
(B) anticyclonic
(C) irrotational
(D) divergent
Answer: (B, D)
161. The Rossby number of a synoptic system with a length scale of 1000 km, characteristic velocity scale of 10 m s-1 at a latitude where the Coriolis parameter equals 10−4 s−1, is _______. (Round off to two decimal places)
Answer: (0.08 to 0.12)
162. The ratio of scattering efficiency of red light of wavelength 0.65 μm to blue light of wavelength 0.45 μm by air molecules in the atmosphere is _____. (Round off to two decimal places)
Answer: (0.22 to 0.24)
Q.163 – Q.175 Carry TWO marks Each
163. An unsaturated moist air parcel undergoes adiabatic ascent in atmosphere without mixing with surrounding air. Air is so clean that there is no possibility for heterogeneous nucleation. Which one of the following plots depicts the vertical variation of water vapor pressure (shown as continuous line) and saturation water vapor pressure (shown as dotted/dashed line) of the parcel?
(A) P
(B) Q
(C) R
(D) S
Answer: (A)
164. A fluid is in solid body rotation in a cylindrical container of radius R rotating with an angular velocity Ω = (0, 0, Ω). The circulation per unit area around a circular loop in the horizontal plane of radius r(r < R), whose center coincides with the axis of rotation is
(A) 2Ω
(B) Ω2
(C) Ω/2
(D) Ω/4
Answer: (A)
165. Consider a layer of atmosphere where temperature increases with height. If the concentration of a vertically well-mixed greenhouse gas suddenly increases in this layer, then an immediate consequence is that
(A) infrared radiation leaving the top of the layer decreases.
(B) infrared radiation leaving the top of the layer increases.
(C) infrared radiation leaving the top of the layer remains unchanged.
(D) the layer becomes optically thinner to infrared radiation.
Answer: (B)
166. Consider an atmosphere where the mole fractions of N2, Ar and CO2 are 7.81 × 10−1, 9.34 × 10−3 and 4.05 × 10−4, respectively. This atmosphere exchanges gases with sea water below having temperature and salinity of 20 °C and 35 psu, respectively. In the absence of biological and chemical activity, relative concentrations of dissolved gases in the surface sea water at equilibrium are ordered as
(A) [N2] > [Ar] > [CO2]
(B) [CO2] > [N2] > [Ar]
(C) [N2] > [CO2] > [Ar]
(D) [Ar] > [CO2] > [N2]
Answer: (C)
167. Gravitational forces exerted by the Sun and the Moon are mainly responsible for ocean tides. Which of the following statement(s) regarding ocean tides is/are correct?
(A) Tidal amplitude corresponding to diurnal period is larger than that of the semi-diurnal period.
(B) Diurnal time period of lunar forced tides is longer than that of the solar forced tides.
(C) Tidal amplitudes are larger during a solar eclipse compared to that during a lunar eclipse.
(D) Tides are absent during equinoxes.
Answer: (B, C)
168. Which of the following statement(s) is/are true about northern hemisphere tropical cyclones?
(A) They have a warm core.
(B) Their low-level flow is cyclonic.
(C) Strong wind shear in the vertical is required for their intensification.
(D) They are characterized by upper-level divergence.
Answer: (A, B, D)
169. In gradient wind balance, which of the following statement(s) is/are true for flow around a region of low pressure in the northern hemisphere?
(A) The flow is clockwise.
(B) The flow is anti-clockwise.
(C) The wind speed is faster than the geostrophic wind.
(D) The wind speed is slower than the geostrophic wind.
Answer: (B, D)
170. Which of the following statement(s) is/are true regarding biogeochemical cycle
in the ocean?
(A) Shutdown of the biological pump in the ocean would have resulted in higher CO2 concentration in the atmosphere compared to present-day.
(B) If atmospheric CO2 concentration increases, solubility pump would lead to a decrease in dissolved inorganic carbon in the ocean.
(C) All carbon sequestered by marine photosynthesis settles down on the ocean floor as organic matter.
(D) Calcification (the process of making shells and skeletons) by marine organisms in the surface ocean layer would lead to an increase in the surface ocean CO2.
Answer: (A, D)
171. Consider the atmosphere to be a heat engine, which converts absorbed radiation to kinetic energy of winds. Let the global mean radiation absorbed be 200 Wm−2. In steady-state, if the global mean kinetic energy dissipation is 10 Wm−2, then the efficiency of the atmospheric heat engine is ________%. (Round off to one decimal place)
Answer: (4.9 to 5.1)
172. A drifter on the surface of the ocean performs inertial oscillation. The speed of the drifter is 2 m s−1 and the Coriolis parameter at the latitude is 2×10−4 s−1. The radius of the inertial oscillation is _______ km. (Round off to the nearest integer)
Answer: (9 to 11)
173. Consider a tornado in cyclostrophic balance. The tangential wind speed at a radial distance of 500 m from the center of the tornado is _______ m s−1, if the pressure gradient at that location in the radial direction is 5 N m−3. Assume the density of air to be 1 kg m−3. (Round off to the nearest integer)
Answer: (49 to 51)
174. Consider two weather stations A and B having the same altitude. Station B is 5 km north of Station A and is always 2 K warmer than Station A. A steady northerly wind blows at 1 m s−1. The change in temperature at Station A in 2 hours is ________ K. (Round off to one decimal place)
Answer: (2.8 to 3.0)
175. Assume the Earth is in radiative equilibrium with effective radiative temperature of 255 K. If the planetary albedo increases by 0.05, then the effective radiative temperature of the planet will be _______ K. (Round off to the nearest integer)
1. Inhaling the smoke from a burning _________ could _________ you quickly.
(A) tire / tier
(B) tire / tyre
(C) tyre / tire
(D) tyre / tier
Answer: (C)
2. A sphere of radius r cm is packed in a box of cubical shape.
What should be the minimum volume (in cm3) of the box that can enclose the sphere?
(A) r3/8
(B) r3
(C) 2r3
(D) 8r3
Answer: (D)
3. Pipes P and Q can fill a storage tank in full with water in 10 and 6 minutes, respectively. Pipe R draws the water out from the storage tank at a rate of 34 litres per minute. P, Q and R operate at a constant rate.
If it takes one hour to completely empty a full storage tank with all the pipes operating simultaneously, what is the capacity of the storage tank (in litres)?
(A) 26.8
(B) 60.0
(C) 120.0
(D) 127.5
Answer: (C)
4. Six persons P, Q, R, S, T and U are sitting around a circular table facing the center not necessarily in the same order. Consider the following statements:
P sits next to S and T.
Q sits diametrically opposite to P.
The shortest distance between S and R is equal to the shortest distance between T and U.
Based on the above statements, Q is a neighbor of
(A) U and S
(B) R and T
(C) R and U
(D) P and S
Answer: (C)
5. A building has several rooms and doors as shown in the top view of the building given below. The doors are closed initially.
What is the minimum number of doors that need to be opened in order to go from the point P to the point Q?
(A) 4
(B) 3
(C) 2
(D) 1
Answer: (C)
Q.6 – Q. 10 Carry TWO marks each.
6. Rice, a versatile and inexpensive source of carbohydrate, is a critical component of diet worldwide. Climate change, causing extreme weather, poses a threat to sustained availability of rice. Scientists are working on developing Green Super Rice (GSR), which is resilient under extreme weather conditions yet gives higher yields sustainably.
Which one of the following is the CORRECT logical inference based on the information given in the above passage?
(A) GSR is an alternative to regular rice, but it grows only in an extreme weather
(B) GSR may be used in future in response to adverse effects of climate change
(C) GSR grows in an extreme weather, but the quantity of produce is lesser than regular rice
(D) Regular rice will continue to provide good yields even in extreme weather
Answer: (B)
7. A game consists of spinning an arrow around a stationary disk as shown below. When the arrow comes to rest, there are eight equally likely outcomes. It could come to rest in any one of the sectors numbered 1, 2, 3, 4, 5, 6, 7 or 8 as shown. Two such disks are used in a game where their arrows are independently spun. What is the probability that the sum of the numbers on the resulting sectors upon spinning the two disks is equal to 8 after the arrows come to rest?
(A) 1/16
(B) 5/64
(C) 3/32
(D) 7/64
Answer: (D)
8. Consider the following inequalities.
(i) 3p − q< 4
(ii) 3q − p< 12
Which one of the following expressions below satisfies the above two inequalities?
(A) p + q < 8
(B) p + q = 8
(C) 8 ≤ p + q < 16
(D) p + q ≥ 16
Answer: (A)
9. Given below are three statements and four conclusions drawn based on the statements.
Statement 1: Some engineers are writers.
Statement 2: No writer is an actor.
Statement 3: All actors are engineers.
Conclusion I: Some writers are engineers.
Conclusion II: All engineers are actors.
Conclusion III: No actor is a writer.
Conclusion IV: Some actors are writers.
Which one of the following options can be logically inferred?
(A) Only conclusion I is correct
(B) Only conclusion II and conclusion III are correct
(C) Only conclusion I and conclusion III are correct
(D) Either conclusion III or conclusion IV is correct
Answer: (C)
10. Which one of the following sets of pieces can be assembled to form a square with a single round hole near the center? Pieces cannot overlap.
Answer: (C)
Textile Engineering and Fibre Science
Q.11 – Q.35 Carry ONE mark Each
11. The number of solution(s) of the system of linear equations
x + y + z = 0
x – y + z = 0
x + 2y – z = 0
is
(A) 1
(B) 0
(C) Infinite
(D) More than one but finite
Answer: (A)
12.
(A) 1
(B) 0
(C) 1/2
(D) 2
Answer: (MTA)
13. An integrating factor of the differential equation xdy + (1 – y)dx = 0 is
(A) 1/x
(B) x
(C) ex
(D) 1/x2
Answer: (A OR D)
14. Cotton fibre has maximum amount of cellulose in
(A) Cuticle
(B) Primary cell wall
(C) Secondary cell wall
(D) Lumen
Answer: (C)
15. High extensibility of wool fibre is due to
(A) Presence of scales
(B) α-helix structure of proteins
(C) Cross-linking
(D) β-sheet structure of proteins
Answer: (B)
16. In a comber, the component that rotates both in the forward and backward directions is
(A) Nipper
(B) Top comb
(C) Cylinder comb
(D) Detaching roller
Answer: (D)
17. Yarn that has helically twisted fibres at the core and belts/wrappers on the surface is
(A) Ring yarn
(B) Rotor yarn
(C) Compact yarn
(D) Air-vortex yarn
Answer: (B)
18. The ingredient that is NOT used in sizing formulations is
(A) Starch
(B) Polyvinyl acetate
(C) Polyvinyl alcohol
(D) Polycarbonate
Answer: (D)
19. The machine that uses ‘Horn gears’ is
(A) Warp knitting
(B) Circular braiding
(C) Sectional warping
(D) Shuttle loom
Answer: (B)
20. Direct measurement of degree of thickening (θ) of cotton fibre is carried out using
(A) AFIS
(B) HVI
(C) Caustic soda method
(D) Double compression method
Answer: (A)
21. A relatively flat middle zone in a comb sorter diagram indicates
(A) Higher fibre length variation
(B) Lower fibre length variation
(C) Higher mean length
(D) Lower mean length
Answer: (B)
22. Scouring and cold mercerisation of cotton are carried out by treatment with aqueous sodium hydroxide. The process parameters that differ in the two processes are
(A) Temperature and alkali concentration only
(B) Temperature and treatment time only
(C) Treatment time and alkali concentration only
(D) Temperature, treatment time and alkali concentration
Answer: (D)
23. Woven fabrics can be dyed in open width form in
(A) Jigger and winch
(B) Jigger and jet dyeing machine
(C) Winch and beam dyeing machine
(D) Jigger and beam dyeing machine
Answer: (D)
24. The determinant of a 3 × 3 matrix A is 30. If 2 and 3 are two Eigenvalues of A,
then the third Eigenvalue of A (in integer) is _______.
Answer: (5 to 5)
25. A fair coin is tossed five times. The probability of obtaining at most two “HEAD” (correct up to 1 decimal place) is _______.
Answer: (0.4 to 0.6)
26. Molecular weight (g/mol) of polypropylene with a degree of polymerisation of 1000 (rounded off to nearest integer) is ________.
Answer: (42000 to 43000)
27. Polydispersity index of a polymer is 5 and its weight average molecular weight is 8400 g/mol. The number average molecular weight (g/mol) of the polymer (in integer) is _______.
Answer: (1680 to 1680)
28. A three-bladed beater is running with an angular velocity of 600 rpm and delivering material at a rate of 600 kg/h. Number of strikes per kg of delivered material (in integer) is ______.
Answer: (180 to 180)
29. Assume that there is no compression of roving during winding and each coil of a layer is placed directly over the coil of the previous layer. A full roving bobbin consisting of 50 layers of roving is wound on an empty bobbin of 60 mm diameter. If the diameter of the roving is 1 mm, then the diameter (mm) of the full bobbin (in integer) is ______.
Answer: (160 to 160)
30. A yarn is unravelled from a woven fabric specimen of 1 m × 1 m size. If the length of the straightened yarn is 1.1 m, then the crimp percentage (in integer) is _________.
Answer: (10 to 10)
31. In a projectile loom, the energy stored in a torsion rod just before picking is proportional to rn. If r is the radius of torsion rod, then the value of n (in integer) is _______.
Answer: (4 to 4)
32. Cusick drape test on a fabric specimen results in a drape coefficient of 0.7. If the total mass of the paper ring is 3.0 g, then the mass (g) of the paper with shadowed area (correct up to 1 decimal place) is _______.
Answer: (2.0 to 2.2)
33. If moisture regain of polyester and cotton is 0.4 % and 8.5 %, respectively, then moisture regain (%) of 70:30 polyester-cotton blend (correct up to 2 decimal places)is ______.
Answer: (2.66 to 3.00)
34. A pad bath for flame retardant finishing is prepared by mixing 300 g/Ldi ammonium phosphate (DAP) aqueous solution with 60 g/L softener solution inthe ratio of 2:1 (v/v). The concentration (g/L) of DAP in the resultant solution (in integer) is ______.
Answer: (200 to 200)
35. If the reflectance of a dyed fabric at λmax is 10 %, then the colour strength value(K/S) of the dyed fabric (correct up to 2 decimal places) is ______.
Answer: (4.00 to 4.10)
Q.36 – Q.65 Carry TWO marks Each
36. If the probability density function of a continuous random variable X is given by
then the value of a is
(A) 0.2
(B) 0.1
(C) 0.5
(D) 0.4
Answer: (B)
37. Let f : R2→ R (R is the set of real numbers) be defined by
If fx(0, 0) and fy(0, 0) denote partial derivatives of f with respect to x and y at the point (0, 0), respectively, then fx(0, 0) and fy(0, 0), respectively, are
(A) 1 and 1
(B) 1 and 2
(C) 1 and −1
(D) 2 and 1
Answer: (C)
38. Match the properties listed in Group I with the corresponding measuring techniques given in Group II. The correct option is
(A) P-1, Q-2, R-4, S-3
(B) P-3, Q-1, R-4, S-2
(C) P-3, Q-2, R-4, S-1
(D) P-3, Q-2, R-1, S-4
Answer: (B)
39. Determine the correctness or otherwise of the following Assertion [a] and Reason[r].
[a]: In viscose rayon manufacturing process, the fibres develop a skin-core
structure.
[r]: During extrusion, the polymer molecules near the wall of the spinneret tend to orient less as compared to molecules at the centre of the fibre.
(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].
[a]: Para-aramid fibres have better mechanical properties as compared to meta-aramid fibres
[r]: The chemical structure of para-aramid fibres allows them to pack closely
(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. Keeping the speed of all other components of a carding machine unchanged, the angular velocity of a cylinder with damaged wire points in an area of 2 cm × 2 cm is doubled. Wavelength of the periodic fault in the card sliver would be
(A) Same
(B) Halved
(C) Doubled
(D) Tripled
Answer: (B)
42. Determine the correctness or otherwise of the following Assertion [a] and Reason[r].
[a]: As compared to parallel wound yarn packages, ring bobbins exhibit lower
tendency of slough off during unwinding
[r]: The main winding layers in the ring bobbins are separated by cross-winding layers
(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)
43. A set of yarns is produced with same linear density. If these yarns follow helical model and their diameter is inversely proportional to twist (number of turns per unit length), then the yarns have the same
(A) Packing density
(B) Twist multiplier
(C) Twist angle of surface fibres
(D) Area of cross-section
Answer: (C)
44. Consider the following statements for a shuttle loom having linear (straight line)displacement profile for the picker:
P. The maximum actual acceleration of shuttle depends on loom speed and alacrity of picking system
Q. The maximum actual velocity of shuttle depends on loom speed
R. The maximum actual acceleration and maximum actual velocity of shuttle occur at the same time
S. Nominal displacement of shuttle is inversely proportional to the angular
movement of crank shaft
The combination of TRUE statements is
(A) P and Q
(B) Q and R
(C) R and S
(D) P and R
Answer: (A)
45. Eight-end regular sateen fabric can be woven with move (step) numbers of
(A) 2 or 8
(B) 1 or 7
(C) 3 or 5
(D) 4 or 6
Answer: (C)
46. Consider the following components of a needle:
P. Shank
Q. Beard
R. Barb
S. Latch
The combination of correct components of a needle in a needle punching non woven machine is
(A) P and Q
(B) Q and R
(C) R and S
(D) P and R
Answer: (D)
47. The schematic of elastic recovery of a textile material is given below
Where
AB = original length; BD = total extension; CD = elastic extension;
BC = permanent set
With reference to the above schematic, consider the following statements:
P. For perfectly elastic material, BC = 0
Q. For perfectly elastic material, CD = 0
R. For perfectly plastic material, BC = 0
S. For perfectly plastic material, CD = 0
The combination of TRUE statements is
(A) P and Q
(B) Q and R
(C) R and S
(D) P and S
Answer: (D)
48. Consider the following statements with reference to testing of cotton fibre in HVI:
P. Strength is measured in single fibre form
Q. Strength is measured in fibre bundle form
R. Fineness is measured by air flow method
S. Fineness is determined by measuring fibre diameter
The combination of TRUE statements is
(A) P and Q
(B) Q and R
(C) R and S
(D) P and R
Answer: (B)
49. Determine the correctness or otherwise of the following Assertion [a] and Reason[r].
[a]: Increase resistant finishing process of cotton with DMDHEU, curing is not carried out in steam
[r]: Steam causes DMDHEU to self-polymerise rather than cross link cotton
(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)
50. Consider the following statements with respect to a cotton fabric which has been fully desized and bleached but not scoured:
P. It has residual seed coat fragments
Q. It has poor water absorbency
R. It has high whiteness index
S. It has high crease recovery
The combination of TRUE statements is
(A) P, Q and R
(B) Q, R and S
(C) P, R and S
(D) P, Q and S
Answer: (A)
51. In a dye identification test, a dyed fabric is immersed in an aqueous alkaline solution of a reducing agent. The colour of the dyed fabric changes and some dye bleeds out in the solution. The correct combination of the fabric and dye is
(A) Wool and acid dye
(B) Polyester and disperse dye
(C) Cotton and vat dye
(D) Acrylic and basic dye
Answer: (C)
52. Assuming the step size h = 1, the numeric value (rounded off to 2 decimal places)of the definite integral
obtained using Simpson’s rule is _____.
Answer: (1.29 to 1.33)
53. Let yʹ and yʹʹ denote the first and second order derivatives of y with respect to
x, respectively. Let y(x) be a solution of the initial value problem:
yʹʹ − 3yʹ + 2y = 0, y(0) = 1, yʹ(0) = 3.
Then yʹʹ(0) (in integer) is ________.
Answer: (7 to 7)
54. The Gibb’s free energy equation for a system undergoing phase transition is given by ΔG = ΔH – TΔS, where ΔG is the change in Gibb’s free energy, ΔH is the change in enthalpy, ΔS is the change in entropy and T is the temperature in Kelvin.
During melting transition, two systems A and B, show no difference in ΔH but Bexhibits 10 % lower ΔS than A. The ratio of melting temperature of B to that of A(rounded off to 2 decimal places) is _______.
Answer: (1.10 to 1.12)
55. A monofilament gets extruded at a speed of 10 m/min from a spinneret of 0.2 mm diameter. In order to ensure a spin draw ratio of 11, the first godet roller with a diameter of 70 cm has to rotate with an angular velocity (rpm) of (rounded off to nearest integer) _______.
Answer: (49 to 51)
56. Nine slivers having same mean linear density are doubled on a draw frame. If the standard deviation of linear density of each sliver is 0.3 k tex, then the standard deviation (ktex) of linear density of the doubled sliver (correct up to 1 decimal place) is _________.
Answer: (0.8 to 1.0)
57. The twist angle (degree) of surface fibres in a yarn with density of 700 kg/m3 and twist multiplier of 6000 m−1∙tex5 (rounded off to nearest integer), is ______.
Answer: (38 to 40)
58. In a multiplicative type tensioner, the angle of wrap is 90° and the coefficient of friction between the yarn and the guide is 0.2. If the input yarn tension is 10 cN,then the output yarn tension (cN) is (rounded off to 1 decimal place) _______.
Answer: (13.5 to 13.9)
59. A take-up motion is shown below. The number of teeth on gear A, B, C, D and E are 60, 20, 40, 25 and 50, respectively. The circumference of the take-up roller is 40 cm. If one tooth is broken on gear B, then the wavelength (cm) of the fault in fabric (in integer) is ______.
Answer: (10 to 10)
60. The tensile load (F) in Newton (N) and the elongation (ε) in cm of a yarn are related as follows F = 2ε2 + ε
If the breaking elongation of the yarn is 10 cm, then the work of rupture (N∙m) of yarn (rounded off to 2 decimal places) is _____.
Answer: (7.10 to 7.25)
61. Under steady-state thermal conditions, the temperature at various locations in a two-plate Tog meter is as shown in the Figure given below. If the thermal resistance of the standard bottom plate is 1.5 K/W, then the thermal resistance (K/W) of fabric specimen (correct up to 1 decimal place) is ______.
Answer: (4.7 to 4.9)
62. For a wool fibre strand, the relationship between Vr(limit CV % of linear density)and N (average number of fibres in the cross-section of the strand) is given below
For the above relationship, the CV % of linear density of wool fibre (rounded off to2 decimal places) is ______.
Answer: (50.20 to 50.60)
63. The breaking load of a cotton yarn, with a twist multiplier of 4 tpi∙Ne−5, is 2.5 N.If the twist (number of turns per inch) of yarn is 20, then the tenacity (cN/tex) of the yarn (rounded off to 2 decimal places) is ______.
Answer: (10.50 to 10.70)
64. A cotton fabric is dyed at 5 % shade (owf) using a monofunctional reactive dye.The molecular weight of the dye and cellobiose unit is 400 and 342, respectively. If all the hydroxyl groups in cellulose are accessible for reaction, the percentage of unreacted hydroxyl groups of cellulose remaining after dyeing (rounded off to 2 decimal places) is _______.
Answer: (99.20 to 99.40)
65. A polyester fabric of 150 cm width and areal density of 300 g/m2 is printed at a speed of 60 m/min. The solid content of the print paste is 50 %. After printing and drying, the areal density of the printed fabric becomes 400 g/m2. The consumption(kg/h) of the print paste (in integer) is _______.
2. A sum of money is to be distributed among P, Q, R, and S in the proportion 5 : 2 : 4 : 3, respectively.
If R gets Rs 1000 more than S, what is the share of Q (in Rs)?
(A) 500
(B) 1000
(C) 1500
(D) 2000
Answer: (D)
3. A trapezium has vertices marked as P, Q, R and S (in that order anticlockwise). The side PQ is parallel to side SR.
Further, it is given that, PQ = 11 cm, QR = 4 cm, RS = 6 cm and SP = 3 cm.
What is the shortest distance between PQ and SR (in cm)?
(A) 1.80
(B) 2.40
(C) 4.20
(D) 5.76
Answer: (B)
4. The figure shows a grid formed by a collection of unit squares. The unshaded unit square in the grid represents a hole.
What is the maximum number of squares without a “hole in the interior” that can be formed within the 4 × 4 grid using the unit squares as building blocks?
(A) 15
(B) 20
(C) 21
(D) 26
Answer: (B)
5. An art gallery engages a security guard to ensure that the items displayed are protected. The diagram below represents the plan of the gallery where the boundary walls are opaque. The location the security guard posted is identified such that all the inner space (shaded region in the plan) of the gallery is within the line of sight of the security guard.
If the security guard does not move around the posted location and has a 360o view, which one of the following correctly represents the set of ALL possible locations among the locations P, Q, R and S, where the security guard can be posted to watch over the entire inner space of the gallery.
(A) P and Q
(B) Q
(C) Q and S
(D) R and S
Answer: (C)
Q.6 – Q.10 Carry TWO marks each.
6. Mosquitoes pose a threat to human health. Controlling mosquitoes using chemicals may have undesired consequences. In Florida, authorities have used genetically modified mosquitoes to control the overall mosquito population. It remains to be seen if this novel approach has unforeseen consequences.
Which one of the following is the correct logical inference based on the information in the above passage?
(A) Using chemicals to kill mosquitoes is better than using genetically modified mosquitoes because genetic engineering is dangerous
(B) Using genetically modified mosquitoes is better than using chemicals to kill mosquitoes because they do not have any side effects
(C) Both using genetically modified mosquitoes and chemicals have undesired consequences and can be dangerous
(D) Using chemicals to kill mosquitoes may have undesired consequences but it isnot clear if using genetically modified mosquitoes has any negative consequence
Answer: (D)
7. Consider the following inequalities.
(i) 2x − 1 > 7
(ii) 2x − 9 < 1
Which one of the following expressions below satisfies the above two inequalities?
(A) x ≤ −4
(B) −4 <x ≤ 4
(C) 4 <x< 5
(D) x ≥ 5
Answer: (C)
8. Four points P(0, 1), Q(0, −3), R(−2, −1), and S(2, −1) represent the vertices of a quadrilateral.
What is the area enclosed by the quadrilateral?
(A) 4
(B) 4√2
(C) 8
(D) 8√2
Answer: (C)
9. In a class of five students P, Q, R, S and T, only one student is known to have copied in the exam. The disciplinary committee has investigated the situation and recorded the statements from the students as given below.
Statement of P: R has copied in the exam.
Statement of Q: S has copied in the exam.
Statement of R: P did not copy in the exam.
Statement of S: Only one of us is telling the truth.
Statement of T: R is telling the truth.
The investigating team had authentic information that S never lies.
Based on the information given above, the person who has copied in the exam is
(A) R
(B) P
(C) Q
(D) T
Answer: (B)
10. Consider the following square with the four corners and the center marked as P, Q, R, S and T respectively.
Let X, Y and Z represent the following operations:
X: rotation of the square by 180 degree with respect to the
S-Q axis.
Y: rotation of the square by 180 degree with respect to the P-R axis.
Z: rotation of the square by 90 degree clockwise with respect to the axis perpendicular, going into the screen and passing through the point T.
Consider the following three distinct sequences of operation (which are applied
in the left to right order).
(1) XYZZ
(2) XY
(3) ZZZZ
Which one of the following statements is correct as per the information provided above?
(A) The sequence of operations (1) and (2) are equivalent
(B) The sequence of operations (1) and (3) are equivalent
(C) The sequence of operations (2) and (3) are equivalent
(D) The sequence of operations (1), (2) and (3) are equivalent
Answer: (B)
Statistics
Q.11 – Q.35 Carry ONE mark Each
11. Let M be a 2 × 2 real matrix such that (I + M)−1 = I – αM, where α is a non-zero real number and I is the 2 × 2 identity matrix. If the trace of the matrix M is 3, then the value of 𝛼 is
(A) 3/4
(B) 1/3
(C) 1/2
(D) 1/4
Answer: (D)
12. Let {X(t)}t≥0 be a linear pure death process with death rate μi = 5i,, i = 0.1, …, N, N ≥ Suppose that pi(t) = P(X(t) = i). Then the system of forward Kolmogorov’s equations is
Answer: (B)
13. Let S2 be the variance of a random sample of size n > 1 from a normal population with an unknown mean μ and an unknown finite variance σ2 > 0. Consider the following statements:
(I) S2 is an unbiased estimator of σ2, and S is an unbiased estimator of σ.
(II) is a maximum likelihood estimator of σ2, and is a maximum likelihood estimator of σ.
Which of the above statements is/are true?
(A) (I) only
(B) (II) only
(C) Both (I) and (II)
(D) Neither (I) nor (II)
Answer: (B)
14. Let f : ℝ2 → ℝ be a function defined by
Then which one of the following statements is true?
(A) f is bounded and ∂f/∂x is unbounded on ℝ2
(B) f is unbounded and ∂f/∂x is bounded on ℝ2
(C) Both f and ∂f/∂x are unbounded on ℝ2
(D) Both f and ∂f/∂x are bounded on ℝ2
Answer: (B)
15. Let X1, X2, … , Xn be a random sample from a distribution with cumulative distribution function F(x). Let the empirical distribution function of the sample be Fn(x). The classical Kolmogorov-Smirnov goodness of fit test statistic is given by
Consider the following statements:
(I) The distribution of Tn is the same for all continuous underlying
distribution functions F(x).
(II) Dn converges to 0 almost surely, as n → ∞.
Which of the above statements is/are true?
(A) (I) only
(B) (II) only
(C) Both (I) and (II)
(D) Neither (I) nor (II)
Answer: (C)
16. Consider the following transition matrices P1 and P2 of two Markov chains:
Then which one of the following statements is true?
(A) Both P1 and P2 have unique stationary distributions
(B) P1 has a unique stationary distribution, but P2 has infinitely many stationary distributions
(C) P1 has infinitely many stationary distributions, but P2 has a unique stationary distribution
(D) Neither P1 nor P2 has unique stationary distribution
Answer: (C)
17. Let X1, X2, …, X20 be a random sample of size 20 from N6(μ, ∑), with det(∑) ≠ 0, and suppose both μ and ∑ are unknown. Let
Consider the following two statements:
(I) The distribution of 19 S is W6(19, ∑) (Wishart distribution of order 6 with 19 degrees of freedom).
(II) The distribution of (X3 − μ)T S−1(X3 − μ) is χ62 (Chi-square distribution with 6 degrees of freedom).
Then which of the above statements is/are true?
(A) (I) only
(B) (II) only
(C) Both (I) and (II)
(D) Neither (I) nor (II)
Answer: (A)
18. Let X1, X2, …, X3 be a random sample from the distribution
Let χ2α,n denote the value of a Chi-square random variable Y with n degrees of freedom such that P(Y > χ2α,n = α. If x1, x2, …, x18 is a realization of this random sample, then, based on the sufficient statistic which one of the following is a 98% confidence interval for θ?
Answer: (A)
19. Let X1, X2, …, Xn be a random sample from a population f (x; θ), where θ is a parameter. Then which one of the following statements is NOT true?
(A) is a complete and sufficient statistic for θ, if x = 0, 1, 2, …, and θ > 0
(B) is a complete and sufficient statistic for θ, if −∞ < x < ∞, θ > 0
(C) f(x, θ) = θxθ−1, 0 x < 1, θ > 0 has monotone likelihood ratio property in
(D) X(n) – X(1) is ancillary statistic for θ if f(x; θ) = 1, 0 < θ < x < θ +1, where X(1) = min{X1, X2, …, Xn) and X(n) = max[X1, X2, …, Xn}
Answer: (B)
20. A random sample X1, X2, …, X6 of size 6 is taken from a Bernoulli distribution with the parameter θ. The null hypothesis H0 : θ = 1/2 is to be tested against the alternative hypothesis H1 : θ > 1/2, based on the statistic If the value of Y corresponding to the observed sample values is 4, then the 𝑝-value of the test statistic is
(A) 21/32
(B) 9/64
(C) 11/32
(D) 7/64
Answer: (C)
21. Let be a sequence of positive real numbers satisfying with a1 = 3 and an < 7 for all n ≥
Consider the following statements:
(I) {an} is monotonically increasing.
(II) {an} converges to a value in the interval [3, 7]
Then which of the above statements is/are true?
(A) (I) only
(B) (II) only
(C) Both (I) and (II)
(D) Neither (I) nor (II)
Answer: (C)
22. Let M be any square matrix of arbitrary order 𝑛 such that M2 = 0 and the nullity of M is 6. Then the maximum possible value of n (in integer) is ______
Answer: (12 to 12)
23. Consider the usual inner product in ℝ4. Let u ∈ ℝ4 be a unit vector orthogonal to the subspace
If v = (1, −2, 1, 1)T, and the vectors u and v – αu, α ∈ ℝ, are orthogonal, then the value of α2 (rounded off to two decimal places) is equal to _______
Answer: (0.25 to 0.25)
24. Let {B(t)}t≥0 be a standard Brownian motion and let ϕ (∙) be the cumulative distribution function of the standard normal distribution. If α > 0, then the value of α (in integer) is equal to ____
Answer: (22 to 22)
25. Let X and Y be two independent exponential random variables with E(X2) = 1/2 and E(Y2) = 2/9. Then P(X < 2Y) (rounded off to two decimal places) is equal to ______
Answer: (0.55 to 0.59)
26. Let X be a random variable with the probability mass function x = 1, 2, 3 …. . Then the value of (rounded off to two decimal places) is equal to _______
Answer: (2.30 to 2.32)
27. Let Xi, i = 1, 2, …, n, be i.i.d. random variables from a normal distribution with mean 1 and variance 4 Let If Var(Sn) denotes the variance of Sn, then the value of (in integer) is equal to ______
Answer: (23 to 23)
28. At a telephone exchange, telephone calls arrive independently at an average rate of 1 call per minute, and the number of telephone calls follows a Poisson distribution. Five time intervals, each of duration 2 minutes, are chosen at random. Let p denote the probability that in each of the five time intervals at most 1 call arrives at the telephone exchange. Then e10 p (in integer) is equal to ______
Answer: (243 to 243)
29. Let X be a random variable with the probability density function
where c is a constant and [x] denotes the greatest integer less than or equal to x. If A = [1/2, 2], then P(X ∈ A) (rounded off to two decimal places) is equal to ______
Answer: (0.57 to 0.59)
30. Let X and Y be two random variables such that the moment generating function of X is M(t) and the moment generating function of Y is where t ∈ (−h, h), h > 0. If the mean and the variance of X are 1/2 and 1/4, respectively, then the variance of Y (in integer) is equal to _______
Answer: (1 to 1)
31. Let Xi, i = 1, 2, … n, be i.i.d. random variables with the probability density function
where Γ(∙)denotes the gamma function. Also, let If converges to N(0, σ2) in distribution, then σ2 (rounded off to two decimal places) is equal to ________
Answer: (1.18 to 1.19)
32. Consider a Poisson process {X(t), t ≥ 0}. The probability mass function of X(t) is given by
If C(t1, t2) is the covariance function of the Poisson process, then the value of C(5, 3) (in integer) is equal to ______
Answer: (12 to 12)
33. A random sample of size 4 is taken from the distribution with the probability density function
If the observed sample values are 6, 5, 3, 6, then the method of moments estimate (in integer) of the parameter θ, based on these observations, is ______
Answer: (15 to 15)
34. A company sometimes stops payments of quarterly dividends. If the company pays the quarterly dividend, the probability that the next one will be paid is 0.7. If the company stops the quarterly dividend, the probability that the next quarterly dividend will not be paid is 0.5. Then the probability (rounded off to three decimal places) that the company will not pay quarterly dividend in the long run is ______
Answer: (0.375 to 0.375)
35. Let X1, X2, …, X8 be a random sample taken from a distribution with the probability density function
Let F8(x) be the empirical distribution function of the sample. If α is the variance of F8(2), then 128α (in integer) is equal to ______
Answer: (3 to 3)
Q.36 – Q.65 Carry TWO marks Each
36. Let M be a 3 × 3 real symmetric matrix with eigenvalues −1, 1, 2 and the corresponding unit eigenvectors u, v, w respectively. Let x and y be two vectors in ℝ3 such that
Mx = u +2(v + w) and M2y = u – (v + 2w).
Considering the usual inner product in ℝ3, the value of |x + y|2, where |x + y| is the length of vector x + y, is
(A) 1.25
(B) 0.25
(C) 0.75
(D) 1
Answer: (A)
37. Consider the following infinite series:
Which of the above series is/are conditionally convergent?
(A) S1 only
(B) S2 only
(C) Both S1 and S2
(D) Neither S1 nor S2
Answer: (C)
38. Let (3, 6)T, (4, 4)T, (5, 7)T and (4, 7)T be four independent observations from a bivariate normal distribution with the mean vector μ and the covariance matrix ∑. Let be the maximum likelihood estimates of μ and ∑, respectively, based on these observations. Then is equal to
Answer: (A)
39. Let follow N3(μ, ∑) with where a ∈ ℝ. Suppose that the partial correlation coefficient between X2 and X3, keeping X1 fixed is 5/7. Then a is equal to
(A) 1
(B) 3/2
(C) 2
(D) 1/2
Answer: (A)
40. If the line y = αx, α ≥ √2, divides the area of the region
R: = {(x, y) ∈ ℝ2| 0 ≤ x ≤ √y, 0 ≤ y ≤ 2}
into two equal parts, then the value of α is equal to
(A) 3/√2
(B) 2√2
(C) √2
(D) 5/2√2
Answer: (A)
41. Let (X, Y, Z) be a random vector with the joint probability density function
Then which one of the following points is on the regression surface of X on (Y, Z) ?
Answer: (A)
42. A random sample X of size one is taken from a distribution with the probability density function
If x/θ is used as a pivot for obtaining the confidence interval for θ, hen which one of the following is an 80% confidence interval (confidence limits rounded off to three decimal places) for θ based on the observed sample value x = 10?
(A) (10.541, 31.623)
(B) (10.987, 31.126)
(C) (11.345, 30.524)
(D) (11.267, 30.542)
Answer: (A)
43. Let X1, X2, …, X7 be a random sample from a normal population with mean 0 and variance θ > 0. Let
Consider the following statements:
(I) The statistics K and K12 + X22 + … + X72 are independent.
(II) 7K/2 has an F-distribution with 2 and 7 degrees of freedom.
(III) E(K2) = 8/63.
Then which of the above statements is/are true?
(A) (I) and (II) only
(B) (I) and (III) only
(C) (II) and (III) only
(D) (I) only
Answer: (B)
44. Consider the following statements:
(I) Let a random variable X have the probability density function Then there exist i.i.d. random variables X1 and X2 such that X and X1 – X2 have the same distribution.
(II) Let a random variable Y have the probability density function
Then there exist i.i.d. random variables Y1 and Y2 such that Y and Y1 – Y2 have the same distribution.
Then which of the above statements is/are true?
(A) (I) only
(B) (II) only
(C) Both (I) and (II)
(D) Neither (I) nor (II)
Answer: (A)
45. Suppose X1, X2, …, Xn, … are independent exponential random variables with the mean 1/2. Let the notation o. denote ‘infinitely often’. Then which of the following is/are true?
Answer: (A, B, D)
46. Let {Xn}, n ≥ 1, be a sequence of random variables with the probability with the probability mass functions
Let X be a random variable with P(X = 0) = 1. Then which of the following statements is/are true?
(A) Xn converges to X in distribution
(B) Xn converges to X in probability
(C) E(Xn) → E(X)
(D) There exists a subsequence of {Xn} such that converges to X almost surely
Answer: (A, B, D)
47. Let M be any 3 × 3 symmetric matrix with eigenvalues 1, 2 and 3. Let N be any 3 × 3 matrix with real eigenvalues such that MN + NTM = 3I, where I is the 3 × 3 identity matrix. Then which of the following cannot be eigenvalue(s) of the matrix N ?
(A) 1/4
(B) 3/4
(C) 1/2
(D) 7/4
Answer: (A, D)
48. Let M be a 3 × 2 real matrix having a singular value decomposition as M = USVT, where the matrix U is a 3 × 3 orthogonal matrix, and V is a 2 × 2 orthogonal matrix. Then which of the following statements is/are true?
(A) The rank of the matrix M is 1
(B) The trace of the matrix MTM is 4
(C) The largest singular value of the matrix (MTM)−1MT is 1
(D) The nullity of the matrix M is 1
Answer: (B, C)
49. Let X be a random variable such that
where ℤ denotes the set of all integers. If ϕx(t), t ∈ ℝ, denotes the characteristic function of X, then which of the following is/are true?
(A) ϕx(a) = 1
(B) ϕx(∙) is periodic with period a
(C) | ϕx(t)| < 1 for al t ≠ a
(D)
Answer: (A, B)
50. Which of the following real valued functions is/are uniformly continuous on [0, ∞)?
(A) sin2x
(B) x sin x
(C) sin(sin x)
(D) sin(x sin x)
Answer: (A, C)
51. Two independent random samples, each of size 7, from two populations yield the following values:
If Mann-Whitney U test is performed at 5% level of significance to test the null hypothesis H0: Distributions of the populations are same, against the alternative hypothesis H1: Distributions of the populations are not same, then the value of the test statistic U (in integer) for the given data, is ______
Answer: (15 to 15)
52. Consider the multiple regression model
Y = β0 + β1X1 + β2X2 + β3X3 + ϵ,
where ϵ is normally distributed with mean 0 and variance σ2 > 0, and β0, β1, β2, β3 are unknown parameters. Suppose 52 observations of (Y, X1, X2, X3) yield sum of squares due to regression as 18.6 and total sum of squares as 79.23. Then, for testing the null hypothesis H0 : β1 = β2 = β3 = 0 against the alternative hypothesis H1 : βi ≠ 0 for some i = 1, 2, 3, the value of the test statistic (rounded off to three decimal places), based on one way analysis of variance, is _______
Answer: (4.907 to 4.909)
53. Suppose a random sample of size 3 is taken from a distribution with the probability density function
If p is the probability that the largest sample observation is at least twice the smallest sample observation, then the value of p (rounded off to three decimal places) is ______
Answer: (0.436 to 0.439)
54. Let a linear model Y = β0 + β1X + ϵ be fitted to the following data, where ϵ is normally distributed with mean 0 and unknown variance σ2 > 0.
Let denote the ordinary least-square estimator of at X = 6, and the variance of Then the value of the real constant c (rounded off to one decimal place) is equal to ______
Answer: (1.8 to 1.8)
55. Let 0, 1, 1, 2, 0 be five observations of a random variable X which follows a Poisson distribution with the parameter θ > 0. Let the minimum variance unbiased estimate of P(X ≤ 1), based on this data, be α. Then 54α (in integer) is equal to ______
Answer: (512 to 512)
56. While calculating Spearman’s rank correlation coefficient, based on n observations {(xi, yi), i = 1, 2 …, n} from a paired data, it is found that xi are distinct for all i ≥ 2, x1 = x2 and where di = rank(xi) – rank(yi). Then the minimum possible value of n3 – n (in integer) is ________
Answer: (60 to 60)
57. In a laboratory experiment, the behavior of cats are studied for a particular food preference between two foods A and B. For an experiment, 70% of the cats that had food A will prefer food A, and 50% of the cats that had food B will prefer food A. The experiment is repeated under identical conditions. If 40% of the cats had food A in the first experiment, then the percentage (rounded off to one decimal place) of cats those will prefer food A in the third experiment, is ______
Answer: (61.5 to 61.7)
58. A random sample of size 5 is taken from a distribution with the probability density function
where θ is an unknown parameter. If the observed values of the random sample are 3, 6, 4, 7, 5, then the maximum likelihood estimate of the 1/8th quantile of the distribution (rounded off to one decimal place) is ____
Answer: (3.5 to 3.5)
59. Consider a gamma distribution with the probability density function
with β > 0. Then, for β = 2, the value of the Cramer-Rao lower bound (rounded off to one decimal place) for the variance of any unbiased estimator of β2, based on a random sample of size 8 from this distribution, is ______
Answer: (1.6 to 1.6)
60. Let X1, X2, X3, X4 be a random sample of size four from a Bernoulli distribution with the parameter θ, 0 < θ < 1. Consider the null hypothesis H0 : θ = 1/4 against the alternative hypothesis H1 : θ > 1/4. Suppose H0 is rejected if and only if X1 + X2 + X3 + X4 > 2. If α is the probability of Type I error for the test and γ(θ) is the power function of the test, then the value of 16α + 7γ(1/2) (in integer) is equal to _______
Answer: (3 to 3)
61. Given that Φ(1.645) = 0.95 and Φ(2.33) = 0.99, where Φ(⋅) denotes the cumulative distribution function of a standard normal random variable. For a random sample X1, X2, …, Xn from a normal population N(μ, 22), where μ is unknown, the null hypothesis H0 : μ = 10 to be tested against the alternative hypothesis H1 : μ = 12. Suppose that a test that rejects H0 if the sample mean is large, is used. Then the smallest value of n (in integer) such that Type I error is 0.05 and Type II error is at most 0.01, is ______
Answer: (16 to 16)
62. Let Y1 < Y2 < … < Yn be the order statistics of a random sample of size n from a continuous distribution, which is symmetric about its mean μ. Then the smallest value of n (in integer) such that P(Y1 < μ < Yn) ≥99, is ______
Answer: (8 to 8)
63. If P(x, y, z) is a point which is nearest to the origin and lies on the intersection of the surfaces z = xy + 5 and x + y + z = 1. Then the distance (in integer) between the origin and the point P is ______
Answer: (3 to 3)
64. Let X and Y be random variables such that X is uniformly distributed over (0, 4), and the conditional distribution of Y given X = x is uniformly distributed over (0, x2/4). Then E(Y2) (rounded off to three decimal places) is equal to _____
Answer: (1.065 to 1.069)
65. Let X = (X1, X2, X3)T be a random vector with the distribution N3(μ, Σ), where
Then E(X1|(X2 = 4, X3 = 7)) (in integer) is equal to _____
1. Inhaling the smoke from a burning _________ could _________ you quickly.
(A) tire / tier
(B) tire / tyre
(C) tyre / tire
(D) tyre / tier
Answer: (C)
2. A sphere of radius r cm is packed in a box of cubical shape.
What should be the minimum volume (in cm3) of the box that can enclose the sphere?
(A) r3/8
(B) r3
(C) 2r3
(D) 8r3
Answer: (D)
3. Pipes P and Q can fill a storage tank in full with water in 10 and 6 minutes, respectively. Pipe R draws the water out from the storage tank at a rate of 34 litres per minute. P, Q and R operate at a constant rate.
If it takes one hour to completely empty a full storage tank with all the pipes operating simultaneously, what is the capacity of the storage tank (in litres)?
(A) 26.8
(B) 60.0
(C) 120.0
(D) 127.5
Answer: (C)
4. Six persons P, Q, R, S, T and U are sitting around a circular table facing the center not necessarily in the same order. Consider the following statements:
• P sits next to S and T.
• Q sits diametrically opposite to P.
• The shortest distance between S and R is equal to the shortest distance between T and U.
Based on the above statements, Q is a neighbor of
(A) U and S
(B) R and T
(C) R and U
(D) P and S
Answer: (C)
5. A building has several rooms and doors as shown in the top view of the building given below. The doors are closed initially.
What is the minimum number of doors that need to be opened in order to go from the point P to the point Q?
(A) 4
(B) 3
(C) 2
(D) 1
Answer: (C)
Q.6 – Q. 10 Carry TWO marks each.
6. Rice, a versatile and inexpensive source of carbohydrate, is a critical component of diet worldwide. Climate change, causing extreme weather, poses a threat to sustained availability of rice. Scientists are working on developing Green Super Rice (GSR), which is resilient under extreme weather conditions yet gives higher yields sustainably.
Which one of the following is the CORRECT logical inference based on the information given in the above passage?
(A) GSR is an alternative to regular rice, but it grows only in an extreme weather
(B) GSR may be used in future in response to adverse effects of climate change
(C) GSR grows in an extreme weather, but the quantity of produce is lesser than regular rice
(D) Regular rice will continue to provide good yields even in extreme weather
Answer: (B)
7. A game consists of spinning an arrow around a stationary disk as shown below. When the arrow comes to rest, there are eight equally likely outcomes. It could come to rest in any one of the sectors numbered 1, 2, 3, 4, 5, 6, 7 or 8 as shown. Two such disks are used in a game where their arrows are independently spun. What is the probability that the sum of the numbers on the resulting sectors upon spinning the two disks is equal to 8 after the arrows come to rest?
(A) 1/16
(B) 5/64
(C) 3/32
(D) 7/64
Answer: (D)
8. Consider the following inequalities.
(i) 3p − q< 4
(ii) 3q − p< 12
Which one of the following expressions below satisfies the above two inequalities?
(A) p + q < 8
(B) p + q = 8
(C) 8 ≤ p + q < 16
(D) p + q ≥ 16
Answer: (A)
9. Given below are three statements and four conclusions drawn based on the statements.
Statement 1: Some engineers are writers.
Statement 2: No writer is an actor.
Statement 3: All actors are engineers.
Conclusion I: Some writers are engineers.
Conclusion II: All engineers are actors.
Conclusion III: No actor is a writer.
Conclusion IV: Some actors are writers.
Which one of the following options can be logically inferred?
(A) Only conclusion I is correct
(B) Only conclusion II and conclusion III are correct
(C) Only conclusion I and conclusion III are correct
(D) Either conclusion III or conclusion IV is correct
Answer: (C)
10. Which one of the following sets of pieces can be assembled to form a square with a single round hole near the center? Pieces cannot overlap.
Answer: (C)
Production and Industrial Engineering
Q.11 – Q.35 Carry ONE mark Each
11. If a, b and c are three vectors, the vector triple product (a×b) ×c is given by
(A) (a∙c)b− (a∙b)c
(B) (a∙b)c − (a∙c)b
(C) (a∙c)b− (b∙c)a
(D) (b∙c)a− (a∙c)b
Answer: (C)
12. The numerical integration of the function y = 2x + 5 is carried out between
x = 1 and x = 3, by using ordinates at x = 1, 2 and 3. Which one of the following statements is TRUE?
(A) Simpson’s 1/3 rule will provide exact result but trapezoidal rule will not.
(B) Trapezoidal rule will provide exact result but Simpson’s 1/3 rule will not.
(C) Both Simpson’s 1/3 and trapezoidal rules will provide exact result.
(D) Neither Simpson’s 1/3 rule nor trapezoidal rule will provide exact result.
Answer: (C)
13. Which one of the following metals has a face-centered cubic (FCC) structure?
(A) Alpha iron
(B) Chromium
(C) Magnesium
(D) Aluminum
Answer: (D)
14. If G denotes the shear modulus of an isotropic material, then the maximum possible value of Young’s modulus of the material is
(A) G
(B) 2 G
(C) 3 G
(D) 4 G
Answer: (C)
15. Match the casting methods with products.
(A) P-3, Q-1, R-2
(B) P-2, Q-3, R-1
(C) P-3, Q-2, R-1
(D) P-2, Q-1, R-3
Answer: (A)
16. In injection blow molding of plastic beverage bottles, the blowing is accomplished by
(A) hot water
(B) hot air
(C) hot oil
(D) alcohol
Answer: (B)
17. In an electro-discharge machining process, the discharge voltage is Vb. The energy dissipated per spark across the inter-electrode gap is proportional to
(A) Vb0.5
(B) Vb
(C) Vb2
(D) Vb3
Answer: (C)
18. Match the codes used in CNC part programming with their functions.
(A) P-2, Q-3, R-4, S-1
(B) P-2, Q-1, R-4, S-3
(C) P-4, Q-1, R-2, S-3
(D) P-4, Q-2, R-3, S-1
Answer: (B)
19. The control chart for a number of defects in a welded joint is
(A)
(B) R – chart
(C) c – chart
(D) p – chart
Answer: (C)
20. Which one of the following statements is TRUE?
(A) Concurrent engineering is a non-integrated approach for designing a product.
(B) Concurrent engineering carries out all product development functions in a sequential manner.
(C) Concurrent engineering reduces the lead time for the product development.
(D) Concurrent engineering increases the lead time for the product development.
Answer: (C)
21. Match the therblig symbols with their meanings.
(A) P-4, Q-3, R-1, S-2
(B) P-4, Q-3, R-2, S-1
(C) P-3, Q-4, R-1, S-2
(D) P-3, Q-4, R-2, S-1
Answer: (A)
22. Match the types of layout with the types of production.
(A) P-2, Q-3, R-1
(B) P-3, Q-1, R-2
(C) P-2, Q-1, R-3
(D) P-3, Q-2, R-1
Answer: (A)
23. Matrix A as a product of two other matrices is given by
The value of det(A) is________. [round off to nearest integer]
Answer: (0 to 0)
24. The order of the following differential equation is _______. [in integer]
Answer: (1 to 1)
25. An operator manufactures 10 identical spur gears in a lot. One spur gear is defective in the lot. Three spur gears are drawn at random without replacement.The probability of getting all three gears as non-defective is _______.[round off to two decimal places]
Answer: (0.69 to 0.71)
26. In a slider crank mechanism (schematic shown in the figure), the crank rotates at 60 revolutions per minute. The radius of the crank is 30 mm and the length of the connecting rod is 120 mm. The average speed (in mm/s) of the piston over one revolution of the crank is __________. [round off to nearest integer]
Answer: (119 to 121)
27. Water (kinematic viscosity v = 1 × 10−6 m2/s) is flowing through a circular horizontal pipe of diameter 8 mm. If the flow is laminar and fully developed with a maximum axial velocity of 0.5 m/s, the Reynolds number is _________.[round off to nearest integer]
Answer: (1995 to 2005)
28. Yielding starts in a material when the principal stresses are 100 MPa, 100 MPa and 200 MPa. As per the von Mises criterion, yield stress (in MPa) of the material is ______. [round off to nearest integer]
Answer: (99 to 101)
29. A single-point cutting tool with zero rake angle is used for orthogonal machining.If the chip-compression ratio is 1.25, then the shear angle (in degree) during machining is_______. [round off to one decimal place]
Answer: (38.0 to 39.0)
30. It is required to cut a single-start thread of 2 mm pitch in a lathe machine with a single-start lead screw of 4 mm pitch. For one revolution of the workpiece, the number of revolution of the lead screw is ________. [round off to two decimal places]
Answer: (0.40 to 0.60)
31. The absolute deviations of 8 points from the datum line of a surface are 10, 15, 12,10, 13, 12, 20 and 25 μm. The root mean square value of the surface roughness(in μm) is________. [round off to one decimal place]
Answer: (15.0 to 16.0)
32. In a machine there are two motors, but only one motor is needed for the functioning of the machine. The reliabilities of the motors are 0.90 and 0.70. The overall reliability of the machine is________. [round off to two decimal places]
Answer: (0.96 to 0.98)
33. If the inter arrival time is exponential and 8 customers per hour arrive in a bank, then the probability of no arrival of customer during a period of 15 minutes is _______. [round off to two decimal places]
Answer: (0.12 to 0.15)
34. A company buys a machine worth Rs. 65000, which has a salvage value of ₹ 5000.The annual depreciation cost is Rs. 10000 based on the straight line depreciation method. The useful life (in year) of the machine is ________. [in integer]
Answer: (6 to 6)
35. A project comprises of seven activities. The expected durations of activities and their variances are as follows:
The critical path consists of activities B, E and G. The standard deviation (in minute)of the project duration is ________. [round off to two decimal places]
Answer: (2.90 to 3.10)
Q.36 – Q.65 Carry TWO marks Each
36. If a matrix is squared, then
(A) both eigenvalues and eigenvectors must change
(B) both eigenvalues and eigenvectors are retained
(C) eigenvalues get squared but eigenvectors are retained
(D) eigenvalues are retained but eigenvectors change
Answer: (C)
37. Consider the following ordinary differential equation:
Given that c1 and c2 are constants, the general solution of the differential equation is
(A) y = (c1 + c2x) ex
(B) y = c1ex/2 + c2ex
(C) y = c1ex + c2e2x
(D) y = (c1 + c2x)ex/2
Answer: (D)
38. A market survey with a sample size of 1000 was conducted for a parameter that follows normal distribution. The confidence interval was estimated as [500, 700]with a mean of 600. It is now desired to reduce the confidence interval to [550, 650].The sample size for achieving the desired interval at the same confidence level is
(A) 1000
(B) 4000
(C) 9000
(D) 16000
Answer: (B)
39. A eutectoid steel with 100% austenite is cooled from a temperature of 750°C to a room temperature of 35° Match the cooling methods with transformed structures.
(A) P-1, Q-2, R-3, S-4
(B) P-2, Q-3, R-4, S-1
(C) P-3, Q-4, R-2, S-1
(D) P-3, Q-4, R-1, S-2
Answer: (C)
40. In the three-member truss shown in the figure, AC = BC. An external force of 10 kN is applied at B, parallel to AC. The force in the member BC is
(A) zero
(B) 10 kN (tensile)
(C) 10 kN (compressive)
(D) 7.07 kN (tensile)
Answer: (B)
41. Match the processing steps related to production of powder metallurgy parts with their descriptions.
(A) P-1, Q-5, R-2, S-3
(B) P-3, Q-2, R-1, S-5
(C) P-2, Q-3, R-1, S-4
(D) P-2, Q-5, R-1, S-4
Answer: (C)
42. In an assembly comprising shaft and hole, the nominal sizes with tolerances are specified as
The type of fit is
(A) Clearance fit
(B) Interference fit
(C) Transition fit
(D) Running fit
Answer: (C)
43. In a manufacturing system, four different types of products (P, Q, R and S) are produced. The batch size of each product is 2×107. The numbers of defective units are 60, 71, 80 and 55, for P, Q, R and S, respectively. Which one of the following statements is TRUE?
(A) All products conform to six sigma standard.
(B) Only product S conforms to six sigma standard.
(C) Except R, all other products conform to six sigma standard.
(D) Products P and S conform to six sigma standard.
Answer: (D)
44. Match the processes of product development with their characteristics.
(A) P-2, Q-4, R-1, S-3
(B) P-2, Q-3, R-1, S-4
(C) P-4, Q-3, R-1, S-2
(D) P-4, Q-3, R-2, S-1
Answer: (A)
45. The value of is _________. [round off to one decimal place]
Answer: (1.4 to 1.6)
46. A thick-cylinder has inner diameter of 20 mm and outer diameter of 40 mm. It is subjected to an internal pressure of 100 MPa. Follow the convention of taking tensile stress as positive and compressive stress as negative. The sum of radial and hoop stresses (in MPa) at a radius of 15 mm is ________. [round off to two decimal places]
Answer: (66.00 to 67.00)
47. A shaft is used to transmit a power of 10 kW. The shear yield stress of the material is 150 MPa and factor of safety is 2. The shaft rotates at 1440 revolutions per minute. The diameter of the shaft (in mm) based on static strength is _________. [round off to two decimal places]
Answer: (16.00 to 17.00)
48. Air at an initial temperature and pressure of 15°C and 1 bar, respectively is heated in an irreversible process. The final temperature and pressure are 303°C and 2 bar,respectively. Take gas constant for air as R = 287 J/kg-K, the ratio of the specific heats as γ = 1.4, and treat air as a calorically perfect gas. The change of entropy(in J/kg-K) in the process is ________. [round off to nearest integer]
Answer: (495 to 499)
49. During a hot-working process, the homologous temperature is 0.8. The melting point of the work metal is 800 °C. The temperature (in °C) during hot-working is _________. [round off to nearest integer]
Answer: (584 to 586)
50. A workpiece of 30 mm diameter and 40 mm height is compressed between two platens in an open die forging process. Assume a perfectly plastic material with a flow stress of 300 MPa. The ideal forging load (in kN) at 30% reduction (in height)is _________. [round off to nearest integer]
Answer: (300 to 306)
51. In a gas tungsten arc welding process under steady state condition, the input voltage and current are measured as 18 V and 160 A, respectively. Heat loss during creation of arc is 40% of the input power. Heat loss through convection and radiation from the workpiece is 800 W. The effective power (in W) utilized to melt the workpiece is ______. [round off to nearest integer]
Answer: (926 to 930)
52. During straight turning of a 20 mm diameter steel bar at a spindle speed of 400 revolutions per minute (RPM) with an HSS tool, a tool life of 10 minute was observed. When the same bar was turned at 200 RPM, the tool life increased to 40 minute. The tool life (in minute) while machining the bar at 300 RPMis __________. [round off to nearest integer]
Answer: (16 to 19)
53. A cylindrical workpiece is turned using two different tools. Tool 1 has zero nose radius; side and end cutting edge angles are 20° and 10°, respectively. Tool 2 has 0.5 mm nose radius. Both the tools machine at a feed of 0.2 mm/rev. The ratio of ideal maximum height of unevenness on the surface produced by Tool 1 to that produced by Tool 2 is __________. [round off to one decimal place]
Answer: (2.9 to 3.7)
54. For an electrochemical machining process
where y is the inter-electrode gap in mm at time t in minute, and f is the feed of the tool in mm/minute. The value ofλ is 6 × 10−3 cm2/minute. For maintaining a constant inter-electrode gap of 0.1 mm, the feed (in mm/minute) should be __________.[round off to one decimal place]
Answer: (5.9 to 6.1)
55. The worktable of an open loop positioning system is driven by a lead screw with a pitch of 4 mm. The lead screw is connected to the shaft of a stepper motor. A gear of 80 teeth mounted on the stepper motor shaft meshes with a gear of 20 teeth mounted on the lead screw. The step angle of the stepper motor is 9°. The number of pulses required to move the table by 200 mm is _________. [in integer]
Answer: (498 to 502)
56. The diameter of a cylindrical cavity is measured by using two spherical steel balls of diameters 3 cm and 4 cm. The balls are placed inside the cavity such that the bigger ball is above the smaller one as shown in the figure. If the depth of cavity is 6 cm, then the diameter (in cm) of cavity is ________. [round off to two decimal places]
Answer: (5.93 to 5.97)
57. In a mobile screen manufacturing process on a mass scale basis, 5 samples of size 80 are inspected. Consider a p-chart with ±3σ limits (σ is the standard deviation).The numbers of defective items are given in the table.
The upper control limit of the defective item (in fraction defective) is _________. [round off to two decimal places]
Answer: (0.15 to 0.18)
58. In a factory, 100 bulbs are in use. The table lists the cumulative probability of the failure of a bulb for various durations.
The factory follows the individual replacement policy. If the cost of replacing a bulb is Rs. 300, then the expected cost (in Rs.) of replacement per month is ________.[round off to nearest integer]
Answer: (8570 to 8701)
59. A company procures 384 parts annually. The annual holding cost per part is Rs. 30. If the ordering cost is Rs. 1000, then the economic order quantity is __________.[in integer]
Answer: (160 to 160)
60. A time study engineer recorded the cycle time (in minute) for machining of a component. The recorded time study data is provided in the table. The performance rating of the worker is 110%. The standard time for machining (in minute) the component by assuming 10% allowance is ________. [round off to nearest integer]
Answer: (53 to 54)
61. A machine component is to be processed at 5 workstations sequentially. The table provides the cycle time (in second) of each workstation. In mass production, the number of components produced per hour (in steady state) is [in integer]
Answer: (40 to 40)
62. A vaccine has to be distributed from two warehouses to three hospitals. The supplies at warehouses W1 and W2 are 200 and 150, respectively. The demands at hospitals H1, H2, and H3 are 100, 150 and 125, respectively. The transportation cost (in Rs.) pervaccine is as follows:
The initial basic feasible solution using the Northwest-corner method provides the total transportation cost (in Rs.) as ________. [round off to nearest integer]
Answer: (2190 to 2210)
63. Consider the linear programming problem:.
Maximize z = 20x1 + 6x2 + Px3,
subject to
8x1 + 2x2 + 3x3≤ 250, (C1)
4x1 + 3x2≤ 150, (C2)
2x1 + x3≤ 50, (C3)
x1, x2, x3≥ 0.
The optimal solution is given as x1* = 0, x*2 = 50 and x*3 = 50. The dual variables of constraints C1, C2 and C3 are y1, y2 and y3, respectively. The optimal values of dual variables are y1* = 0, y*2 = 2 and y*3 = 8. The value of parameter P in the objective function is _________. [round off to one decimal place]
Answer: (7.9 to 8.1)
64. A company is planning to produce 24 electric cars per day. The setup cost of the plant is estimated as Rs. 19476 million and the variable cost is ₹ 0.6 million per car.The car will be sold at a price of Rs. 1.5 million. The number of days required for achieving the break even is ________. [round off to nearest integer]
Answer: (900 to 905)
65. A company forecasts the weekly demand of oxygen cylinders using exponential smoothing method with smoothing constant α = 0.2. The actual demands in Week 1, Week 2, Week 3 and Week 4 were 375, 412, 592 and 439 units,respectively. The forecasted demand for Week 3 was 500 units. The forecast (in unit) for the Week 5 is ________. [in integer]
2. Two straight lines pass through the origin (x0, y0) = (0, 0). One of them passes through the point (x1, y1) = (1, 3) and the other passes through the point (x2, y2) = (1, 2).
What is the area enclosed between the straight lines in the interval [0, 1] on the x-axis?
(A) 0.5
(B) 1.0
(C) 1.5
(D) 2.0
Answer: (A)
3. If
p : q = 1 : 2
q : r = 4 : 3
r : s = 4 : 5
and u is 50% more than 𝑠, what is the ratio p ∶ u?
(A) 2 : 15
(B) 16 : 15
(C) 1 : 5
(D) 16 : 45
Answer: (D)
4. Given the statements:
P is the sister of Q.
Q is the husband of R.
R is the mother of S.
T is the husband of P.
Based on the above information, T is ______ of S.
(A) the grandfather
(B) an uncle
(C) the father
(D) a brother
Answer: (B)
5. In the following diagram, the point R is the center of the circle. The lines PQ and ZV are tangential to the circle. The relation among the areas of the squares, PXWR, RUVZ and SPQT is
(A) Area of SPQT = Area of RUVZ = Area of PXWR
(B) Area of SPQT = Area of PXWR − Area of RUVZ
(C) Area of PXWR = Area of SPQT − Area of RUVZ
(D) Area of PXWR = Area of RUVZ − Area of SPQT
Answer: (B)
6. Healthy eating is a critical component of healthy aging. When should one start eating healthy? It turns out that it is never too early. For example, babies who start eating healthy in the first year are more likely to have better overall health as they get older.
Which one of the following is the CORRECT logical inference based on the
information in the above passage?
(A) Healthy eating is important for those with good health conditions, but not for others
(B) Eating healthy can be started at any age, earlier the better
(C) Eating healthy and better overall health are more correlated at a young age, but not older age
(D) Healthy eating is more important for adults than kids
Answer: (B)
7. P invested Rs. 5000 per month for 6 months of a year and Q invested Rs. x per month for 8 months of the year in a partnership business. The profit is shared in proportion to the total investment made in that year.
If at the end of that investment year, Q receives 4/9 of the total profit, what is the value of x (in Rs)?
(A) 2500
(B) 3000
(C) 4687
(D) 8437
Answer: (B)
8.
The above frequency chart shows the frequency distribution of marks obtained by a set of students in an exam.
From the data presented above, which one of the following is CORRECT?
(A) mean > mode > median
(B) mode > median > mean
(C) mode > mean > median
(D) median > mode > mean
Answer: (B)
9. In the square grid shown on the left, a person standing at P2 position is required to move to P5 position.
The only movement allowed for a step involves, “two moves along one
direction followed by one move in a perpendicular direction”. The permissible directions for movement are shown as dotted arrows in the right.
For example, a person at a given position Y can move only to the positions marked X on the right.
Without occupying any of the shaded squares at the end of each step, the minimum number of steps required to go from P2 to P5 is
(A) 4
(B) 5
(C) 6
(D) 7
Answer: (B)
10.
Consider a cube made by folding a single sheet of paper of appropriate shape.
The interior faces of the cube are all blank. However, the exterior faces that are not visible in the above view may not be blank.
Which one of the following represents a possible unfolding of the cube?
Answer: (MTA)
Physics
Q.11 – Q.35 Carry ONE mark Each
11. For the Op-Amp circuit shown below, choose the correct output waveform corresponding to the input Vin = 1.5 sin 20πt (in Volts). The saturation voltage for this circuit is Vsat = ±10 V.
Answer: (A)
12. Match the order of β – decays given in the left column to appropriate clause in the right column. Here X(Iπ) and Y(Iπ) are nuclei with intrinsic spin I and parity π.
(A) 1 – i, 2 – ii, 3 – iii, 4 – iv
(B) 1 – iv, 2 – i, 3 – ii, 4 – iii
(C) 1 – i, 2 – iii, 3 – ii, 4 – iv
(D) 1 – iv, 2 – ii, 3 – iii, 4 – i
Answer: (B)
13. What is the maximum number of free independent real parameters specifying an n-dimensional orthogonal matrix?
(A) n(n – 2)
(B) (n – 1)2
(C)
(D)
Answer: (C)
14. An excited state of Ca atom is [Mg]3p54s23d1. The spectroscopic terms corresponding to the total orbital angular momentum are
(A) S, P, and D
(B) P, D, and F
(C) P and D
(D) S and P
Answer: (B)
15. On the surface of a spherical shell enclosing a charge free region, the electrostatic potential values are as follows: One quarter of the area has potential ϕ0, another quarter has potential 2ϕ0 and the rest has potential 4ϕ0. The potential at the centre of the shell is
(You can use a property of the solution of Laplace’s equation.)
Answer: (A)
16. A point charge q is performing simple harmonic oscillations of amplitude A at angular frequency ω. Using Larmor’s formula, the power radiated by the charge is proportional to
(A) q ω2 A2
(B) q ω4 A2
(C) q2 ω2 A2
(D) q2 ω4 A2
Answer: (D)
17. Which of the following relationship between the internal energy U and the Helmholtz’s free energy F is true?
Answer: (A)
18. If nucleons in a nucleus are considered to be confined in a three-dimensional cubical box, then the first four magic numbers are
(A) 2, 8, 20, 28
(B) 2, 8, 16, 24
(C) 2, 8, 14, 20
(D) 2, 10, 16, 28
Answer: (C)
19. Consider the ordinary differential equation
yʹʹ − 2xyʹ + 4y = 0
and its solution y(x) = a + bx + cx2. Then
(A) a = 0, c = −2b ≠ 0
(B) c = −2a ≠ 0, b = 0
(C) c = −2a ≠ 0, c = 0
(D) c = 2a ≠ 0, b = 0
Answer: (B)
20. For an Op-Amp based negative feedback, non-inverting amplifier, which of the following statements are true?
(A) Closed loop gain < Open loop gain
(B) Closed loop bandwidth < Open loop bandwidth
(C) Closed loop input impedance > Open loop input impedance
(D) Closed loop output impedance < Open loop output impedance
Answer: (A, C, D)
21. From the pairs of operators given below, identify the ones which commute. Here l and j correspond to the orbital angular momentum and the total angular momentum, respectively.
(A) l2, j2
(B) j2, jz
(C) j2, lz
(D) lz, jz
Answer: (A, B, D)
22. For normal Zeeman lines observed || and ⊥ to the magnetic field applied to an atom, which of the following statements are true?
(A) Only π-lines are observed || to the field
(B) σ-lines ⊥ to the field are plane polarized
(C) π-lines ⊥ to the field are plane polarized
(D) Only σ-lines are observed || to the field
Answer: (B, C, D)
23. Pauli spin matrices satisfy
(A) σα σβ − σβ σα = iϵαβγ σγ
(B) σα σβ − σβ σα = 2iϵαβγ σγ
(C) σα σβ + σβ σα = ϵαβγ σγ
(D) σα σβ + σβ σα = 2δαβ
Answer: (B, D)
24. For the refractive index n = nr(ω) + inim(ω) of a material, which of the
following statements are correct?
(A) nr can be obtained from nim and vice versa
(B) nim could be zero
(C) n is an analytic function in the upper half of the complex ω plane
(D) n is independent of ω for some materials
Answer: (A, C)
25. Complex function f(z) = z + |z – a|2 (a is a real number) is
(A) continuous at (a, a)
(B) complex-differentiable at (a, a)
(C) complex-differentiable at (a, 0)
(D) analytic at (a, 0)
Answer: (A, C)
26. If g(k) is the Fourier transform of f(x), then which of the following are true?
(A) g(−k) = +g∗(k) implies f(x) is real
(B) g(−k) = −g∗(k) implies f(x) is purely imaginary
(C) g(−k) = +g∗(k) implies f(x) is purely imaginary
(D) g(−k) = −g∗(k) implies f(x) is real
Answer: (A, B)
27. The ordinary differential equation (1 – x2)yʹʹ − xyʹ + 9y = 0 has a regular singularity at
(A) -1
(B) 0
(C) +1
(D) no finite value of x
Answer: (A, C)
28. For a bipolar junction transistor, which of the following statements are true?
(A) Doping concentration of emitter region is more than that in collector and base region
(B) Only electrons participate in current conduction
(C) The current gain β depends on temperature
(D) Collector current is less than the emitter current
Answer: (A, C, D)
29. Potassium metal has electron concentration of 1.4 × 1028 m−3 and the corresponding density of states at Fermi level is 6.2 × 1046 Joule−1 m−3. If the Pauli paramagnetic susceptibility of Potassium is n × 10−k in standard scientific form, then the value of k (an integer) is __________ (Magnetic moment of electron is 9. 3 × 10−24 Joule T−1; permeability of free space is 4π × 10−7 Tm A−1)
Answer: (6 to 6)
30. A power supply has internal resistance RS and open load voltage VS = 5 V. When a load resistance RL is connected to the power supply, a voltage drop of VL = 4 V is measured across the load. The value of RL/RS is _______ (Round off to the nearest integer)
Answer: (4 to 4)
31. Electric field is measured along the axis of a uniformly charged disc of radius 25 cm. At a distance d from the centre, the field differs by 10% from that of an infinite plane having the same charge density. The value of 𝑑 is _______cm. (Round off to one decimal place)
Answer: (2.4 to 2.6)
32. In a solid, a Raman line observed at 300 cm−1 has intensity of Stokes line four times that of the anti-Stokes line. The temperature of the sample is _______K. (Round off to the nearest integer) (1 cm−1 ≡ 1.44 K)
Answer: (311 to 312)
33. An electromagnetic pulse has a pulse width of 10−3 The uncertainty in the momentum of the corresponding photon is of the order of 10−N kg m s−1, where N is an integer. The value of 𝑁 is ____________ (speed of light = 3 × 108 m s−1, h = 6.6 × 10−34 J s)
Answer: (39 to 40)
34. The wave function of a particle in a one-dimensional infinite well of size 2a at a certain time is Probability of finding the particle in n = 2 state at that time is ______% (Round off to the nearest integer)
Answer: (33 to 34)
35. A spectrometer is used to detect plasma oscillations in a sample. The spectrometer can work in the range of 3 × 1012 rad s−1 to 30 × 1012 rad s−1. The minimum carrier concentration that can be detected by using this spectrometer is n × 1021 m−3. The value of n is ________ (Round off to two decimal places)
(Charge of an electron = −1.6 × 10−1 C, mass of an electron = 9.1 × 10−31 kg and ϵ0 = 8.85 × 10−12 C2 N−1 m−2)
Answer: (2.70 to 2.96)
Q.36 – Q.65 Carry TWO marks Each
36. Consider a non-interacting gas of spin 1 particles, each with magnetic moment μ, placed in a weak magnetic field B, such that The average magnetic moment of a particle is
Answer: (A)
37. Water at 300 K can be brought to 320 K using one of the following processes.
Process 1: Water is brought in equilibrium with a reservoir at 320 K directly.
Process 2: Water is first brought in equilibrium with a reservoir at 310 K and then with the reservoir at 320 K.
Process 3: Water is first brought in equilibrium with a reservoir at 350 K and then with the reservoir at 320 K.
The corresponding changes in the entropy of the universe for these processes are ∆S1, ∆S2 and ∆S3, respectively. Then
(A) ∆S1 > ∆S2 > ∆S3
(B) ∆S3 > ∆S1 > ∆S2
(C) ∆S3 > ∆S2 > ∆S1
(D) ∆S1 > ∆S2 > ∆S3
Answer: (B)
38. A student sets up Young’s double slit experiment with electrons of momentum p incident normally on the slits of width w separated by distance d. In order to observe interference fringes on a screen at a distance D from the slits, which of the following conditions should be satisfied?
Answer: (B)
39. Consider a particle in three different boxes of width L. The potential inside the boxes vary as shown in figures (i), (ii) and (iii) with The corresponding ground-state energies of the particle are E1, E2 and E3, respectively. Then
(A) E2 > E1 > E3
(B) E3 > E1 > E2
(C) E2 > E3 > E1
(D) E3 > E2 > E1
Answer: (A)
40. In cylindrical coordinates (s, φ, z), which of the following is a Hermitian operator?
Answer: (C)
41. A particle of mass 1 kg is released from a height of 1 m above the ground. When it reaches the ground, what is the value of Hamilton’s action for this motion in J s? (g is the acceleration due to gravity; take gravitation potential to be zero on the ground)
Answer: (D)
42. If is a constant of motion of a two-dimensional isotropic harmonic oscillator with Lagrangian then α is
(A) +k/m
(B) –k/m
(C) −2k/m
(D) 0
Answer: (A)
43. In a two-dimensional square lattice, frequency ω of phonons in the long wavelength limit changes linearly with the wave vector k. Then the density of states of phonons is proportional to
(A) ω
(B) ω2
(C) √ω
(D) 1/√ω
Answer: (A)
44. At T = 0 K, which of the following diagram represents the occupation probability P(E) of energy states of electrons in a BCS type superconductor?
Answer: (A)
45. For a one-dimensional harmonic oscillator, the creation operator (a†) acting on the nth state where 𝑛 = 0, 1, 2, …, gives The matrix representation of the position operator for the first three rows and columns is
Answer: (C)
46. A piston of mass m is fitted to an airtight horizontal cylindrical jar. The cylinder and piston have identical unit area of cross-section. The gas inside the jar has volume V and is held at pressure P = Patmosphere. The piston is pushed inside the jar very slowly over a small distance. On releasing, the piston performs an undamped simple harmonic motion of low frequency. Assuming that the gas is ideal and no heat is exchanged with the atmosphere, the frequency of the small oscillations is proportional to
Answer: (B)
47. A paramagnetic salt of mass m is held at temperature T in a magnetic field H. If S is the entropy of the salt and M is its magnetization, then dG = −SdT −MdH, where G is the Gibbs free energy. If the magnetic field is changed adiabatically by ΔH → 0 and the corresponding infinitesimal changes in entropy and temperature are ΔS and ΔT, then which of the following statements are correct
(A)
(B) ∆S = 0
(C)
(D) ∆T = 0
Answer: (B, C)
48. A particle of mass m is moving inside a hollow spherical shell of radius a so that the potential is
The ground state energy and wave function of the particle are E0 and R(r), respectively. Then which of the following options are correct?
Answer: (A, B, D)
49. A particle of unit mass moves in a potential If the angular
momentum of the particle is L = 0.5 √V0, then which of the following statements are true?
(A) There are two equilibrium points along the radial coordinate
(B) There is one stable equilibrium point at r1 and one unstable equilibrium point at r2 > r1
(C) There are two stable equilibrium points along the radial coordinate
(D) There is only one equilibrium point along the radial coordinate
Answer: (A, B)
50. In a diatomic molecule of mass M, electronic, rotational and vibrational energy scales are of magnitude Ee, ER and EV, respectively. The spring constant for the vibrational energy is determined by Ee. If the electron mass is m then
Answer: (A, C)
51. Electronic specific heat of a solid at temperature T is C = γT, where γ is a constant related to the thermal effective mass (meff) of the electrons. Then which of the following statements are correct?
(A) γ ∝ meff
(B) meff is greater than free electron mass for all solids
(C) Temperature dependence of C depends on the dimensionality of the solid
(D) The linear temperature dependence of C is observed at T ≪ Debye temperature
Answer: (D)
52. In a Hall effect experiment on an intrinsic semiconductor, which of the following statements are correct?
(A) Hall voltage is always zero
(B) Hall voltage is negative if the effective mass of holes is larger than those of electrons
(C) Hall coefficient can be used to estimate the carrier concentration in the semiconductor
(D) Hall voltage depends on the mobility of the carriers
Answer: (D)
53. A parallel plate capacitor with spacing d and area of cross-section A is connected to a source of voltage V. If the plates are pulled apart quasistatically to a spacing of 2d, then which of the following statements are correct?
(A) The force between the plates at spacing 2d is
(B) The work done in moving the plates is
(C) The energy transferred to the voltage source is
(D) The energy of the capacitor reduces by
Answer: (A, C, D)
54. A system with time independent Hamiltonian H(q, p) has two constants of motion f(q, p) and g(q, p). Then which of the following Poisson brackets are always zero?
(A) {H, f + g}
(B) {H, {f, g}}
(C) {H + f, g}
(D) {H, H + fg}
Answer: (A, B, D)
55. In the action-angle variables (I1, I2, θ1, θ2), consider the Hamiltonian H = 4I1I2 and 0 ≤ θ1, θ2 < 2π. Let Which of the following are possible plots of the trajectories with different initial conditions in θ1-θ2 plane?
Answer: (B, C)
56. A particle of mass m in the x-y plane is confined in an infinite two-dimensional well with vertices at (0, 0), (0, L), (L, L), (L, 0). The eigenfunctions of this particle are If perturbation of the form V = Cxy, where C is a real constant, is applied, then which of the following statements are correct for the first excited state?
(A) The unperturbed energy is
(B) The unperturbed energy is
(C) First order energy shift due to the applied perturbation is zero
(D) The shift (δ) in energy due to the applied perturbation is determined by an equation of the form where a and b are real, non-zero constants.
Answer: (B, D)
57. A junction is formed between a metal on the left and an n-type semiconductor on the right. Before forming the junction, the Fermi level EF of the metal lies below that of the semiconductor. Then which of the following schematics are correct for the bands and the I-V characteristics of the junction?
Answer: (A, C)
58. A plane polarized electromagnetic wave propagating in y-z plane is incident at the interface of two media at Brewster’s angle. Taking z = 0 as the boundary between the two media, the electric field of the reflected wave is given by
then which among the following statements are correct?
(A) The angle of refraction is π/6
(B) Ratio of permittivity of the medium of refraction (ϵ2) with respect to the medium on incidence (ϵ1), ϵ2/ϵ1 = 3
(C) The incident wave can have components of its electric field in y-z plane
(D) The angle of reflection is π/6
Answer: (A, B, C)
59. The minimum number of two-input NAND gates required to implement the following Boolean expression is ________.
Answer: (3 to 3)
60. In a nucleus, the interaction is responsible for creating spin-orbit doublets. The energy difference between p1/2 and p3/2 states in units of is ______ (Round off to the nearest integer)
Answer: (3 to 3)
61. Two identical particles of rest mass m0 approach each other with equal and opposite velocity v = 0.5c, where 𝑐 is the speed of light. The total energy of one particle as measured in the rest frame of the other is E = αm0c2. The value of a is _______ (Round off to two decimal places)
Answer: (1.65 to 1.70)
62. In an X-Ray diffraction experiment on a solid with FCC structure, five diffraction peaks corresponding to (111), (200), (220), (311) and (222) planes are observed using 1.54 Å X-rays. On using 3 Å X-rays on the same solid, the number of observed peaks will be
Answer: (1 to 1)
63. For 1 mole of Nitrogen gas, the ratio of entropy change of the gas in processes (I) and (II) mentioned below is ______ (Round off to one decimal place)
(I) The gas is held at 1 atm and is cooled from 300 K to 77 K.
(II) The gas is liquified at 77 K.
(Take Cp = 7.0 cal mol−1 K−1, Latent heat L = 1293.6 cal mol−1)
Answer: (0.5 to 0.7)
64. Frequency bandwidth Δv of a gas laser of frequency v Hz is
where α = 3.44 × 106 m2 s−2 at room temperature and A is the atomic mass of the lasing atom. For 4He-20Ne laser (wavelength = 633 nm), ∆v = n × 109 Hz. The value of n is ________ (Round off to one decimal place)
Answer: (1.2 to 1.4)
65. A current of 1 A is flowing through a very long solenoid made of winding density 3000 turns/m. As shown in the figure, a parallel plate capacitor, with plates oriented parallel to the solenoid axis and carrying surface charge density 6ϵ0 C m−2, is placed at the middle of the solenoid. The momentum density of the electromagnetic field at the midpoint X of the capacitor is n × 10−13 N s m−3. The value of n is ________ (Round off to the nearest integer)
1. After playing _________ hours of tennis, I am feeling _________ tired to walk back.
(A) too / too
(B) too / two
(C) two / two
(D) two / too
Answer: (D)
2. The average of the monthly salaries of M, N and S is Rs. 4000. The average of the monthly salaries of N, S and P is Rs. 5000. The monthly salary of P is Rs. 6000.
What is the monthly salary of M as a percentage of the monthly salary of P?
(A) 50%
(B) 75%
(C) 100%
(D) 125%
Answer: (A)
3. A person travelled 80 km in 6 hours. If the person travelled the first part with a uniform speed of 10 kmph and the remaining part with a uniform speed of 18 kmph.
What percentage of the total distance is travelled at a uniform speed of 10 kmph?
(A) 28.25
(B) 37.25
(C) 43.75
(D) 50.00
Answer: (C)
4. Four girls P, Q, R and S are studying languages in a University. P is learning French and Dutch. Q is learning Chinese and Japanese. R is learning Spanish and French. S is learning Dutch and Japanese.
Given that: French is easier than Dutch; Chinese is harder than Japanese; Dutch is easier than Japanese, and Spanish is easier than French.
Based on the above information, which girl is learning the most difficult pair of languages?
(A) P
(B) Q
(C) R
(D) S
Answer: (B)
5.
A block with a trapezoidal cross-section is placed over a block with rectangular cross section as shown above.
Which one of the following is the correct drawing of the view of the 3D object as viewed in the direction indicated by an arrow in the above figure?
Answer: (A)
Q.6 – Q.10 Carry TWO marks each.
6. Humans are naturally compassionate and honest. In a study using strategically placed wallets that appear “lost”, it was found that wallets with money are more likely to be returned than wallets without money. Similarly, wallets that had a key and money are more likely to be returned than wallets with the same amount of money alone. This suggests that the primary reason for this behavior is compassion and empathy.
Which one of the following is the CORRECT logical inference based on the information in the above passage?
(A) Wallets with a key are more likely to be returned because people do not care about money
(B) Wallets with a key are more likely to be returned because people relate to suffering of others
(C) Wallets used in experiments are more likely to be returned than wallets that are really lost
(D) Money is always more important than keys
Answer: (B)
7. A rhombus is formed by joining the midpoints of the sides of a unit square.
What is the diameter of the largest circle that can be inscribed within the rhombus?
(A) 1/√2
(B) 1/2√2
(C) √2
(D) 2√2
Answer: (A)
8. An equilateral triangle, a square and a circle have equal areas.
What is the ratio of the perimeters of the equilateral triangle to square to circle?
Answer: (B)
9. Given below are three conclusions drawn based on the following three statements.
Statement 1: All teachers are professors.
Statement 2: No professor is a male.
Statement 3: Some males are engineers.
Conclusion I: No engineer is a professor.
Conclusion II: Some engineers are professors.
Conclusion III: No male is a teacher.
Which one of the following options can be logically inferred?
(A) Only conclusion III is correct
(B) Only conclusion I and conclusion II are correct
(C) Only conclusion II and conclusion III are correct
(D) Only conclusion I and conclusion III are correct
Answer: (A)
10. In a 12-hour clock that runs correctly, how many times do the second, minute, and hour hands of the clock coincide, in a 12-hour duration from 3 PM in a day to 3 AM the next day?
(A) 11
(B) 12
(C) 144
(D) 2
Answer: (MTA)
Petroleum Engineering
Q.11 – Q.35 Carry ONE mark Each
11. The value of is
(A) e
(B) 1
(C) 0
(D) 1/e
Answer: (B)
12. The following second order ordinary differential equation has the boundary conditions: y(0) = 0, and y(1) = 1.
The type of above boundary conditions is
(A) Neumann
(B) Dirichlet
(C) Cauchy
(D) Robin
Answer: (B)
13. Let for (x, y) ∈ C2. If C is the circle x2 + y2 = 4 oriented in the anticlockwise direction then equals
(A) 4π
(B) 6π
(C) 7π
(D) 8π
Answer: (A)
14. The general equation for the production rate decline can be expressed as
where, b and d are empirical constants, and q is the production rate.
Match the value of d (Group 1) with the appropriate decline curves (Group 2).
(A) I – P; II – Q; III – R
(B) I – P; II – R; III – Q
(C) I – Q; II – R; III – P
(D) I – Q; II– P; III– R
Answer: (D)
15. The production optimization is evaluated on the basis of discounted revenue to be generated by the projects. The net present value (NPV) for calculating the discounted revenue is defined by
NPV = NPVR – cost
where, NPVR = present value of cash flow discounted at a given rate i.
If ∆Rn is the annual incremental revenue after optimization for nth year, and m is the remaining life of the project at the end of nth year, then which ONE of the following options for NPVR is CORRECT?
Answer: (D)
16. The formation volume factors of oil and water are Bo and Bw, respectively.
The CORRECT relationship between the fractional water cut at the surface condition (fws) and the fractional water cut at the reservoir condition (fw) is
Answer: (D)
17. Which ONE of the following is used to support the packer against the casing while expanding the rubber sealing element?
(A) Blast joints
(B) Slips
(C) Landing nipples
(D) Side pocket mandrels
Answer: (B)
18. ‘Cupola’ offshore storage tank is an example of
(A) floating storage type.
(B) above-water storage type.
(C) submerged storage type.
(D) platform storage type.
Answer: (C)
19. The liquid shrinkage curves for different types of crude oil are shown in the following figure.
Which curve represents the Black Oil?
(A) I
(B) II
(C) III
(D) IV
Answer: (B)
20. The dynamic mud inflow rate and mud outflow rate profiles are shown in the following figure.
Identify the “Hole ballooning” and the “Lost circulation” phenomena.
(A) Case 1 – Hole ballooning; Case 3 – Lost circulation
(B) Case 2 – Lost circulation; Case 3 – Hole ballooning
(C) Case 1 – Lost circulation; Case 2 – Hole ballooning
(D) Case 2 – Hole ballooning; Case 3 – Lost circulation
Answer: (B)
21. What is the maximum permissible limit of ‘oil and grease’ in discharged waste water from a petroleum industry as per the guidelines of Central Pollution Control Board(CPCB), India?
(A) 5 ppm
(B) 10ppm
(C) 30ppm
(D) 50ppm
Answer: (B)
22. The Timur chart for estimating the permeability is the plot between
(A) Porosity and Water Saturation
(B) True Resistivity and Water Saturation
(C) Porosity and Irreducible Water Saturation
(D) Porosity and True Resistivity
Answer: (C)
23. The logging tool(s) preferred for the measurement of formation resistivity in a well drilled with oil-based mud is/are
(A) Dual Laterolog
(B) Compensated Neutron Log
(C) Compensated Density Log
(D) Induction Log
Answer: (D)
24. Which of the following properties of Matrix are CORRECT?
(A) Singular
(B) Positive definite
(C) Symmetric
(D) Diagonal
Answer: (B, C)
25. Simpson’s one-third rule will give the exact value of the integral, (where a, b, b0, b1, b2, …,bn are numeric constants), if the values of n are
(A) 1
(B) 2
(C) 3
(D) 4
Answer: (A, B, C)
26. Which of the following are NOT CORRECT during the operating cycle of a
‘sucker rod pump’?
(A) Standing valve is open during the upward stroke.
(B) Standing valve is closed during the upward stroke.
(C) Travelling valve is closed during the upward stroke.
(D) Travelling valve is open during the upward stroke.
Answer: (B, D)
27. Which of the following statements related to the ‘enriched gas drive’ are CORRECT?
(A) The enriching components are transferred from the oil to the gas.
(B) The enriched gas drive is an example of immiscible enhanced oil recovery.
(C) A miscible zone is formed between the injected gas and the reservoir oil.
(D) In enriched gas drive, the viscous fingering results in poor sweep efficiency.
Answer: (C, D)
28. Select the CORRECT statements for the injection-production well pattern.
(A) Inverted 5-spot drive includes four injectors at the corners and the producer at the centre.
(B) Regular 7-spot drive includes six injectors at the corners and the producer at the centre.
(C) Staggered-line drive involves staggered injectors and producers.
(D) Crestal injection involves positioning of the wells along the periphery of the reservoir.
Answer: (B, C)
The flammable gas detector works on which of the following phenomena?
(A) Catalytic
(B) Paramagnetic
(C) Electrochemical
(D) Photoionisation
Answer: (A, D)
30. A drilling mud with high gel strength is undesirable because it
(A) retards the separation of cuttings and entrained gas at the surface.
(B) leads to the lost circulation.
(C) creates swabbing action beneath the bit while pulling the string.
(D) leads to the hole ballooning.
Answer: (MTA)
31. Which of the following Logging tool combinations are required to estimate the Hydrocarbon Initial in Place (HCIP)?
(A) Resistivity Log, Neutron Log and Gamma Ray Log
(B) Sonic Log, Neutron Log and Gamma Ray Log
(C) Resistivity Log, Density Log and Gamma Ray Log
(D) Neutron Log, Density Log and Sonic Log
Answer: (A, C)
32. A homogeneous sandstone reservoir is under a radial steady state flow. The wellbore radius is 0.1 m. The formation near the wellbore is damaged up to 0.9 m from the sand face. The permeability impairment results in k/ks = 5, where k is the permeability in the undamaged region and ks is that of the damaged region. The value of skin factor is _________ (rounded off to two decimal places).
Answer: (9.00 to 9.40)
33. A reservoir is producing oil at 7000 stb/day with a producing gas to oil ratio (GOR)of 2000 scf/stb. At a certain point of time, the reservoir pressure is monitored and decided to be maintained at a constant pressure of 2500 psi using water injection.
The PVT properties estimated at 2500 psi are:
Bubble point pressure = 3000 psi
Oil formation volume factor = 1.2 rb/stb
Water formation volume factor = 1.0 rb/stb
Gas formation volume factor = 0.0012 rb/scf
Solution GOR = 300 scf/stb
The initial water injection rate (stb/day) required to maintain oil production at 7000 stb/day is ____________ (rounded off to the nearest integer).
Answer: (22675 to 22685)
34. An oil well is drilled using an 8.5-inch drill bit at a penetration rate of 30 ft/hr.The rotary speed is 20 rpm and the weight on the bit is 3500 lb. The value of the‘d’ exponent for the drilled section is ________ (rounded off to two decimal places).
Answer: (0.69 to 0.70)
35. A vertical wellbore is drilled with a 12.25-inch drill bit. While drilling, the bit could drill a total rock volume of 385 ft3 in 6.5 hr. After drilling, the hole diameter throughout the depth is found to be 12.49 inch. The average rate of penetration is _______ ft/hr (rounded off to two decimal places).
Answer: (68.00 to 70.00)
Q.36 – Q.65 Carry TWO marks Each
36. A real gas is produced from a gas reservoir at a constant temperature of 30°The compressibility factor (Z) is observed to change with pressure (P) at a rate of The difference in the compressibility of the real gas from the ideal gas at a given pressure (P) and temperature (T) is
(A) Z
(B) Z2
(C) √Z
(D) 1/Z2
Answer: (A)
37. A brine solution is being injected at a velocity (u) downward through a tubing of diameter (d) inclined at an angle of θ from vertical with gravitational acceleration g. Which ONE of the following options is CORRECT for the velocity (u) and the angle (θ) such that the ratio of frictional pressure drop to the gravitational pressure drop is four times the Fanning friction factor?
(A) u = (2gd)1/2; θ = 30°
(B) u = gd; θ = 30°
(C) u = (gd)1/2; θ = 60°
(D) u = gd1/2; θ = 30°
Answer: (C)
38. Which ONE of the following options is the CORRECT match of contaminants and their effluent treatment techniques?
(I) Suspended solids P. Ion exchange
(II) Biodegradable organics Q. Filtration
(III) Heavy metals R. Trickling filters
(IV) Suspended oil and grease S. Flocculation
(A) I – P ; II – Q ; III – R ; IV – S
(B) I – Q ; II – R ; III – P ; IV – S
(C) I – Q ; II – S ; III – P ; IV – R
(D) I – R ; II – S ; III – Q ; IV – P
Answer: (B)
39. Capillary pressure (Pc) vs water saturation (Sw) curves for different sand stone reservoirs (I, II, III and IV) are given in the following figure.
Which reservoir has the most uniform pore size distribution?
(A) I
(B) II
(C) III
(D) IV
Answer: (D)
40. Flow tests are conducted for oil well in reservoirs P, Q, R and S having different parameters as given in the following table. In all the four cases the wells are tested at 1200 stb/day.
Identify the reservoir in which the pressure transient reaches earliest at a point 2000 ft away from the wellbore.
(A) P
(B) Q
(C) R
(D) S
Answer: (C)
41. Identify the CORRRECT match for the flow regimes (Group 1) with the corresponding slopes of the pressure derivative (Group 2) used in the type curve analysis.
(A) I – P; II – Q; III – R; IV – S
(B) I – Q; II – S; III – R; IV – P
(C) I – R; II – S; III – Q; IV – P
(D) I – S; II – P; III – Q; IV – R
Answer: (C)
42. The log data obtained for a particular well section are shown in the following figures.Identify the CORRECT interpretations for different zones.
Answer: (C)
43. Well testing is to be conducted on the bounded sandstone reservoirs as shown in the following figures. All the reservoirs have the same drainage area, rock and fluid properties, and well bore conditions.
Which of the following statements are CORRECT for the given reservoirs?
(A) Pseudo steady flow regime will develop first in Reservoir 1.
(B) Infinite acting behavior will stop first in Reservoir 2.
(C) Infinite acting behavior will sustain the longest in Reservoir 1.
(D) Pressure depletion will be the fastest in Reservoir 3.
Answer: (C, D)
44. An exploratory well is planned to be drilled in a basin that extends up to a depth of 5000 m. The surface temperature is 30°C. The geothermal gradient of the basin is 0.025°C/m. Select the possible range(s) of depth at which the potential oil bearing zones can be encountered.
(A) 800 m to 950 m
(B) 1500 m to 1650 m
(C) 3100 m to 3150 m
(D) 4550 m to 4600 m
Answer: (B, C)
45. The following data are given for an oil well scheduled for a draw down test.
If the well is tested at a constant rate, the ‘Wellbore Storage Effect’ would sustain for__________ hours (rounded off to two decimal places).
Answer: (48.00 to 52.00)
46. During the core analysis, the following data are measured at laboratory and reservoir conditions.
The capillary pressure at the laboratory condition is 50 psi. The calculated capillary pressure using the Leverett J-function at the reservoir condition is ______ psi(rounded off to two decimal places).
Answer: (36.00 to 37.00)
47. The total oil production rate (measured at the bottom hole conditions) from avolumetric reservoir is 200 bbl/day (1 bbl = 5.615 ft3) at the flowing bottom hole pressure (FBHP) of 3000 psi. The reservoir has the following properties:
Considering a radial flow under pseudo steady state, the bottom hole pressure after 180 days is __________ psi (rounded off to two decimal places).
Answer: (2280.00 to 2290.00)
48. An incompressible fluid (density = 40 lb/ft3) flows at a steady state through a linear porous media with the following properties:
The absolute value of the difference between the actual fluid velocity (ft/day) atθ = 0° and θ = 10° is __________ (rounded off to three decimal places).
Answer: (0.165 to 0.175)
49. An oil well (wellbore radius = 0.5 inch) in a heavy oil reservoir (drainage radius =745 ft, oil viscosity = 500 cP) is being operated at 200 rb/day and 150 psi under the radial steady state flow regime. A huff and puff steam injection is planned to reduce the oil viscosity to 35 cP. The steam soaks into the reservoir up to a distance of 65 ft from the centre of the wellbore. The new production rate at the down hole condition after the steam stimulation is _________ rb/day (rounded off to two decimal places).
Answer: (661.0 to 664.0)
50. If Z is the standard normal variable having mean 0 and standard deviation 1, then the probability of occurrence of Z in the range of −3 to 3 is ________ (rounded off to three decimal places).
Answer: (0.996 to 0.999)
51. In a three dimensional xyz -space, if and then the value of (a + b + c) is _____ (in integer).
Answer: (1 to 1)
52. The local minimum value of the real function f(x) = 2x3 – 21x2 + 36x – 20 is _____ (in integer)
Answer: (-128 to -128)
53. Consider the following ordinary differential equation
The initial value is y(0) = 1 and the step-size is 0.1. Solving this differential equation by Euler’s first-order method, the value of y(0.2) is ________ (rounded off to three decimal places).
Answer: (1.001 to 1.001)
54. In a horizontal circular pipe, liquid and gas are flowing concurrently at the same superficial velocity. However, the average velocity of the gas is greater than the average velocity of liquid. If the slip velocity is equal to the superficial velocity of each of the phases, the fractional liquid holdup is _______ (rounded off to two decimal places).
Answer: (0.60 to 0.65)
55. A 1 kg-mol bottled gas consists of the following composition at 30°C.
The equilibrium vapour composition of n-Butane in mol % is ________ (rounded off to two decimal places).
Answer: (18.00 to 19.00)
56. A crude oil with a flow rate of 1000 kg/hr is to be cooled using water in a double-pipe counter-flow heat exchanger from a temperature of 80°C to 40° The water enters the exchanger at 20°C and leaves at 40°C. The specific heat capacities of the oil and the water at constant pressure are 2 kJ kg−1 K−1 and 4.2 kJ kg−1 K−1, respectively. The overall heat transfer coefficient is 0.25 kW m−2 K−1. Neglecting the heat loss and using the log mean temperature difference (LMTD) method, the minimum heat exchanger area (m2) required for the operation is _______ (rounded off to two decimal places).
Answer: (3.00 to 3.15)
57. In an oil reservoir undergoing water flooding, the areal and vertical sweep efficiencies are 0.75 and 0.85, respectively. The average water saturation behind the flood front is 0.63 at breakthrough, and the initial water saturation is 0.17. If the initial volume of in-situ oil at the start of water flooding is 3200 rb, the amount of oil produced during the water flooding is _______ rb (rounded off to two decimal places).
Answer: (1120.00 to 1143.00)
58. The initial water saturation in an oil reservoir with a free gas cap is 30%. The initial gas saturation is 40%. At the end of water flooding, all the free gases are dissolved due to the elevated pressure and the oil formation volume factor reaches a value of 1.20 rb/stb. The final water saturation at the end of water flooding is 50%. If the two-phase formation volume factor at the initiation of the water flood is 2.3 rb/stb,the pore-to-pore displacement efficiency under the current reservoir condition is ______ % (rounded off to one decimal place).
Answer: (MTA)
59. The station survey data during the directional drilling at two locations are given below.
The calculated dogleg severity (dogleg angle per 100 m of drilled section)is ________ (rounded off to one decimal place).
Answer: (8.1 to 8.3)
60. A sandstone reservoir has the formation top at a depth of 3421 ft from the surface as shown in the following figure. The reservoir is logged with a modular dynamic tester(MDT). At a depth of 3425 ft, the formation pressure is recorded as 1560 psi and the sampled crude has a density of 35°API.
Considering a normal hydrostatic pressure gradient (brine density of 1.04 g/cc) and a capillary displacement pressure of 1.2 psi, the oil water contact (OWC) is found at a depth of _________ ft from the surface (rounded off to two decimal places).
Answer: (3435.00 to 3670.00)
61. The drill pipes and drill collars with a combined length of 2500 m are held on the hook without rotation and mud flow. The specific gravity of the mud in the annulus is 1.5 and that inside the drill string is 1.4. The material density of the drill pipe and drill collar is 7850 kg/m3. The specifications of drill pipes and drill collars are given below.
The overall weight acting on the hook is _______ kN (rounded off to two decimal places).
Answer: (3870 to 4070)
62. A drilling rig is designed with 12 lines strung between the crown block and the traveling block. The hoisting system has an output power of 650 HP(1 HP = 33000 lb-ft/min). When the drill string is pulled up with a speed of 52.5ft/min, the tension in the fast line reads 46180 lb. Assume that the rig utilizes all the available output power of draw works and the drill string is pulled at a constant system efficiency. If the drill string is pulled at the same output power and the tension in the fast line is 35690 lb, then the pullout speed of the drill string is ________ ft/min(rounded off to one decimal place).
Answer: (67.0 to 69.0)
63. In a sandstone reservoir, the density log reads 2.11 g/cc and sonic log reads 90 μs/ft.The other parameters are given below:
Matrix density (ρma) = 2.68 g/cc
Fluid density (ρfl) = 1.0 g/cc
Compressional wave travel time in matrix (∆tma) = 54 μs/ft
Compressional wave travel time in fluid(∆tfl) = 189μs/ft
The calculated secondary porosity of the reservoir is ______ % (rounded off tothe nearest integer).
Answer: (6 to 8)
64. The Waxman-Smits equation to estimate water saturation for shaly sands is given as,
where, B is cation mobility (mΩ−1 meq−1 ml−1) and Qv is cation exchange capacity per pore volume (meq ml−1). The values of other parameters are:
As per the given dataset, the calculated water saturation (sw) in oil zoneis ____________ % (rounded off to the nearest integer).
Answer: (MTA)
65. The hydrogen index (HI) of a potential source rock is 500. If 400 g of the same rock produces 6000 mg of hydrocarbons during a thermal pyrolys is at the maximum temperature, the calculated total organic content (TOC) of the rock is _________ weight % (rounded off to one decimal place).
2. A sum of money is to be distributed among P, Q, R, and S in the proportion 5 : 2 : 4 : 3, respectively.
If R gets Rs 1000 more than S, what is the share of Q (in Rs)?
(A) 500
(B) 1000
(C) 1500
(D) 2000
Answer: (D)
3. A trapezium has vertices marked as P, Q, R and S (in that order anticlockwise). The side PQ is parallel to side SR.
Further, it is given that, PQ = 11 cm, QR = 4 cm, RS = 6 cm and SP = 3 cm.
What is the shortest distance between PQ and SR (in cm)?
(A) 1.80
(B) 2.40
(C) 4.20
(D) 5.76
Answer: (B)
4. The figure shows a grid formed by a collection of unit squares. The unshaded unit square in the grid represents a hole.
What is the maximum number of squares without a “hole in the interior” that can be formed within the 4 × 4 grid using the unit squares as building blocks?
(A) 15
(B) 20
(C) 21
(D) 26
Answer: (B)
5. An art gallery engages a security guard to ensure that the items displayed are protected. The diagram below represents the plan of the gallery where the boundary walls are opaque. The location the security guard posted is identified such that all the inner space (shaded region in the plan) of the gallery is within the line of sight of the security guard.
If the security guard does not move around the posted location and has a 360o view, which one of the following correctly represents the set of ALL possible locations among the locations P, Q, R and S, where the security guard can be posted to watch over the entire inner space of the gallery.
(A) P and Q
(B) Q
(C) Q and S
(D) R and S
Answer: (C)
Q.6 – Q.10 Carry TWO marks each.
6. Mosquitoes pose a threat to human health. Controlling mosquitoes using chemicals may have undesired consequences. In Florida, authorities have used genetically modified mosquitoes to control the overall mosquito population. It remains to be seen if this novel approach has unforeseen consequences.
Which one of the following is the correct logical inference based on the information in the above passage?
(A) Using chemicals to kill mosquitoes is better than using genetically modified mosquitoes because genetic engineering is dangerous
(B) Using genetically modified mosquitoes is better than using chemicals to kill mosquitoes because they do not have any side effects
(C) Both using genetically modified mosquitoes and chemicals have undesired consequences and can be dangerous
(D) Using chemicals to kill mosquitoes may have undesired consequences but it is not clear if using genetically modified mosquitoes has any negative consequence
Answer: (D)
7. Consider the following inequalities.
(i) 2x − 1 > 7
(ii) 2x − 9 < 1
Which one of the following expressions below satisfies the above two inequalities?
(A) x ≤ −4
(B) −4 <x ≤ 4
(C) 4 <x< 5
(D) x ≥ 5
Answer: (C)
8. Four points P(0, 1), Q(0, −3), R(−2, −1), and S(2, −1) represent the vertices of a quadrilateral.
What is the area enclosed by the quadrilateral?
(A) 4
(B) 4√2
(C) 8
(D) 8√2
Answer: (C)
9. In a class of five students P, Q, R, S and T, only one student is known to have copied in the exam. The disciplinary committee has investigated the situation and recorded the statements from the students as given below.
Statement of P: R has copied in the exam.
Statement of Q: S has copied in the exam.
Statement of R: P did not copy in the exam.
Statement of S: Only one of us is telling the truth.
Statement of T: R is telling the truth.
The investigating team had authentic information that S never lies.
Based on the information given above, the person who has copied in the exam is
(A) R
(B) P
(C) Q
(D) T
Answer: (B)
10. Consider the following square with the four corners and the center marked as P, Q, R, S and T respectively.
Let X, Y and Z represent the following operations:
X: rotation of the square by 180 degree with respect to the
S-Q axis.
Y: rotation of the square by 180 degree with respect to the P-R axis.
Z: rotation of the square by 90 degree clockwise with respect to the axis perpendicular, going into the screen and passing through the point T.
Consider the following three distinct sequences of operation (which are applied
in the left to right order).
(1) XYZZ
(2) XY
(3) ZZZZ
Which one of the following statements is correct as per the information provided above?
(A) The sequence of operations (1) and (2) are equivalent
(B) The sequence of operations (1) and (3) are equivalent
(C) The sequence of operations (2) and (3) are equivalent
(D) The sequence of operations (1), (2) and (3) are equivalent
Answer: (B)
Naval Architecture and Marine Engineering
Q.11 – Q.35 Carry One mark Each
11. Let A be a real non-zero square matrix of order n. If the homogeneous system of linear equations Ax = 0 has only trivial solution, then
(A) the matrix A is singular
(B) the determinant of A is zero
(C) λ = 0 is an eigenvalue of A
(D) for any n-vector 𝑏, the system of linear equations Ax = b has a unique solution
Answer: (D)
12. Let z = x + iy, where x and y are real numbers. Consider the complex functions:
f(z) = (x2 – y2) + i2xy
and
g(z) = 2xy + i (x2 – y2).
Then on the complex plane,
(A) f(z) is analytic and g(z) is not analytic
(B) both f(z) and g(z) are analytic
(C) both f(z) and g(z) are not analytic
(D) f(z) is not analytic and g(z) is analytic
Answer: (A)
13. If a population has exponential distribution with mean 1, then its median is
(A) e
(B) 1
(C) loge 2
(D) loge 3
Answer: (C)
14. Let ωf be the excitation frequency of a sinusoidal load and ωn be the natural frequency of a single degree of freedom system. Then the dynamic response of the system is highly affected by the stiffness of the system when
(A) ωf = ωn
(B) 0 <ωf<ωn
(C) 0 <ωn<ωf
(D) ωf = 0
Answer: (B)
15. A truck loaded with a half-filled water tank is moving at a constant horizontal acceleration a. The acceleration due to gravity is g. At steady state, the angle θ made by the free surface with the horizontal plane is
(A) sin−1 (a/g)
(B) tan−1 (g/a)
(C) tan−1 (a/g)
(D) sin−1 (g/a)
Answer: (C)
16. Which one of the following combinations of elementary flows will lead to an ideal flow past a deeply submerged circular cylinder with circulation?
(A) Source, sink and uniform flow
(B) Doublet, uniform flow and vortex
(C) Doublet and vortex
(D) Source and uniform flow
Answer: (B)
17. A 10000 tonne displacement container ship’s main propulsion engine has a brake power equal to 46 MW and its service speed is 25 knots. Considering the engine brake power as double the effective power of the ship, then the ship resistance at the service speed lies in between ________ kN.
(A) 3285 and 3315
(B) 6785 and 6815
(C) 885 and 915
(D) 1785 and 1815
Answer: (D)
18. The margin line used for the floodable length calculation of a ship is
(A) 76 mm above the ship’s baseline
(B) 76 mm inside the zero-buttock line in the profile view of the ship’s lines plan
(C) a line drawn 76 mm parallel to and below the watertight main deck at side
(D) a line drawn 76 mm parallel to and below the watertight main deck along the ship’s center line if the ship has camber
Answer: (C)
19. Consider a rectangular box barge of length 80 m, breadth 20 m and depth 15 m floating at an even draught of 10 m. Assume that the heave added mass of the vessel is equal to its mass displacement and the acceleration due to gravity is 9.81 m/s2. The heave natural period of the vessel lies in between ________ s.
(A) 1 and 5
(B) 6 and 10
(C) 11 and 15
(D) 16 and 20
Answer: (B)
20. A 1:20 scaled model of a surface ship is tested in a towing tank. The model is towed at 3 m/s and drag force measured is 10 N. The velocity of the prototype and the drag force acting on the prototype, respectively, are ______ m/s and _______ kN.
(A) 60.4 and 80
(B) 13.4 and 80
(C) 13.4 and 4
(D) 60.4 and 4
Answer: (B)
21. In a diesel engine, the ignition is initiated by the
(A) spark
(B) preheating of the fuel
(C) heating due to the compression of intake air
(D) preheating of the intake air
Answer: (C)
22. In an internal combustion engine, supercharging is the process of supplying intake air at a pressure
(A) higher than that of the ambient
(B) lower than that of the fuel
(C) higher than that of the fuel
(D) lower than that of the ambient
Answer: (A)
23. The most desirable property amongst the following for a lubricating oil is
(A) high density
(B) high dynamic viscosity
(C) low density
(D) low dynamic viscosity
Answer: (B)
24. If is the Fourier cosine series of the function
f(x) = sin x, 0 < x <π,
then which of the following are TRUE?
(A) a0 + a1 = 4/π
(B) a0 = 4/π
(C) a0 + a1 = 2/π
(D) a1 = 2/π
Answer: (A, B)
25. A simply supported beam is loaded with a uniformly distributed load (UDL) acting vertically downwards. Which of the following statements are TRUE with regard to strain energy?
(A) It increases with increase in UDL
(B) It increases with increase in cross-sectional area of the beam
(C) It is independent of the length of the beam
(D) It is dependent on Young’s modulus of elasticity
Answer: (A, D)
26. Which of the following flows are represented by the velocity field,
(A) Incompressible flow
(B) Compressible flow
(C) Irrotational flow
(D) Rotational flow
Answer: (A, C)
27. If a ship enters shallow water from deep water, maintaining the same speed, then which of the following are TRUE?
(A) Resistance increases
(B) Trim changes
(C) Resistance decreases
(D) Draught increases
Answer: (A, B, D)
28. For a rigid vessel at sea, which of the following statements are TRUE?
(A) Static and dynamic environmental loads are dependent on the structural strength of the vessel
(B) Static and dynamic environmental loads are NOT dependent on the structural strength of the vessel
(C) Static and dynamic environmental loads are dependent on the geometry of the vessel
(D) Static and dynamic environmental loads are NOT dependent on the geometry of the vessel
Answer: (B, C)
29. Which of the following are TRUE for pressure, temperature and density of a thermodynamic system?
(A) path functions
(B) point functions
(C) inexact differentials
(D) exact differentials
Answer: (B, D)
30. Let f(x, y, z) = xy + yz + xz. If a point (0, 0, λ) lies on the tangent plane to the surface f(x, y, z) = 3 at the point (1, 1, 1) then the value of λ is _____.
Answer: (3 to 3)
31. The beam fixed at end A and simply supported at C with a roller is shown in the figure. If B is an internal hinge and a concentrated load of 10 kN is acting at D and a uniformly distributed load (UDL) of 10 kN/m is acting on member AB, then the magnitude of bending moment at the fixed end A is ________ kNm.
Answer: (15 to 15)
32. The laminar and turbulent boundary layer thickness of a flat plate are given by respectively, where x is the distance from the leading edge and Rex is the Reynolds number at x-location.
The kinematic viscosity of the fluid is 10−6 m2/s. A 100 m long plate is moving at a speed of 10 m/s. The boundary layer thickness at the rear end of the plate is ________ m (rounded off to two decimal places).
Answer: (0.58 to 0.59)
33. The diameter and rotating speed of a cargo ship propeller are 7.5 m and 120 RPM, respectively. An open water test is to be performed in a towing tank with a propeller model of 300 mm diameter. The corresponding propeller model speed is ________ RPM.
Answer: (600 to 600)
34. Assume that a ship has length L = 200 m and operates at a design speed U = 12 m/s. If in a turning circle maneuver, the ship exhibits a steady turning diameter of 6L, then the yaw rate of the ship is ______ rad/s (correct to two decimal places).
Answer: (0.02 to 0.02)
35. If the maximum static deflection of a shaft is 5 mm, then the estimated critical speed using Rayleigh-Ritz method is ______ RPM (rounded off to nearest integer).
Answer: (422 to 424)
Q.36 – Q.65 Carry TWO marks Each
36. The value of the line integral
along the circle C: x2 + y2 = 1, z = 1 oriented in the clockwise sense as seen from the origin, is
(A) 2π
(B) 4π
(C) 6π
(D) 8π
Answer: (C)
37. A column of height 20 m is fixed at both ends. If Young’s modulus of elasticity is 17 × 109 N/m2 and moment of inertia is 3.255 × 10−4 m4, then the first critical load of buckling of the column lies between __________ kN.
(A) 501 and 520
(B) 521 and 540
(C) 541 and 560
(D) 561 and 580
Answer: (C)
38. In a potential flow field, if the stream function ψ = xy2, then the velocity potential ϕ is
Answer: (D)
39. For a container ship, the propeller open water efficiency, thrust deduction fraction and wake fraction are 0.60, 0.19 and 0.25, respectively. If the relative rotative efficiency of the propeller is 1.0, then the hull efficiency and quasi-propulsive efficiency of the propeller, respectively, are
(A) 1.080 and 0.648
(B) 0.608 and 0.556
(C) 0.926 and 0.648
(D) 0.926 and 0.556
Answer: (A)
40. Consider the wave elevation spectrum Sηη(ω) as shown in the figure. Then, the significant wave height is ______ m.
(A) 2
(B) 4
(C) 6
(D) 8
Answer: (D)
41. If ∆hm and ∆hf are the enthalpy drops across the moving and fixed blades of a turbine stage, then the degree of reaction is
Answer: (C)
42. Let
Which of the following are TRUE?
(A) M is singular
(B) where I is the identity matrix of order 3
(C) M has three distinct eigenvalues
(D) M has three linearly independent eigenvectors
Answer: (B, D)
43. Which of the following statements are TRUE about the assumptions adopted in Euler’s column theory?
(A) Length of the column is very large in comparison to its cross-sectional dimensions
(B) Effect of the axial compressive stress is smaller than the effect of bending stress on column buckling
(C) Column fails only by transverse loads
(D) Column fails only by buckling
Answer: (A, B, D)
44. An autonomous underwater vehicle is made of a long cylinder with a semi-ellipsoid at the forward end and a hemisphere at the aft end as shown in the figure. The origin of the reference frame is located at the centroid of the cylinder.
The positive x, y and z axes, respectively, are pointing towards forward, port and upward directions. The surge, sway and heave motions are represented by indices 1-2-3 and roll, pitch and yaw motions are represented by indices 4-5-6, respectively.
If A = [Aij] is the added mass matrix, then which of the following are NOT zero?
(A) A15
(B) A35
(C) A46
(D) A26
Answer: (B, D)
45. If a ship hull is subdivided into different watertight compartments, which of the following statements are TRUE?
(A) It improves the ship stability in damaged conditions
(B) It increases the ship hull strength
(C) It reduces the ship intact stability
(D) It provides more options to carry different types of cargo
Answer: (A, B, D)
46. Consider the midship section of a vessel with the centerline (CL) and neutral axis (NA) as shown in the figure. Assume that the cross-section is symmetric about the centerline, the plate thickness is uniform throughout the section and h1< h2.
When the vessel is subjected to a vertical bending moment in its upright condition,which of the following statements are TRUE?
(A) Magnitude of shear stress is maximum at points P and S
(B) Magnitude of shear stress is minimum at points Q and U
(C) Magnitude of bending stress is maximum at points S and T
(D) Magnitude of bending stress is minimum at points Q and U
Answer: (C, D)
47. For a simple vapour compression refrigeration, which of the following thermodynamic cycles (1-2-3-4) are possible? Here, T, P, s and h indicate temperature, pressure, specific entropy and specific enthalpy, respectively.
Answer: (A, B)
48. Which of the following statements are TRUE for a fluid flow over a deeply
submerged body?
(A) D’Alembert’s paradox states that a deeply submerged body in a real fluid flow experiences no drag force
(B) D’Alembert’s paradox states that a deeply submerged body in an ideal fluid flow experiences no drag force
(C) The wall shear stress at the point of flow separation on the body is zero
(D) Dimples/dentures on a body surface facilitate earlier transition to turbulent flow which delays the boundary layer separation
Answer: (B, C, D)
49. An Otto cycle has states 1 and 2 at the beginning and the end of the compression stroke, respectively. The states 3 and 4 are at the beginning and the end of the expansion stroke, respectively.
Let the compression ratio of the cycle be r, specific heat ratio of air beγ, specific heat of air at constant volume beCv and P, v and T be pressure, specific volume and temperature of the air, respectively. Then, which of the following expressions represent the thermal efficiency of the cycle?
Answer: (A, C)
50. Let y(x) be the solution of the differential equation
yʹʹ – 4yʹ – 12y = 3e5x
Then y(1) is ______ (rounded off to nearest integer).
Answer: (339 to 341)
51. We have two coins. One is biased with the probability for head being 1.0 and the other is a fair coin. One coin is chosen at random and is tossed twice. If we obtain head both times, then the probability of the chosen coin being a fair coin is ______ (correct to one decimal place).
Answer: (0.2 to 0.2)
52. An element, as shown in the figure, is subjected to stresses σx = 500 N/m2, σy = 300 N/m2 and τ = 120 N/m2.
If σ1 and σ2 are the principal stresses, then the absolute value of the angleφ is ______ degree (rounded off to one decimal place).
Answer: (24.5 to 25.5)
53. An under-damped single degree of freedom system is freely oscillating with an initial amplitude A. The initial velocity of the system is zero. After five cycles of oscillation, the amplitude reduces to A/2.
Then the damping ratio of the system is ______ % (rounded off to one decimal place) of critical damping.
Answer: (2.1 to 2.3)
54. A system with two degrees of freedom, as shown in the figure, has masses m1 = 200 kg and m2 = 100 kg and stiffness coefficients k1 = k2 = 200 N/m. Then the lowest natural frequency of the system is ____ rad⁄s (rounded off to one decimal place).
Answer: (0.7 to 0.8)
55. A horizontal cylinder of 1.0 m diameter is placed transversely at the aft of a ship and is completely immersed in water. The cylinder rotates at 100 RPM and inflow velocity is 10 m/s. Water density is 1000 kg/m3. Assuming an ideal planar flow, the lift force/unit length acting on the cylinder is _______ kN/m (rounded off to one decimal place).
Answer: (163.3 to 165.5)
56. Consider a steady flow through a horizontal nozzle. The nozzle inlet area is 1 m2 and the outlet area is 0.05 m2. At the outlet, the flow discharges to atmosphere. Assuming the flow to be incompressible and frictionless, and the density of the fluid as 1 kg/m3, the gauge pressure required at the nozzle inlet to produce an outlet speed of 100 m/s is ______ N/m2 (rounded off to nearest integer).
Answer: (4987 to 4988)
57. A rectangular barge has length (L) of 100 m, breadth (B) of 18 m and depth (D) of 10 m. It is subdivided transversely into four equal compartments of equal length with the end compartments loaded fully with oil of density = 0.9 tonne/m3. The barge floats in water having a density of 1000 kg/m3. If the hull structural weight is ignored, then the transverse metacentric height of the barge is _______ m (correct to two decimal places).
Answer: (3.25 to 3.25)
58. A propeller rotating at a speed of 108 RPM behind the ship produces a thrust of 720 kN with a torque of 700 kNm, when it travels at a speed of 15 knots. In open water, this propeller rotating at the same speed, produces the same thrust at an advance speed of 12 knots, and develops the same torque at an advance speed of 12.3 knots. Then, the average of the wake fractions is _______ (correct to two decimal places).
Answer: (0.19 to 0.19)
59. Consider a point source in a uniform flow of velocity U = 4 m/s along the positive x-axis as shown in the figure. Assume a two-dimensional steady potential flow. The potential due to the point source is given by loge(r), where r2 = x2 + y2.
Then the magnitude of the distance d between the point source and the stagnation point is _________ m (rounded off to two decimal places).
Answer: (0.24 to 0.26)
60. Consider a ship with one half of its midship cross-section, as shown in the figure, with moulded breadth B of 30 m and moulded depth D of 9 m.
Assume the following:
The deck, side shell and bottom plate have the same thickness
The yield stress of the material is 240 MPa
The section is subjected to a vertical bending moment of 712.8 MNm
Ignore the self-moment of inertia of the deck and bottom plating in calculations.The distance of the fiber farthest from the neutral axis can be considered excluding the plate thickness.
If the maximum bending stress is equal to the yield stress, then the plate thickness is ________ mm (rounded off to one decimal place).
Answer: (9.5 to 10.5)
61. Consider a ship with a forward speed U (A) of 9.81 m/s moving in deep waters. A wave is incident at an angle β = 120° to the longitudinal axis of the ship as shown in figure. Assume acceleration due to gravity g = 9.81 m/s2. If a person onboard the ship observes the encounter period of the incident wave to be 4.187 s, then the actual period of the wave is ______ s (rounded off to one decimal place).
Answer: (6.2 to 6.4)
62. An air standard Otto cycle has a compression ratio of 6 and a mean effective pressure of 1000 kPa. Assume that the specific heat ratioγas 1.4 and specific gas constant R as 0.287 kJ/kgK for the air. If the pressure and temperature at the beginning of the compression stroke are 100 kPa and 300 K, respectively, then the specific work output of the cycle is _____kJ/kg (rounded off to one decimal place).
Answer: (716.5 to 718.5)
63. If methane (CH4) gas reacts with air at a stoichiometric proportion, then the air fuel ratio of the combustion process is _________ (rounded off to one decimal place).
Answer: (16.7 to 17.7)
64. In a vapour compression refrigeration cycle using R134 as the refrigerant, the enthalpies are (i) 240 kJ/kg at the beginning of the compression, (ii) 275 kJ/kg at the end of the compression and (iii) 96 kJ/kg at the beginning of the throttling.
Then the coefficient of performance of the cycle is ________ (rounded off to one decimal place).
Answer: (4.0 to 4.2)
65. Consider a steady incompressible laminar flow between two parallel long plates separated by a distance h = 1 m as shown in the figure. The bottom plate is fixed, and the flow is driven by the motion of the upper plate alone. No externally imposed pressure exists.
If the upper plate has a velocity of U = 10 m/s, the kinematic viscosity of the fluid is 10−6 m2/s and the density of the fluid is 103 kg/m3, then the shear stress at the bottom plate is _______ N/m2 (correct to two decimal places).
2. A sum of money is to be distributed among P, Q, R, and S in the proportion 5 : 2 : 4 : 3, respectively.
If R gets Rs 1000 more than S, what is the share of Q (in Rs)?
(A) 500
(B) 1000
(C) 1500
(D) 2000
Answer: (D)
3. A trapezium has vertices marked as P, Q, R and S (in that order anticlockwise). The side PQ is parallel to side SR.
Further, it is given that, PQ = 11 cm, QR = 4 cm, RS = 6 cm and SP = 3 cm.
What is the shortest distance between PQ and SR (in cm)?
(A) 1.80
(B) 2.40
(C) 4.20
(D) 5.76
Answer: (B)
4. The figure shows a grid formed by a collection of unit squares. The unshaded unit square in the grid represents a hole.
What is the maximum number of squares without a “hole in the interior” that can be formed within the 4 × 4 grid using the unit squares as building blocks?
(A) 15
(B) 20
(C) 21
(D) 26
Answer: (B)
5. An art gallery engages a security guard to ensure that the items displayed are protected. The diagram below represents the plan of the gallery where the boundary walls are opaque. The location the security guard posted is identified such that all the inner space (shaded region in the plan) of the gallery is within the line of sight of the security guard.
If the security guard does not move around the posted location and has a 360o view, which one of the following correctly represents the set of ALL possible locations among the locations P, Q, R and S, where the security guard can be posted to watch over the entire inner space of the gallery.
(A) P and Q
(B) Q
(C) Q and S
(D) R and S
Answer: (C)
Q.6 – Q.10 Carry TWO marks each.
6. Mosquitoes pose a threat to human health. Controlling mosquitoes using chemicals may have undesired consequences. In Florida, authorities have used genetically modified mosquitoes to control the overall mosquito population. It remains to be seen if this novel approach has unforeseen consequences.
Which one of the following is the correct logical inference based on the information in the above passage?
(A) Using chemicals to kill mosquitoes is better than using genetically modified mosquitoes because genetic engineering is dangerous
(B) Using genetically modified mosquitoes is better than using chemicals to kill mosquitoes because they do not have any side effects
(C) Both using genetically modified mosquitoes and chemicals have undesired consequences and can be dangerous
(D) Using chemicals to kill mosquitoes may have undesired consequences but it isnot clear if using genetically modified mosquitoes has any negative consequence
Answer: (D)
7. Consider the following inequalities.
(i) 2x − 1 > 7
(ii) 2x − 9 < 1
Which one of the following expressions below satisfies the above two inequalities?
(A) x ≤ −4
(B) −4 <x ≤ 4
(C) 4 <x< 5
(D) x ≥ 5
Answer: (C)
8. Four points P(0, 1), Q(0, −3), R(−2, −1), and S(2, −1) represent the vertices of a quadrilateral.
What is the area enclosed by the quadrilateral?
(A) 4
(B) 4√2
(C) 8
(D) 8√2
Answer: (C)
9. In a class of five students P, Q, R, S and T, only one student is known to have copied in the exam. The disciplinary committee has investigated the situation and recorded the statements from the students as given below.
Statement of P: R has copied in the exam.
Statement of Q: S has copied in the exam.
Statement of R: P did not copy in the exam.
Statement of S: Only one of us is telling the truth.
Statement of T: R is telling the truth.
The investigating team had authentic information that S never lies.
Based on the information given above, the person who has copied in the exam is
(A) R
(B) P
(C) Q
(D) T
Answer: (B)
10. Consider the following square with the four corners and the center marked as P, Q, R, S and T respectively.
Let X, Y and Z represent the following operations:
X: rotation of the square by 180 degree with respect to the
S-Q axis.
Y: rotation of the square by 180 degree with respect to the P-R axis.
Z: rotation of the square by 90 degree clockwise with respect to the axis perpendicular, going into the screen and passing through the point T.
Consider the following three distinct sequences of operation (which are applied
in the left to right order).
(1) XYZZ
(2) XY
(3) ZZZZ
Which one of the following statements is correct as per the information provided above?
(A) The sequence of operations (1) and (2) are equivalent
(B) The sequence of operations (1) and (3) are equivalent
(C) The sequence of operations (2) and (3) are equivalent
(D) The sequence of operations (1), (2) and (3) are equivalent
Answer: (B)
Metallurgical Engineering
Q.11 – Q.29 Multiple Choice Question (MCQ), carry ONE mark each
11. The Taylor series expansion around x = 0 of the function truncated to first two terms is _______
Answer: (A)
12. According to Sieverts’ law, the equilibrium solubility of N2 (gas) in molten steel is proportional to _________
Given: Equilibrium partial pressure of N2 (gas) is pN2
(A) pN2
(B) √pN2
(C) 1/pN2
(D) pN22
Answer: (B)
13. Titanium is produced commercially by ______
(A) smelting reduction of TiO2
(B) thermal dissociation of TiH2
(C) reduction of TiCl4 by Mg
(D) reduction of TiO2 by H2
Answer: (C)
14. Magnesium treatment is carried out to produce _______ cast iron.
(A) white
(B) gray
(C) spheroidal graphite
(D) malleable
Answer: (C)
15. The sequence of peaks corresponding to the planes (in the order of increasing 2θ) observed in the X-ray diffractogram of a pure copper powder sample is ______
(A) 111, 200, 220, 311
(B) 110, 200, 211, 220
(C) 110, 200, 211, 311
(D) 111, 200, 311, 220
Answer: (A)
16. Which one of the following Non Destructive Testing (NDT) techniques CANNOT be used to identify volume defects in the interior of a casting?
(A) Ultrasonic testing
(B) X-ray computed tomography
(C) Dye-penetrant testing
(D) Gamma ray radiography
Answer: (C)
17. Neutral point in rolling is defined as the point along the surface of contact between the roll and the sheet, where the surface velocity of the roll is _______
(A) zero
(B) half the velocity of the sheet
(C) twice the velocity of the sheet
(D) equal to the velocity of the sheet
Answer: (D)
18. In fluid flow, the dimensionless number that describes the transition from laminar to turbulent flow is _______
(A) Reynolds number
(B) Schmidt number
(C) Biot number
(D) Prandtl number
Answer: (A)
19. Which one of the following elements has the slowest removal rate from hot metal in basic oxygen furnace (BOF) steelmaking?
(A) Carbon
(B) Sulfur
(C) Silicon
(D) Phosphorus
Answer: (B)
20. Match the nature of bonding (Column I) with material (Column II)
Column I Column II
(P) Ionic (1) Diamond
(Q) Covalent (2) Silver
(R) Metallic (3) NaCl
(S) Secondary (4) Solid argon
(A) P – 4, Q – 3, R – 2, S – 1
(B) P – 2, Q – 1, R – 3, S – 4
(C) P – 3, Q – 1, R – 4, S – 2
(D) P – 3, Q – 1, R – 2, S – 4
Answer: (D)
21. Which one of the following figures illustrates a lap joint with fillet weld?
(A) I
(B) II
(C) III
(D) IV
Answer: (B)
22. The CCT diagram of a eutectoid steel with a superimposed cooling curve is shown in the figure. The microstructure at room temperature (RT) after this heat treatment is ________
(A) pearlite only
(B) pearlite + retained austenite
(C) martensite only
(D) pearlite + martensite
Answer: (D)
23. Given that V is a closed volume in space bounded by the surface S with unit normal is any non-zero vector and is the gradient operator, then the volume integral is equal to the surface integral by virtue of _______
(A) Stokes Curl theorem
(B) Reynolds transport theorem
(C) Buckingham Pi theorem
(D) Gauss divergence theorem
Answer: (D)
24. In green sand moulding, the casting defect resulting from the displacement of mould cavity by an oversized core is known as ________
(A) crush
(B) hot tear
(C) blow
(D) fin
Answer: (A)
25. Which one of the following modern practices is used for retarding the solution loss reaction in blast furnace iron making?
(A) High top pressure
(B) Bell-less top
(C) Pulverized coal injection
(D) Rotating chute for burden distribution
Answer: (A)
26. For a material that undergoes strain hardening, necking instability occurs during tensile testing when ________
Given: σ = true stress and ϵ = true strain.
Answer: (C)
27. Match the processes (Column I) with the corresponding defects (Column II).
Column I Column II
(P) Extrusion (1) Earing
(Q) Deep drawing (2) Cold shut
(R) Forging (3) Edge cracking
(S) Rolling (4) Fir-tree cracking
(A) P − 1, Q − 4, R −2, S − 3
(B) P − 2, Q − 1, R − 4, S − 3
(C) P − 4, Q − 1, R − 3, S − 2
(D) P − 4, Q − 1, R − 2, S − 3
Answer: (D)
28. With increase in carbon content (up to 2 mass%) in Fe-C alloy, which one of the following statements is correct with respect to the lattice parameters (c and a) of BCT martensite?
(A) Both c and a increase
(B) c increases but a decreases
(C) c decreases but a increases
(D) Both c and a decrease
Answer: (B)
29. With reference to the stress intensity factor, find the correct match of nomenclature (Column A) with the mode of deformation applied to the crack (Column B).
Column A Column B
(P) Mode I (X) Forward shear mode
(Q) Mode II (Y) Parallel shear mode
(R) Mode III (Z) Crack opening mode
(A) P − Z, Q − Y, R − X
(B) P − Z, Q − X, R − Y
(C) P − Y, Q − X, R − Z
(D) P − Y, Q − Z, R − X
Answer: (B)
Q.30 – Q.33 Multiple Selection Question (MSQ), carry ONE mark each
30. In continuous casting of steel, mould flux is used for _____
(A) lubrication
(B) reducing heat loss
(C) inclusion control
(D) reducing solidification shrinkage
Answer: (A, B, C)
31. Identify the correct statement(s) with respect to the role of nickel as an alloying element in steels.
(A) It increases the Ms temperature
(B) It is an austenite stabiliser
(C) It decreases the Ms temperature
(D) It is a carbide former
Answer: (B, C)
32. While designing a material for high temperature application, which of the following characteristic(s)/attribute(s) is(are) desirable for achieving better creep resistance?
(A) Fine grain size
(B) FCC crystal structure
(C) High melting point
(D) Cold worked microstructure
Answer: (B, C)
33. Given the strain rate dislocation density (ρ), dislocation velocity (v), which of the following relationship(s) is(are) correct? Assume that Orowan equation for plastic flow due to the dislocation movement is obeyed.
Answer: (B, D)
Q.34 – Q.35 Numerical Answer Type (NAT), carry ONE mark each
34. A set of observations with normal distribution of error as ±1.96σ (where σ is standard deviation) is equivalent to the confidence interval of ________% (round off to the nearest integer).
Answer: (95 to 95)
35. A Newtonian incompressible liquid is contained between two parallel metal plates separated by 10−3 m (see figure). A stress of 5 Pa is required to maintain the upper plate in motion with a constant speed of 2 m∙s−1 in the horizontal direction relative to the bottom plate.
The viscosity of liquid contained between the plates is _______ × 10−3 Pa∙s (answer rounded off to 1 decimal place).
Answer: (2.5 to 2.5)
Q.36 – Q.42 Multiple Choice Question (MCQ), carry TWO marks each
36. The general solution to the following differential equation is _______, where A and B are constants
(A) y = A sin(2t) + B
(B) y = A sin(2t) + B cos(2t)
(C) y = A e2t + Be−2t
(D) y = A e2t + B t e2t
Answer: (D)
37. Which one of the following equations will fail to converge to a root with an initial guess value of x = 0.5, using the Newton-Raphson method?
(A) x(1 – x) = 0
(B) ex – 3x2 = 0
(C) x – ln(3x) = 0
(D) tan(x) – x = 0
Answer: (A)
38. Match the following mineral processing operations (Column I) with the corresponding physical principles (Column II)
(A) P − 2, Q − 4, R − 1, S − 3
(B) P − 2, Q − 3, R − 1, S − 4
(C) P − 3, Q − 1, R − 4, S − 2
(D) P − 1, Q − 4, R − 2, S − 3
Answer: (A)
39. Figures P, Q, R and S schematically show the atomic dipole moments in the absence of external magnetic field. Which one of the following is the correct mapping of nature of magnetism to atomic dipole moments?
(A) P – Diamagnetism, Q – Antiferromagnetism, R – Paramagnetism, S – Ferromagnetism
(B) P – Ferromagnetism, Q – Antiferromagnetism, R – Diamagnetism, S – Paramagnetism
(C) P – Paramagnetism, Q – Ferromagnetism, R – Diamagnetism, S – Antiferromagnetism
(D) P – Ferromagnetism, Q – Diamagnetism, R – Antiferromagnetism, S – Paramagnetism
Answer: (B)
40. Find the correct match between dislocation reactions (Column A) to the descriptions (Column B)
(A) P − 3, Q − 2, R − 1
(B) P − 3, Q − 1, R − 2
(C) P − 2, Q − 3, R − 1
(D) P − 2, Q − 1, R − 3
Answer: (B)
41. Match the phenomena (Column I) with the descriptions (Column II)
(A) P − 1, Q − 2, R − 3, S − 4
(B) P − 1, Q − 2, R − 4, S − 3
(C) P − 3, Q − 4, R − 1, S − 2
(D) P − 3, Q − 1, R − 4, S − 2
Answer: (C)
42. For a 3×3 matrix, the value of the determinant is −48 and the trace is 8. If one of the eigenvalues is 4, the other two are ________
(A) 2, −3
(B) 1, −3
(C) 6, −2
(D) −4, 0
Answer: (C)
43. Which of the following statement(s) is(are) TRUE about black body radiation?
(A) Among all radiation emitted by an ideal black body at room temperature, the most intense radiation falls in the visible light spectrum
(B) The total emissive power of an ideal black body is proportional to the square of its absolute temperature
(C) The emissive power of an ideal black body peaks at a wavelength λ which is inversely proportional to its absolute temperature
(D) The radiant energy emitted by an ideal black body is greater than that emitted by the non-black body at all temperatures above 0 K
Answer: (C, D)
44. Which of the following parameter(s) influence(s) the melting rate of the consumable wire in a gas metal arc welding process?
(A) Stick-out length
(B) Welding speed
(C) Welding current
(D) Diameter of the consumable wire
Answer: (A, C, D)
45. A non-rotating smooth solid spherical object is fixed in the stream of an inviscid incompressible fluid of density ρ (see figure). The flow is horizontal, slow, steady, and fully developed far from the object as shown by the streamline arrows near point O. Which of the following statement(s) is(are) TRUE?
(Note: B is the center of the sphere and the straight horizontal line OAB intersects the surface of the sphere at the point A.)
(A) The velocity of the fluid at the point A is zero
(B) The fluid pressure at the point A exceeds that at point O by the amount ρv2/2, where v is the fluid velocity at point O
(C) Fluid moving precisely along OA will turn perpendicular to OA to circumvent the object
(D) On each side of the central streamline OA, the flow will be deflected round the object
Answer: (A, B, D)
Q.46 – Q.65 Numerical Answer Type (NAT), carry TWO marks each
46. From high temperature tensile testing, the flow stress (measured at the same value of strain) of an alloy was found to be 50 MPa at a strain rate of 0.1 s−1 and 70 MPa at a strain rate of 10 s−1. The strain rate sensitivity parameter is _______ (round off to 3 decimal places).
Answer: (0.069 to 0.075)
47. A spherical gas bubble of radius 0.01 mm is entrapped in molten steel held at 1773 K. If the pressure outside the bubble is 1.5 bar, the pressure inside the bubble is _____ bar (round off to 1 decimal place).
Given: 1 bar = 105 Pa and the surface tension of the steel at 1773 K is 1.4 N⋅ m−1.
Answer: (4.3 to 4.3)
48. What is the equilibrium pco/pco2 ratio for the given reaction at 1873 K? (round off to 2 decimal places)
Mo(s) + O2(g) ↔ MoO2(s)
Given : ∆fG°1873 = −262300 J; and ∆rG°1873 = −120860 J for the reaction CO(g) + 0.5O2(g) ↔ CO2(g); R = 8.314 J∙K−1∙mol−1.
is 1.2327 V at 873 K. Activity of Pb in the Au-Pb alloy is 0.72 and the activity of PbCl2 in the electrolyte is 0.18. The standard Gibbs energy of formation of
PbCl2(liquid) at 873 K is _______ kJ∙mol−1 (round off to 1 decimal place).
Given : R = 8.314 J∙K−1∙mol−1 and F = 96500 C∙mol−1.
Answer: (-233.5 to -232.5)
50. Consider a tilt boundary of misorientation of 2° in an aluminium grain. The lattice parameter of aluminium is 0.143 nm. The spacing between the dislocations that form the tilt boundary is ____________ nm (round off to 2 decimal places).
Answer: (2.86 to 2.93)
51. Molten steel at 1873 K weighing 100 metric tons is desulfurized using 1250 kg of synthetic slag by equilibration. If the sulfur content in the steel is reduced from 0.015 mass% to 0.0025 mass%, the desulfurizing index is _______ (round off to the nearest integer).
Answer: (400 to 400)
52. High cycle fatigue data for an alloy at various alternating stresses, σa (see figure) is given below
A specimen of this alloy is subjected to multiple stress cycles sequentially in the following order: (i) first 5000 cycles at σa = 400 MPa followed by (ii) 25000 cycles at σa = 300 MPa and finally (iii) at σa = 500 MPa. Assuming that Miner’s law is obeyed, the number of cycles to failure at the final applied stress of 500 MPa is _________.
Answer: (250 to 250)
53. The partial molar enthalpy of Au in Ag-Au melt containing 25 mol% Au at 1400 K is −8300 J∙mol−1. Assuming regular solution behavior, the activity of Au in the melt is _______ (round off to 3 decimal places).
Given : R = 8.314 J∙K−1∙mol−1
Answer: (0.121 to 0.125)
54. A rectangular block made of Material I and Material II of identical cross sections (as shown in the figure) has a temperature (T) of 435 K and 400 K at the bottom and top surfaces, respectively. Assuming purely steady state conductive heat transfer, the temperature at the interface is _______ K (round off to nearest integer).
(Given: The two parts of the block made of Material I and Material II have equal thickness of 25 mm each. The thermal conductivities of Material I and Material II are 50 W∙m−1 ∙ K−1 and 200 W∙m−1∙K−1, respectively.)
Answer: (406 to 408)
55. During solidification of a pure metal, the radius of critical nucleus at an undercooling of 10 K is ________ × 10−9 m (answer rounded off to 1 decimal place).
Given: solid/liquid interface energy = 0.177 J∙m−2,
melting point of the metal = 1356 K and
latent heat of fusion = 1.88 × 109 J∙m−3
Answer: (25.1 to 25.9)
56. The concentration C of a solute (in units of atoms∙mm−3) in a solid along x direction (for x > 0) follows the expression
C = a1x2 + a2x
where x is in mm, a1 are in units of atoms∙mm−5 and atoms∙mm−4, respectively. Assuming a1 = a2 = 1, the magnitude of flux at x = 2 mm is ______ × 10−3 atoms∙mm−2∙s−1(answer rounded off to the nearest integer).
Given: diffusion coefficient of the solute in the solid is 3 × 10−3 mm2∙s−1.
Answer: (15 to 15)
57. Assuming that Dulong-Petit law is valid for a monoatomic solid, the ratio of heat capacities Cp/Cv at 500 K is _____ (round off to 3 decimals).
Given: molar volume = 7 × 10−6 m3∙mol−1,
isothermal compressibility = 8 × 10−12 Pa−1,
isobaric expansivity = 6 × 10−5K−1 and R = 8.314 J∙K−1∙mol−1.
Answer: (1.059 to 1.071)
58. A sieve made of steel wire of diameter 53 μm has an aperture size of 74 μm. Its mesh number is ______ (round off to the nearest integer).
Answer: (197 to 201)
59. Steel plates are welded autogenously using Gas Tungsten Arc welding with an arc heat transfer efficiency of 0.65. The first weld is made using a welding current of 200 A at an arc voltage of 18 V with a welding speed of 0.002 m∙s−1 The second weld is made at a welding speed of 0.0022 m∙s−1 with the same arc voltage. If both the welds have identical heat input, the welding current of the second weld is _________ A (round off to the nearest integer).
Answer: (220 to 220)
60. A cylindrical specimen of an Al alloy with diameter of 30 mm is cold extruded to a diameter of 20 mm. If the flow behavior of the alloy is expressed by the equation, σ = 350 ϵ3 MPa, the ideal plastic work of deformation per unit volume is ________ × 106 J (answer rounded off to the nearest integer).
Answer: (200 to 210)
61. The integral of the function f(x) = 0.2 + 10x2 estimated by the trapezoidal rule with a single segment from x = 0 to x = 1 is _______ (round off to 1 decimal place).
Answer: (5.1 to 5.3)
62. Air at 300 K is passed at a mass flow rate of 1.5 kg ∙ s−1 through a metallic tube of inner diameter 0.08 m. Inner wall temperature of the tube is maintained at 700 K. Temperature of the air leaving the tube is 600 K. Assuming that heat transfer occurs entirely by steady state convection, length of the tube is ________ m (round off to 2 decimal places).
Given: the coefficient of convective heat transfer from tube wall to air is 500 W∙m−2K−1. Assume specific heat capacity of air to be constant and equal to 1080 J∙kg−1∙K−1 and π = 3.14
Answer: (16.55 to 18.55)
63. Given the stress tensor
the maximum shear stress is _________ MPa (round off to the nearest integer).
Answer: (70 to 70)
64. A set of 11 (x, y) data points is least-squares fitted to a quadratic polynomial. If the sum of squares of error is 2.4, the variance of error is ________ (round off to 1 decimal place).
Answer: (0.3 to 0.3)
65. The equilibrium microstructure of an alloy A-B consists of two phases α and β in the molar proportion 2:1. If the overall composition of the alloy is 70 mol% B and the composition of β is 90 mol% B, the composition of α is ______ (in mol% B) (round off to the nearest integer).
2. A sum of money is to be distributed among P, Q, R, and S in the proportion 5 : 2 : 4 : 3, respectively.
If R gets Rs 1000 more than S, what is the share of Q (in Rs)?
(A) 500
(B) 1000
(C) 1500
(D) 2000
Answer: (D)
3. A trapezium has vertices marked as P, Q, R and S (in that order anticlockwise). The side PQ is parallel to side SR.
Further, it is given that, PQ = 11 cm, QR = 4 cm, RS = 6 cm and SP = 3 cm.
What is the shortest distance between PQ and SR (in cm)?
(A) 1.80
(B) 2.40
(C) 4.20
(D) 5.76
Answer: (B)
4. The figure shows a grid formed by a collection of unit squares. The unshaded unit square in the grid represents a hole.
What is the maximum number of squares without a “hole in the interior” that can be formed within the 4 × 4 grid using the unit squares as building blocks?
(A) 15
(B) 20
(C) 21
(D) 26
Answer: (B)
5. An art gallery engages a security guard to ensure that the items displayed are protected. The diagram below represents the plan of the gallery where the boundary walls are opaque. The location the security guard posted is identified such that all the inner space (shaded region in the plan) of the gallery is within the line of sight of the security guard.
If the security guard does not move around the posted location and has a 360o view, which one of the following correctly represents the set of ALL possible locations among the locations P, Q, R and S, where the security guard can be posted to watch over the entire inner space of the gallery.
(A) P and Q
(B) Q
(C) Q and S
(D) R and S
Answer: (C)
Q.6 – Q.10 Carry TWO marks each.
6. Mosquitoes pose a threat to human health. Controlling mosquitoes using chemicals may have undesired consequences. In Florida, authorities have used genetically modified mosquitoes to control the overall mosquito population. It remains to be seen if this novel approach has unforeseen consequences.
Which one of the following is the correct logical inference based on the information in the above passage?
(A) Using chemicals to kill mosquitoes is better than using genetically modified mosquitoes because genetic engineering is dangerous
(B) Using genetically modified mosquitoes is better than using chemicals to kill mosquitoes because they do not have any side effects
(C) Both using genetically modified mosquitoes and chemicals have undesired consequences and can be dangerous
(D) Using chemicals to kill mosquitoes may have undesired consequences but it isnot clear if using genetically modified mosquitoes has any negative consequence
Answer: (D)
7. Consider the following inequalities.
(i) 2x − 1 > 7
(ii) 2x − 9 < 1
Which one of the following expressions below satisfies the above two inequalities?
(A) x ≤ −4
(B) −4 <x ≤ 4
(C) 4 <x< 5
(D) x ≥ 5
Answer: (C)
8. Four points P(0, 1), Q(0, −3), R(−2, −1), and S(2, −1) represent the vertices of a quadrilateral.
What is the area enclosed by the quadrilateral?
(A) 4
(B) 4√2
(C) 8
(D) 8√2
Answer: (C)
9. In a class of five students P, Q, R, S and T, only one student is known to have copied in the exam. The disciplinary committee has investigated the situation and recorded the statements from the students as given below.
Statement of P: R has copied in the exam.
Statement of Q: S has copied in the exam.
Statement of R: P did not copy in the exam.
Statement of S: Only one of us is telling the truth.
Statement of T: R is telling the truth.
The investigating team had authentic information that S never lies.
Based on the information given above, the person who has copied in the exam is
(A) R
(B) P
(C) Q
(D) T
Answer: (B)
10. Consider the following square with the four corners and the center marked as P, Q, R, S and T respectively.
Let X, Y and Z represent the following operations:
X: rotation of the square by 180 degree with respect to the
S-Q axis.
Y: rotation of the square by 180 degree with respect to the P-R axis.
Z: rotation of the square by 90 degree clockwise with respect to the axis perpendicular, going into the screen and passing through the point T.
Consider the following three distinct sequences of operation (which are applied
in the left to right order).
(1) XYZZ
(2) XY
(3) ZZZZ
Which one of the following statements is correct as per the information provided above?
(A) The sequence of operations (1) and (2) are equivalent
(B) The sequence of operations (1) and (3) are equivalent
(C) The sequence of operations (2) and (3) are equivalent
(D) The sequence of operations (1), (2) and (3) are equivalent
Answer: (B)
Mining Engineering
Q.11 – Q.35 Carry ONE mark Each
11. The value of is
(A) 0
(B) 1
(C) −n
(D) n
Answer: (C)
12. A velocity field in Cartesian coordinate system is expressed as
where p(0) = 0
If div v= 0, p(z)is
(A) 0
(B) −2z
(C) 2
(D) 2z
Answer: (B)
13. The constant term of the Fourier coefficients of the periodic function
is
(A) k
(B) 2k
(C) 2π
(D) 0
Answer: (D)
14. Two vectors x and y are shown in the figure. The projection vector of x on y is
(A)
(B) x × y
(C)
(D)
Answer: (A)
15. A deposit has the grade attribute X ∈ [0, 30] with a density function 𝑓(x). For a cut-off grade xc, the proportion of the ore in the deposit is given by
Answer: (A)
16. The drilling technique applicable for mineral exploration is
(A) Percussive drilling
(B) Tricone roller drilling
(C) Rotary-percussive drilling
(D) Diamond core drilling
Answer: (D)
17. Match the rock with its metamorphosed form
(A) P-II, Q-IV, R-I, S-III
(B) P-III, Q-I, R-IV, S-II
(C) P-IV, Q-III, R-I, S-II
(D) P-II, Q-III, R-IV, S-I
Answer: (A)
18. Identify the WRONG statement:
Break-even stripping ratio
(A) takes into account the maximum pit slope that is safe
(B) helps in determining the volume of the overburden
(C) presents the maximum possible mine size that is economical
(D) takes into account the life of the mine
Answer: (D)
19. A square pattern of blasting is shown in the figure. For the case of simultaneous blast, identify the zone of no fragmentation
(A) P
(B) Q
(C) R
(D) S
Answer: (C)
20. In the truss shown in the figure, the force in the member BD, in kN is_____.
(A) 7
(B) 5
(C) 2
(D) 0
Answer: (D)
21. The correct vertical stress profile in the case of tributary area method for pillar design is
(A) I
(B) II
(C) III
(D) IV
Answer: (C)
22. The bottom section of a stoping block has dimensions 200 m × 40 m. If the modified RMR of rock mass is 50, the appropriate method of mining on the basis of Laubscher’s chart in the figure is
(A) Shrinkage stoping
(B) Cut and fill
(C) Block Caving
(D) Sublevel stoping
Answer: (B)
23. Match the machine with its component.
(A) P-III, Q-IV, R-I, S-II
(B) P-IV, Q-III, R-I, S-II
(C) P-III, Q-IV, R-II, S-I
(D) P-IV, Q-III, R-II, S-I
Answer: (A)
24. Which one of the following is NOT a notifiable disease as per Indian mining legislation?
(A) Silicosis
(B) Noise induced hearing loss
(C) Nystagmus
(D) Asbestosis
Answer: (C)
25. If the ambient lapse rate is higher than the dry adiabatic lapse rate, the atmosphere is
(A) stable
(B) neutral
(C) unstable
(D) strongly stable
Answer: (C)
26. Identify the WRONG statement:
The application of controlled air recirculation in an underground work place can
(A) increase the air velocity at the work place
(B) lead to increased concentration of contaminants in the work place
(C) require the installation of an additional fan in the system
(D) lead to overall ventilation cost savings
Answer: (B)
27. The correct order of pavement layers for a haul road from top to bottom is
(A) Wearing course → Base → Sub base → Sub grade
(B) Wearing course → Sub base → Base → Sub grade
(C) Wearing course → Sub grade → Sub base → Base
(D) Wearing course → Base → Sub grade → Sub base
Answer: (A)
28. A mining company produces iron ore and sells to another company. Royalty to be paid is on the basis of
(A) quantity of ore produced
(B) quantity of ore sold
(C) difference between the quantities of ore produced and sold
(D) net profit
Answer: (B)
29. The cost of a screw compressor with an estimated life of 15 years is Rs. 21,00,000. If the depreciation of the compressor charged, using ‘sum-of-the-years-digits’ method, at the end of 4th year is Rs. 2,00,000, the salvage value, in Rs. is_______. (round off to one decimal place)
Answer: (100000.0 to 100000.0)
30. A safety device consists of two independent critical components X1 and X2. The failure of any one or both of these components can cause an accident. The failure probabilities of components X1 and X2 are 0.2 and 0.1, respectively. The probability of occurrence of an accident is_______. (round off to two decimal places)
Answer: (0.28 to 0.28)
31. In a levelling survey, a reading is taken as 2.25 m. However, along the line of sight there is deflection of 20 cm with respect to vertical position of the staff. The correct reading, in m is_______. (round off to two decimal places)
Answer: (2.20 to 2.30)
32. Water flows through a vertical sand column of cross sectional area 4000 mm2 and length 300 mm. For a water head of 600 mm, quantity of seepage water is 100 mm3/min. The hydraulic conductivity of the sand column, in mm/min is_______. (round off to three decimal places)
Answer: (0.012 to 0.013)
33. The modified Lauffer diagram as shown in the figure relates to roof span, RMR and stand-up time. In a metal mine, roof span of a drive is 4 m. If the RMR of the rock mass changes from 40 to 60, then the stand-up time increases by a factor of________. (round off to two decimal places)
Answer: (50.00 to 70.00)
34. In a friction winder, the skip accelerates to a steady speed over a time span of 15 s from the start. The torque vs. time diagram for the winding cycle is shown in the figure. The deceleration time in seconds is_______. (round off to one decimal place)
Answer: (10.0 to 10.0)
35. At a measurement station, the air quality parameters PM5, NO2 and O3 have the AQI sub-index values as 180, 96, and 84, respectively. The AQI for the station is_______. (in integer)
Answer: (180 to 180)
Q.36 – Q.65 Carry TWO marks Each
36. Match the drilling pattern with mining operation
(A) P→II, Q→III, R→I, S→II
(B) P→III, Q→IV, R→I, S→II
(C) P→II, Q→I, R→IV, S→III
(D) P→III, Q→IV, R→II, S→I
Answer: (D)
37. The closest match of the scatter plot between the variables X and Y with the approximate attribute is
(A) P→I, Q→II, R→III, S→IV
(B) P→II, Q→I, R→IV, S→III
(C) P→III, Q→IV, R→I, S→II
(D) P→IV, Q→II, R→III, S→I
Answer: (D)
38. A 3-point borehole extensometer is installed to identify the location of a single discontinuity plane in a hanging wall rock by measuring deformations at three locations as shown in the figure. The absolute readings of deformations measured on two different dates are listed in the table. Based on the measured data the most likely inference is
(A) Discontinuity between Anchor-1 and Anchor-2
(B) Discontinuity between Anchor-2 and Anchor-3
(C) Discontinuity between Anchor-3 and excavation boundary
(D) No noticeable discontinuity
Answer: (B)
39. Match the semi-variogram shape with the model name and the property
(A) P→III→E, Q→II→F, R→IV→E, S→I→G
(B) P→II→F, Q→I→G, R→III→E, S→IV→E
(C) P→IV→G, Q→III→F, R→II→E, S→I→E
(D) P→II→E, Q→I→E, R→III→F, S→IV→G
Answer: (A)
40. In a uniaxial compressive strength test, a rock sample of diameter 50 mm fails at an angle of 60° as shown in the figure. If the peak load at failure is 120 kN, the normal and shear stresses on failure plane respectively, in MPa are_______ and _____.
(A) 15.28 and 26.46
(B) 26.46 and 15.28
(C) 57.02 and -15.28
(D) -15.28 and 15.28
Answer: (A)
41. A coal mining company examines the option of buying two types of dumpers with the following details.
In order to minimize the operating cost, the optimum fleet of dumpers of Type-1
and Type-2, respectively are
(A) 20, 15
(B) 0, 30
(C) 0, 31
(D) 40, 0
Answer: (A)
42. Let f(x) be a continuous and differentiable function on [3, 18]. If f(3) = −50 and f ′ (x) ≤ 20, then the largest possible value of f(18), is_______. (in integer)
Answer: (250 to 250)
43. Let where TR and T are temperatures in degree centigrade of a room and thermometer, respectively, and t denotes time in minutes. A thermometer at a reading of 2°C is brought in a room of temperature 40° Two minutes later, the thermometer reads 15°C. The time elapsed in minutes when the thermometer reads 39.5°C, is_______. (round off to two decimal places)
Answer: (20.40 to 20.80)
44. In a health centre, the probability of ‘full occupancy’ of COVID beds for a day is 0.8. Assuming Binomial probability distribution, the probability of full occupancy exactly for 5 days in a week, is _______. (round off to three decimal places)
Answer: (0.251 to 0.299)
45. Following information is given for a drilling operation to be carried out for overburden removal in a surface mine.
Volume of rock blasted per round, m3 : 3,20,000
Number of blast holes : 100
Drill hole diameter (D), mm : 200
Length of subgrade drilling : 8D
Stemming length : 25D
Bench height, m : 30
Powder factor, m3/kg : 3.2
The amount of explosive per unit length of charge in kg/m, is _______. (round off to two decimal places)
Answer: (36.00 to 39.00)
46. The shaft-top coordinates of two vertical shafts are given below. The depth of the shaft A and B are 200 m and 149 m, respectively.
The downward gradient of the line joining the bottom of the two shafts in degrees, is _______. (round off to two decimal places)
Answer: (0.90 to 1.13)
47. The oxygen-balanced equation for explosive ANFO is given below.
3NH4NO3 + CH2 → 7H2O + CO2 + 3N2
For 100 litre of fuel oil having density 850 kg/m3, the amount of ammonium nitrate to be mixed, in kg, is_______. (round off to two decimal places)
Answer: (1453.00 to 1458.00)
48. Two weightless cables of equal length and cross sectional area are hanging from a ceiling as shown in the figure. They are connected by a horizontal light bar of length 1.0 m and pulled by a force, F. The modulus of elasticity of Cable-1 and Cable-2 are 50 GPa and 200 GPa, respectively. If the deformation in both the cables is equal, the distance x, in m is_______. (round off to one decimal place)
Answer: (0.8 to 0.8)
49. A circular tunnel of radius 3 m is constructed in a hydrostatic stress field of 15 MPa. The modulus of elasticity and Poisson’s ratio of the rock are 5 GPa and 0.25, respectively. A uniform support pressure pi is applied at tunnel boundary to restrict the radial deformation at the tunnel boundary to 4 mm. The value of pi in MPa is_______. (round off to two decimal places)
Answer: (9.50 to 9.75)
50. The extraction ratio during development of a bord and pillar panel is 0.15 in a flat coal seam. The panel is further extracted by widening the galleries, and the extraction ratio changes to 0.25. The percentage change in pillar stress, considering tributary area method, is_______. (round off to two decimal places)
Answer: (13.00 to 14.00)
51. In a small metal mine a battery powered locomotive hauls a train of mine tubs such that:
The weight of the train of mine tubs, tonne : 3.0
The coefficient of friction between the wheels and the rails : 0.06
The coefficient of adhesion between the loco wheels and the rails : 0.2
Time required from the start to reach speed of 1.8 m/s through constant acceleration, min : 3.0
Upward gradient to be negotiated : 1 in 20
The minimum weight of the locomotive in tonnes to meet these design requirements, is _______. (round off to one decimal place)
Answer: (3.7 to 3.8)
52. A pump lifts mine water of density 1020 kg/m3, at 250 m3/hr from a depth of 150 m. The overall pumping efficiency is 68%. Considering a head loss of 15 m due to pipe friction and shock, the motor input power, in kW is_______. (round off to two decimal places)
Answer: (165.00 to 170.00)
53. In a surface mine bench, overburden is removed by the shovel-dumper combination. For the dumper:
Time required at the loading station : 3.0 min
Time required at the unloading station : 1.0 min
Distance between loading and unloading stations : 4.5 km
Average speed during loaded travel : 12.0 km/hr
Average speed during empty travel : 18.0 km/hr
Minimum number of dumpers required to avoid idle time of the shovel, is _______. (in integer)
Answer: (14 to 14)
54. In a bord and pillar development panel, headings of 4.4 m × 2.5 m are advanced using solid blasting. The average pull per round of blast is 1.2 m. On an average 12 faces are blasted per day. Density of coal is 1500 kg/m3. The mine operates in three shifts. If the average daily employment is 330 persons, labour productivity (OMS) of the panel in tonne, is_______. (round off to two decimal places)
Answer: (0.70 to 0.75)
55. In a longwall face, the full seam thickness of 3 m is cut by a shearer with a web of depth 0.7 m. The hauling speed of shearer during cutting is 12 m/min. The trough cross-section of AFC is 0.4 m2 and the average loading coefficient is 0.7. In order to evacuate coal from the face without spillage, the speed of AFC, in m/s is_______. (round off to one decimal place)
Answer: (1.4 to 1.6)
56. A city is spread over an area of 20 km × 40 km. Wind, at an average speed of 4 m/s, enters perpendicular to the 20 km long side. On a winter day the inversion layer exists over the city at a height of 100 m. PM1 is emitted from the city at a rate of 1 kg/s. The steady state PM1 concentration in the city air, in μg/m3, assuming Box model, is_______. (round off to one decimal place)
Answer: (125.0 to 125.0)
57. The point ‘A’ as shown in the Coward flammability diagram represents the gas composition of a sealed-off area of a coal mine. The volume of the sealed-off area is 10000 m3. Inert gas is proposed to be injected into the sealed-off area so that the gas composition comes below the LEL (lower explosibility limit). The minimum volume of the inert gas required (at the same pressure as that of the sealed-off area), in m3 (round off to one decimal place)
Answer: (2000.0 to 2400.0)
58. An underground workshop has dimensions of 8 m length, 6 m width and 4 m height. Four identical luminaires are placed at the four corners of the roof. Each luminaire is of 100 W capacity with luminous efficacy of 100 lumen/W. Light is transmitted spherically from luminaires and there are no reflections. The illumination on the horizontal plane at the centre of the floor, in lux is_______. (round off to two decimal places)
Answer: (45.00 to 50.00)
59. An underground AC plant requires the delivery of 250 US gpm (15.85 US gpm = 1.0 lps) of chilled water. For this purpose, ice-pellets at 0°C temperature (latent heat of melting, 334 kJ/kg) are mixed with water at 20°C (specific heat 4.18 kJ/kg°C) on the surface. The mixture is adiabatically transported to the underground location such that the water at 7°C becomes available for the AC plant. The requirement of ice-pellets in tonne/hr to meet the design condition, is ______. (round off to two decimal places)
Answer: (7.00 to 7.50)
60. An intake shaft has resistance of 0.05 Ns2/m8 up to a depth of 400 m. The airflow rate is 100 m3/s and the average density is 1.2 kg/m3. A barometer reads 99.375 kPa when placed on surface. Considering acceleration due to gravity is 9.81 m/s2, the reading of the barometer at the depth of 400 m, in kPa is_______. (round off to two decimal places)
Answer: (103.50 to 103.60)
61. The net present values (NPV) of two mining project proposals A and B are as given.
NPVA = −0.01i2 – 0.02i + 4.44
NPVB = −0.03i2 – 0.01i + 6.55
where, i is discount rate.
The required rate of return for which both the proposals have equal possibility of acceptance and rejection, is _______. (round off to two decimal places)
Answer: (10.00 to 11.00)
62. The value of is ______. (round off to two decimal places)
Answer: (0.25 to 0.25)
63. A coal seam of uniform thickness 12 m is dipping at an angle 30° as shown in the figure. The ultimate pit is demarcated based on allowable instantaneous stripping ratio of 10 m3/tonne and safe slope angle of 45°. The density of coal is 1.41 tonne/m3. The length, L in m is_______. (round off to two decimal places)
Answer: (320.00 to 330.00)
64. A mine has a reserve of 150 million tonne (Mt) and is designed for a maximum production capacity of 5 Mt per year. In the first year the production is 2 Mt and it increases by 20% each year. The reserve in Mt that remains at the end of 15 years, is_______. (round off to two decimal places)
Answer: (84.80 to 85.50)
65. Information on Activity-Time duration of a project is provided below
The expected project duration in weeks, is_______. (in integer)