GATE Entrance Paper 2021 | ENTRANCE INDIA

GATE Exam 2021 Computer Science and Information Technology (CS-1) Question Paper With Answer Key

June 8, 2023June 13, 2022 by suresh84

GATE-2021

CS-1: Computer Science and Information Technology

GA-General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. The ratio of boys to girls in a class is 7 to 3.

Among the options below, an acceptable value for the total number of students in the class is:

(A) 21

(B) 37

(D) 73

Answer: (C)

2. A polygon is convex if, for every pair of points, P and Q belonging to the polygon, the line segment PQ lies completely inside or on the polygon.

Which one of the following is NOT a convex polygon?

Answer: (A)

3. Consider the following sentences:

(i) Everybody in the class is prepared for the exam.

(ii) Babu invited Danish to his home because he enjoys playing chess.

Which of the following is the CORRECT observation about the above two sentences?

(A) (i) is grammatically correct and (ii) is unambiguous

(B) (i) is grammatically incorrect and (ii) is unambiguous

(D) (i) is grammatically incorrect and (ii) is ambiguous

Answer: (C)

4. A circular sheet of paper is folded along the lines in the directions shown. The paper, after being punched in the final folded state as shown and unfolded in the reverse order of folding, will look like _______.

Answer: (A)

5. _____ is to surgery as writer is to ________

Which one of the following options maintains a similar logical relation in the above sentence?

(A) Plan, outline

(B) Hospital, library

(D) Medicine, grammar

Answer: (C)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

6. We have 2 rectangular sheets of paper, M and N, of dimensions 6 cm × 1 cm each. Sheet M is rolled to form an open cylinder by bringing the short edges of the sheet together. Sheet N is cut into equal square patches and assembled to form the largest possible closed cube. Assuming the ends of the cylinder are closed, the ratio of the volume of the cylinder to that of the cube is _______

(A) π/2

(B) 3/π

(D) 3π

Answer: (C)

Details of prices of two items P and Q are presented in the above table. The ratio of cost of item P to cost of item Q is 3:4. Discount is calculated as the difference between the marked price and the selling price. The profit percentage is calculated as the ratio of the difference between selling price and cost, to the cost

The discount on item Q, as a percentage of its marked price, is ______

(A) 25

(B) 12.5

(D) 5

Answer: (C)

8. There are five bags each containing identical sets of ten distinct chocolates. One chocolate is picked from each bag.

The probability that at least two chocolates are identical is ___________

(A) 0.3024

(B) 0.4235

(D) 0.8125

Answer: (C)

9. Given below are two statements 1 and 2, and two conclusions I and II.

Statement 1: All bacteria are microorganisms.

Statement 2: All pathogens are microorganisms.

Conclusion I: Some pathogens are bacteria.

Conclusion II: All pathogens are not bacteria.

Based on the above statements and conclusions, which one of the following options is logically CORRECT?

(A) Only conclusion I is correct

(B) Only conclusion II is correct

(D) Neither conclusion I nor II is correct.

Answer: (C OR D)

10. Some people suggest anti-obesity measures (AOM) such as displaying calorie information in restaurant menus. Such measures sidestep addressing the core problems that cause obesity: poverty and income inequality.

Which one of the following statements summarizes the passage?

(A) The proposed AOM addresses the core problems that cause obesity.

(B) If obesity reduces, poverty will naturally reduce, since obesity causes poverty.

(D) AOM are addressing the problem superficially.

Answer: (D)

Computer Science and Information Technology (CS, Set-1)

Q.1 – Q.10 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Suppose that L₁ is a regular-language and L₂ is a context-free language. Which one of the following languages is NOT necessarily context-free?

(A) L₁ ⋂ L₂

(B) L₁ ⋅ L₂

(D) L₁ ⋃ L₂

Answer: (C)

2. Let P be an array containing n integers. Let t be the lowest upper bound on the under of comparisons of the array elements, required to find the minimum and maximum values in an arbitrary array of n elements. Which one of the following choices is correct?

(A) t > 2n – 2

(B)

(D) t > [log₂(n)] and t ≤ n

Answer: (C)

3. Consider the following three functions.

f₁ = 10ⁿ f₂ = n^{log n} f₃ n^√n

Which one of the following options arranges the functions in the increasing order of asymptotic growth rate ?

(A) f₃, f₂, f₁

(B) f₂, f₁, f₃

(D) f₂, f₃, f₁

Answer: (D)

4. Consider the following statements,

S₁ : The sequence of procedure calls corresponds to a preorder traversal of the activation tree.

S₂ : The sequence of procedure returns corresponds to a postorder traversal of the activation tree.

Which one of the following options is correct?

(A) S₁ is true and S₂ is false

(B) S₁ is false and S₂ is true

(D) S₁ is false and S₂ is false

Answer: (C)

5. Consider the following statements.

S₁ : Every SLR(1) grammar is unambiguous but there are certain unambiguous grammas that are not SLR(1)

S₂ : For any context-free grammar, there is a parser that takes at most O(n³) time to parse a string of length n.

Which one of the following options is correct?

(A) S₁ is true and S₂ is false

(B) S₁ is false and S₂ is true

(D) S₁ is false and S₂ is false

Answer: (C)

6. Let the representation of a number in base 3 be 210. What is the hexadecimal representation of the number?

(A) 15

(B) 21

(D) 528

Answer: (A)

7. Let p and q be two propositions. Consider the following two formulae in propositional logic.

Which one of the following choices is correct?

(A) Both S₁ and S₂ are tautologies

(B) S₁ is a tautology but S₂ is not a tautology.

(D) Neither S₁ nor S₂ is a tautology

Answer: (B)

8. Consider the following two statements.

S₁ : Destination MAC address of an ARP reply is a broadcast address.

S₂ : Destination MAC address of an ARP request is a broadcast address.

Which one of the following choices is correct?

(A) Both S₁ and S₂ are true.

(B) S₁ is true and S₂ is false.

(D) Both S₁ and S₂ are false

Answer: (C)

9. Consider the following array.

Which algorithm out of the following options uses the least number of comparisons (among the array elements) to sort the above array in ascending order?

(A) Selection sort

(B) Mergesort

(D) Quicksort using the last element as pivot

Answer: (C)

10. A binary search tree T contains n distinct elements. What is the time complexity of picking an element in T that is smaller than the maximum element in T?

(A) Θ(n log n)

(B) Θ(n)

(D) Θ(1)

Answer: (D)

11. In the context of operating systems, which of the following statement is/are correct with respect to paging?

(A) Paging helps solve the issue of external fragmentation.

(B) Page size has no impact on internal fragmentation.

(D) Multi-level paging is necessary to support pages of different sizes.

Answer: (A; C)

12. Let denote an encoding of an automation M. Suppose that ∑ = {0, 1}.Which of the following languages is/are NOT recursive?

Answer: (D)

13. Suppose a database system crashes gain while recovering from a previous crash. Assume check pointing is not done by the database either during the transactions or during recovery.

Which of the following statements is/are correct?

(A) The same undo and redo list will be used while recovering again.

(B) The system cannot recover any further.

(D) The database will become inconsistent.

Answer: (A)

14. Which of the following standard C library functions will always invoke a system call when executed from a single-threaded process in a UNIX/Linux operating system?

(A) exit

(B) malloc

(D) strlen

Answer: (A; C)

15. Consider a linear list based directory implementation in a file system. Each directory is a list of nodes, where each node contains the file name along with the file metadata, such as the list of pointers to the data blocks. Consider a given directory foo.

Which of the following operations will necessarily require a full scan of foo for successful completion?

(A) Creation of a new file in foo

(B) Deletion of an existing file from foo

(D) Opening of an existing file in foo

Answer: (A; C)

Q.16 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks)

16. In an undirected connected planar graph G, there are eight vertices and five faces. The number of edges in G is ______.

Answer: (11 to 11)

17. Consider the following undirected graph with edge weights as shown:

The number of minimum-weight spanning trees of the graph is _____.

Answer: (3 to 3)

18. The lifetime of a component of a certain type is a random variable whose probability density function is exponentially distributed with parameter 2. For a randomly picked component of this type, the probability that its lifetime exceeds the expected lifetime (rounded to 2 decimal places) is ______.

Answer: (0.35 to 0.39)

19. There are 6 jobs with distinct difficulty levels, and 3 computers with distinct processing speeds. Each job is assigned to a computer such that:

– The fastest computer gets the toughest job and the slowest computer gets the easiest job.

-Every computer gets at least one job.

The number of ways in which this can be done is _______

Answer: (65 to 65)

20. Consider the following expression.

The value of the above expression ( rounded to 2 decimal places) is ________

Answer: (0.25 to 0.25)

21. Consider the following sequence of operations of an empty stack.

Consider the following sequence of operations on any empty queue.

The value of s + q is ______.

Answer: (86 to 86)

22. Consider a computer system with a byte-addressable primary memory of size 2³² Assume the computer system has a direct-mapped cache of size 32 KB (1 KB = 2¹⁰ bytes), and each cache block is of size 64 bytes.

The size of the tag field is ______ bits.

Answer: (17 to 17)

23. A relation r(A, B) in a relational database has 1200 tuples. The attribute A has integer values ranging from 6 to 20, and the attribute B has integer values ranging from 1 to 20. Assume that the attributes A and B are independently distributed.

The estimated number of tuples in the output of σ _(A>10)_⋁_(B=18)(r) is _________.

Answer: (819 to 820 OR 205 to 205)

24. Consider the following representation of a number in IEEE 754 single-precision floating point format with a bias of 127.

S:1 E: 10000001 F: 111110000000000000000000

Here S, E and F denote the sign, exponent and fraction components of the floating point representation.

The decimal value corresponding to the above representation (rounded to 2 decimal places) is _______.

Answer: (-7.75 to -7.75)

25. Three processes arrive at time zero with CPU bursts of 16, 20 and 10 milliseconds. If the scheduler has prior knowledge about the length of the CPU bursts, the minimum achievable average waiting time for these three processes in a non-preemptive scheduler (round to nearest integer) is ______ milliseconds.

Answer: (12 to 12)

Q.26 – Q.39 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: -2/3)

26. Consider the following grammar (that admits a series of declarations, followed by expressions) and the associated syntax directed translation (SDT) actions, given as pseudo-code:

With respect to the above grammar, which one of the following choices is correct?

(A) The actions can be used to correctly type-check any syntactically correct program.

(B) The actions can be used to type-check syntactically correct integer variable declarations and integer expressions.

(D) The actions will lead to an infinite loop.

Answer: (B)

27. The following relation records the age of 500 employees of a company, where empNo (indicating the employee number) is the key:

Consider the following relational algebra expression:

What does the above expression generate?

(A) Employee numbers of only those employees whose age is the maximum.

(B) Employee numbers of only those employees whose age is more than the age of exactly one other employee.

(D) Employee numbers of all employees whose age is the minimum.

Answer: (C)

28. Consider a 3-bit counter, designed using T flip-flops, as shown below:

Assuming the initial state of the counter given by PQR as 000, what are the next three states?

(A) 011, 101, 000

(B) 001, 010, 111

(D) 001, 010, 000

Answer: (A)

29. Assume that a 12-bit hamming codeword consisting of 8-bit data and 4 check bits is d₈d₇d₆d₅c₈d₄d₃d₂c₄d₁c₂c₁, where the data bits and the check bits are given in the following tables:

Which one of the following choices gives the correct values of x and y?

(A) x is 0 and y is 0.

(B) x is 0 and y is 1.

(D) x is 1 and y is 1.

Answer: (A)

30. Consider the following recurrence relation.

Which one of the following options is correct?

(A) T(n) = Θ(n^5/2)

(B) T(n) = Θ(n log n)

(D) T(n) = Θ((log n)^5/2

Answer: (C)

31. Consider the following context-free grammar where the set of terminals is {a, b, c, d, f}.

The following is a partially-filled LL(1) parsing table.

Which one of the following choices represents the correct combination for the numbered cells in the parsing table (“blank” denotes that the corresponding cell is empty)?

Answer: (A)

32. Let r_i(z) and w_i(z) denote read and write operations respectively on a data item z by a transaction T_i. Consider the following two schedules.

Which one of the following option sis correct?

(A) S₁ is conflict serializable, and S₂ is not conflict serializable

(B) S₁ is not conflict serializable, and S₂ is conflict serializable.

(D) Neither S₁ nor S₂ is conflict serializable.

Answer: (B)

33. Consider the relation R(P, Q, S, T, X, Y, Z W) with the following functional dependencies.

PQ → X; P → YX; Q → Y; Y → ZW

Consider the decomposition of the relation R into the constituent relations according to the following two decomposition schemes.

D₁: R = {(P, Q, S, T); (P, T, X); (Q, Y); (Y, Z, W)]

D₂: R = [(P, Q, S); (T, X), (Q, Y); (Y, Z, W)]

Which one of the following options is correct?

(A) D₁ is a lossless decomposition, but D₂ is a lossy decomposition.

(B) D₁ is a lossy decomposition, but D₂ is a lossless decomposition.

(D) Both D₁ and D₂ are lossy decompositions.

Answer: (A)

34. Let G be a group of order 6, and H be a subgroup of G such that 1 < |H| < 6. Which one of the following options is correct?

(A) Both G and H are always cyclic.

(B) G may not be cyclic, but H is always cyclic.

(D) Both G and H may not be cyclic.

Answer: (B)

35. Consider the two statements.

Which one of the following choices is correct?

(A) Both S₁ and S₂ are true

(B) S₁ is true, but S₂ is false.

(D) Both S₁ and S₂ are false

Answer: (D)

36. Let G = (V, E) be an undirected unweighted connected graph. The diameter of G is defined as:

Let M be the adjacency matrix of G.

Define graph G₂ on the same set of vertices with adjacency matrix N, where

Which one of the following statements is true?

(A)

(B)

(D) diam(G) < diam(G₂) ≤ 2 diam(G)

Answer: (A)

37. Consider the following ANSI C program.

Which one of the following options is correct?

(A) The program will not compile successfully.

(B) The program will compile successfully and output 1- when executed.

(D) The program will compile successfully and output 13 when executed.

Answer: (B)

38. Consider the following language.

L = {w ∈ {0, 1}* | w ends with the substring 011}

Which one of the following deterministic finite automata accepts L?

Answer: (D)

39. For a Turing machine M, denotes an encoding of M. Consider the following two languages.

Which one of the following options is correct?

(A) Both L₁ and L₂ are decidable

(B) L₁ is decidable and L₂ is undecidable

(D) Both L₁ and L₂ are undecidable

Answer: (A)

Q.40 – Q.47 Multiple Select Question (MSQ), carry two mark each (no negative marks).

40. Define R_n to be the maximum amount earned by cutting a rod of length n meters into one or more pieces of integer length and selling them. For i > 0, let p[i] denote the selling price of a rod whose length is i meters. Consider the array of prices:

p[1] = 1, p[2] = 5, p[3] = 8, p[4] 9, p[5] = 10, p[6] = 17, p[7] = 18

Which of the following statements is/are correct about R₇?

(A) R₇ = 18

(B) R₇ = 19

(D) R₇ cannot be achieved by a solution consisting of three pieces.

Answer: (A; C)

41. An articulation point in a connected graph is a vertex such that removing the vertex and its incident edges disconnects the graph into two or more connected components.

Let T be a DFS tree obtained by doing DFS in a connected undirected graph G. Which of the following options is/are correct?

(A) Root of T can never be an articulation point in G.

(B) Root of T is an articulation point in G if and only if it has 2 or more children.

(D) If u is an articulation point in G such that x is an ancestor of u in T and y is a descendent of u in T, then all paths from x to y in G must pass through u.

Answer: (B)

42. Consider the following Boolean expression.

Which of the following Boolean expressions is/are equivalent to (complement of F)?

Answer: (B; C; D)

43. A relation R is said to be circular if aRb and bRc together imply cRa. Which of the following options is/are correct?

(A) If a relation S is reflexive and symmetric, then S is an equivalence relation.

(B) If a relation S is circular and symmetric, then S is an equivalence relation.

(D) If a relation S is transitive and circular, then S is an equivalence relation.

Answer: (C)

44. A TCP server application is programmed to listen on port number P on host S. A TCP client is connected to the TCP server over the network.

Consider that while the TCP connection was active, the server machine S crashed and rebooted. Assume that the client does not use the TCP keep alive timer. Which of the following behaviors is/are possible?

(A) If the client was waiting to receive a packet, it may wait indefinitely.

(B) The TCP server application on S can listen on P after reboot.

(D) If the client sends a packet after the server reboot, it will receive a FIN segment.

Answer: (A; B; C)

45. Consider two hosts P and Q connected through a router R. The maximum transfer unit (MTU) value of the link between P and R is 1500 bytes, and between R and Q is 820 bytes.

A TCP segment of size 1400 bytes was transferred from P to Q through R, with IP identification value as 0 x1234. Assume the IP header size is 20 bytes. Further, the packet is allowed to be fragmented, i.e., Don’t Fragment (DF) flag in the IP header is not set by P.

Which of the following statements is/are correct?

(A) Two fragments are created at R and the IP datagram size carrying the second fragment is 620 bytes.

(B) If the second fragment is lost, R will resent the fragment with the IP identification value 0x1234.

(D) TCP destination port can be determined by analyzing only the second fragment.

Answer: (A; C)

46. Consider the following pseudocode, where S is a semaphore initialized to 5 in line ≠2 and counter is a shared variable initialized to 0 in line ≠ Assume that the increment operation in line ≠7 is not atomic.

If five threads execute the function parop concurrently,, which of the following program behavior(s) is/are possible?

(A) The value of counter is 5 after all the threads successfully complete the execution of parop.

(B) The value of counter is 1 after all the threads successfully complete the execution of parop.

(D) There is a deadlock involving all the threads.

Answer: (A; B; D)

47. Consider a dynamic hashing approach for 4-bit integer keys:

(1) There is a main has table of size 4.

(2) The 2 least significant bits of a key is used index into the main has table.

(3) Initially, the main has table entries are empty.

(4) Thereafter, when more keys are hashed into it, to resolve collisions, the set of all keys corresponding to a main hash table entry is organized as a binary tree that grows on demand.

(5) First, the 3^rd least significant bit is used to divided the keys into left and right subtrees.

(6) To resolve more collisions, each node of the binary tree is further sub-divided into left and right subtrees based on the 4^th least significant bit.

(7) A split is done only if it is needed i.e.., only when there is a collision.

Consider the following state of the hash table.

Which of the following sequences of key insertions can cause the above state of the hash table (assume the keys are in decimal notation)?

(A) 5, 9, 4, 13, 10, 7

(B) 9, 5, 10, 6, 7, 1

(D) 9, 5, 13, 6, 10, 14

Answer: (C)

Q.48 – Q.55Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

48. Consider the following ANSI-C function:

Let Z be an array of 10 elements with Z[i] = 1, for all i such that 0 ≤ i ≤ 9. The value returned by SimpleFunction(Z, 10, 2) is ______.

Answer: (1023 to 1023)

49. Consider the sliding window flow-control protocol operating between a sender and a receiver over a full-duplex error-free link. Assume the following:

• The time taken for processing the data frame by the receiver is negligible.

• The time taken for processing the acknowledgement frame by the sender is negligible.

• The sender has infinite number of frames available for transmission.

• The size of the data frame is 2,000 bits and the size of the acknowledgement frame is 10 bits.

• The link data rate in each direction is 1 Mbps (= 10⁶ bits per second).

• One way propagation delay of the link is 100 milliseconds.

The minimum value of the sender’s window size in terms of the number of frames, (rounded to the nearest integer) needed to achieve a link utilization of 50% is _______.

Answer: (50 to 52)

50. Consider the following C code segment:

In a complier, this code segment is represented internally as a directed acyclic graph (DAG). The number of nodes in the DAG is ________.

Answer: (6 to 6)

51. In a pushdown automaton P = (Q, ∑, Γ, δ, q₀, F) a transition of the form,

where p, q ∈ Q, a ∈ ∑ ⋃ {ϵ], and X, Y ∈ Γ ⋃ {ϵ}, represents (q, Y) ∈ δ(p, a, X).

Consider the following pushdown automaton over the input alphabet ∑ = {a, b} and stack alphabet Γ = {≠, A}.

The number of strings of length 100 accepted by the above pushdown automaton is ______.

Answer: (50 to 50)

52. Consider the following matrix.

The largest eigenvalue of the above matrix is ______.

Answer: (3 to 3)

53. A five-stage pipeline has stage delays of 150, 120, 150, 160 and 140 nanoseconds. The registers that are used between the pipeline stages have a delay of 5 nanoseconds each.

The total time to execute 100 independent instructions on this pipeline, assuming there are no pipeline stalls, is _________ nanoseconds.

Answer: (17160 to 17160)

54. A sender (S) transmits a signal, which can be one of the two kinds: H and L with probabilities 0.1 and 0.9 respectively, to a receiver (R).

In the graph below, the weight of edge (u, v) is the probability of receiving v when u is transmitted, where u, v ∈ {H, L}. For example, the probability that the received signal is L given the transmitted signal was H, is 0.7.

If the received signal is H, the probability that the transmitted signal was H (rounded to 2 decimal places) is ________.

Answer: (0.04 to 0.04)

55. Consider the following instruction sequence where registers R1, R2 and R3 are general purpose and MEMORY[X] denotes the content at the memory location X.

Assume that the content of the memory location 5000 is 10, and the content of the register R3 is 3000. The content of each of the memory locations from 3000 to 3010 is 50. The instruction sequence starts from the memory location 1000. All the numbers are in decimal format. Assume that the memory is byte addressable.

After the execution of the program, the content of memory location 3010 is _______.

Answer: (50 to 50)

GATE Exam 2021 Chemical Engineering (CH) Question Paper With Answer Key

June 8, 2023June 13, 2022 by suresh84

GATE-2021

CH: Chemical Engineering

GA-General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. The ratio of boys to girls in a class is 7 to 3.

Among the options below, an acceptable value for the total number of students in the class is:

(A) 21

(B) 37

(D) 73

Answer: (C)

2. A polygon is convex if, for every pair of points, P and Q belonging to the polygon, the line segment PQ lies completely inside or on the polygon.

Which one of the following is NOT a convex polygon?

Answer: (A)

3. Consider the following sentences:

(i) Everybody in the class is prepared for the exam.

(ii) Babu invited Danish to his home because he enjoys playing chess.

Which of the following is the CORRECT observation about the above two sentences?

(A) (i) is grammatically correct and (ii) is unambiguous

(B) (i) is grammatically incorrect and (ii) is unambiguous

(D) (i) is grammatically incorrect and (ii) is ambiguous

Answer: (C)

Answer: (A)

5. _____ is to surgery as writer is to ________

Which one of the following options maintains a similar logical relation in the above sentence?

(A) Plan, outline

(B) Hospital, library

(D) Medicine, grammar

Answer: (C)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

(A) π/2

(B) 3/π

(D) 3π

Answer: (C)

The discount on item Q, as a percentage of its marked price, is ______

(A) 25

(B) 12.5

(D) 5

Answer: (C)

8. There are five bags each containing identical sets of ten distinct chocolates. One chocolate is picked from each bag.

The probability that at least two chocolates are identical is ___________

(A) 0.3024

(B) 0.4235

(D) 0.8125

Answer: (C)

9. Given below are two statements 1 and 2, and two conclusions I and II.

Statement 1: All bacteria are microorganisms.

Statement 2: All pathogens are microorganisms.

Conclusion I: Some pathogens are bacteria.

Conclusion II: All pathogens are not bacteria.

Based on the above statements and conclusions, which one of the following options is logically CORRECT?

(A) Only conclusion I is correct

(B) Only conclusion II is correct

(D) Neither conclusion I nor II is correct.

Answer: (C OR D)

Which one of the following statements summarizes the passage?

(A) The proposed AOM addresses the core problems that cause obesity.

(B) If obesity reduces, poverty will naturally reduce, since obesity causes poverty.

(D) AOM are addressing the problem superficially.

Answer: (D)

Chemical Engineering (CH)

Q.1 – Q.15 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. An ordinary differential equation (ODE), with an initial condition y(0) = 1, has the analytical solution y = e^2x.

Using Runge-Kutta second order method, numerically integrate the ODE to calculate y at x = 0. 5 using a step size of h = 0. 5.

If the relative percentage error is defined as, then the value of ε at x = 0.5 is ________.

(A) 0.06

(B) 0.8

(D) 8.0

Answer: (D)

2. The function cos(x) is approximated using Taylor series around x = 0 as cos(x) ≈ 1 + a x + bx² + cx³ + d x⁴. The values of a, b, c and d are

(A) a = 1, b = −0.5, c = −1, d = −0.25

(B) a = 0, b = −0.5, c = 0, d = 0.042

(D) a = −0.5, b = 0, c = 0.042, d = 0

Answer: (B)

3. The heat of combustion of methane, carbon monoxide and hydrogen are P, Q and R respectively. For the reaction below, CH₄ + H₂O → CO + 3H₂ the heat of reaction is given by

(A) P − Q − 3R

(B) Q + 3R − P

(D) Q + R − P

Answer: (A)

4. A batch settling experiment is performed in a long column using a dilute dispersion containing equal number of particles of type A and type B in water (density 1000 kg m^–3) at room temperature.

Type A are spherical particles of diameter 30 μm and density 1100 kg m^–3.

Type B are spherical particles of diameter 10 μm and density 1900 kg m^–3.

Assuming that Stokes’ law is valid throughout the duration of the experiment, the settled bed would

(A) consist of a homogeneous mixture of type A and type B particles

(B) consist of type B particles only

(D) be completely segregated with type A particles on top of type B particles

Answer: (A)

5. A three-dimensional velocity field is given by V = 5x²y i + Cy j − 10xyz k, where i,j, k are the unit vectors in x, y, z directions, respectively, describing a cartesian coordinate system. The coefficient C is a constant. If V describes an incompressible fluid flow, the value of C is

(A) −1

(B) 0

(D) 5

Answer: (B)

6. Heat transfer coefficient for a vapor condensing as a film on a vertical surface is given by

(A) Dittus-Boelter equation

(B) Nusselt theory

(D) Sieder-Tate equation

Answer: (B)

7. In a double-pipe heat exchanger of 10 m length, a hot fluid flows in the annulus and a cold fluid flows in the inner pipe. The temperature profiles of the hot (T_h) and cold (T_c) fluids along the length of the heat exchanger (x, such that x ≥ 0), are given by

Th(x) = 80 − 3x

Tc(x) = 20 + 2x

where T_h and T_c are in °C, and x is in meter.

The logarithmic mean temperature difference (in °C) is

(A) 24.6

(B) 27.9

(D) 50.0

Answer: (B)

8. For a shell-and-tube heat exchanger, the clean overall heat transfer coefficient is calculated as 250 Wm^–2K^–1 for a specific process condition. It is expected that the heat exchanger may be fouled during the operation, and a fouling resistance of 0.001 m²KW^–1 is prescribed. The dirt overall heat transfer coefficient is _____ W m^–2 K^–1.

(A) 100

(B) 150

(D) 250

Answer: (C)

9. In reverse osmosis, the hydraulic pressure and osmotic pressure at the feed side of the membrane are P₁ and π₁, respectively. The corresponding values are P₂ and π₂ at the permeate side. The membrane, feed, and permeate are at the same temperature. For equilibrium to prevail, the general criterion that should be satisfied is

(A) π₁ = π₂

(B) P₁ = P₂

(D) P₁ – π₁ = P₂ – π₂

Answer: (D)

10. Ethylene adsorbs on the vacant active sites V of a transition metal catalyst according to the following mechanism.

If NT, NV and denote the total number of active sites, number of vacant active sites and number of adsorbed C2H4 molecules, respectively, the balance on the total number of active sites is given by

Answer: (B)

11. Which of the following is NOT a standard to transmit measurement and control signals?

(A) 4 – 20 mA

(B) 3 – 15 psig

(D) 1 – 5 VDC

Answer: (C)

12. A feedforward controller can be used only if

(A) the disturbance variable can be measured

(B) the disturbance variable can be manipulated

(D) regulatory control is not required

Answer: (A)

13. Turnover ratio is defined as

Answer: (B)

14. A principal amount is charged a nominal annual interest rate of 10%. If the interest rate is compounded continuously, the final amount at the end of one year would be

(A) higher than the amount obtained when the interest rate is compounded monthly

(B) lower than the amount obtained when the interest rate is compounded annually

(D) equal to the amount obtained when using an effective interest rate of 27.18%

Answer: (A)

15. Match the common name of chemicals in Group – 1 with their chemical formulae in Group – 2.

The correct combination is:

(A) P – III, Q – II, R – I

(B) P – III, Q – I, R – II

(D) P – II, Q – I, R – III

Answer: (C)

Q.16 – Q.18 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).

16. For the function the CORRECT statement(s) is/are

(A) f(x) is continuous at x = 1

(B) f(x) is differentiable at x = 1

(D) f(x) is differentiable at x = 0

Answer: (A; B; C)

17. Feed solution F is contacted with solvent B in an extraction process. Carrier liquid in the feed is A and the solute is C. The ternary diagram depicting a single ideal stage extraction is given below. The dashed lines represent the tie-lines.

The CORRECT option(s) is/are

(A) For the tie-lines shown, concentration of solute in the extract is higher than that in the raffinate

(B) Maximum amount of solvent is required if the mixture composition is at W

(D) U represents the raffinate composition if the mixture composition is at M

Answer: (A; C; D)

18. The inherent characteristics of three control valves P, Q and R are shown in the figure.

The CORRECT option(s) is/are

(A) P is a quick opening valve

(B) Q is a quick opening valve

(D) R is an equal percentage valve

Answer: (A; D)

Q.19 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

19. A source placed at the origin of a circular sample holder (radius r = 1 m) emits particles uniformly in all directions. A detector of length l = 1 cm has been placed along the perimeter of the sample holder. During an experiment, the detector registers 14 particles.

The total number of particles emitted during the experiment is ______.

Answer: (8790 to 8800)

20. A, B, C and D are vectors of length 4.

It is known that B is not a scalar multiple of A. Also, C is linearly independent of A and B. Further, D = 3 A + 2 B + C.

The rank of the matrix is _______.

Answer: (3 to 3)

21. The van der Waals equation of state is given by

where P_r, T_r and v_r represent reduced pressure, reduced temperature and reduced molar volume, respectively. The compressibility factor at critical point (z_c) is 3/8.

If v_r = 3 and T_r = 4/3, then the compressibility factor based on the van der Waals equation of state is _________ (round off to 2 decimal places).

Answer: (0.83 to 0.85)

22. Consider a steady flow of an incompressible, Newtonian fluid through a smooth circular pipe. Let α_laminar and α_turbulent denote the kinetic energy correction factors for laminar and turbulent flow through the pipe, respectively. For turbulent flow through the pipe

Here, is the average velocity, V0 is the centerline velocity, and n is a parameter. The ratio of average velocity to the centerline velocity for turbulent flow through the pipe is given by

For n = 7, the value of is ______ (round off to 2 decimal places.)

Answer: (0.52 to 0.54)

23. The molar heat capacity at constant pressure Cp (in J mol^–1 K^–1) for n-pentane as a function of temperature (T in K) is given by 46 + 45.4 × 10⁻³T – 14.1 × 10⁻⁶ T². Take R = 8.314 J mol⁻¹K⁻¹.

At 1000 K, the rate of change of molar entropy of n-pentane with respect to temperature at constant pressure is ___________ J mol^–1 K^–2 (round off to 2

decimal places).

Answer: (0.27 to 0.29)

24. The following homogeneous liquid phase reactions are at equilibrium.

The values of rate constants are given by: k₁ = 0.1 s^–1, k^–1 = 0.2 s^–1, k₂ = 1 s^–1 k_–2 = 10 s^–1, k₃ = 10 s^–1.

The value of rate constant k^–3 is ______________ s^–1 (round off to 1 decimal

place).

Answer: (0.5 to 0.5)

25. A company invests in a recovery unit to separate valuable metals from effluent streams. The total initial capital investment of this unit is Rs. 10 lakhs. The recovered metals are worth Rs. 4 lakhs per year.

If the annual return on this investment is 15%, the annual operating costs should be ________ lakhs of rupees (correct to 1 decimal place).

Answer: (2.5 to 2.5)

Q.26 – Q.33 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

26. Let A be a square matrix of size n × n (n > 1). The elements of A = {a_ij} are given by

The determinant of A is

(A) 0

(B) 1

(D) (n!)²

Answer: (D)

27. Consider a fluid confined between two horizontal parallel plates and subjected to shear flow.

In the first experiment, the plates are separated by a distance of 1 mm. It is found that a shear stress of 2 N m^–2 has to be applied to keep the top plate moving with a velocity of 2 m s^–1, while the other plate is fixed.

In the second experiment, the plates are separated by a distance of 0.25 mm. It is found that a shear stress of 3 N m^–2 has to be applied to keep the top plate moving with a velocity of 1 m s^–1, while the other plate is fixed.

In the range of shear rates studied, the rheological character of the fluid is

(A) Newtonian

(B) Pseudoplastic

(D) Ideal and inviscid

Answer: (B)

28. Water of density 1000 kg m^–3 flows in a horizontal pipe of 10 cm diameter at an average velocity of 0.5 m s^–1. The following plot shows the pressure measured at various distances from the pipe entrance.

Using the data shown in the figure, the Fanning friction factor in the pipe when the flow is FULLY DEVELOPED is

(A) 0.0012

(B) 0.0074

(D) 0.0106

Answer: (B)

29. In a solvent regeneration process, a gas is used to strip a solute from a liquid in a countercurrent packed tower operating under isothermal condition. Pure gas is used in this stripping operation. All solutions are dilute and Henry’s law, y* = mx, is applicable. Here, y* is the mole fraction of the solute in the gas phase in equilibrium with the liquid phase of solute mole fraction x, and m is the Henry’s law constant.

Let x₁ be the mole fraction of the solute in the leaving liquid, and x₂ be the mole fraction of solute in the entering liquid.

When the value of the ratio of the liquid-to-gas molar flow rates is equal to m, the overall liquid phase Number of Transfer Units, NTUOL, is given by

Answer: (A)

30. Which of these symbols can be found in piping and instrumentation diagrams?

(A) (Q) and (S) only

(B) (P), (Q) and (R) only

(D) (P), (Q), (R) and (S)

Answer: (C)

31. It is required to control the volume of the contents in the jacketed reactor shown in the figure.

Which one of the following schemes can be used for feedback control?

(A) Measure L101 and manipulate valve V-2

(B) Measure T101 and manipulate valve V-1

(D) Measure F101 and manipulate valve V-1

Answer: (C)

32. Which of the following is NOT a necessary condition for a process under closed-loop control to be stable?

(A) Dead-time term(s) must be absent in the open-loop transfer function

(B) Roots of the characteristic equation must have negative real part

(D) Open-loop transfer function must have an amplitude ratio less than 1 at the critical frequency

Answer: (A)

33. Match the reaction in Group – 1 with the reaction type in Group – 2.

The correct combination is:

(A) P – II, Q – III, R – I, S – IV

(B) P – III, Q – IV, R – I, S – II

(D) P – I, Q – IV, R – III, S – II

Answer: (B)

Q.34 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

34. To solve an algebraic equation f(x) = 0, an iterative scheme of the type x_n+1 = g(x_n) is proposed, where

At the solution x = s, g’(s) = 0 and g’’(s) ≠ 0.

The order of convergence for this iterative scheme near the solution is __________.

Answer: (2 to 2)

35. The probability distribution function of a random variable X is shown in the following figure.

From this distribution, random samples with sample size n = 68 are taken. If is the sample mean, the standard deviation of the probability distribution of , i.e. is ______ (round off to 3 decimal places).

Answer: (0.069 to 0.071)

36. For the ordinary differential equation

with initial conditions y(0) = y'(0) = y”(0) = ”'(0) = 0, the value of _______ (round off to 3 decimal places).

Answer: (0.161 to 0.169)

37. Formaldehyde is produced by the oxidation of methane in a reactor. The following two parallel reactions occur.

CH₄ + O₂ → HCHO + H₂O

CH₄ + 2O₂ → CO₂ + 2H₂O

Methane and oxygen are fed to the reactor. The product gases leaving the reactor include methane, oxygen, formaldehyde, carbon dioxide and water vapor.

60 mol s–1 of methane enters the reactor. The molar flowrate (in mol s^–1) of CH₄, O₂ and CO₂ leaving the reactor are 26, 2 and 4, respectively. The molar flowrate of oxygen entering the reactor is _______________ mol s^–1.

Answer: (40 to 40)

38. The combustion of carbon monoxide is carried out in a closed, rigid and insulated vessel. 1 mol of CO, 0.5 mol of O₂ and 2 mol of N₂ are taken initially at 1 bar and 298 K, and the combustion is carried out to completion.

The standard molar internal energy change of reaction (∆u°_R) for the combustion of carbon monoxide at 298 K = –282 kJ mol^–1. At constant pressure, the molar heat capacities of N₂ and CO₂ are 33.314 J mol^–1 K^–1 and 58.314 J mol^–1 K^–1, respectively. Assume the heat capacities to be independent of temperature, and the gases are ideal. Take R = 8.314 J mol^–1 K^–1.

The final pressure in the vessel at the completion of the reaction is _______ bar (round off to 1 decimal place).

Answer: (8.9 to 9.1)

39. A gaseous mixture at 1 bar and 300 K consists of 20 mol % CO₂ and 80 mol% inert gas.

Assume the gases to be ideal. Take R = 8.314 J mol^–1 K^–1.

The magnitude of minimum work required to separate 100 mol of this mixture at 1 bar and 300 K into pure CO₂ and inert gas at the same temperature and pressure is __________ kJ (round off to nearest integer).

Answer: (124 to 126)

40. A binary liquid mixture consists of two species 1 and 2. Let γ and x represent the activity coefficient and the mole fraction of the species, respectively. Using a molar excess Gibbs free energy model, ln γ₁ x₁and ln γ₂ vs. x₁ are plotted. A tangent drawn to the ln γ₁ vs. x₁ curve at a mole fraction of x₁ = 0. 2 has a slope = −1.728.

The slope of the tangent drawn to the ln γ₂ vs. x₁ curve at the same mole fraction is ______ (correct to 3 decimal places).

Answer: (0.432 to 0.432)

41. Consider a tank filled with 3 immiscible liquids A, B and C at static equilibrium, as shown in the figure. At 2 cm below the liquid A – liquid B interface, a tube is connected from the side of the tank. Both the tank and the tube are open to the atmosphere.

At the operating temperature and pressure, the specific gravities of liquids A, B and C are 1, 2 and 4, respectively. Neglect any surface tension effects in the calculations. The length of the tube L that is wetted by liquid B is _____________ cm.

Answer: (8 to 8)

42. Seawater is passed through a column containing a bed of resin beads.

Density of seawater = 1025 kg m^–3

Density of resin beads = 1330 kg m^–3

Diameter of resin beads = 50 μm

Void fraction of the bed at the onset of fluidization = 0.4

Acceleration due to gravity = 9.81 m s^–2

The pressure drop per unit length of the bed at the onset of fluidization is ___________ Pa m^–1 (round off to nearest integer).

Answer: (1790 to 1800)

43. A straight fin of uniform circular cross section and adiabatic tip has an aspect ratio (length/diameter) of 4. If the Biot number (based on radius of the fin as the characteristic length) is 0.04, the fin efficiency is __________ % (round off to nearest integer).

Answer: (42 to 44)

44. A double-effect evaporator is used to concentrate a solution. Steam is sent to the first effect at 110°C and the boiling point of the solution in the second effect is 63.3° The overall heat transfer coefficient in the first effect and second effect are 2000 W m^–2 K^–1 and 1500 W m^–2 K^–1, respectively. The heat required to raise the temperature of the feed to the boiling point can be neglected. The heat flux in the two evaporators can be assumed to be equal.

The temperature at which the solution boils in the first effect is _______ °C (round off to nearest integer).

Answer: (89 to 91)

45. Consider a solid slab of thickness 2L and uniform cross section A. The volumetric rate of heat generation within the slab is ġ (W m^–3). The slab loses heat by convection at both the ends to air with heat transfer coefficient h. Assuming steady state, one-dimensional heat transfer, the temperature profile within the slab along the thickness is given by:

where k is the thermal conductivity of the slab and T_s is the surface temperature. If T_s = 350 K, ambient air temperature T_∞ = 300 K, and Biot number (based on L as the characteristic length) is 0.5, the maximum temperature in the slab is ___________ K (round off to nearest integer).

Answer: (362 to 363)

46. A distillation column handling a binary mixture of A and B is operating at total reflux. It has two ideal stages including the reboiler. The mole fraction of the more volatile component in the residue (x_W) is 0.1. The average relative volatility α_AB is 4. The mole fraction of A in the distillate (x_D) is ___________ (round off to 2 decimal places).

Answer: (0.63 to 0.65)

47. In a batch drying experiment, a solid with a critical moisture content of 0.2 kg H₂O/kg dry solid is dried from an initial moisture content of 0.35 kg H₂O/kg dry solid to a final moisture content of 0.1 kg H₂O/kg dry solid in 5 h. In the constant rate regime, the rate of drying is 2 kg H₂O/(m².h).

The entire falling rate regime is assumed to be uniformly linear. The equilibrium moisture content is assumed to be zero.

The mass of the dry solid per unit area is ___________ kg/m² (round off to nearest integer).

Answer: (34 to 35)

48. As shown in the figure below, air flows in parallel to a freshly painted solid surface of width 10 m, along the z-direction.

The equilibrium vapor concentration of the volatile component A in the paint, at the air-paint interface, is C_A,i. The concentration C_A decreases linearly from this value to zero along the y-direction over a distance δ of 0.1 m in the air phase. Over this distance, the average velocity of the air stream is 0.033 m s^–1 and its velocity profile (in m s-1) is given by v_z(y) = 10 y²

where y is in meter.

Let C_A,m represent the flow averaged concentration. The ratio of C_A,m to C_A,i , is _______________ (round off to 2 decimal places).

Answer: (0.24 to 0.26)

49. The following isothermal autocatalytic reaction, A + B → 2B (−r_A) = 0.1C_AC_B (mol L⁻¹ s⁻¹) is carried out in an ideal continuous stirred tank reactor (CSTR) operating at steady state. Pure A at 1 mol L^–1 is fed, and 90% of A is converted in the CSTR. The space time of the CSTR is ___________ seconds.

Answer: (100 to 100)

50. Reactant A decomposes to products B and C in the presence of an enzyme in a well-stirred batch reactor. The kinetic rate expression is given by

If the initial concentration of A is 0.02 mol L^–1, the time taken to achieve 50% conversion of A is _________ min (round off to 2 decimal places).

Answer: (4.44 to 4.51)

51. The following homogeneous, irreversible reaction involving ideal gases, A → B + C (−r_A) = 0.5C_A (mol L⁻¹s⁻¹) is carried out in a steady state ideal plug flow reactor (PFR) operating at isothermal and isobaric conditions. The feed stream consists of pure A, entering at 2 m s^–1.

In order to achieve 50% conversion of A, the required length of the PFR is _____________ meter (round off to 2 decimal places).

Answer: (3.49 to 3.61)

52. A system has a transfer function When a step change of magnitude M is given to the system input, the final value of the system output is measured to be 120. The value of M is ___________.

Answer: (40 to 40)

53. A process has a transfer function Initially the process is at steady state with x(t = 0) = 0. 4 and y(t = 0) = 100. If a step change in x is given from 0.4 to 0.5, the maximum value of y that will be observed before it reaches the new steady state is ___________ (round off to 1 decimal place).

Answer: (102.4 to 102.6)

54. Operating labor requirements L in the chemical process industry is described in terms of the plant capacity C (kg day^–1) over a wide range (10³ – 10⁶) by a power law relationship L = αC^β

where α and β are constants. It is known that

L is 60 when C is 2 × 10⁴

L is 70 when C is 6 × 10⁴

The value of L when C is 10⁵ kg day^–1 is ______________ (round off to nearest integer).

Answer: (73 to 77)

55. A viscous liquid is pumped through a pipe network in a chemical plant. The annual pumping cost per unit length of pipe is given by

The annual cost of the installed piping system per unit length of pipe is given by C_piping = 45.92D

Here, D is the inner diameter of the pipe in meter, q is the volumetric flowrate of the liquid in m³ s^–1 and μ is the viscosity of the liquid in Pa.s. and the volumetric flow rate of the liquid is 10^–4 m³ s^–1, the economic inner diameter of the pipe is ________ meter (round off to 3 decimal places).

Answer: (0.014 to 0.016)

GATE Exam 2021 Civil Engineering (CE-2) Question Paper With Answer Key

June 8, 2023June 13, 2022 by suresh84

GATE-2021

CE2: Civil Engineering

GA-General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. (i) Arun and Aparna are here.

(ii) Arun and Aparna is here.

(iii) Arun’s families is here.

(iv) Arun’s family is here.

Which of the above sentences are grammatically CORRECT?

(A) (i) and (ii)

(B) (i) and (iv)

(D) (iii) and (iv)

Answer: (B)

3. Two identical cube shaped dice each with faces numbered 1 to 6 are rolled simultaneously. The probability that an even number is rolled out on each dice is:

(A) 1/36

(B) 1/12

(D) 1/4

Answer: (D)

4. ⊕ and ⊙ are two operators on numbers p and q such that p ⊙ q = p – q, and p ⊕ q – p × q

Then, (9 ⊙ (6 ⊕ 7)) ⨀ (7 ⊕ (6 ⊙ 5) =

(A) 40

(B) -26

(D) -40

Answer: (D)

5. Four persons P, Q, R and S are to the seated in a row, R should not be seated at the second position from the left end of the row. The number of distinct seating arrangement possible is:

(A) 6

(B) 9

(D) 24

Answer: (C)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

6. On a planar field, you travelled 3 units East from a point O. Next you travelled 4 units South to arrive at point P. Then you travelled from P in the North-East direction such that you arrive at a point that is 6 units East of point O. Next, you travelled in the North-West direction, so that you arrive at point Q that is 18 units North of Point P.

The distance of point Q to point O, in the same units, should be_____

(A) 3

(B) 4

(D) 6

Answer: (C)

7. The author said, “Musicians rehearse before their concerts. Actors rehearse their roles before the opening of a new play, On the other hand, I find it strange that many public speakers think key can just walk on to the stage and start speaking. In my opinion, it is no less important for public speakers to rehearse their talks.”

Based on the above passage, which one of the following is TRUE?

(A) The author is of the opinion that rehearsing is important for musicians, actors and public speakers.

(B) The author is of the opinion that rehearsing is less important for public speakers than for musicians and actors.

(D) The author is of the opinion that rehearsal is more important for actors than musicians.

Answer: (A)

8. (1) Some football players play cricket.

(2) All cricket players play hockey.

Among the options given below, the statement that logically follows from the two statements 1 and 2 above, is:

(A) No football player plays hockey.

(B) Some football players play hockey.

(D) All hockey players play football.

Answer: (B)

9. In the figure shown above, PQRS is a square. The shaded portion is formed by the intersection of sectors of circles with radius equal to the side of the square and centers at S and Q.

The probability that any point picked randomly within the square falls in the shaded area is______

(A)

(B) 1/2

(D) π/4

Answer: (C)

10. In an equilateral triangle PQR, side PQ is divided into four equal parts, side QR is divided into six equal parts and side PR is divided into eight equal parts. The length of each subdivided part in cm is an integer.

The minimum area of the triangle PQR possible, in cm², is

(A) 18

(B) 24

(D) 144√3

Answer: (D)

Civil Engineering (CE, Set-2)

Q.1 – Q.16 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. The value of is

(A) 0

(B) 1.0

(D) ∞

Answer: (A)

2. The rank of the matrix is

(A) 1

(B) 2

(D) 4

Answer: (C)

3. The unit normal vector to the surface X² + Y² + Z² – 48 = 0 at the point (4, 4, 4) is

Answer: (B)

4. If A is a square matrix then orthogonality property mandates

(A) AA^T = I

(B) AA^T = 0

(D) AA^T = A²

Answer: (A)

5. In general, the CORRECT sequence of surveying operations is

(A) Field observations → Reconnaissance → Data analysis → Map making

(B) Data analysis → Reconnaissance → Field observations → Map making

(D) Reconnaissance → Data analysis → Field observations → Map making

Answer: (C)

6. Strain hardening of structural steel means

(A) experiencing higher stress than yield stress with increased deformation

(B) strengthening steel member externally for reducing strain experienced

(D) decrease in the stress experienced with increasing strain

Answer: (A)

7. A single story building model is shown in the figure. The rigid bar of mass ‘m’ is supported by three massless elastic columns whose ends are fixed against rotation. For each of the columns, the applied lateral force (P) and corresponding moment (M) are also shown in the figure. The lateral deflection (δ) of the bar is given by where L is the effective length of the column, E is the Young’s modulus of elasticity and I is the area moment of inertia of the column cross-section with respect to its neutral axis.

For the lateral deflection profile of the columns as shown in the figure, the natural frequency of the system for horizontal oscillation is

Answer: (A)

8. Seasoning of timber for use in construction is done essentially to

(A) increase strength and durability

(B) smoothen timber surfaces

(D) cut timber in right season and geometry

Answer: (A)

9. In case of bids in Two-Envelop System, the correct option is

(A) Technical bid is opened first

(B) Financial bid is opened first

(D) Either of the two (Technical and Financial) bids can be opened first

Answer: (A)

10. The most appropriate triaxial test to assess the long-term stability of an excavated clay slope is

(A) consolidated drained test

(B) unconsolidated undrained test

(D) unconfined compression test

Answer: (A)

11. As per the Unified Soil Classification System (USCS), the type of soil represented by ‘MH’ is

(A) Inorganic silts of high plasticity with liquid limit more than 50%

(B) Inorganic silts of low plasticity with liquid limit less than 50%

(D) Inorganic clays of low plasticity with liquid limit more than 50%

Answer: (A)

12. The ratio of the momentum correction factor to the energy correction factor for a laminar flow in a pipe is

(A) 1/2

(B) 2/3

(D) 3/2

Answer: (B)

13. Relationship between traffic speed and density is described using a negatively sloped straight line. If v_f is the free-flow speed then the speed at which the maximum flow occurs is

(A) 0

(B) v_f/4

(D) v_f

Answer: (C)

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

Assertion [a]: One of the best ways to reduce the amount of solid wastes is to reduce the consumption of raw materials.

Reason [r]: Solid wastes are seldom generated when raw materials are converted to goods for consumption.

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

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

(D) [a] is true but [r] is false

Answer: (D)

15. The hardness of a water sample is measured directly by titration with 0.01 M solution of ethylenediamine tetraacetic acid (EDTA) using eriochrome black T (EBT) as an indicator. The EBT reacts and forms complexes with divalent metallic cations present in the water. During titration, the EDTA replaces the EBT in the complex. When the replacement of EBT is complete at the end point of the titration, the colour of the solution changes from

(A) blue-green to reddish brown

(B) blue to colourless

(D) wine red to blue

Answer: (D)

16. The softening point of bitumen has the same unit as that of

(A) distance

(B) temperature

(D) viscosity

Answer: (B)

Q.17 Multiple Select Question (MSQ), carry ONE mark (no negative marks).

17. Which of the following statement(s) is/are correct?

(A) Increased levels of carbon monoxide in the indoor environment result in the formation of carboxyhemoglobin and the long term exposure becomes a cause of cardiovascular diseases.

(B) Volatile organic compounds act as one of the precursors to the formation of photochemical smog in the presence of sunlight.

(C) Long term exposure to the increased level of photochemical smog becomes a cause of chest constriction and irritation of the mucous membrane.

(D) Increased levels of volatile organic compounds in the indoor environment will result in the formation of photochemical smog which is a cause of cardiovascular diseases.

Answer: (A; B; C)

Q.18 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

18. The value (round off to one decimal place) of is______

Answer: (0.0 to 0.0)

19. A solid circular torsional member OPQ is subjected to torsional moments as shown in the figure (not to scale). The yield shear strength of the constituent material is 160 MPa.

The absolute maximum shear stress in the member (in MPa, round off to one decimal place) is ______________

Answer: (14 to 16)

20. A propped cantilever beam XY, with an internal hinge at the middle, is carrying a uniformly distributed load of 10 kN/m, as shown in the figure.

The vertical reaction at support X (in kN, in integer) is _____________

Answer: (30 to 30)

21. The internal (d_i) and external (d_o) diameters of a Shelby sampler are 48 mm and 52 mm, respectively. The area ratio (A_r) of the sampler (in %, round off to two decimal places) is ____________

Answer: (17.25 to 17.45)

22. A 12-hour unit hydrograph (of 1 cm excess rainfall) of a catchment is of a triangular shape with a base width of 144 hour and a peak discharge of 23 m³/s. The area of the catchment (in km2, round off to the nearest integer) is ____________

Answer: (595 to 598)

23. A lake has a maximum depth of 60 m. If the mean atmospheric pressure in the lake region is 91 kPa and the unit weight of the lake water is 9790 N/m³, the absolute pressure (in kPa, round off to two decimal places) at the maximum depth of the lake is ___________

Answer: (677.50 to 679.50)

24. In a three-phase signal system design for a four-leg intersection, the critical flow ratios for each phase are 0.18, 0.32, and 0.22. The total loss time in each of the phases is 2 s. As per Webster’s formula, the optimal cycle length (in s, round off to the nearest integer) is _______.

Answer: (48 to 52)

25. A horizontal angle θ is measured by four different surveyors multiple times and the values reported are given below.

The most probable value of the angle θ (in degree, round off to two decimal places) is _________

Answer: (36 to 36)

Q.26 – Q.35 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

26. If k is a constant, the general solution of will be in the form of

(A) y = xln( kx)

(B) y = k ln(kx)

(D) y = xkln(k)

Answer: (A)

27. The smallest eigenvalue and the corresponding eigenvector of the matrix respectively are

Answer: (A)

28. A prismatic steel beam is shown in the figure.

The plastic moment, M_p calculated for the collapse mechanism using static method and kinematic method is

Answer: (C)

29. A frame EFG is shown in the figure. All members are prismatic and have equal flexural rigidity. The member FG carries a uniformly distributed load w per unit length. Axial deformation of any member is neglected.

Considering the joint F being rigid, the support reaction at G is

(A) 0.375 wL

(B) 0.453 wL

(D) 0.500 wL

Answer: (C)

30. A clay layer of thickness H has a preconsolidation pressure p_c and an initial void ratio e₀. The initial effective overburden stress at the mid-height of the layer is p₀. At the same location, the increment in effective stress due to applied external load is Δ_p. The compression and swelling indices of the clay are Cc and Cs, respectively. If p₀ < p_c < (p₀ + ∆p), then the correct expression to estimate the consolidation settlement (s_c ) of the clay layer is

Answer: (B)

31. A rectangular open channel of 6 m width is carrying a discharge of 20 m³/s. Consider the acceleration due to gravity as 9.81 m/s² and assume water as incompressible and inviscid. The depth of flow in the channel at which the specific energy of the flowing water is minimum for the given discharge will then be

(A) 0.82 m

(B) 1.04 m

(D) 3.18 m

Answer: (B)

32. Read the statements given below.

(i) Value of the wind profile exponent for the ‘very unstable’ atmosphere is smaller than the wind profile exponent for the ‘neutral’ atmosphere.

(ii) Downwind concentration of air pollutants due to an elevated point source will be inversely proportional to the wind speed.

(iii)Value of the wind profile exponent for the ‘neutral’ atmosphere is smaller than the wind profile exponent for the ‘very unstable’ atmosphere.

(iv) Downwind concentration of air pollutants due to an elevated point source will be directly proportional to the wind speed.

Select the correct option.

(A) (i) is False and (iii) is True

(B) (i) is True and (iv) is True

(D) (iii) is False and (iv) is False

Answer: (D)

33. A water filtration unit is made of uniform-size sand particles of 0.4 mm diameter with a shape factor of 0.84 and specific gravity of 2.55. The depth of the filter bed is 0.70 m and the porosity is 0.35. The filter bed is to be expanded to a porosity of 0.65 by hydraulic backwash. If the terminal settling velocity of sand particles during backwash is 4.5 cm/s, the required backwash velocity is

(A) 5.79 × 10⁻³ m/s

(B) 6.35 × 10⁻³ m/s

(D) 0.75 cm/s

Answer: (B)

34. For a given traverse, latitudes and departures are calculated and it is found that sum of latitudes is equal to +2.1 m and the sum of departures is equal to –2.8 m. The length and bearing of the closing error, respectively, are

(A) 3.50 m and 53°7’48” NW

(B) 2.45 m and 53°7’48” NW

(D) 3.50 m and 53.13° SE

Answer: (A)

35. From laboratory investigations, the liquid limit, plastic limit, natural moisture content and flow index of a soil specimen are obtained as 60%, 27%, 32% and 27, respectively. The corresponding toughness index and liquidity index of the soil specimen, respectively, are

(A) 0.15 and 1.22

(B) 0.19 and 6.60

(D) 6.60 and 0.19

Answer: (C)

Q.36 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

36. A function is defined in Cartesian coordinate system as f (x, y) = xe^y. The value of the directional derivative of the function (in integer) at the point (2, 0) along the direction of the straight line segment from point (2, 0) to point (1/2, 2) is _______

Answer: (1 to 1)

37. An elevated cylindrical water storage tank is shown in the figure. The tank has inner diameter of 1.5 m. It is supported on a solid steel circular column of diameter 75 mm and total height (L) of 4 m. Take, water density = 1000 kg/m³ and acceleration due to gravity = 10 m/s².

If elastic modulus (E) of steel is 200 GPa, ignoring self-weight of the tank, for the supporting steel column to remain unbuckled, the maximum depth (h) of the water permissible (in m, round off to one decimal place) is _________

Answer: (2.5 to 2.9)

38. A prismatic fixed-fixed beam, modelled with a total lumped-mass of 10 kg as a single degree of freedom (SDOF) system is shown in the figure.

If the flexural stiffness of the beam is 4π² kN/m, its natural frequency of vibration (in Hz, in integer) in the flexural mode will be __________

Answer: (10 to 10)

39. A perfectly flexible and inextensible cable is shown in the figure (not to scale). The external loads at F and G are acting vertically.

The magnitude of tension in the cable segment FG (in kN, round off to two decimal places) is ____________

Answer: (8.10 to 8.40)

40. A fire hose nozzle directs a steady stream of water of velocity 50 m/s at an angle of 45° above the horizontal. The stream rises initially but then eventually falls to the ground. Assume water as incompressible and inviscid. Consider the density of air and the air friction as negligible, and assume the acceleration due to gravity as 9.81 m/s². The maximum height (in m, round off to two decimal places) reached by the stream above the hose nozzle will then be ________________

Answer: (63.50 to 63.90)

41. A rectangular cross-section of a reinforced concrete beam is shown in the figure. The diameter of each reinforcing bar is 16 mm. The values of modulus of elasticity of concrete and steel are 2.0 × 10⁴ MPa and 2.1 × 10⁵ MPa, respectively.

The distance of the centroidal axis from the centerline of the reinforcement (x) for the uncracked section (in mm, round off to one decimal place) is _______

Answer: (129.0 to 130.0)

42. The activity details for a small project are given in the Table.

The total time (in days, in integer) for project completion is __________

Answer: (56 to 56)

43. An equipment has been purchased at an initial cost of Rs.160000 and has an estimated salvage value of Rs. 10000. The equipment has an estimated life of 5 years. The difference between the book values (in ₹, in integer) obtained at the end of 4th year using straight line method and sum of years digit method of depreciation is______

Answer: (20000 to 20000)

44. A rectangular footing of size 2.8 m × 3.5 m is embedded in a clay layer and a vertical load is placed with an eccentricity of 0.8 m as shown in the figure (not to scale). Take Bearing capacity factors: N_c = 5.14, N_q = 1.0, and N_γ = 0.0; Shape factors: s_c = 1.16, s_q = 1.0 and s_γ = 1.0; Depth factors: d_c = 1.1, d_q = 1.0 and d_γ = 1.0; and Inclination factors: ic = 1.0 and iq = 1.0 and i_γ = 1.0.

Using Meyerhoff’s method, the load (in kN, round off to two decimal places) that can be applied on the footing with a factor of safety of 2.5 is ________

Answer: (439.00 to 442.00)

45. The soil profile at a road construction site is as shown in figure (not to scale). A large embankment is to be constructed at the site. The ground water table (GWT) is located at the surface of the clay layer, and the capillary rise in the sandy soil is negligible. The effective stress at the middle of the clay layer after the application of the embankment loading is 180 kN/m². Take unit weight of water, γ_w = 9.81 kN/m³.

The primary consolidation settlement (in m, round off to two decimal places) of the clay layer resulting from this loading will be _______

Answer: (0.32 to 0.34)

46. Numerically integrate, f (x) =10x − 20x² from lower limit a = 0 to upper limit b = 0.5. Use Trapezoidal rule with five equal subdivisions. The value (in units, round off to two decimal places) obtained is _______

Answer: (0.38 to 0.42)

47. The void ratio of a clay soil sample M decreased from 0.575 to 0.510 when the applied pressure is increased from 120 kPa to 180 kPa. For the same increment in pressure, the void ratio of another clay soil sample N decreases from 0.600 to 0.550. If the ratio of hydraulic conductivity of sample M to sample N is 0.125, then the ratio of coefficient of consolidation of sample M to sample N (round off to three decimal places) is _______

Answer: (0.090 to 0.105)

48. The hyetograph in the figure corresponds to a rainfall event of 3 cm.

If the rainfall event has produced a direct runoff of 1.6 cm, the ϕ-index of the event (in mm/hour, round off to one decimal place) would be_______

Answer: (4.2 to 4.2)

49. A venturimeter as shown in the figure (not to scale) is connected to measure the flow of water in a vertical pipe of 20 cm diameter.

Assume g = 9.8 m/s². When the deflection in the mercury manometer is 15 cm, the flow rate (in lps, round off to two decimal places) considering no loss

in the venturimeter is _________

Answer: (49.0 to 50.0)

50. A reservoir with a live storage of 300 million cubic metre irrigates 40000 hectares (1 hectare = 10⁴ m²) of a crop with two fillings of the reservoir. If the base period of the crop is 120 days, the duty for this crop (in hectares per cumec, round off to integer) will then be _______

Answer: (689 to 693)

51. An activated sludge process (ASP) is designed for secondary treatment of 7500 m³/day of municipal wastewater. After primary clarifier, the ultimate BOD of the influent, which enters into ASP reactor is 200 mg/L. Treated effluent after secondary clarifier is required to have an ultimate BOD of 20 mg/L. Mix liquor volatile suspended solids (MLVSS) concentration in the reactor and the underflow is maintained as 3000 mg/L and 12000 mg/L, respectively. The hydraulic retention time and mean cell residence time are 0.2 day and 10 days, respectively. A representative flow diagram of the ASP is shown below.

The underflow volume (in m³/day, round off to one decimal place) of sludge

wastage is _________

Answer: (37.0 to 38.0)

52. A grit chamber of rectangular cross-section is to be designed to remove particles with diameter of 0.25 mm and specific gravity of 2.70. The terminal settling velocity of the particles is estimated as 2.5 cm/s. The chamber is having a width of 0.50 m and has to carry a peak wastewater flow of 9720 m³/d giving the depth of flow as 0.75 m. If a flow-through velocity of 0.3 m/s has to be maintained using a proportional weir at the outlet end of the chamber, the minimum length of the chamber (in m, in integer) to remove 0.25 mm particles completely is ______

Answer: (9 to 9)

53. In an aggregate mix, the proportions of coarse aggregate, fine aggregate and mineral filler are 55%, 40% and 5%, respectively. The values of bulk specific gravity of the coarse aggregate, fine aggregate and mineral filler are 2.55, 2.65 and 2.70, respectively. The bulk specific gravity of the aggregate mix (round off to two decimal places) is _______

Answer: (2.58 to 2.61)

54. The stopping sight distance (SSD) for a level highway is 140 m for the design speed of 90 km/h. The acceleration due to gravity and deceleration rate are 9.81 m/s2 and 3.5 m/s², respectively. The perception/reaction time (in s, round off to two decimal places) used in the SSD calculation is________

Answer: (1.90 to 2.10)

55. For a 2° curve on a high speed Broad Gauge (BG) rail section, the maximum sanctioned speed is 100 km/h and the equilibrium speed is 80 km/h. Consider dynamic gauge of BG rail as 1750 mm. The degree of curve is defined as the angle subtended at its center by a 30.5 m arc. The cant deficiency for the curve (in mm, round off to integer) is __________

Answer: (55 to 59)

GATE Exam 2021 Civil Engineering (CE-1) Question Paper With Answer Key

June 8, 2023June 13, 2022 by suresh84

GATE-2021

CE1: Civil Engineering

GA-General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Getting to the top is ___________than staying on top.

(A) more easy

(B) much easy

(D) easier

Answer: (D)

2. The mirror image of the above text about the x-axis is

Answer: (B)

3. In a company, 35% of the employees drink coffee, 40% of the employees drink tea and 10% of the employees drink both tea and coffee. What % of employees drink neither tea nor coffee?

(A) 15

(B) 25

(D) 40

Answer: (C)

4. ⊕ and ⨀ are two operators on numbers p and q such that

If x ⊕ y = 2 ⊙ 2, then x =

(A) y/2

(B) y

(D) 2y

Answer: (B)

5. Four persons P, Q, R and S are to be seated in a row, all facing the same direction, but not necessarily in the same order. P and R cannot sit adjacent to each other. S should be seated to the right of Q. The number of distinct seating arrangements possible is:

(A) 2

(B) 4

(D) 8

Answer: (C)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

6. Statement: Either P marries Q or X marries Y

Among the options below, the logical NEGATION of the above statement is:

(A) P does not marry Q and X marries Y.

(B) Neither P marries Q nor X marries Y.

(D) P marries Q and X marries Y.

Answer: (B)

7. Consider two rectangular sheets, Sheet M and Sheet N of dimensions 6 cm x 4 cm each.

Folding operation 1: The sheet is folded into half by joining the short edges of the current shape.

Folding operation 2: The sheet is folded into half by joining the long edges of the current shape.

Folding operation 1 is carried out on Sheet M three times.

Folding operation 2 is carried out on Sheet N three times.

The ratio of perimeters of the final folded shape of Sheet N to the final folded shape of Sheet M is ______.

(A) 13 : 7

(B) 3 : 2

(D) 5 : 13

Answer: (A)

8. Five line segments of equal lengths, PR, PS, QS, QT and RT are used to form a star as shown in the figure above.

The value of θ, in degrees, is ______

(A) 36

(B) 45

(D) 108

Answer: (A)

9. A function, λ, is defined by

The value of the expression is:

(A) −1

(B) 0

(D) 16

Answer: (B)

10. Humans have the ability to construct worlds entirely in their minds, which don’t exist in the physical world. So far as we know, no other species possesses this ability. This skill is so important that we have different words to refer to its different flavors, such as imagination, invention and innovation.

Based on the above passage, which one of the following is TRUE?

(A) No species possess the ability to construct worlds in their minds.

(B) The terms imagination, invention and innovation refer to unrelated skills.

(D) Imagination, invention and innovation are unrelated to the ability to construct mental worlds.

Answer: (C)

Civil Engineering (CE, Set-1)

Q.1 – Q.16 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. The rank of matrix is

(A) 1

(B) 2

(D) 4

Answer: (B)

2. If and then Q^TP^T is

Answer: (D)

3. The shape of the cumulative distribution function of Gaussian distribution is

(A) Horizontal line

(B) Straight line at 45 degree angle

(D) S-shaped

Answer: (D)

4. A propped cantilever beam EF is subjected to a unit moving load as shown in the figure (not to scale). The sign convention for positive shear force at the left and right sides of any section is also shown.

The CORRECT qualitative nature of the influence line diagram for shear force at G is

Answer: (B)

5. Gypsum is typically added in cement to

(A) prevent quick setting

(B) enhance hardening

(D) decrease heat of hydration

Answer: (A)

6. The direct and indirect costs estimated by a contractor for bidding a project is Rs.160000 and Rs. 20000 respectively. If the mark up applied is 10% of the bid price, the quoted price (in ₹) of the contractor is

(A) 200000

(B) 198000

(D) 182000

Answer: (A)

7. In an Oedometer apparatus, a specimen of fully saturated clay has been consolidated under a vertical pressure of 50 kN/m² and is presently at equilibrium. The effective stress and pore water pressure immediately on increasing the vertical stress to 150 kN/m², respectively are

(A) 150 kN/m²and 0

(B) 100 kN/m² and 50 kN/m²

(D) 0 and 150 kN/m²

Answer: (C)

8. A partially-saturated soil sample has natural moisture content of 25% and bulk unit weight of 18.5 kN/m³. The specific gravity of soil solids is 2.65 and unit weight of water is 9.81 kN/m³. The unit weight of the soil sample on full saturation is

(A) 21.15 kN/m³

(B) 19.03 kN/m³

(D) 18.50 kN/m³

Answer: (B)

9. If water is flowing at the same depth in most hydraulically efficient triangular and rectangular channel sections then the ratio of hydraulic radius of triangular section to that of rectangular section is

(A) 1/√2

(B) √2

(D) 2

Answer: (A)

10. ‘Kinematic viscosity’ is dimensionally represented as

(A) M/LT

(B) M/L²T

(D) L²/T

Answer: (D)

11. Which one of the following statements is correct?

(A) Pyrolysis is an endothermic process, which takes place in the absence of oxygen.

(B) Pyrolysis is an exothermic process, which takes place in the absence of oxygen.

(D) Combustion is an exothermic process, which takes place in the absence of oxygen.

Answer: (A)

12. Which one of the following is correct?

(A) The partially treated effluent from a food processing industry, containing high concentration of biodegradable organics, is being discharged into a flowing river at a point P. If the rate of degradation of the organics is higher than the rate of aeration, then dissolved oxygen of the river water will be lowest at point P.

(B) The most important type of species involved in the degradation of organic matter in the case of activated sludge process based wastewater treatment is chemoheterotrophs.

(D) A young lake characterized by low nutrient content and low plant productivity is called eutrophic lake.

Answer: (B)

13. The liquid forms of particulate air pollutants are

(A) dust and mist

(B) mist and spray

(D) fly ash and fumes

Answer: (B)

14. The shape of the most commonly designed highway vertical curve is

(A) circular (single radius)

(B) circular (multiple radii)

(D) spiral

Answer: (C)

15. A highway designed for 80 km/h speed has a horizontal curve section with radius 250 m. If the design lateral friction is assumed to develop fully, the required super elevation is

(A) 0.02

(B) 0.05

(D) 0.09

Answer: (B)

16. Which of the following is NOT a correct statement?

(A) The first reading from a level station is a ‘Fore Sight’.

(B) Basic principle of surveying is to work from whole to parts.

(D) Planimeter is used for measuring ‘area’.

Answer: (A)

Q.17 Multiple Select Question (MSQ), carry ONE mark (no negative marks).

17. Which of the following is/are correct statement(s)?

(A) Back Bearing of a line is equal to Fore Bearing ±180°.

(B) If the whole circle bearing of a line is 270°, its reduced bearing is 90° NW.

(D) In the case of fixed hair stadia tachometry, the staff intercept will be larger, when the staff is held nearer to the observation point.

Answer: (A; B; C)

Q.18 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

18. Consider the limit:

The limit (correct up to one decimal place) is __________.

Answer: (0.5 to 0.5)

19. The volume determined from ∭_V 8 xyz dV for V = [2, 3] × [1, 2] × [0, 1] will be (in integer) ______

Answer: (15 to 15)

20. The state of stress in a deformable body is shown in the figure. Consider transformation of the stress from the x-y coordinate system to the X-Y coordinate system. The angle θ, locating the X-axis, is assumed to be positive when measured from the x-axis in counter-clockwise direction.

The absolute magnitude of the shear stress component σ_xy (in MPa, round off to one decimal place) in x-y coordinate system is ___________

Answer: (95 to 97)

21. The equation of deformation is derived to be y = x² – xL for a beam shown in the figure.

The curvature of the beam at the mid-span (in units, in integer) will be _______

Answer: (2 to 2)

22. A truss EFGH is shown in the figure, in which all the members have the same axial rigidity R. In the figure, P is the magnitude of external horizontal forces acting at joints F and G.

If R = 500 ×10³ kN, P = 150 kN and L = 3 m, the magnitude of the horizontal displacement of joint G (in mm, round off to one decimal place) is _________

Answer: (0.9 to 0.9)

23. The cohesion (c), angle of internal friction (ϕ) and unit weight (γ) of a soil are 15 kPa, 20° and 17.5 kN/m³, respectively. The maximum depth of unsupported excavation in the soil (in m, round off to two decimal places) is ____________

Answer: (4.80 to 5.00)

24. Two reservoirs are connected through a homogeneous and isotropic aquifer having hydraulic conductivity (K) of 25 m/day and effective porosity (η) of 0.3 as shown in the figure (not to scale). Ground water is flowing in the aquifer at the steady state.

If water in Reservoir 1 is contaminated then the time (in days, round off to one decimal place) taken by the contaminated water to reach to Reservoir 2 will be_______

Answer: (2400 to 2400)

25. A signalized intersection operates in two phases. The lost time is 3 seconds per phase. The maximum ratios of approach flow to saturation flow for the two phases are 0.37 and 0.40. The optimum cycle length using the Webster’s method (in seconds, round off to one decimal place) is ______

Answer: (60.7 to 61.1)

Q.26 – Q.35 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

26. The solution of the second-order differential equation with boundary conditions y(0) = 1 and y(1) = 3 is

(A) e⁻^x + (3e – 1)xe⁻^x

(B) e⁻^x – (3e – 1)xe⁻^x

(C)

(D)

Answer: (A)

27. The value of using the trapezoidal rule with four equal subintervals is

(A) 1.718

(B) 1.727

(D) 2.718

Answer: (B)

28. A 50 mL sample of industrial wastewater is taken into a silica crucible. The empty weight of the crucible is 54.352 g. The crucible with the sample is dried in a hot air oven at 104°C till a constant weight of 55.129 g. Thereafter, the crucible with the dried sample is fired at 600°C for 1 h in a muffle furnace, and the weight of the crucible along with residue is determined as 54.783 g. The concentration of total volatile solids is __________.

(A) 15540 mg/L

(B) 8620 mg/L

(D) 1700 mg/L

Answer: (C)

29. A wedge M and a block N are subjected to forces P and Q as shown in the figure. If force P is sufficiently large, then the block N can be raised. The weights of the wedge and the block are negligible compared to the forces P and Q. The coefficient of friction (μ) along the inclined surface between the wedge and the block is 0.2. All other surfaces are frictionless. The wedge angle is 30°.

The limiting force P, in terms of Q, required for impending motion of block N

to just move it in the upward direction is given as P = αQ. The value of the coefficient ‘α’ (round off to one decimal place) is

(A) 0.6

(B) 0.5

(D) 0.9

Answer: (D)

30. Contractor X is developing his bidding strategy against Contractor Y. The ratio of Y’s bid price to X’s cost for the 30 previous bids in which Contractor X has competed against Contractor Y is given in the Table

Based on the bidding behaviour of the Contractor Y, the probability of winning against Contractor Y at a mark up of 8% for the next project is

(A) 0%

(B) more than 0% but less than 50%

(D) 100%

Answer: (B)

31. Based on drained triaxial shear tests on sands and clays, the representative variations of volumetric strain (∆V/V) with the shear strain (γ) is shown in the figure.

Choose the CORRECT option regarding the representative behaviour exhibited by Curve P and Curve Q.

(A) Curve P represents dense sand and over consolidated clay, while Curve Q represents loose sand and normally consolidated clay

(B) Curve P represents dense sand and normally consolidated clay, while Curve Q represents loose sand and over consolidated clay

(C) Curve P represents loose sand and over consolidated clay, while Curve Q represents dense sand and normally consolidated clay

(D) Curve P represents loose sand and normally consolidated clay, while Curve Q represents dense sand and over consolidated clay

Answer: (A)

32. A fluid flowing steadily in a circular pipe of radius R has a velocity that is everywhere parallel to the axis (centerline) of the pipe. The velocity distribution along the radial direction is where r is the radial distance as measured from the pipe axis and U is the maximum velocity at r = 0. The average velocity of the fluid in the pipe is

(A) U/2

(B) U/3

(D) (5/6)U

Answer: (A)

33. A water sample is analyzed for coliform organisms by the multiple-tube fermentation method. The results of confirmed test are as follows:

The most probable number (MPN) of coliform organisms for the above results is to be obtained using the following MPN Index.

The MPN of coliform organisms per 100 mL is

(A) 1100000

(B) 110000

(D) 110

Answer: (B)

34. Ammonia nitrogen is present in a given wastewater sample as the ammonium ion (NH₄⁺) and ammonia (NH₃). If pH is the only deciding factor for the proportion of these two constituents, which of the following is a correct statement?

(A) At pH above 9.25, only NH₄⁺ will be present.

(B) At pH below 9.25, NH₃ will be predominant.

(D) At pH 7.0, NH₄⁺ will be predominant.

Answer: (D)

35. On a road, the speed – density relationship of a traffic stream is given by u k = − 70 0.7 (where speed, u, is in km/h and density, k, is in veh/km). At the capacity condition, the average time headway will be

(A) 0.5 s

(B) 1.0 s

(D) 2.1 s

Answer: (D)

Q.36 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

36. The values of abscissa (x) and ordinate (y) of a curve are as follows:

By Simpson’s 1/3rd rule, the area under the curve (round off to two decimal places) is ____________

Answer: (20.00 to 21.00)

37. Vehicular arrival at an isolated intersection follows the Poisson distribution. The mean vehicular arrival rate is 2 vehicle per minute. The probability (round off to two decimal places) that at least 2 vehicles will arrive in any given 1-minute interval is __________

Answer: (0.58 to 0.60)

38. Refer the truss as shown in the figure (not to scale).

If load, F = 10√3 kN, moment of inertia, I = 8.33 × 10⁶ mm⁴ , area of cross-section, A = 10⁴ mm², and length, L = 2 m for all the members of the truss, the compressive stress (in kN/m², in integer) carried by the member Q-R is _______

Answer: (490 to 510)

39. A prismatic cantilever prestressed concrete beam of span length, L = 1.5 m has one straight tendon placed in the cross-section as shown in the following figure (not to scale). The total prestressing force of 50 kN in the tendon is applied at dc = 50 mm from the top in the cross-section of width, b = 200 mm and depth, d = 300 mm.

If the concentrated load, P = 5 kN, the resultant stress (in MPa, in integer) experienced at point ‘Q’ will be ________

Answer: (0 to 0)

40. A column is subjected to a total load (P) of 60 kN supported through a bracket connection, as shown in the figure (not to scale).

The resultant force in bolt R (in kN, round off to one decimal place) is ______________

Answer: (27.0 to 29.0)

41. Employ stiffness matrix approach for the simply supported beam as shown in the figure to calculate unknown displacements/rotations. Take length, L = 8 m; modulus of elasticity, E = 3 × 10⁴ N/mm²; moment of inertia, I = 225 × 10⁶ mm⁴

The mid-span deflection of the beam (in mm, round off to integer) under P = 100 kN in downward direction will be ________

Answer: (100 to 130)

42. A square plate O-P-Q-R of a linear elastic material with sides 1.0 m is loaded in a state of plane stress. Under a given stress condition, the plate deforms to a new configuration O-P’-Q’-R’ as shown in the figure (not to scale). Under the given deformation, the edges of the plate remain straight.

The horizontal displacement of the point (0.5 m, 0.5 m) in the plate O-P-Q-R (in mm, round off to one decimal place) is ___________

Answer: (2.4 to 2.6)

43. A small project has 12 activities – N, P, Q, R, S, T, U, V, W, X, Y, and Z. The relationship among these activities and the duration of these activities are given in the Table.

The total float of the activity “V” (in weeks, in integer) is ___________

Answer: (0 to 0)

44. The soil profile at a construction site is shown in the figure (not to scale). Ground water table (GWT) is at 5 m below the ground level at present. An old well data shows that the ground water table was as low as 10 m below the ground level in the past. Take unit weight of water, γ_w = 9.81 kN/m³.

The over consolidation ratio (OCR) (round off to two decimal places) at the mid-point of the clay layer is __________

Answer: (1.18 to 1.26)

45. A retaining wall of height 10 m with clay backfill is shown in the figure (not to scale). Weight of the retaining wall is 5000 kN per m acting at 3.3 m from the toe of the retaining wall. The interface friction angle between base of the retaining wall and the base soil is 20°. The depth of clay in front of the retaining wall is 2.0 m. The properties of the clay backfill and the clay placed in front of the retaining wall are the same. Assume that the tension crack is filled with water. Use Rankine’s earth pressure theory. Take unit weight of water, γ_w = 9.81 kN/m³.

The factor of safety (round off to two decimal places) against sliding failure of the retaining wall after ignoring the passive earth pressure will be _________

Answer: (4.20 to 4.35)

46. A combined trapezoidal footing of length L supports two identical square columns (P₁ and P₂) of size 0.5 m × 0.5 m, as shown in the figure. The columns P₁ and P₂ carry loads of 2000 kN and 1500 kN, respectively.

If the stress beneath the footing is uniform, the length of the combined footing L (in m, round off to two decimal places) is _________

Answer: (5.70 to 5.90)

47. An unsupported slope of height 15 m is shown in the figure (not to scale), in which the slope face makes an angle 50° with the horizontal. The slope material comprises purely cohesive soil having undrained cohesion 75 kPa. A trial slip circle KLM, with a radius 25 m, passes through the crest and toe of the slope and it subtends an angle 60° at its center O. The weight of the active soil mass (W, bounded by KLMN) is 2500 kN/m, which is acting at a horizontal distance of 10 m from the toe of the slope. Consider the water table to be present at a very large depth from the ground surface.

Considering the trial slip circle KLM, the factor of safety against the failure of slope under undrained condition (round off to two decimal places) is __________

Answer: (1.94 to 1.98)

48. An unlined canal under regime conditions along with a silt factor of 1 has a width of flow 71.25 m. Assuming the unlined canal as a wide channel, the corresponding average depth of flow (in m, round off to two decimal places) in the canal will be __________

Answer: (2.80 to 2.95)

49. A cylinder (2.0 m diameter, 3.0 m long and 25 kN weight) is acted upon by water on one side and oil (specific gravity = 0.8) on other side as shown in the figure.

The absolute ratio of the net magnitude of vertical forces to the net magnitude of horizontal forces (round off to two decimal places) is __________

Answer: (0.35 to 0.40)

50. A tube-well of 20 cm diameter fully penetrates a horizontal, homogeneous and isotropic confined aquifer of infinite horizontal extent. The aquifer is of 30 m uniform thickness. A steady pumping at the rate of 40 litres/s from the well for a long time results in a steady drawdown of 4 m at the well face. The subsurface flow to the well due to pumping is steady, horizontal and Darcian and the radius of influence of the well is 245 m. The hydraulic conductivity of the aquifer (in m/day, round off to integer) is _________

Answer: (34 to 38)

51. A baghouse filter has to treat 12 m³/s of waste gas continuously. The bag house is to be divided into 5 sections of equal cloth area such that one section can be shut down for cleaning and/or repairing, while the other 4 sections continue to operate. An air-to-cloth ratio of 6.0 m³/min-m² cloth will provide sufficient treatment to the gas. The individual bags are of 32 cm in diameter and 5 m in length. The total number of bags (in integer) required in the bag house is __________

Answer: (30 to 30)

52. A secondary clarifier handles a total flow of 9600 m³/d /d from the aeration tank of a conventional activated-sludge treatment system. The concentration of solids in the flow from the aeration tank is 3000 mg/L. The clarifier is required to thicken the solids to 12000 mg/L, and hence it is to be designed for a solid flux of 3.2 kg/m².h. The surface area of the designed clarifier for thickening (in m², in integer) is ___________

Answer: (375 to 375)

53. Spot speeds of vehicles observed at a point on a highway are 40, 55, 60, 65 and 80 km/h. The space-mean speed (in km/h, round off to two decimal places) of the observed vehicles is ________

Answer: (55.50 to 58.50)

54. The longitudinal section of a runway provides the following data:

The effective gradient of the runway (in %, round off to two decimal places) is _____

Answer: (0.30 to 0.34)

55. Traversing is carried out for a closed traverse PQRS. The internal angles at vertices P, Q, R and S are measured as 92°, 68°, 123°, and 77°, respectively. If fore bearing of line PQ is 27°, fore bearing of line RS (in degrees, in integer) is_______

Answer: (196 to 196 OR 218 to 218)

GATE Exam 2021 Biomedical Engineering (BM) Question Paper With Answer Key

June 8, 2023June 13, 2022 by suresh84

GATE-2021

BM: Biomedical Engineering

GA-General Aptitude

Q 1 – Q5 Carry one mark each. ( for each wrong answer: −1/3)

1. (i) Arun and Aparna are here.

(ii) Arun and Aparna is here.

(iii) Arun’s families is here.

(iv) Arun’s family is here.

Which of the above sentences are grammatically CORRECT?

(A) (i) and (ii)

(B) (i) and (iv)

(D) (iii) and (iv)

Answer: (B)

3. Two identical cube shaped dice each with faces numbered 1 to 6 are rolled simultaneously. The probability that an even number is rolled out on each dice is:

(A) 1/36

(B) 1/12

(D) 1/4

Answer: (D)

4. ⊕ and ⊙ are two operators on numbers p and q such that p ⊙ q = p – q, and p ⊕ q – p × q

Then, (9 ⊙ (6 ⊕ 7)) ⨀ (7 ⊕ (6 ⊙ 5) =

(A) 40

(B) -26

(D) -40

Answer: (D)

5. Four persons P, Q, R and S are to the seated in a row, R should not be seated at the second position from the left end of the row. The number of distinct seating arrangement possible is:

(A) 6

(B) 9

(D) 24

Answer: (C)

Q.6 – Q. 10 carry two marks (for each wrong answer: −2/3)

The distance of point Q to point O, in the same units, should be_____

(A) 3

(B) 4

(D) 6

Answer: (C)

Based on the above passage, which one of the following is TRUE?

(A) The author is of the opinion that rehearsing is important for musicians, actors and public speakers.

(B) The author is of the opinion that rehearsing is less important for public speakers than for musicians and actors.

(D) The author is of the opinion that rehearsal is more important for actors than musicians.

Answer: (A)

8. (1) Some football players play cricket.

(2) All cricket players play hockey.

Among the options given below, the statement that logically follows from the two statements 1 and 2 above, is:

(A) No football player plays hockey.

(B) Some football players play hockey.

(D) All hockey players play football.

Answer: (B)

9. In the figure shown above, PQRS is a square. The shaded portion is formed by the intersection of sectors of circles with radius equal to the side of the square and centers at S and Q.

The probability that any point picked randomly within the square falls in the shaded area is______

(A)

(B) 1/2

(D) π/4

Answer: (C)

The minimum area of the triangle PQR possible, in cm², is

(A) 18

(B) 24

(D) 144√3

Answer: (D)

Biomedical Engineering (BM)

Q.1 – Q.25 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. For to be a valid probability distribution function of a random variable X, the value of q is _____.

(A) 2

(B) π

(D) −π

Answer: (A)

2. Given a scalar function the directional derivative of V in the direction of the vector field 3yi – 3xj at the point (1, 1) is _____. (Note: i and j are the unit vectors along the x and y directions, respectively.)

(A) √18

(B) 0

(D) 3/2

Answer: (B)

3. Three resistive loads are connected to ideal voltage and current sources as shown in the circuit below. The voltage VAB across the terminals A and B is equal to ________ V.

(A) +10

(B) −10

(D) +6

Answer: (B)

4. An ideal inductor with an inductance value of 1/3 H is connected to a 50 Hz sinusoidal AC voltage source. The energy stored in the inductor is 6 J. The value of the maximum power delivered to the inductor is ____ W.

(A) 1200π

(B) 600π

(D) 0

Answer: (A)

5. Let X(jω) denote the Fourier transform of x(t). If then (where ω = 2πf)

(A) 10π

(B) 100

(D) 20π

Answer: (C)

6. In the circuit shown below, Y is a 2-bit (Y₁Y₀) output of the combinational logic. What is the maximum value of Y for any given digital inputs, A₁A₀ and B₁B₀?

(A) 01

(B) 10

(D) 11

Answer: (A)

7. In the block diagram shown below, an analog signal, V_IN = sin(2π10⁶t) is quantized by a 10-bit Nyquist ADC. Later, 4 LSBs are dropped and 6 MSBs are converted to an analog signal (V_OUT) while using a 6-bit DAC. Assume uniform distribution for the quantization noise. The peak SQNR at the output of DAC is _____ dB.

(A) 61.96

(B) 25.84

(D) 37.88

Answer: (D)

8. For a linear stable second order system, if the unit step response is such that the peak time is twice the rise time, then the system is _____.

(A) underdamped

(B) undamped

(D) critically damped

Answer: (B)

9. Which of the following displacement sensors is known to have a high sensitivity and a relatively larger measurement range?

(A) Strain gauge

(B) Capacitive sensor

(D) Piezoelectric sensor

Answer: (C)

10. Which of the following temperature sensors is used in contact-type digital thermometers for measuring body temperature?

(A) Thermocouple

(B) Thermistor

(D) Infrared LED-photodetector pair

Answer: (B)

11. The pH of blood in a healthy human is precisely in the range of ______.

(A) 7.10 – 8.10

(B) 6.95 – 7.05

(D) 7.35 – 7.45

Answer: (D)

12. Which of the following is a cranial bone in the human body?

(A) Occipital

(B) Mandible

(D) Sternum

Answer: (A)

13. Which of the following glands produces the thyroid stimulating hormone (TSH)?

(A) Thyroid

(B) Parathyroid

(D) Pineal

Answer: (C)

14. Which of the following causes Myocardial Infarction (MI)?

(A) Obstruction in one of the arteries supplying blood to the heart

(B) Obstruction in one of the arteries supplying blood to the brain

(D) Obstruction in one of the veins draining blood from the brain

Answer: (A)

15. If we consider blood as a suspension of RBCs in a Newtonian fluid, the shear forces experienced by the RBCs during blood flow would ___________.

(A) Randomize the orientation of blood cells

(B) Align RBCs along their long axes with streamlines

(D) Create an equal distribution of RBCs aligned in their long and short axes

Answer: (B)

16. As shown in the figure, the water contact angles of surfaces A and B are θA and θB, respectively. Based on the figure, which of the following statements given below is TRUE?

(A) Surface A is hydrophilic and surface B is hydrophobic

(B) Surface A is hydrophobic and surface B is hydrophilic

(D) Both surfaces are hydrophobic

Answer: (A)

17. Which of the following is a bone resorbing cell?

(A) Osteoblasts

(B) Osteoclasts

(D) Osteocalcin

Answer: (B)

Q.18 – Q.20 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).

18. Which of the following statements are CORRECT in the context of planar X-ray imaging?

(A) Using fast X-ray screen improves spatial resolution

(B) Using fast X-ray screen worsens spatial resolution

(D) Decreasing tube current increases signal to noise ratio

Answer: (B; C)

19. While comparing parallel fiber and pinnate muscles of a given volume, which of the following statements are TRUE?

(A) Pinnate muscles provide more muscle force

(B) Parallel fiber muscles provide more muscle force

(D) Parallel fiber muscles facilitate better muscle shortening

Answer: (A; D)

20. Which of the following may cause failure of bone implants?

(A) Stress shielding – reduction of bone density due to removal of a typical stress from bone by an implant

(B) Aseptic loosening – loss of bond between bone and implant in the absence of an infection

(D) Osseointegration – formation of a direct interface between an implant and a bone, without intervening soft tissues

Answer: (A; B; C)

Q.21 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

21. The minimum value, fmin, of the function given below is _________. (rounded off to the nearest integer)

Answer: (-6 to -6)

22. A continuous time transfer function is converted to a discrete time transfer function H(z) using a bilinear transform at 100 MHz sampling rate. The pole of H(z) is located at z = ____.

Answer: (1 to 1)

23. Consider a type 2, unity feedback system. The intersection of the initial −40 dB/dec segment, of its Bode plot, with the zero dB line occurs at a frequency of 2 rad/s. The acceleration error constant of the system K_a is ___.

Answer: (4 to 4)

24. The radioactivity of a radionuclide with decay constant of 3. 22 × 10⁻⁵ s⁻¹is 6 mCi at 10:30 AM. The radioactivity of the radionuclide at 4:30 PM on the same day will be _________ mCi. (rounded off to two decimal places)

Answer: (2.96 to 3.02)

25. A polymeric scaffold has been developed for cartilage tissue engineering. To understand the biodegradability of the material, this polymeric scaffold with a dry weight of 20 mg is kept in a lysozyme solution for 7 days. At the end of 7 days, the scaffold is freeze-dried, and the dry weight is measured to be 18 mg. The degradation of the polymeric scaffold after 7 days is ______ %.

Answer: (10 to 10)

Q.26 – Q.42 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

26. The Trace and Determinant of a 2 × 2 nonsingular matrix A are 12 and 32, respectively. The eigen values of A⁻¹are ____ and _____.

(A) 0.6, 0.8

(B) 0.25, 0.125

(D) 1/12, 1/32

Answer: (B)

27. A unit step input is applied to a system with impulse response at t = 0. The output of the system y(t) at t = 0⁺ is ______.

(A) 1

(B) −ω_z/ω_p

(D) 0

Answer: (C)

28. Consider the following first order partial differential equation, also known as the transport equation with initial conditions given by y(x, 0) = sin x, − ∞ < x < ∞. The value of y(x, t) at x = π and t = π/6 is _______.

(A) 1

(B) 2

(D) 0.5

Answer: (D)

29. In the circuit shown below, V_s = 100 V, R₁ = 30 Ω, R₂ = 60 Ω, R₃ = 90 Ω, R₄ = 45 Ω, and R₅ = 30 Ω. The current flowing through resistor R₃ is ___ A. (rounded off to two decimal places)

(A) +0.30

(B) +0.21

(D) −0.30

Answer: (B)

30. x[n] is convolved with h[n] to give y[n]. If y[2] = 1 and y[3] = 0, h[0] =______. (Graphs are not uniformly scaled)

(A) 1.85

(B) −2.50

(D) 2.38

Answer: (D)

31. In the block diagram shown below, an infinite tap FIR filter with transfer function H(z) = Y(z)/X(z) is realized. If the value of α is ______.

(A) 2

(B) 1/√2

(D) √2

Answer: (B)

32. An analog signal is sampled at 100 MHz to generate 1024 samples. Only these samples are used to evaluate 1024-point FFT. The separation between adjacent frequency points (ΔF) in FFT is __________ kHz.

(A) 102.16

(B) 97.66

(D) 95.63

Answer: (B)

33. In the circuit diagram shown below, all OPAMPs are ideal with infinite gain and bandwidth. V_OUT/V_IN for this circuit is ______.

(A) 5.00

(B) 5.33

(D) 6.00

Answer: (C)

34. In the circuit diagram shown below, NMOS is in saturation region, μ_nC_ox = 200 μ_A/V², width W = 40 μm, length L = 1 μm, the threshold voltage is 0.4 V, and the ratio of body-effect transconductance (g_mb) to transconductance (g_m) is 0.1. A small input voltage vin is applied at the bulk-terminal to produce a small change in the output voltage v_out. The dc gain for v_out/v_in is _______. (Neglect channel-length modulation for NMOS and all intrinsic capacitors)

(A) −0.4

(B) −4.0

(D) −3.6

Answer: (A)

35. As shown in the circuit below, a constant voltage source is connected to two ideal resistors.

The voltage drop across a resistor is measured using two different voltmeters V1 and V2 at five different time instances and the following values are recorded from V1 and V2.

Which of the following is TRUE?

(A) V1 is less accurate, V2 is more precise

(B) V1 is more accurate, V2 is more precise

(D) V1 is more accurate, V2 is less precise

Answer: (B)

36. The closed-loop characteristic equation of a system is given by s⁴ + 2s³ + 8s² + 8s + 16 = 0.

The frequency of oscillations of this closed-loop system at steady state is ______ rad/s.

(A) 1

(B) 2

(D) 4

Answer: (B)

37. Match the following in the context of biomaterial characterization:

(A) P-L, Q-N, R-K, S-M

(B) P-N, Q-M, R-K, S-L

(D) P-M, Q-K, R-N, S-L

Answer: (B)

38. In comparison to ECG amplifiers, the surface-EMG amplifiers have

(A) A comparable gain and smaller bandwidth

(B) A comparable gain and larger bandwidth

(D) At least 20 dB lower gain and a smaller bandwidth

Answer: (B)

39. Match the following organs with their functions:

(A) P-M, Q-N, R-K, S-L

(B) P-N, Q-M, R-K, S-L

(D) P-L, Q-M, R-K, S-N

Answer: (B)

40. An RF pulse is applied to acquire an axial MR image at the isocenter of a 1.5T MRI scanner with slice thickness of 2.5 mm. Assuming a gradient field strength of 2 Gauss/cm is applied and Gyromagnetic ratio of protons is 42.58 MHz/T, the RF pulse bandwidth required for slice selection is _______ kHz.

(A) 1.06

(B) 2.13

(D) 13.31

Answer: (B)

41. A longitudinal pressure wave travelling inside a muscle tissue is incident at an angle of 60° at the interface between the muscle and kidney. Let the wave impedance be Z_muscle = 1.70 × 10⁵g cm⁻² s⁻¹, Z_kidney = 1.62 × 10⁵g cm⁻² s⁻¹ and wave velocities in muscle and kidney tissues be 1590 and 1560 m/s respectively. The transducer centre frequency is 1.5 MHz. The pressure wave propagation angle in the kidney tissue and intensity transmission coefficient at the tissue interface are ________degrees (rounded off to the nearest integer) and ______ (rounded off to two decimal places), respectively.

(A) 58, 0.24

(B) 30, 0.68

(D) 30, 0.99

Answer: (C)

42. A novel biomaterial was tested for its tensile properties. The experiment was conducted using a cylindrical sample of this material, which was 10 cm long with 1 cm diameter. When a tensile force of 50 kN was applied, this cylindrical sample elongated by 4 mm. Based on the experimental results described above and the tensile moduli of different tissues given in the table below, this biomaterial would be a suitable replacement for __________.

(A) Bone

(B) Tendon

(D) Articular cartilage

Answer: (A)

Q.43 – Q.45 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).

43. In the circuit shown below, R₁= 2 Ω, R₂= 1 Ω, L₁= 2 H, and L₂= 0.5 H. Which of the following describe(s) the characteristics of the circuit?

(A) Second order high pass filter

(B) Second order low pass filter

(D) Overdamped system

Answer: (B; D)

44. An inexperienced clinician was measuring the cardiac output of a healthy human by thermo dilution technique. A 2.0 mL of cold saline solution of volume (V_i) at 7 °C was injected at the entrance of the right atrium. The change in blood temperature at the pulmonary artery was measured to be −20 Kelvin. second. The cardiac output F was calculated using the following formula

where Q is the heat content of injectate in Joules, given by V_i∆T_iρ_ic_i and ∆T_i is the temperature difference between the injectate and blood. It was assumed that the density of blood (ρ_b in kg/m³) and the specific heat

capacity of blood (c_b in J/(kg. K)) were respectively equal to that of the injectate ρ_i and c_i.

The clinician realized that there was an error in the measurement of F. Which of the following is TRUE?

(A) Cardiac output is too low because the cold saline volume was too small

(B) Cardiac output is too low because is too large

(D) Cardiac output is too high because is too small

Answer: (A; B)

45. Which of the following statements about smooth muscles are TRUE?

(A) Smooth muscles are found in the walls of hollow organs

(B) Smooth muscles are controlled by the autonomic nervous system

(D) Smooth muscles are made up of striated cells

Answer: (A; B; C)

Q.46 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

46. Consider a unity feedback system with closed loop transfer function

The steady state error with respect to a unit ramp input is ____. (rounded off to one decimal place)

Answer: (0.1 to 0.1)

47. The diameter of a renal artery lumen in humans is 5 mm. If the mean velocity of the blood flowing in the renal artery is 40 cm/s, the density of blood (ρ) is 1060 kg/m3, and the viscosity of blood (μ) is 3 cP, the Reynolds number for the blood flowing in the renal artery is ________ (rounded off to the nearest integer).

Answer: (700 to 710)

48. A drug manufacturer believes that there is a 95% chance that the drug controller will approve a new drug the company plans to distribute if the results of the current testing show that the drug causes no side effects. The manufacturer further believes that there is a 0.50 probability that the drug will be approved even if the test shows side effects. A physician working for the drug manufacturer believes there is a 0.20 probability that tests will show side effects. If the drug is approved by the drug controller, the probability that the drug causes side effects is ______. (rounded off to three decimal places)

Answer: (0.111 to 0.121)

49. In a measurement process, groups A and B recorded 10 and 15 values, respectively. The arithmetic means and standard deviations of group A are μ_A = 35, σ_A = 0.4 and group B are μ_B = 38, σ_B = 0.6, respectively. The standard deviation for the combined set of group A and group B measurements is ____. (rounded off to two decimal places)

Answer: (1.54 to 1.58)

50. In the circuit given below, V_s = 50 V. Let the circuit reach steady state for the SPDT switch at position 1. Once the circuit is switched to position 2, the energy dissipated in the resistors is _______ J. (rounded off to one decimal place)

Answer: (0.2 to 0.2)

51. In the circuit shown below, the output voltage V_OUT is ________ V.

Answer: (-10 to -10)

52. A pacemaker was implanted in a cardiac patient. It has a battery of 2.4 A.h (Ampere.hour). It is designed to deliver a rectangular pulse of amplitude 1.5 V for 1 ms ON time for every one second. The electrode – heart resistance is 150 Ω. Assuming the current drained from the battery is negligible, the lifetime of the pacemaker is _____ years. (rounded off to the nearest integer)

Answer: (27 to 28)

53. A radiographic system is using X-ray tube operating at 80 kVp. In order to filter the low energy X-rays, an aluminum (Al) filter of 2.5 mm thickness is used. The Al filter is replaced with a copper (Cu) filter to have the same energy filtered. The mass attenuation coefficients of Al and Cu at 80 kVp are 0.02015 m²/kg and 0.07519 m²/kg, respectively. The densities of Al and Cu are 2699 kg/m³ and 8960 kg/m³ The thickness of the new Cu filter is ______ mm. (rounded off to two decimal places)

Answer: (0.15 to 0.25)

54. In a radioactive isotope, N nuclei are needed to produce radioactivity level of 2 mCi. Assuming decay constant of 3. 22 × 10⁻⁵ s⁻¹ and atomic weight of 98 g/mol and Avogadro’s number = 6. 02 × 10²³ mol⁻¹, the mass of N radionuclide is __________ picograms. (rounded off to the nearest integer)

Answer: (372 to 376)

55. A PZT crystal of thickness 1 mm and wave velocity 4000 m/s is emitting a longitudinal pressure wave, which is incident on a blood vessel at an angle of 30°. The doppler shift in the ultrasound wave for a blood flow of 10 cm/s and wave velocity in the soft tissue of 1540 m/s is ______ Hz.

Answer: (222 to 228)

GATE Exam 2021 Architecture and Planning (AR) Question Paper With Answer Key

June 8, 2023June 13, 2022 by suresh84

GATE-2021

AR-Architecture and Planning

GA-General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. (i) Arun and Aparna are here.

(ii) Arun and Aparna is here.

(iii) Arun’s families is here.

(iv) Arun’s family is here.

Which of the above sentences are grammatically CORRECT?

(A) (i) and (ii)

(B) (i) and (iv)

(D) (iii) and (iv)

Answer: (B)

3. Two identical cube shaped dice each with faces numbered 1 to 6 are rolled simultaneously. The probability that an even number is rolled out on each dice is:

(A) 1/36

(B) 1/12

(D) 1/4

Answer: (D)

4. ⊕ and ⊙ are two operators on numbers p and q such that p ⊙ q = p – q, and p ⊕ q – p × q

Then, (9 ⊙ (6 ⊕ 7)) ⨀ (7 ⊕ (6 ⊙ 5) =

(A) 40

(B) -26

(D) -40

Answer: (D)

5. Four persons P, Q, R and S are to the seated in a row, R should not be seated at the second position from the left end of the row. The number of distinct seating arrangement possible is:

(A) 6

(B) 9

(D) 24

Answer: (C)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

The distance of point Q to point O, in the same units, should be_____

(A) 3

(B) 4

(D) 6

Answer: (C)

Based on the above passage, which one of the following is TRUE?

(A) The author is of the opinion that rehearsing is important for musicians, actors and public speakers.

(B) The author is of the opinion that rehearsing is less important for public speakers than for musicians and actors.

(D) The author is of the opinion that rehearsal is more important for actors than musicians.

Answer: (A)

8. (1) Some football players play cricket.

(2) All cricket players play hockey.

Among the options given below, the statement that logically follows from the two statements 1 and 2 above, is:

(A) No football player plays hockey.

(B) Some football players play hockey.

(D) All hockey players play football.

Answer: (B)

9. In the figure shown above, PQRS is a square. The shaded portion is formed by the intersection of sectors of circles with radius equal to the side of the square and centers at S and Q.

The probability that any point picked randomly within the square falls in the shaded area is______

(A)

(B) 1/2

(D) π/4

Answer: (C)

The minimum area of the triangle PQR possible, in cm², is

(A) 18

(B) 24

(D) 144√3

Answer: (D)

Architecture and Planning (AR)

Q.1 – Q.25 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. As per National Building Code of India, 2016, the function of an Automatic Rescue Device is to

(A) bring a stuck lift to the nearest landing level.

(B) control fire in electrical system at plenum level.

(D) trigger fire sprinkler system.

Answer: (A)

2. Which among the following acronyms represents a thermal comfort index?

(A) PMV

(B) NDVI

(D) PCA

Answer: (A)

3. Indian satellite sensor that can be used for very high resolution mapping of urban areas is

(A) LANDSAT.

(B) CARTOSAT.

(D) MODIS.

Answer: (MTA)

4. What is the smallest entity of raster data used in GIS?

(A) Line

(B) Pixel

(D) Polygon

Answer: (B)

5. The correct sequence of stages during firing/burning of bricks is

(A) Dehydration – Oxidation – Vitrification – Cooling.

(B) Vitrification – Dehydration – Oxidation – Cooling.

(D) Cooling – Oxidation – Vitrification – Dehydration.

Answer: (A)

6. Industry Foundation Classes (IFC) in BIM is

(A) a module used to improve energy savings.

(B) an algorithm related to the precision of the BIM model.

(D) an object oriented data model to facilitate interoperability.

Answer: (D)

7. As per urban design principles proposed by Gordon Cullen, Rashtrapati Bhavan, New Delhi, is an example of

(A) Serial Vision.

(B) Pinpointing.

(D) Here and there.

Answer: (A)

8. A waste water pipe connecting two inspection chambers (IC) is laid at a slope of 1:200. The Invert Level of the starting IC is -450 mm. The Invert level of the second pit at a distance of 40 m from the first IC is

(A) -650 mm.

(B) -200 mm.

(D) -550 mm.

Answer: (A)

9. From the images P, Q and R given below, select the corresponding land use categories according to Alonso’s Bid Rent Theory.

(A) P–Manufacturing; Q–Residential; R–Retail

(B) P–Retail; Q–Residential; R–Manufacturing

(D) P–Retail; Q–Manufacturing; R–Residential

Answer: (D)

10. The urban land use model based on the concept of a polycentric city is known as

(A) Burgess Model.

(B) Harris and Ullman model.

(D) Homer Hoyt’s model.

Answer: (B)

11. The total head or total lift against which a pump works includes suction lift, discharge lift and

(A) cone of depression.

(B) salvage lift.

(D) frictional head loss.

Answer: (D)

12. The two components for measuring time of concentration for storm water are

(A) overland flow time and retention time.

(B) overland flow time and gutter flow time.

(D) retention time and inlet time.

Answer: (B)

13. The traffic assignment technique where the traffic arranges itself in congested networks such that the journey time in all used routes between an Origin-Destination pair are equal and less than those that would be experienced in all unused routes. This is known as

(A) System equilibrium.

(B) All–or–nothing.

(D) Incremental.

Answer: (C)

14. What is the dependent variable in a regression based trip generation model?

(A) Population of Traffic Analysis Zone

(B) Number of trips

(D) Number of households

Answer: (B)

15. The curve traced by a point on a circle rolling inside another circle is known as

(A) hypocycloid.

(B) helix.

(D) hyperbola.

Answer: (A)

16. The law of Primate City was first proposed by

(A) Samuel A. Stouffer.

(B) Colin Clark.

(D) Harold Hotelling.

Answer: (C)

17. In the European Union which constitutes the cities namely, London, Paris, Brussels, Amsterdam, Cologne, Frankfurt, Munich and Milan, lie within a linear megalopolitan zone known as

(A) Purple Zone.

(B) Golden Polygon.

(D) Yellow Corridor.

Answer: (C)

18. An urban governance tool to mobilize financial resources by permitting additional FAR over and above the prescribed FAR by imposing a charge or fee for the same is known as

(A) Betterment Levy.

(B) Impact Fee.

(D) Floor Area Incentive Tax.

Answer: (MTA)

19. Identify the colour palette that is created using any three equally spaced hues around the colour wheel.

(A) Split – complementary

(B) Analogous

(D) Complementary

Answer: (C)

20. Coefficient of Performance (COP) for heat pump is used to calculate

(A) the number of air changes.

(B) the Energy Efficiency Ratio.

(D) the Indoor Air Quality index.

Answer: (B)

21. Freight flows are converted to truck flows using

(A) Volume factor.

(B) Weight factor.

(D) Distance load factor.

Answer: (C)

22. Rebound hammer test is used to measure

(A) permeability of concrete.

(B) bond stress between rebar and concrete.

(D) tensile strength of concrete.

Answer: (C)

23. Which type of temporary supporting structure can be used in case of rebuilding the lower part of a load bearing wall at ground floor above plinth level?

(A) Dead Shore

(B) Pit Underpinning

(D) Needle Scaffolding

Answer: (A)

24. During earthquake, soft storey failure in a building is due to

(A) shear failure initiated by short column effect.

(B) stress discontinuity initiated by abrupt changes of stiffness.

(D) drift of building storey initiated by pounding effect.

Answer: (B)

25. Following five activities are associated with construction contract management. Choose the option showing the correct progressive sequence of the activities.

(A) R – Q – P – T – S

(B) S – P – R – T – Q

(D) S – T – P – R – Q

Answer: (C)

Q.26 – Q.36 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

26. Match the acronym in Group I with the particulars in Group II.

(A) P–3, Q–5, R–4, S–2

(B) P–4, Q–3, R–1, S–2

(D) P–5, Q–3, R–4, S–1

Answer: (D)

27. Match the buildings in Group I with their corresponding architect in Group II.

(A) P–4, Q–3, R–1, S–2

(B) P–2, Q–4, R–2, S–5

(D) P–2, Q–3, R–4, S–5

Answer: (D)

28. Match the heritage conservation charters in Group I with their focus areas in Group II.

(A) P–3, Q–1, R–4, S–5

(B) P–5, Q–4, R–1, S–2

(D) P–4, Q–1, R–3, S–2

Answer: (C)

29. Match the Buildings (name of architects) in Group I with the abstractions used in Group II.

(A) P–4, Q–2, R–1, S–3

(B) P–5, Q–1, R–4, S–3

(D) P–5, Q–2, R–4, S–1

Answer: (B)

30. Match the names of the gardens in Group I with their type in Group II.

(A) P–3, Q–1, R–2, S–4

(B) P–5, Q–1, R–4, S–3

(D) P–5, Q–4, R–1, S–3

Answer: (B)

31. Match the various types of impurities present in water in Group I with the appropriate water treatment process given in Group II.

(A) P–2, Q–5, R–3, S–4

(B) P–3, Q–4, R–1, S–2

(D) P–3, Q–5, R–1, S–4

Answer: (D)

32. Match the temples in Group I with their style of Architecture in Group II

(A) P–3, Q–1, R–2, S–5

(B) P–3, Q–4, R–2, S–1

(D) P–5, Q–1, R–4, S–2

Answer: (A)

33. Match the urban form/structure in Group I with their respective proponents in Group II.

(A) P–4, Q–1, R–5, S–3

(B) P–5, Q–1, R–4, S–2

(D) P–3, Q–4, R–1, S–2

Answer: (C)

34. Match the elements in Group I to their description in Group II.

(A) P–3, Q–1, R–5, S–4

(B) P–4, Q–3, R–1, S–2

(D) P–5, Q–1, R–2, S–4

Answer: (D)

35. Match the position of feet in Group I to the most appropriate description of stability of human body in Group II.

(A) P–5, Q–5, R–2, S–1

(B) P–5, Q–3, R–1, S–2

(D) P–4, Q–3, R–2, S–1

Answer: (B)

36. Match the buildings in Group I with their corresponding structural systems in Group II.

(A) P–5 , Q–3 , R–4 , S–1

(B) P–3 , Q–5 , R–1 , S–2

(D) P–5 , Q–1 , R–4 , S–2

Answer: (D)

Q.37 – Q.43 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).

37. Choose the correct options with respect to cycle track design as per Indian Road Congress guidelines.

(A) The minimum width of cycle track is 3 m if overtaking is to be provided for

(B) Cycle tracks may be provided when peak hour cycle traffic is 400 or more on routes with a traffic of 100 to 200 vehicles/hour

(D) Cyclist should have a clear view of at least 80 m

Answer: (A, B)

38. As per the Right to Fair Compensation and Transparency in Land Acquisition, Rehabilitation and Resettlement Act, 2013, for which purposes can the urgency clause for land acquisition be invoked?

(A) National defence and security purposes

(B) Affordable housing program

(D) Emergency arising out of natural calamities

Answer: (A, D)

39. Which of the following international treaties are related to Climate Change and global warming?

(A) Cartagena protocol, 2000

(B) Copenhagen summit, 2001

(D) Paris Agreement, 2016

Answer: (B, D OR D)

40. Which of the following algorithms are used for finding the shortest path in an urban transportation network?

(A) Logit

(B) Huff

(D) Dijkstra

Answer: (C, D)

41. Which of the following statements are true with respect to surface paint?

(A) Paint is glossy when Pigment Volume Concentration is high

(B) Vehicle is the volatile part of the paint

(D) High VOC content is preferred in paints

Answer: (B, C)

42. As per the Solid Waste Management Rules 2016, which among the following are ‘Duties of waste generators’?

(A) Segregate and store waste generated in four separate streams namely, combustible, non-combustible, organic and domestic hazardous waste

(B) Store construction and demolition waste separately within own premise before disposal

(D) Compost horticulture waste and garden waste separately within own premise

Answer: (B, C)

43. Choose the correct options with regard to activated sludge process.

(A) The activated sludge process is an aerobic process

(B) The entire settled sludge is sent back to the aeration tank

(D) In aeration tanks, sewage is aerated and agitated for a few hours

Answer: (A, D)

44. A rectangular hall having dimension of 8.0 m × 14.0 m × 4.0 m has total 4 windows (1.5 m ×0 m each) and 2 doors (1.0 m × 2.0 m each).

The coefficients of absorption are given below. Considering all windows open and doors closed, the reverberation time in seconds is _______.

[round off to 2 decimal places]

Answer: (0.82 to 0.86)

45. If surface conductance of external surface is 20 W/m²°C, absorbance of the surface is 0.66 and U value of the wall is 1.2 W/m²°C, the solar gain factor of a wall is ______. [round off to 2 decimal places]

Answer: (0.03 to 0.05)

46. The initial cost of a property is INR 4,00,000 and its future life is 30 years. Considering the scrap value as 10% of its initial cost and rate of interest as 5%, the sinking fund (deposited at the end of year) for the property is INR _______.

[round off to 2 decimal places]

Answer: (5405.00 to 5422.00)

47. Reading in the staff stationed at P measured by a dumpy level is 3.5 m. The dumpy level is stationed at Q. The Reference Level (RL) at point P is 96.5 m and the height of the dumpy level is 1.25 m. The RL at point Q is _______ m.

[round off to 2 decimal places]

Answer: (98.75 to 98.75)

48. A circular cricket field of 180 m diameter is illuminated by four floodlight towers. The floodlight towers are equally spaced along the perimeter of the field. The height of the floodlight tower is 48 m. Using ‘Inverse Square Law’, the illumination level at the center of the field is found as 750 Lux. Each tower is consisting of 50 lamps. The rating of each lamp is 700 Watt. The efficacy of each lamp is _______ Lumen /Watt. [round off to 2 decimal places]

Answer: (117.00 to 119.00 OR 1483.00 to 1496.00)

49. A building is constructed on a plot measuring 70 m × 40 m. The utilized FAR of the building is 1.5. An energy audit team found that the average monthly electricity bill of the building is INR 2,94,000. The unit cost of the electricity is INR 7. The Building Energy Index is __________ kW-hr/m²/year. [in integer]

Answer: (120 to 120)

50. A simply-supported steel beam made of an I-section has a span of 8 m. The beam is carrying a uniformly distributed load of 15 kN/m. The overall depth of the beam is 450 mm. The moment of inertia of the beam section is 18000 cm⁴. The maximum bending stress in the beam will be _________ N/mm². [in integer]

Answer: (150 to 150)

51. The slenderness ratio of a circular column of diameter 300 mm and effective height 3 m is __________. [in integer]

Answer: (40 to 40)

52. A construction project consists of following five activities. The immediate successor activity relationship and duration of each activity are mentioned in the table below.

The total duration of the project is _______ weeks. [in integer]

Answer: (12 to 12)

53. It is proposed to have ceramic tile flooring in a room having internal clear dimension of 1.8 m × 2.4 m. Tile sizes are 300 mm × 300 mm. The door opening is 900 mm and the door is flushed with the internal face of the wall. The height of skirting is 600 mm. The number of ceramic tiles required for internal flooring and skirting is _______.[in integer]

Answer: (98 to 98)

54. In a housing project, 75% of the permissible FAR was utilised after constructing four numbers eight storey MIG towers with identical floor area of 400 sqm. If three numbers seven storey LIG towers with identical floor area are built utilising the remaining FAR, the floor area of each LIG tower is _______ sqm.

[round off to 2 decimal places]

Answer: (MTA)

55. Using the following values of thermal conductance, surface conductance and thermal resistance, the U value across the given wall cross-section is _______W/m²° [round off to 2 decimal places]

Answer: (MTA)

GATE Exam 2021 Agricultural Engineering (AG) Question Paper With Answer Key

June 8, 2023June 13, 2022 by suresh84

GATE-2021

AG : Agricultural Engineering

General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. The people ___________ were at the demonstration were from all sections of society.

(A) whose

(B) which

(D) whom

Answer: (C)

2. A transparent square sheet shown above is folded along the dotted line. The folded sheet will look like ________.

Answer: (C)

3. For a regular polygon having 10 sides, the interior angle between the sides of the polygon, in degrees, is:

(A) 396

(B) 324

(D) 144

Answer: (D)

4. Which one of the following numbers is exactly divisible by (11¹³ +1) ?

(A) 11²⁶ + 1

(B) 11³³ + 1

(D) 11⁵² – 1

Answer: (D)

5. Oasis is to sand as island is to ________

Which one of the following options maintains a similar logical relation in the above sentence?

(A) Stone

(B) Land

(D) Mountain

Answer: (C)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

6. The importance of sleep is often overlooked by students when they are preparing for exams. Research has consistently shown that sleep deprivation greatly reduces the ability to recall the material learnt. Hence, cutting down on sleep to study longer hours can be counterproductive.

Which one of the following statements is the CORRECT inference from the above passage?

(A) Sleeping well alone is enough to prepare for an exam. Studying has lesser benefit.

(B) Students are efficient and are not wrong in thinking that sleep is a waste of time.

(D) To do well in an exam, adequate sleep must be part of the preparation.

Answer: (D)

7. In the figure shown above, each inside square is formed by joining the midpoints of the sides of the next larger square. The area of the smallest square (shaded) as shown, in cm² is:

(A) 12.50

(B) 6.25

(D) 1.5625

Answer: (C)

8. Let X be a continuous random variable denoting the temperature measured. The range of temperature is [0, 100] degree Celsius and let the probability density function of X be f(x) = 0.01 for 0 ≤ X ≤ 100.

The mean of X is _____

(A) 2.5

(B) 5.0

(D) 50.0

Answer: (D)

9. The number of students passing or failing in an exam for a particular subject are presented in the bar chart above. Students who pass the exam cannot appear for the exam again. Students who fail the exam in the first attempt must appear for the exam in the following year. Students always pass the exam in their second attempt.

The number of students who took the exam for the first time in the year 2 and the year 3 respectively, are __________.

(A) 65 and 53

(B) 60 and 50

(D) 55 and 48

Answer: (D)

10. Seven cars P, Q, R, S, T, U and V are parked in a row not necessarily in that order. The cars T and U should be parked next to each other. The cars S and V also should be parked next to each other, whereas P and Q cannot be parked next to each other. Q and S must be parked next to each other. R is parked to the immediate right of V. T is parked to the left of U.

Based on the above statements, the only INCORRECT option given below is:

(A) There are two cars parked in between Q and V.

(B) Q and R are not parked together.

(D) Car P is parked at the extreme end.

Answer: (A)

Agricultural Engineering (AG)

Q.1 – Q.10 Multiple Choice Question (MCQ), carry ONE marks each (for each wrong answer: – 1/3).

1. Let the vector be a differentiable vector function of Cartesian coordinates x, y and z. The curl of the vector is given by curl =

Answer: (C)

2. If x is an integer with x > 1, the solution of is

(A) Zero

(B) 0.5

(D) ∞

Answer: (B)

3. In a tyre axis system as defined by Society of Automotive Engineers, the moment acting about z-axis is called

(A) aligning torque

(B) over turning torque

(D) lateral moment

Answer: (A)

4. Pitting is a process of

(A) mixing of pulses with red earth

(B) mixing of pulses with edible oil

(D) beating of oil seeds for oil extraction

Answer: (C)

5. During ploughing with a tractor mounted mould board plough, the mast of three point hitch system would be

(A) inclined 5 to 20° with horizontal

(B) nearly vertical

(D) parallel to the rear axle of the tractor

Answer: (B)

6. The hydrologic reservoir routing methods use

(A) Bernoulli’s equation only

(B) hydrologic continuity equation only

(D) both the hydraulic momentum and hydrologic continuity equations

Answer: (B)

7. While assessing the intensity of agricultural drought, a negative value of aridity index indicates that the area is classified as

(A) severely arid

(B) moderately arid

(D) non-arid

Answer: (B)

8. The approximate relationship between Sediment Delivery Ratio (SDR) and drainage area (A) shows that SDR varies

(A) directly with A^0.2

(B) inversely with A^0.2

(D) inversely with A

Answer: (B)

9. One-dimensional generalized heat conduction equation representing temperature distribution in a sphere, based on thermal conductivity k, specific heat capacity C_p, density ρ, and energy generation E, can be written as where the value of n is

(A) 1

(B) 2

(D) 4

Answer: (B)

10. In butter, the fishy flavor defect is due to the decomposition of

(A) α-lactalbumin

(B) β-lactoglobulin

(D) lecithin

Answer: (D)

11. In a field test of drip irrigation system having an application efficiency of 90%, the minimum, maximum and average flow rates are found to be 45 L∙h⁻¹, 65 L∙h⁻¹ and 50 L∙h⁻¹, respectively. The manufacturer’s coefficient of variation of the emitter is 0.07. If there is one emitter per plant, the drip irrigation efficiency in percent is ________. [round off to 2 decimal places]

Answer: (73.70 to 73.85)

12. Trace of the matrix is _______. [in integer]

Answer: (18 to 18)

13. The probabilities of A and B are given by P(A) = 0.35 and P(B) = 0.25, respectively. If A and B are mutually exclusive so that P(A⋃B) = P(A) + P(B), then the value of P(A/A⋃B) is _________. [round off to 3 decimal places]

Answer: (0.583 to 0.584)

14. Stoichiometric air-fuel ratio of an SI engine is 14.7:1. If equivalence ratio (λ) is 0.92, the actual air-fuel ratio maintained during the engine operation is ______. [round off to 2 decimal places]

Answer: (13.47 to 13.57 OR 15.93 to 16.03)

15. While harvesting paddy with a self-propelled vertical conveyor reaper with a cutter bar of width 60 cm, the power required for cutting and propelling are measured to be 300 W and 350 W, respectively. If the power required for conveying the cut crop is 50% of the power required for cutting, the power required by the header unit of the vertical conveyor reaper in W will be ________. [answer in integer]

Answer: (450 to 450)

16. A gear pump has a displacement of 120 cm³ rev^-1 and it runs at 1500 rpm against a system pressure of 18 MPa. If the torque efficiency of the pump is 90%, actual torque required to run the pump in N∙m is _______. [round off to 2 decimal places]

(Take π = 3.14)

Answer: (380.00 to 383.00)

17. Useful soil reaction forces acting on a tractor drawn mould board plough during operation are 2.0 kN, 0.9 kN and 0.6 kN along longitudinal, transverse and vertical directions, respectively. The soil-metal friction angle is 25°. Neglecting the effects of weight of the implement and the vertical soil reaction, the estimated draft in N is _______. [round off to one decimal place]

Answer: (2400.0 to 2440.0)

18. Cohesionless soil is naturally deposited and makes a slope of infinite extent having slope angle of 25°. If the effective angle of internal friction of this soil is 30°, the factor of safety of slope is _______. [round off to 2 decimal places]

Answer: (1.22 to 1.25)

19. A pump, discharging water at a rate of 80 L∙s⁻¹, is used to irrigate 2 ha of land in 10 h. On irrigation, moisture content of the soil (on weight basis) in the root zone depth of 50 cm is increased from 18% to 30%. If bulk density of the soil is 1500 kg∙m⁻³, water application efficiency in per cent is _______.

[round off to 2 decimal places]

Answer: (62.25 to 62.75)

20. Pumping test is carried out at a constant discharge of 5400 L∙min⁻¹ for 24 h in a main well of 30 cm diameter penetrated 25 m below the static water table. The water level in observation wells located at 30 m and 90 m away from the main well are lowered by 1.11 m and 0.53 m, respectively. Considering steady state flow condition, drawdown estimated in the main well in m is _______.

[round off to 2 decimal places] (Take π = 3.14)

Answer: (4.00 to 4.25)

21. The observed concentrations of magnesium (Mg²⁺), sodium (Na⁺), and bicarbonate (HCO₃⁻) in saturated extract of a soil sample taken from the root zone are 5.68 meq∙L⁻¹, 9.90 meq∙L⁻¹, and 11.20 meq∙L⁻¹, respectively. If the concentration ratio of HCO₃⁻/Ca²⁺ is 2.8, the sodium adsorption ratio is ________. [round off to 2 decimal places]

Answer: (4.50 to 4.50)

22. Fresh potatoes of mass 1000 kg are dried from 14% to 93% total solids. If 7% of original potatoes is lost in peeling, the product yield from fresh potatoes in percent is ________. [answer in integer]

Answer: (14.0 to 14.0)

23. In an ordinary chimney, the draught is 12 mm of water column. Assuming density of water to be 1000 kg∙m⁻³, the pressure difference between the outside air and gas at the base of the chimney in Pa is ________. [round off to one decimal place]

Answer: (117.1 to 118.1)

24. A ball mill of 200 cm diameter grinds solid materials while operating with 10 cm size balls. If the same ball mill is used for wet grinding, charged with 20 cm diameter balls, the change in the operating speed in rpm is _______. [round off to 2 decimal places] (Take π = 3.14 and g = 9.81 m∙s⁻²)

Answer: (3.60 to 4.20)

25. Rushton turbine having an impeller diameter of 20 cm and operating at a stirrer speed of 200 rpm is used in a mixing tank. If the tank receives air at a volumetric flow rate of 0.2 m³∙min⁻¹, the non-dimensional Froude number, N_Fr is ______. [round off to 2 decimal places]

Answer: (0.21 to 0.31)

Q.26 – Q.38 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

26. Solution of the differential equation y′′ + y′ + 0. 25y = 0 with the initial values y(0) = 3. 0 and y′(0) = −3. 5 is

(A) y = (3 − 2x) e^0.5x

(B) y = (3 − 2x) e^−0.25x

(D) y = (2 − 3x) e^−0.5x

Answer: (C)

27. A shear annulus with inner and outer diameters of 240 mm and 300 mm, respectively is used to measure shear strength of soil in the field. When it is inserted into the soil and rotated, the torque measured at the soil failure is 50 N∙ Shear strength of the soil in kPa is

(Take π = 3.14)

(A) 14.49

(B) 18.94

(D) 28.98

Answer: (A)

28. A bushy crop with stem cross-sectional diameter 6 mm is to be cut by impact force at a height of 50 mm above the soil surface. Based on the entire stem cross-section, the modulus of elasticity is 1500 N∙mm⁻² and ultimate tensile strength is 35 N∙mm⁻². The force in N that would cause failure of the stem due to bending is

(Take π = 3.14)

(A) 14.84

(B) 23.52

(D) 44.53

Answer: (A)

29. A solar panel has length of 1.3 m and width of 0.65 m. The solar cells cover 90% of the panel area and its conversion efficiency is 13.7%. For a total solar radiation of 750 W∙m⁻², the panel output voltage is 18 V at its maximum power output. If two such panels are connected in series to supply power to run a thresher, the current in A that can be supplied by the two panels at the maximum power output is

(A) 2.17

(B) 3.01

(D) 8.68

Answer: (C)

30. A fertilizer drill with a row to row spacing of 40 cm, discharges 38 g of fertilizer per row per revolution of the metering wheel. The metering wheel is driven through a chain transmission system by ground wheel having 60 cm diameter. Neglecting skid of the ground wheel, for an application rate of 200 kg∙ha⁻¹, the speed ratio of ground wheel to metering wheel will be

(Take π = 3.14)

(A) 1.40 : 1

(B) 2.52 : 1

(D) 4.76 : 1

Answer: (B)

31. A sample of wet sandy-clay loam soil of mass 135 kg is collected for laboratory tests. The wet density, water content (weight basis) and specific gravity of solids of this soil sample are 1.8 g∙cm⁻³, 18%, and 2.7, respectively. The dry density (in g∙cm⁻³) and porosity (in per cent) of the soil sample, respectively, are

(A) 1.53 and 43.50

(B) 1.53 and 77.00

(D) 1.65 and 77.00

Answer: (A)

32. It is proposed to develop bench terraces in an area having land slope of 10%. If the vertical interval between the bench terraces is 2.5 m and the batter slope is 100%, working width (in m) and the area lost for cultivation (in per cent), respectively will be

(A) 22.50 and 0.05

(B) 25.00 and 0.50

(D) 25.00 and 10.45

Answer: (C)

33. While carrying out a traverse survey ABCDA′ using a theodolite with the originating station A, the departures and latitudes of the lines, as obtained, are shown in the following figure (not drawn to scale). It is seen that, due to the observational errors, the originating station A and its computed station A′ are not the same. For this survey, the ‘closing error’ in m is

(A) 6.33

(B) 7.62

(D) 35.21

Answer: (B)

34. The shape of the Instantaneous Unit Hydrograph (IUH) of a catchment is an isosceles triangle with a peak of 60 m³∙s⁻¹ and time to peak of 3 h. If the constant base flow is 7.5 m³∙s⁻¹, the peak of the 3 h Unit Hydrograph (UH) in m³∙s⁻¹ is

(A) 43.33

(B) 50.83

(D) 60.00

Answer: (A)

35. Match the following hulling mechanism in column 1 with the corresponding machine in column 2

(A) P-3, Q-2, R-4, S-1

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

(D) P-4, Q-3, R-1, S-2

Answer: (A)

36. Match the correct items in column 1 with column 2

(A) P-1, Q-2, R-4, S-3

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

(D) P-4, Q-3, R-2, S-1

Answer: (D)

37. A 30 μm thick membrane having 3 m² surface area is used to separate NaCl from a solution at steady state condition. The mass transfer coefficient of NaCl at the solution side is 1×10⁻⁶ m∙s⁻¹ and that at the other side of the membrane is 3×10⁻⁷ m∙s⁻¹. Concentration of NaCl in the solution is 0.03 g∙(100 mL)⁻¹ and, that on the other side of the membrane is assumed to be zero. Permeability of the membrane is 9×10-6 m∙s⁻¹. The rate of removal of the NaCl by the membrane in g∙h⁻¹ is

(A) 0.73

(B) 0.81

(D) 0.93

Answer: (A)

38. In a size reduction operation, the power required to crush 2 ton of feed material per hour is 7.2 kW. Eighty per cent of the feed and product material pass through 4.75 mm and 0.5 mm sieve openings, respectively. The work index of the material is

(A) 6.5

(B) 7.4

(D) 14.8

Answer: (C)

Q.39 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

39. A nine-member committee of an Agricultural University consists of 4 B. Tech., 3 M. Tech., and 2 Ph. D. students. It is decided to remove three students from the committee at random. The probability of removing 2 students from the same category and the third one from any other category is__________.

[round off to 3 decimal places]

Answer: (0.654 to 0.656)

40. Summation of eigenvalues of a matrix is _______.

Answer: (10 to 10)

41. During operation of a two-wheel drive tractor with a total weight of 20 kN in pure sandy soil (angle of internal friction is 26.5°), the weight distribution at the front and rear axles are found to be 35% and 65%, respectively. If extra weight of 2.5 kN is added to each of the rear wheels, the change in maximum thrust developed by the tractor in per cent will be ________. [round off to 2 decimal places]

Answer: (38.20 to 38.60)

42. A tractor PTO driven rotavator with a rotor radius 30 cm has 20 L-shaped blades each of width 12 cm. These blades are fixed at a radial distance of 7 cm from the center of the rotor shaft to the brackets attached to the rotor shaft. When this rotavator is operated at a forward speed of 4.5 km∙h⁻¹ and at a depth of 12 cm, the resultant soil force of 150 N tangential to the rotor circumference acts at the middle of the blade width. The torsional moment acting on the blade in N∙m is _______. [round off to one decimal place]

Answer: (8.90 to 9.10)

43. Fixed cost per year and variable cost per hour of a tractor were estimated based on its annual usage of 800 h. The total cost of operation was found to be Rs. 540 per hour. It was later re-estimated and found that total cost of operation would be Rs. 510 per hour, if the annual hours of use were increased to 1000 h. Considering all the components of annual usage cost to be the same, the variable cost in Rs. per hour would be ___________. [answer in integer]

Answer: (395.0 to 395.0)

44. Two meshed involute gears transmit 1.0 kW power. The pressure angle is 200 and the pitch circle diameter of the large gear rotating at a speed of 600 rpm is 20 cm. If only a pair of teeth meshes at a time, the normal force acting between the meshed teeth in N will be _______. [round off to one decimal place]

(Take π = 3.14)

Answer: (165.0 to 176.0)

45. A horizontal axis lift type wind rotor of diameter 4 m is used to run a pump at a wind velocity of 15 km∙h⁻¹ at standard atmospheric pressure and temperature (density of air is 1.23 kg∙m⁻³). If velocity of wind leaving the rotor blade is reduced to one-third of the approaching wind velocity, the thrust acting on the blade of the wind rotor in N is ____________. [round off to 2 decimal places]

Answer: (118.90 to 119.60)

46. A small watershed receives rainfall of 90 mm in a day. For this watershed, irrespective of the land use, the amount of initial abstraction can be considered as 25% of the potential maximum retention (S) of soil. Initially, the entire watershed was under forest with S = 136 mm, which was converted into cultivated land with S = 64 mm. The change in the daily runoff volume due to this land use alteration for this specific rainfall event in percent is __________.

[round off to one decimal place]

Answer: (142.9 to 143.6)

47. The most economical trapezoidal channel section with 1:1 (horizontal : vertical) side slope is designed to carry a maximum of 40 cm depth of water at its full capacity. If the bed slope of the channel is 1:2500 and the Manning’s roughness coefficient of channel section is 0.01, the estimated discharge capacity of the channel in m³∙s⁻¹is ________. [round off to 2 decimal places]

Answer: (0.18 to 0.22)

48. A windbreak, 15 m in height and 200 m in length, is established to protect the land from wind erosion in an arid area. The minimum wind velocity at the height of 15 m above the ground required to move the most erodible soil fraction is 9.6 m∙s⁻¹. If 5-year return period wind velocity at 15 m height is 16 m∙s⁻¹ and the wind direction deviates 20° from the line perpendicular to the windbreak, the area protected by the windbreak in ha is _________.

[round off to 2 decimal places]

Answer: (2.70 to 3.00)

49. Water is discharged from a tank through a rectangular orifice of width 1.5 m and height 1.2 m. The water level in the tank is 3.5 m above the top edge of the orifice. If the coefficient of discharge of this orifice is 0.62, the discharge through the orifice in m³∙s⁻¹ is ____________. [round off to 2 decimal places]

(Take acceleration due to gravity, g = 9.81 m∙s⁻²)

Answer: (9.90 to 10.10)

50. Two fully penetrating wells are dug 1.4 km apart in a homogenous confined aquifer. The difference in their piezometric levels is 4.0 m. The groundwater flow is steady and unidirectional. If the aquifer has a hydraulic conductivity of 3.5 m∙day⁻¹ and effective porosity of 40%, the time taken for water to move from one well to the other in days is __________. [in integer]

Answer: (56000 to 56000)

51. Food cans are sterilized in a retort to inactivate Clostridium botulinum. Process time (F_o) of this food material is 150 s and the z value is 10°C. Temperatures at the slowest heating region of the food can are measured and the average temperature during time periods 0 to 20 min, 20 to 40 min and 40 to 70 min are 71.1°C, 98.9°C and 110°C, respectively. The actual process time in minutes that is required for equivalent sterilization at 121.1 °C is _________.

[round off to 2 decimal places]

Answer: (2.01 to 3.01)

52. Molecular masses of water and air are 18.02 and 28.97 kg∙(kg mol)⁻¹, respectively. Air in a room is at 40°C under a total pressure of 101.3 kPa absolute and contains water vapour at a partial pressure of 4.0 kPa. If saturated vapour pressure of water at 40 °C is 7.37 kPa, the relative humidity of this air in per cent is ________. [round off to 2 decimal places]

Answer: (52.00 to 54.50)

53. A cylindrical storage bin with an internal diameter of 4 m and a height of 16 m is completely filled with paddy having bulk density of 640 kg∙m⁻³. The angle of internal friction between grain and bin wall is 30° and the ratio of horizontal to vertical pressures is 0.4. When the grain filling rises from 4 m to 16 m in height, the lateral pressure increases by a multiple of__________.

[round off to 2 decimal places]

Answer: (1.60 to 1.70)

54. An air screen grain cleaner unit of capacity one ton∙h⁻¹ with two screens was evaluated with a feed containing 8.5% impurities. During the operation, the clean grain at blower outlet, overflow of 1st screen and underflow of second screen were found to be 0.3%, 1.2% and 0.8%, respectively. If the clean grain contains 0.6% of impurities, the cleaning efficiency of the cleaner unit in per cent would be ________. [round off to one decimal place]

Answer: (93.0 to 94.0)

55. One side of a solid food block of 10 cm thickness is subjected to a heating medium having a film heat transfer coefficient of 70 W∙(m²∙°C)⁻¹. The other side of the food block is being cooled by a medium having a film heat transfer coefficient of 100 W∙(m²∙°C)⁻¹. The food block is having a thermal conductivity of 0.2 W∙(m²∙°C)⁻¹ and the contact area of the block available for heat transfer is 1 m². Heat transfer rate in the block at steady state is 100 J∙s⁻¹. The temperature difference between the two sides of the block in °C is ________.

[round off to 2 decimal places]

Answer: (52.11 to 52.56)

GATE Exam 2021 Aerospace Engineering (AE) Question Paper With Answer Key

June 8, 2023June 13, 2022 by suresh84

GATE-2021

AE : Aerospace Engineering

General Aptitude

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. (i) Arun and Aparna are here.

(ii) Arun and Aparna is here.

(iii) Arun’s families is here.

(iv) Arun’s family is here.

Which of the above sentences are grammatically CORRECT?

(A) (i) and (ii)

(B) (i) and (iv)

(D) (iii) and (iv)

Answer: (B)

3. Two identical cube shaped dice each with faces numbered 1 to 6 are rolled simultaneously. The probability that an even number is rolled out on each dice is:

(A) 1/36

(B) 1/12

(D) 1/4

Answer: (D)

4. ⊕ and ⊙ are two operators on numbers p and q such that p ⊙ q = p – q, and p ⊕ q – p × q

Then, (9 ⊙ (6 ⊕ 7)) ⨀ (7 ⊕ (6 ⊙ 5) =

(A) 40

(B) -26

(D) -40

Answer: (D)

5. Four persons P, Q, R and S are to the seated in a row, R should not be seated at the second position from the left end of the row. The number of distinct seating arrangement possible is:

(A) 6

(B) 9

(D) 24

Answer: (C)

Q.6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong answer: – 2/3).

The distance of point Q to point O, in the same units, should be_____

(A) 3

(B) 4

(D) 6

Answer: (C)

Based on the above passage, which one of the following is TRUE?

(A) The author is of the opinion that rehearsing is important for musicians, actors and public speakers.

(B) The author is of the opinion that rehearsing is less important for public speakers than for musicians and actors.

(D) The author is of the opinion that rehearsal is more important for actors than musicians.

Answer: (A)

8. (1) Some football players play cricket.

(2) All cricket players play hockey.

Among the options given below, the statement that logically follows from the two statements 1 and 2 above, is:

(A) No football player plays hockey.

(B) Some football players play hockey.

(D) All hockey players play football.

Answer: (B)

9. In the figure shown above, PQRS is a square. The shaded portion is formed by the intersection of sectors of circles with radius equal to the side of the square and centers at S and Q.

The probability that any point picked randomly within the square falls in the shaded area is______

(A)

(B) 1/2

(D) π/4

Answer: (C)

The minimum area of the triangle PQR possible, in cm², is

(A) 18

(B) 24

(D) 144√3

Answer: (D)

Aerospace Engineering (AE)

Q.1 – Q.13 carry One marks each (for each wrong answer: -1/3).

1. Consider the differential equation and the boundary conditions y(0) = 1 and The solution to this equation is:

(A) y = (1 + 2x)e⁻^4x

(B) y = (1 – 4x)e⁻^4x

(D) y = (1+4x) e⁻^4x

Answer: (D)

2. u(x, y) is governed by the following equation The nature of this equation is:

(A) linear

(B) elliptic

(D) parabolic

Answer: (B)

3. Consider the velocity field The field is

(A) divergence-free and curl-free

(B) curl-free but not divergence-free

(D) neither divergence-free nor curl-free

Answer: (B)

4. The figures shows schematics of wave patterns at the exit of nozzles A and B operating at different pressure ratios.

Nozzles A and B, respectively, are said to be operating in:

(A) over-expanded mode and under-expanded mode

(B) under-expanded mode and perfectly expanded mode

(D) under-expanded mode and over-expanded mode

Answer: (A)

5. The combustion process in a turbo-shaft engine during ideal operation is:

(A) isentropic

(B) isobaric

(D) isothermal

Answer: (B)

6. How does the specific thrust of a turbojet engine change for a given flight speed with increase in flight altitude?

(A) Increases monotonically

(B) Decreases monotonically

(D) First increases and then decreases

Answer: (A)

7. How does the propulsion efficiency of a turbofan engine, operating at a given Mach number and a given altitude, change with increase in compressor pressure ratio?

(A) Remains constant

(B) Increases monotonically

(D) First decreases and then increases

Answer: (D)

8. A solid propellant rocket producing 25 MN thrust is fired for 150 seconds. The specific impulse of the rocket is 2980 Ns/kg. How much propellant is burned during the rocket operation?

(A) 8390 kg

(B) 82300 kg

(D) 11.2 × 10⁶ kg

Answer: (C)

9. The shape of a supersonic diffuser that slows down an supersonic flow to subsonic flow is

(A) converging

(B) diverging

(D) converging-diverging

Answer: (D)

10. Uniaxial tension test (see the figure) is conducted on two different samples prepared with homogeneous, isotropic materials. One of the materials is brittle, whereas the other is ductile.

Assuming that there is no stress concentration at loading points, the failure would initiate.

(A) along x-x in both materials

(B) along x-x in brittle material and along y-y in ductile material

(D) along y-y in both materials

Answer: (B)

11. For the state of stress as shown in the figure, what is the orientation of the plane with maximum shear stress with respect to the x-axis?

(A) 45°

(B) -45°

(D) -22.5°

Answer: (D)

12. Let V_TAS be the true airspeed of an aircraft flying at a certain altitude where the density of air is ρ, and V_EAS be the equivalent air speed. If ρ₀ is the density of air at sea-level, what is the ratio equal to ?

(A) ρ/ρ₀

(B) ρ₀/ρ

(C)

(D)

Answer: (C)

13. C_m – α variation for a certain aircraft is shown in the figure. Which one of the following statements is true for this aircraft?

(A) The aircraft can trim at a positive α and it is stable.

(B) The aircraft can trim at a positive, α but it is unstable

(D) The aircraft can trim at a negative α, but it is unstable

Answer: (B)

14. Which of the following statement(s) is/are true across an oblique shock (in adiabatic conditions) over a wedge shown below?

(A) Total pressure decreases

(B) Mach number based on velocity tangential to the shock decreases

(D) Mach number based on velocity tangential to the shock remains the same and that based on velocity normal to the shock decreases

Answer: (A, B, C)

15. Which of the following statement(s) is/are true with regards to Kutta condition for flow past airfoils?

(A) It is utilized to determine the circulation on an airfoil.

(B) It is applicable only to airfoils with sharp trailing edge.

(D) The flow leaves the trailing edge smoothly

Answer: (A, B, D)

16. According to the thin airfoil theory, which of the following statement(s) is/are true for a cambered airfoil?

(A) The lift coefficient for an airfoil is directly proportional to the absolute angle of attack.

(B) The aerodynamic center lies at quarter chord point.

(D) Drag coefficient is proportional to the square of lift coefficient.

Answer: (A, B)

17. (round off to nearest integer).

Answer: (0 to 0)

18. Given that ζ is the unit circle in the counter-clockwise direction with its center at origin, the integral (round of to three decimal place).

Answer: (0.02 to 0.03)

19. A single degree of freedom spring-mass-damper system is designed to ensure that the system returns to its original undisturbed position in minimum possible time without overshooting. If the mass of the system is 10 kg, spring stiffness is 17400 N/m and the natural frequency is 13.2 rad/s, the coefficient of damping of the system in Ns/m is _____ (round off to nearest integer).

Answer: (264 to 264 OR 833 to 835)

20. Two cantilever beams (Beam 1 and Beam 2) are made of same homogenous material and have identical cross sections, Beam 1 has length l and Beam 2 has length 2l. Ratio of the first natural frequency of Beam 1 to that of Beam 2 is ______(round off to nearest integer.

Answer: (4 to 4)

21. A free vortex filament (oriented along Z-axis) of strength K= 5 m²/s is placed at the origin as shown in the figure. The circulation around the closed loop ABCDEFA for this flow is ______.

Answer: (0 to 0)

22. A thin-walled cylindrical tank with closed ends, made of homogenous and isotropic material, is pressurized internally. If the hoop (circumferential strain developed in the material is thrice the value of the axial strain then the Poisson’s ratio of the material is ______ (correct up to one decimal place).

Answer: (0.2 to 0.2)

23. A jet aircraft has the following specifications: wing loading = 1800 N/m², wing area = 30 m², drag polar C_D = 0.02 + 0.04C_L² , and C_{L, max} = 1.6. Take density of air at sea level as 1.225 kg/m³.

The speed at which the aircraft achieves maximum endurance in a steady and level flight at sea level is ______ m/s (round off to two decimal places).

Answer: (64.30 to 64.60)

24. An aircraft with twin jet engines has the following specifications:

Thrust produced (per engine) = 8000 N

Spanwise distance between the two engines = 10 m

Wing area = 50 m², Wing span = 10 m

Rudder effectiveness C_nδr = −0.002/deg

Density of air at sea level = 1.225 kg/m³

The rudder deflection, in degrees, required to maintain zero sideslip at 100 m/s in steady and level flight at sea level with a non-functional right engine is ______ (round off to two decimal places).

Answer: (6.50 to 6.60)

25. The velocity required to launch a space shuttle from the surface of the earth to achieve a circular orbit of 250 km altitude is ______ (round off to two decimal places).

For earth, Gm_e = 398,600.4 km³/s² and surface radius R₀ = 6378.14 km.

Answer: (7.75 to 7.77 OR 7750.00 to 7770.00)

Q.26 – Q.30 carry TWO marks each (for each wrong answer: – 2/3).

26. A rigid massless rod pinned at one end has a mass m attached to its other end. The rod is supported by a linear spring of stiffness k as shown in the figure.

The natural frequency of this system is:

(A)

(B)

(C)

(D)

Answer: (A)

27. The figure shows three glasses P, Q and R with water and floating ice cube. Glass P has a solid ice cube, glass Q has an ice cube with a small solid steel ball embedded in it and glass R has an ice cube with an air bubble. After the ice cube melts, the level of water in glasses P, Q and R, respectively:

(A) remains same, increases, and decreases

(B) increases, decreases, and increases

(D) remains same, decreases, and increases

Answer: (C)

28. To estimate aerodynamic loads on an aircraft flying at 100 km/h at standard sea-level conditions, a one-fifth scale model is tested in a variable-density wind tunnel ensuring similarity of inertial and viscous forces. The pressure used in the wind tunnel is 10 times the atmospheric pressure. Assuming ideal gas law to hold and the same temperature conditions in model and prototype, the velocity needed in the wind tunnel test-section is _______.

(A) 25 km/h

(B) 50 km/h

(D) 20 km/h

Answer: (B)

29. The figure shows schematic of a set-up for visualization of non-uniform density field in the test section of a supersonic wind tunnel. This technique of visualization of high speed flows is known as:

(A) schlieren

(B) interferometry

(D) holography

Answer: (C)

30. For a conventional fixed-wing aircraft in a 360° inverted vertical loop maneuver, what is the load factor (n) at the topmost point of the loop? Assume the flight to be steady at the topmost point.

(A) n = 1

(B) n < 1

(D) n > −1

Answer: (D)

31. Which of the following statement(s) is/are true about the function defined as f(x) = e⁻^x |cos x| for x > 0 ?

(A) Differentiable at x = π/2

(B) Differentiable at x = π

(D) Continuous at x = 2π

Answer: (B, D)

32. A two degree of freedom spring-mass system undergoing free vibration with generalized coordinates x₁ and x₂ has natural frequencies ω₁ = 233.9 rad/s and ω₂ = 324.5 rad/s, respectively. The corresponding mode shapes are If the system is disturbed with certain deflections and zero initial velocities, then which of the following statement(s) is/are true?

(A) An initial deflection of x₁ (0) = 6.32 cm and x₂ (0) = −3.16 cm would make the system oscillate with only the second natural frequency.

(B) An initial deflection of x₁ (0) = 2 cm and x₂ = −6.32 cm would make the system oscillate with only the first natural frequency.

(C) An initial deflection of x₁ (0) = 2 cm and x₂ = −2 cm would make the system oscillate with a linear combination of first and second natural frequencies.

(D) An initial deflection of x₁ (0) = 1 cm and x₂ = −6.32 cm cm would make the system oscillate with only the first natural frequency.

Answer: (B, C)

33. A shock moving into a stationary gas can be transformed to a stationary shock by a change in reference frame, as shown in the figure. Which of the following is/are true relating the flow properties in the two reference frames?

Answer: (D)

34. For a conventional fixed-wing aircraft, which of the following statements are true?

(A) Making C_m_α more negative leads to an increase in the frequency of its short-period mode.

(B) Making C_mqmore negative leads to a decreased damping of the short-period mode.

(D) Increasing the size of the vertical fin leads to a higher yaw damping.

Answer: (A, C, D)

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

(A) Service ceiling is higher than absolute ceiling for a piston-propeller aircraft.

(B) For a given aircraft, the stall speed increases with increase in altitude.

(D) For a jet aircraft constrained to fly at constant altitude, there exists an altitude where its range is maximum.

Answer: (B, C, D)

36. A conventional fixed-wing aircraft, with a horizontal tail and vertical fin, in steady and level flight is subjected to small perturbations. Which of the following statement(s) is/are true?

(A) Vertical fin has a stabilizing effect on the lateral stability of the aircraft.

(B) Vertical fin has a destabilizing effect on the directional stability of the aircraft.

(D) Horizontal tail has a stabilizing effect on the longitudinal static stability of the aircraft.

Answer: (A, D)

Q.37 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

37. The ratio of the product of eigenvalues to the sum of the eigenvalues of the given matrix is _______ (round off to nearest integer).

Answer: (8 to 8)

38. The definite integral is evaluated using four equal intervals by two methods – first by the trapezoidal rule and then by the Simpson’s one- third rule. The absolute value of the difference between the two calculations is _______ (round off to two decimal places).

Answer: (0.66 to 0.68)

39. The deflection y of a certain beam of length l and uniform weight per unit length w, is given as where x is the distance from the point of support and EI is a constant. The non-dimensional location x/l, where the deflection of the beam is maximum, is _____ (round off to two decimal places).

Answer: (0.41 to 0.43)

40. A large water tank is fixed on a cart with wheels and a vane (see figure). The wheels of the cart provide negligible resistance for rolling on the fixed support. The cart is tied to the fixed support with a thin horizontal rope. There is a hole of diameter 5 cm on the side of the tank through which a jet of constant velocity of 10 m/s emerges. The jet of water is deflected by the attached vane by 60° (see figure). Assume that the jet velocity remains constant at 10 m/s after emerging from the vane. Take density of water to be 1000 kg/m³. The tension in the connecting rope is _____ N (round off to one decimal place).

Answer: (98.0 to 98.5)

41. A finite wing of elliptic planform with aspect ratio 10, whose section is a symmetric airfoil, is placed in a uniform flow at 5 degrees angle of attack. The induced drag coefficient for the wing is ______ (round off to three decimal places).

Answer: (0.005 to 0.009)

42. Consider a model of a boundary layer with the following velocity profile:

The shape factor, defined as the ratio of the displacement thickness to momentum thickness, for this profile is _____ (round off to 2 decimal places).

Answer: (4.8 to 5.2)

43. An aircraft with a turbojet engine is flying at 270 m/s. The enthalpy of the incoming air at the intake is 260 kJ/kg and the enthalpy of the exhaust gases at the nozzle exit is 912 kJ/kg. The ratio of mass flow rates of fuel and air is equal to 0.019. The chemical energy (heating value) of fuel is 44.5 MJ/kg and the combustion process is ideal. The total loss of heat from the engine to the ambient is 25 kJ per kg of air. The velocity of the exhaust jet is __________m/s (round off to two decimal places).

Answer: (605 to 607)

44. Hot gases are generated at a temperature of 2100 K and a pressure of 14 MPa in a rocket chamber. The hot gases are expanded ideally to the ambient pressure of 0.1 MPa in a convergent-divergent nozzle having a throat area of 0.1 m². The molecular mass of the gas is 22 kg/kmol. The ratio of specific heats (γ) of the gas is 1.32. The value of the universal gas constant (R₀) is 8314 J/kmol-K. The acceleration due to gravity, g, is 9.8 m/s². The specific impulse of the rocket is _______ seconds (round off to two decimal places).

Answer: (216 to 220)

45. A twin-spool turbofan engine is operated at sea level (P_a = 1 bar, T_a = 288 K). The engine has separate cold and hot nozzles. During static thrust test at sea level, the overall mass flow rate of air through the engine and the cold exhaust temperature are measured to be 100 kg/s and 288 K, respectively. The parameters for the engine are:

Fan pressure ratio = 1.6

Overall pressure ratio = 20

Bypass ratio = 3.0

Turbine entry temperature = 1800 K.

The specific heat at constant pressure (Cp) is 1.005 kJ/kg-K and the ratio of specific heats (γ) is 1.4 for air.

Assuming ideal fan and ideal expansion in the nozzle, the sea-level static thrust from the cold nozzle is _____________ kN (round off to two decimal places).

Answer: (20 to 22)

46. At the design conditions, the velocity triangle at the mean radius of a single stage axial compressor is such that the blade angle at the rotor exit is equal to 30°. The absolute velocities at the rotor inlet and exit are equal to 140 m/s and 240 m/s, respectively. The flow velocities relative to the rotor at inlet and exit of the rotor are equal to 240 m/s and 140 m/s, respectively.

The blade speed (U) at the mean radius of the rotor is __________ m/s (round off to two decimal places).

Answer: (274 to 282)

47. A single stage axial turbine has a mean blade speed of 340 m/s at design condition with blade angles at inlet and exit of the rotor being 21° and 55°, respectively. The degree of reaction at the mean radius of the rotor is equal to 0.4. The annulus area at the rotor inlet is 0.08 m² and the density of gas at the rotor inlet is 0.9 kg/m³. The flow rate through the turbine at these conditions is __________ kg/s (round off to two decimal places).

Answer: (18.0 to 19.5)

48. The air flow rate through the gas generator of a turboprop engine is 100 kg/s. The stagnation temperatures at inlet and exit of the combustor are 600 K and 1200 K, respectively. The burner efficiency is 90% and the heating value of the fuel is 40 MJ/kg. The specific heats at constant pressure (Cp) for air and burned gases are 1000 J/kg-K and 1200 J/kg-K, respectively. The flow rate of the fuel being used is _____________ kg/s (round off to two decimal places)..

(Note: Do not neglect the fuel flow rate with respect to the air flow rate)

Answer: (2.35 to 2.50)

49. A rigid horizontal bar ABC, with roller support at A, is pinned to the columns BD and CE at points B and C, respectively as shown in figure. The other end of the column BD is fixed at D, whereas the column CE is pinned at E. A vertical load P is applied on the bar at a distance ‘a’ from point B.

The two columns are made of steel with elastic modulus 200 GPa and have a cross section of 1.5 cm x 1.5 cm. The value of ‘a’ for which both columns buckle simultaneously, is ____________ cm (round off to one decimal place).

Answer: (14.0 to 16.0)

50. A two-cell wing box is shown in the figure. The cell walls are 1.5 mm thick and the shear modulus G = 27 GPa. If the structure is subjected to a torque of 12 kNm, then the wall AD will experience a shear stress of magnitude _________ MPa (round off to one decimal place).

Answer: (2.1 to 2.5)

51. Two cantilever beams AB and DC are in contact with each other at their free ends through a roller as shown in the figure. Both beams have a square cross section of 50 mm x 50 mm, and the elastic modulus E = 70 GPa. If beam AB is subjected to a uniformly distributed load of 20 kN/m, then the compressive force experienced by the roller is ___________ kN (round off to one decimal place).

Answer: (2.2 to 2.6)

52. A 3 m x 1 m signboard is supported by a vertical hollow pole that is fixed to the ground. The pole has a square cross section with outer dimension 250 mm. The yield strength of the pole material is 240 MPa. To sustain a wind pressure of 7.5 kPa, the dimension d of the pole is _________ mm (round off to nearest integer).

Answer: (232 to 238)

53. An airplane weighing 5500 kg is in a steady level flight with a speed of 225 m/s. The pilot initiates a steady pull-up maneuver with a radius of curvature of 775 m. The location of center of gravity (CG), center of pressure on wing (CP) and point of action (T) of tail force are marked in the figure. Use g = 9.81 m/s². Neglect drag on the tail and assume that tail force is vertical. Assuming the engine thrust and drag to be equal, opposite and collinear, the tail force is_____________ kN (round off to one decimal place).

Answer: (14.8 to 15.2)

54. A jet aircraft weighing 10,000 kg has an elliptic wing with a span of 10 m and area 30 m². The C_D0 for the aircraft is 0.025. The maximum speed of the aircraft in steady and level flight at sea level is 100 m/s. The density of air at sea level is 1.225 kg/m³, and take g = 10 m/s². The maximum thrust developed by the engine at sea level is ______ N (round off to two decimal places).

Answer: (9735 to 9797)

55. Consider a jet transport airplane with the following specifications:

Lift curve slope for wing-body