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GATE Exam 2021 Computer Science and Information Technology (CS-2) Question Paper With Answer Key

June 8, 2023June 13, 2022 by suresh84

GATE-2021

CS-2: 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. Gauri said that she can play the keyboard __________ her sister.

(A) as well as

(B) as better as

(D) as worse as

Answer: (A)

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

Answer: (B)

3. If θ is the angle, in degrees, between the longest diagonal of the cube and any one of the edges of the cube, then, cos θ =

(A) 1/2

(B) 1/√3

(D) √3/2

Answer: (B)

4. If then the value of x is:

(A) 2

(B) 4

(D) 8

Answer: (B)

5. Pen : Write :: Knife : _________

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

(A) Vegetables

(B) Sharp

(D) Blunt

Answer: (C)

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

6. Listening to music during exercise improves exercise performance and reduces discomfort. Scientists researched whether listening to music while studying can help students learn better and the results were inconclusive. Students who needed external stimulation for studying fared worse while students who did not need any external stimulation benefited from music.

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

(A) Listening to music has no effect on learning and a positive effect on physical exercise.

(B) Listening to music has a clear positive effect both on physical exercise and on learning.

(C) Listening to music has a clear positive effect on physical exercise. Music has a positive effect on learning only in some students.

(D) Listening to music has a clear positive effect on learning in all students. Music has a positive effect only in some students who exercise.

Answer: (C)

7. A jigsaw puzzle has 2 pieces. One of the pieces is shown above. Which one of the given options for the missing piece when assembled will form a rectangle? The piece can be moved, rotated or flipped to assemble with the above piece.

Answer: (A)

8. The number of students in three classes is in the ratio 3:13:6. If 18 students are added to each class, the ratio changes to 15:35:21.

The total number of students in all the three classes in the beginning was:

(A) 22

(B) 66

(D) 110

Answer: (C)

9. The number of units of a product sold in three different years and the respective net profits are presented in the figure above. The cost/unit in Year 3 was ` 1, which was half the cost/unit in Year 2. The cost/unit in Year 3 was one-third of the cost/unit in Year 1. Taxes were paid on the selling price at 10%, 13% and 15% respectively for the three years. Net profit is calculated as the difference between the selling price and the sum of cost and taxes paid in that year.

The ratio of the selling price in Year 2 to the selling price in Year 3 is ________.

(A) 4:3

(B) 1:1

(D) 1:2

Answer: (A)

10. Six students P, Q, R, S, T and U, with distinct heights, compare their heights and make the following observations.

Observation I: S is taller than R.

Observation II: Q is the shortest of all.

Observation III: U is taller than only one student.

Observation IV: T is taller than S but is not the tallest.

The number of students that are taller than R is the same as the number of students shorter than ______.

(A) T

(B) R

(D) P

Answer: (C)

Computer Science and Information Technology (CS, Set-2)

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

1. Let G be a connected undirected weighted graph. Consider the following two statements.

S₁: There exists a minimum weight edge in G which is present in every minimum spanning tree of G.

S₂: If every edge in has distinct weight, then G has a unique minimum spanning tree.

Which one of the following options 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)

2. Let H be a binary min-heap consisting of n elements implemented as an array. What is the worst case time complexity of an optimal algorithm to find the maximum element is H?

(A) Θ(1)

(B) Θ(log n)

(D) Θ(n log n)

Answer: (C)

3. Consider the following ANSI C program:

Which one of the following phases in a seven-phase C complier will throw an error?

(A) Lexical analyzer

(B) Syntax analyzer

(D) Machine dependent optimizer

Answer: (C)

4. The format of the single-precision floating-point representation of a real number as per the IEEE 754 standard is as follows:

Which one of the following choices is correct with respect to the smallest normalized positive number represented using the standard?

(A) exponent = 00000000 and nmantissa = 000000000000000000000000

(B) exponent = 00000000 and nmantissa = 000000000000000000000001

(D) exponent = 00000001 and nmantissa = 000000000000000000000001

Answer: (C)

5. Which one of the following circuits implements the Boolean function given below?

f(x, y, z) = m₀ + m₁ + m₃ + m₄ + m₅ + m₆, where m_i is the i^th minterm.

Answer: (A)

6. Consider the following statements S1 and S2 about the relational data model:

S1: A relation scheme can have at most one foreign key.

S2: A foreign key in a relation scheme R cannot be used to refer to tuples of R.

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: (D)

7. Consider the three-may handshake mechanism followed during TCP connection establishment between hosts P and Q. Let X and Y be two random 32-bit starting sequence numbers chosen by P and Q respectively. Suppose P sends a TCP connection request message to Q with a TCP segment having SYN bit = 1, SEQ number = X, and ACK bit = 0. Suppose Q accepts the connection request. Which one of the following choices represents the information present in the TCP segment header that is sent by Q to P ?

(A) SYN bit = 1, SEQ number = X + 1, ACK bit = 0, ACK number = Y, FIN bit =0

(B) SYN bit = 0, SEQ number = X+1, ACK bit = 0, ACK number = Y, FIN bit = 1

(D) SYN bit = 1, SEQ number = Y, ACK bit = 1, ACK number = X, FIN bit = 0

Answer: (C)

8. What is the worst-case number of arithmetic operations performed by recursive binary search on a sorted array of size n ?

(A) Θ(√n)

(B) Θ(log₂(n))

(D) Θ(n)

Answer: (B)

9. Let L ⊆ {0, 1}* be an arbitrary regular language accepted by a minimal DFA with k states. Which one of the following languages must necessarily be accepted by a minimal DFA with k states?

(A) L – {01}

(B) L ⋃ {01}

(D) L ∙ L

Answer: (C)

10. Consider the following ANSI C program.

What is the output of the above program?

(A) 14

(B) 20

(D) 30

Answer: (C)

Q.11 – Q.15 Multiple Select Question (MSQ), carry ONE marks each (no negative marks).

11. Consider the following sets, where n ≥

S₁: Set of all n × n matrices with entries from the set {a, b, c}

S₂: Set of all functions from the set {0, 1, 2, …, n² – 1} to the set {0, 1, 2}

Which of the following choice(s) is/are correct?

(A) There does not exist a bijection from S₁ to S₂

(B) There exists a surjection from S₁ to S₂.

(D) There does not exist an injection from S₁ to S₂

Answer: (B; C)

12. Let L₁ be a regular language and L₂ be a context-free language. Which of the following languages is/are context-free?

Answer: (B; C; D)

13. In the context of compilers, which of the following is/are NOT an intermediate representation of the source program?

(A) Three address code

(B) Abstract Syntax Tree (AST)

(D) Symbol table

Answer: (D)

14. Which of the following statement(s) is/are correct in the context of CPU scheduling?

(A) Turnaround time includes waiting time.

(B) The goal is to only maximize CPU utilization and minimize throughput.

(D) Implementing preemptive scheduling needs hardware support.

Answer: (A; C; D)

15. Choose the correct choice(s) regarding the following propositional logic assertion S:

S : ((P ⋀ Q) → R) → ((P ⋀ Q) → (Q → R))

(A) S is neither a tautology nor a contradiction.

(B) S is a tautology.

(D) The antecedent of S is logically equivalent to the consequent of S.

Answer: (B; D)

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

16. Consider a complete binary tree with 7 nodes. Let A denote the set of first 3 elements obtained by performing Breadth-First Search (BFS) starting from the root. Let B denote the set of first 3 elements obtained by performing Depth-First Search (DFS) starting from the root.

The value of |A – B| is _______

Answer: (1 to 1)

17. Consider the following deterministic finite automaton (DFA).

The number of strings of length 8 accepted by the above automaton is _________.

Answer: (256 to 256)

18. If x and y are two decimal digits and (0.1101)₂ = (0.8xy5)₁₀, the decimal value of x + y is ________

Answer: (3 to 3)

19. Consider a set-associative cache of size 2KB (1KB = 2¹⁰ bytes) with cache block size of 64 bytes. Assume that the cache is byte-addressable and a 32-bit address is used for accessing the cache. If the width of the tag field is 22 bits, the associativity of the cache is _________.

Answer: (2 to 2)

20. Consider a computer system with DMA support. The DMA module is transferring one 8-bit character in one CPU cycle from a device to memory through cycle stealing at regular intervals. Consider a 2 MHz processor. If 0.5% processor cycles are used for DMA, the data transfer rate of the device is _______ bits per second.

Answer: (80000 to 80000)

21. A data file consisting of 1,50,000 student-records is stored on a hard disk with block size of 4096 bytes. The data file is sorted on the primary key RollNo. The size of a record pointer for this disk is 7 bytes. Each student-record has a candidate key attribute called ANum of size 12 bytes. Suppose an index file with records consisting of two ields, ANum value and the record pointer to the corresponding student record, is built and stored on the same disk. Assume that the records of data file and index file are not split across disk blocks. The number of blocks in the index file is ________.

Answer: (698 to 698)

22. For a given biased coin, the probability that the outcome of a toss is a head is 0.4. This coin is tossed 1,000 times. Let X denote the random variable whose value is the number of times that head appeared in these 1,000 tosses. The standard deviation of X (rounded to 2 decimal places) is ________.

Answer: (15.00 to 16.00)

23. Consider the following ANSI C function:

The value returned by SomeFunction (15, 255) is ______.

Answer: (15 to 15)

24. Suppose that P is a 4 × 5 matrix sch that every solution of the equation P_x = 0 is a scalar multiple of [2 5 4 3 1]^T. The rank of P is _______.

Answer: (4 to 4)

25. Suppose that f : ℝ → ℝ is a continuous function on the interval [−3, 3] and a differentiable function in the interval (−3, 3) such that for every x in the interval f'(x) ≤ If f(−3) = 7, then f(3) is at most _______.

Answer: (19 to 19)

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

26. Consider the string abbccddeee. Each letter in the string must be assigned a binary code satisfying the following properties:

(1) For any two letters, the code assigned to one letter must not be a prefix of the code assigned to the other letter.

(2) For any two letters of the same frequency, the letter which occurs earlier in the dictionary order is assigned a code whose length is at most the length of the code assigned to the other letter.

Among the set of all binary code assignments which satisfy the above two properties, what is the minimum length of the encoded string?

(A) 21

(B) 23

(D) 30

Answer: (B)

27. Assume a two-level inclusive cache hierarchy, L1 and L2, where L2 is the larger of the two. Consider the following statements.

S₁ : Read misses in a write through L1 cache do not result in writebacks of dirty lines to the L2.

S₂ : Write allocate policy must be used in conjunction with write through caches and no-write allocate policy is used with writeback caches.

Which of the following statements 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: (A)

28. Suppose we want to design a synchronous circuit that processes a string of 0’s and 1’s. Given a string, it produces another string by replacing the first 1 in any subsequence of consecutive 1’s by a 0. Consider the following example.

Input sequence: 00100011000011100

Output sequence : 00000001000001100

A Mealy Machine is a state machine where both the next state and the output are functions of the present state and the current input.

The above mentioned circuit can be designed as a two-state Mealy machine. The states in the Mealy machine can be represented using Boolean values 0 and 1. We denote the current state, the next state, the next incoming bit, and the output bit of the Mealy machine by the variables s, t, b and y respectively.

Assume the initial state of the Mealy machine is 0.

What are the Boolean expressions corresponding to t and y in terms of s and b?

Answer: (B)

29. In an examination, a student can choose the order in which two questions (QuesA and QuesB) must be attempted.

– If the first question is answered wrong, the student gets zero marks.

– If the first question is answered correctly and the second question is not answered correctly, the student gets the marks only for the first question.

-If both the questions are answered correctly, the student gets the sum of the marks of the two questions.

The following table shows the probability of correctly answering a question and the marks of the question respectively.

Assuming that the student always wants to maximize her expected marks in the examination, in which order should she attempt the questions and what is the expected marks for that order (assume that the questions are independent)?

(A) First QuesA and then QuesB. Expected marks 14.

(B) First QuesB and then QuesA. Expected marks 14.

(D) First QuesA and then QuesB. Expected marks 16.

Answer: (D)

30. Consider the following ANSI C code segment:

Assume that the variable y points to a struct (allocated on the heap) containing two fields f1 and f2, and the local variables x, y, z, p, q, and i are allotted registers. Common sub-expression elimination (CSE) optimization is applied on the code. The number of addition and dereference operations (of the form y ->f1 or y->f2) in the optimized code, respectively, are:

(A) 403 and 102

(B) 203 and 2

(D) 303 and 2

Answer: (D)

31. The relation scheme given below is used to store information about the employees of a company, where empId is the key and deptId indicates the department to which the employee is assigned. Each employee is assigned to exactly one department.

Consider the following SQL query:

The above query gives, for each department in the company, the number of female employees whose salary is greater than the average salary of

(A) employees in the department.

(B) employees in the company.

(D) female employees in the company.

Answer: (B)

32. Let S be the following schedule of operations of three transactions T₁, T₂ and T₃ in a relational database system:

R₂(Y), R₁(X), R₃(Z), R₁(Y), W₁(X), R₂(Z), W₂(Y), R₃(X), W₃(Z)

Consider the statement P and Q below:

P: S is conflict-serializable.

Q: If T₃ commits before T₁ finishes, then S is recoverable.

Which one of the following choices is correct?

(A) Both P and Q are true.

(B) P is true and Q is false.

(D) Both P and Q are false.

Answer: (B)

33. A bag has r red balls and b black balls. All balls are identical except for their colours. In a trial, a ball is randomly drawn from the bag, its colour is noted and the ball is placed back into the bag along with another ball of the same colour. Note that the number of balls in the bag will increase by one, after trial. A sequence of four such trials is conducted. Which one of the following choices gives the probability of drawing a red ball in the fourth trial?

Answer: (A)

34. Consider the cyclic redundancy check (CRC) based error detecting scheme having the generator polynomial X³ + X + 1. Suppose the message m₄m₃m₂m₁m₀ = 11000 is to be transmitted. Check bits c₂c₁c₀ are appended at the end of the message by the transmitter using the above CRC scheme. The transmitted bit string is denoted by m₄m₃m₂m₁m₀c₂c₁c₀. The value of the checkbit sequence c₂c₁c₀ is

(A) 101

(B) 110

(D) 111

Answer: (C)

35. Consider the following ANSI C program:

Which one of the statements below is correct about the program?

(A) Upon execution, the program creates a linked-list of five nodes.

(B) Upon execution, the program goes into an infinite loop.

(D) It dereferences an uninitialized pointer that may result in a run-time error.

Answer: (D)

36. Consider the following two statements about regular languages:

S₁: Every infinite regular language contains an undecidable language as a subset.

S₂: Every finite language is regular.

Which one of the following choices is correct ?

(A) Only S₁ is true.

(B) Only S₂is true.

(D) Neither S₁ nor S₂ is true.

Answer: (C)

37. For two n-dimensional real vectors P and Q, the operation s(P, Q) is defined as follows:

Let ℒ be a set of 10-dimensional non-zero real vectors such that for every pair of distinct vectors P, Q, ∈ ℒ s(P, Q) = 0.

(A) 9

(B) 10

(D) 100

Answer: (B)

38. For a statement S in a program, in the context of liveness analysis, the following sets are defined:

USE(S) : the set of variables used in S

IN(S) : the set of variables that are live at the entry of S

OUT(S) : the set of variables that are live at the exit of S

Consider a basic block that consists of two statements, S₁ followed by S₂. Which one of the following statements is correct?

(A) OUT(S₁) = IN(S₂)

(B) OUT(S₁) = IN(S₁) ⋃ USE(S₁)

(D) OUT(S₁) = USE(S₁) ⋃ IN(S₂)

Answer: (A)

39. For constants a ≥ 1 and b > 1, consider the following recurrence defined on the non-negative integers:

Which one of the following options is correct about the recurrence T(n)?

Answer: (C)

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

40. Suppose the following functional dependencies hold on a relation U with attributes P, Q, R, S, and T.

P → QR

RS → T

Which of the following functional dependencies can be inferred from the above functional dependencies?

(A) PS → T

(B) R → T

(D) PS → R

Answer: (A; C; D)

41. For a string 𝓌, we define 𝓌^R to be the reverse of 𝓌. For example if 𝓌 = 01101 then 𝓌^R = 10110.

Which of the following languages is/are context-free?

Answer: (B; C; D)

42. Consider the following multi-threaded code segment (in a mix of C and pseudocode), invoked by two processes P1 and P2, and each of the processes spawns two threads T1 and T2:

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

(A) Both P1 and P2 will print the value of x as 2.

(B) At least one of P1 and P2 will print the value of x as 4.

(D) Both T1 and T2, in both the processes, will print the value of y as 1.

Answer: (A; D)

43. Consider a computer system with multiple shared resource types, with one instance per resource type. Each instance can be owned by only one process at a time. Owning and freeing of resources are done by holding a global lock (L). The following scheme is used to own a resource instance:

Which of the following choice(s) about the above scheme is/are correct?

(A) The scheme ensures that deadlocks will not occur.

(B) The scheme may lead to live-lock.

(D) The scheme violates the mutual exclusion property.

Answer: (A; B; C)

44. If the numerical value of a 2-byte unsigned integer on a little endian computer is 255 more than that on a big endian computer, which of the following choices represent(s) the unsigned integer on a little endian computer?

(A) 0x6665

(B) 0x0001

(D) 0x0100

Answer: (A; D)

45. Consider a computer network using the distance vector routing algorithm in its network layer. The partial topology of the network is as shown below.

The objective is to find the shortest-cost path from the router R to routers P and Q. Assume that R does not initially known the shortest routes to P and Q. Assume that R has three neighbouring routers denotes as X, Y, and Z. During one iteration, R measures its distance to its neighbours X, Y, and Z as 3, 2, and 5, respectively. Router R gets routing vectors from its neighbours that indicate that the distance to router P from routers X, Y and Z are 7, 6, and 5 respectively. The routing vector also indicates that the distance to router Q from routers X, Y, and Z are 4, 6, and 8, respectively. Which of the following statement(s) is/are correct with respect to the new routing table of R, after updation during this iteration?

(A) The distance from R to P will be stored as 10.

(B) The distance from R to Q will be stored as 7.

(D) The next hop router for a packet from R to Q is Z.

Answer: (B; C)

46. Consider the following directed graph:

Which of the following is/are correct about the graph?

(A) The graph does not have a topological order.

(B) A depth-first traversal starting at vertex S classifies three directed edges as back edges.

(D) For each pair of vertices u and v, there is a directed path from u to v.

Answer: (A; B)

47. Which of the following regular expressions represent(s) the set of all binary numbers that are divisible by three? Assume that string ϵ is divisible by three.

(A) (0 + 1(01*0)*1)*

(B) (0 + 11 + 10(1 + 00)*01)*

(D) (0 + 11 + 11(1 + 00)*00)*

Answer: (A; B; C)

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

48. Consider a three-level page table to translate a 39-bit virtual address to a physical address as shown below.

The page is size is 4KB(1KB = 2¹⁰ bytes) and page table entry size at every level is 8 bytes. A process P is currently using 2GB (1GB = 2³⁰ bytes) virtual memory which is mapped to 2GB of physical memory. The minimum amount of memory required for the page table of P across all levels is ______KB.

Answer: (4108 to 4108)

49. Consider the following ANSI C program.

The output of the program upon execution is ________

Answer: (60 to 60)

50. Let S be a set consisting of 10 elements. The number of tuples of the form (A, B) such that A and B are subsets of S, and A ⊆ B is ________

Answer: (59049 to 59049)

51. Consider the following augmented grammar with {#, @, <, >, a, b, c} as the set of terminals.

Answer: (8 to 8)

52. Consider a Boolean function f(w, x, y, z) such that

f(w, 0, 0, z) = 1

f(1, x, 1, z) = x + z

f(w, 1, y, z) = wz + y

The number of literals in the minimal sum-of-products expression of f is _________

Answer: (6 to 6)

53. Consider a pipelined processor with 5 stages, Instruction Fetch (IF), Instruction Decode (ID), Execute (EX), Memory Access (MEM), and Write Back (WB). Each stage of the pipeline, except the EX stage, takes one cycle. Assume that the ID stage merely decodes the instruction and the register read is performed in the EX stage. The EX stage takes one cycle for ADD instruction and two cycles for MUL instruction. Ignore pipeline register latencies.

ADD, MUL, ADD, MUL, ADD, MUL, ADD, MUL

Assume that every MUL instruction is data-dependent on the ADD instruction just before it and every ADD instruction (except the first ADD) is data-dependent on the MUL instruction just before it. The Speedup is defined as follows:

The Speedup achieved in executing the given instruction sequence on the pipelined processor (rounded to 2 decimal places) is _________.

Answer: (1.87 to 1.88)

54. Consider a network using the pure ALOHA medium access control protocol, where each frame is of length 1,000 bits. The channel transmission rate is 1 Mbps (= 10⁶ bits per second). The aggregate number of transmissions across all the nodes (including new frame transmissions and retransmitted frames due to collisions) is modeled as a Poisson process with a rate of 1,000 frames per second. Throughput is defined as the average number of frames successfully transmitted per second. The throughput of the network (rounded to the nearest integer) is _________.

Answer: (130 to 140)

55. In a directed acyclic graph with a source vertex s, the quality-score of a directed path is defined to be the product of the weights of the edges on the path. Further, for a vertex v other than s, the quality-score of v is defined to be the maximum among the quality-scores of all the paths from s to v. The quality-score of s is assumed to be 1.

The sum of the quality-scores of all the vertices in the graph shown above is_________.

Answer: (929 to 929)

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 Biotechnology (BT) Question Paper With Answer Key

June 8, 2023June 13, 2022 by suresh84

GATE-2021

BT-Biotechnology

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)

Biotechnology (BT)

Q.1 – Q.17 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong answer: – 1/3).

1. Coronavirus genome consists of

(A) double-stranded DNA

(B) double-stranded RNA

(D) positive-sense single-stranded RNA

Answer: (D)

2. The enzyme that transcribes the eukaryotic genes encoding precursor ribosomal RNAs (pre-rRNAs) of 28S, 18S and 5.8S rRNAs is

(A) RNA polymerase I

(B) RNA polymerase II

(D) RNA polymerase IV

Answer: (A)

3. Number of unrooted trees in a phylogeny of five sequences is

(A) 3

(B) 15

(D) 945

Answer: (B)

4. Which one of the following methods is used to test the significance of predicted phylogeny?

(A) Bootstrap

(B) Maximum likelihood

(D) Minimum evolution

Answer: (A)

5. The Cartesian coordinates (x, y) of a point A with polar coordinates (4, π/4) is

(A) (√3, 2√2)

(B) (2, 2√3)

(D) (2√2, 2√2)

Answer: (D)

6. The order of genes present in a chromosome is as follows.

Which one of the following rearrangements represents a paracentric inversion?

Answer: (B)

7. Which one of the following statements is INCORRECT about hybridoma production?

(A) Hybridoma cells can use hypoxanthine and thymidine

(B) DNA synthesis in myeloma cells is blocked by aminopterin

(D) Polyethylene glycol is used to fuse myeloma cells to B-cells

Answer: (C)

8. is equal to

(A) 1/2x

(B) 1/x

(D) x

Answer: (B)

9. Which one of the following techniques/tools is NOT used for inserting a foreign gene into a cell?

(A) DNA microarray

(B) Electroporation

(D) Microinjection

Answer: (A)

10. Under standard temperature (T) and pressure (P) conditions, 128g of an ideal gas molecule A occupies a volume of 1L. The gas molecule A obeys the relationship RT PV = 0.25. R and V are universal gas constant and ideal gas volume, respectively. The molecule A is

(A) CO₂

(B) H₂

(D) O₂

Answer: (D)

11. CRISPR-Cas system is associated with

(A) adaptive immunity in eukaryotes

(B) adaptive immunity in prokaryotes

(D) innate immunity in prokaryotes

Answer: (B)

12. The process by which intracellular macromolecules are supplied for lysosomal degradation during nutrient starvation is

(A) apoptosis

(B) autophagy

(D) pinocytosis

Answer: (B)

13. The process and instrumentation diagram for a feedback control strategy to maintain the level (h) of a liquid by regulating a valve (V) in a tank is shown below. F₁ is inlet liquid flow rate, F₂ is outlet liquid flow rate, LT is the liquid level transmitter, LC is the liquid level controller, h_sp is the setpoint value of the liquid level, h_m is the measured value of the liquid level and P_V is the valve pressure.

The manipulating variable(s) is/are

(A) F₁ only

(B) F₂ only

(D) h_sp and P_V only

Answer: (A)

14. A protein without its prosthetic group is known as

(A) apoprotein

(B) hemoprotein

(D) lipoprotein

Answer: (A)

15. The enzyme which adds phosphate group to the free 5’ terminus of a DNA sequence is

(A) adenosine kinase

(B) alkaline phosphatase

(D) terminal deoxynucleotidyl transferase

Answer: (C)

16. Which one of the following is CORRECT about microbial growth medium?

(A) Luria-Bertani broth is a synthetic medium

(B) Nutrient broth is a defined medium

(D) Trypticase soy agar is a complex medium

Answer: (D)

17. The cellular process which utilizes RNA-induced silencing complex to block gene expression is

(A) RNA editing

(B) RNA interference

(D) RNA splicing

Answer: (B)

Q.18 – Q.19 Multiple Select Question (MSQ), carry ONE mark each (no negative marks).

18. Which of the following layer(s) is/are formed from the inner cell mass of the blastocyst?

(A) Ectoderm

(B) Endoderm

(D) Trophectoderm

Answer: (A; B; C)

19. Which of the following cell organelle(s) is/are surrounded by a single phospholipid membrane?

(A) Golgi apparatus

(B) Lysosome

(D) Nucleus

Answer: (A; B)

Q.20 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

20. The sum of the infinite geometric series 1 + 1/3 + 1/3² + 1/3³ + … (rounded off to one decimal place) is ________.

Answer: (1.5 to 1.5)

21. Three balls, colored in blue, green and red, are successively transferred from box A to box B in the order BLUE-GREEN-RED. The probability of a reverse transfer of the balls to the box A in the same order (rounded off to two decimal places) is ________.

Answer: (0.16 to 0.18)

22. Decimal reduction time of a bacterial strain is 20 min. Specific death rate constant in min⁻¹ (rounded off to two decimal places) is ________.

Answer: (0.10 to 0.13)

23. The value of (rounded off to two decimal places) is ________.

Answer: (0.25 to 0.25)

24. A system consists of two reactors, connected by a valve. The first reactor (R1) contains an ideal gas A of volume 5 L and the second reactor (R2) has an ideal gas B of volume 10 L . Initially, the valve is closed and pressure P in R1 and R2 are 9 and 6 atm, respectively. Later, when the valve is opened, the system reaches equilibrium. If the temperature T of both the reactors is maintained constant, the final equilibrium pressure in atm of the system is ________.

Answer: (7 to 7)

25. The enzyme α-amylase used in starch hydrolysis has an affinity constant (K_m) value of 0.005 M. To achieve one-fourth of the maximum rate of hydrolysis, the required starch concentration in mM (rounded off to two decimal places) is ________.

Answer: (1.60 to 1.80)

Q.26 – Q.34 Multiple Choice Question (MCQ), carry TWO mark each (for each wrong answer: – 2/3).

26. Which one of the following represents non-growth associated product formation kinetics in a bioprocess system? X and P denote viable cell and product concentrations, respectively.

Answer: (C)

27. Match enzymes in Group I with their corresponding industrial application in Group II.

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

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

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

Answer: (B)

28. Match separation methods in Group I with associated properties in Group II.

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

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

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

Answer: (D)

29. Match the autoimmune diseases in Group I with the corresponding primarily affected organ in Group II.

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

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

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

Answer: (C)

30. Match hypersensitivity types in Group I with their corresponding condition in Group II.

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

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

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

Answer: (D)

31. Which of the following combinations of plant hormones and their associated function are CORRECT?

(A) P and R only

(B) P and S only

(D) Q and S only

Answer: (C)

32. Which one of the following tools is used to compare all the possible six-open reading frames of a given nucleotide query sequence with all the available six-open reading frames of the nucleotide sequence database?

(A) BLASTN

(B) BLASTX

(D) TBLASTX

Answer: (D)

33. In Neurospora crassa, a mutation in the poky gene results in a slow growth phenotype (poky). The results of four crosses are given below.

Which one of the following explains the inheritance mode of poky?

(A) Episomal inheritance

(B) Mendelian inheritance

(D) X-linked inheritance

Answer: (C)

34. Tertiary structure of a protein consisting of α-helices and β-strands can be determined by

(A) circular dichroism spectroscopy

(B) mass spectrometry

(D) UV spectroscopy

Answer: (C)

Q.35 – Q.38 Multiple Select Question (MSQ), carry TWO mark each (no negative marks).

35. Which of the following statement(s) is/are CORRECT about Agrobacterium tumefaciens?

(A) It contains tumor inducing plasmid

(B) It causes crown gall disease in dicotyledonous plants

(D) It is used in generating transgenic plants

Answer: (A; B; D)

36. Which of the following antimicrobial agent(s) is/are growth factor analog(s)?

(A) 5-Fluorouracil

(B) Isoniazid

(D) Tetracycline

Answer: (A; B; C)

37. Which of the following chemical messenger(s) is/are derivative(s) of tryptophan?

(A) γ-amino butyric acid

(B) Indole acetic acid

(D) Serotonin

Answer: (B; C; D)

38. Which of the following nucleus/nuclei is/are NMR active?

(A) ¹H

(B) ¹³C

(D) ³²S

Answer: (A; B)

Q.39 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative marks).

39. In a Mendel’s dihybrid experiment, a homozygous pea plant with round yellow seeds was crossed with a homozygous plant with wrinkled green seeds.

F₁ intercross produced 560 F₂ progeny. The number of F₂ progeny having both dominant traits (round and yellow) is ________.

Answer: (315 to 315)

40. A 0.1 mL aliquot of a bacteriophage stock having a concentration of 4 × 10⁹ phages mL⁻¹ is added to 0.5 mL of E. coli culture having a concentration of 2 × 10⁸ cells mL⁻¹. The multiplicity of infection is ________.

Answer: (4 to 4)

41. If the area of a triangle with the vertices (k, 0), (2, 0) and (0, −2) is 2 square units, the value of k is ________.

Answer: (0 to 0 OR 4 to 4)

42. In a chemostat with a dilution rate of 0.8 h⁻¹, the steady state biomass concentration and the specific product formation rate are 8 mol m⁻³ and 0.2 (mol product) (mol biomass)⁻¹ h⁻¹, respectively. The steady state product concentration in mol m⁻³ is ______.

Answer: (2 to 2)

43. If the values of two random variables (X, Y) are (121, 360), (242, 364) and (363, 362), the value of correlation coefficient between X and Y (rounded off to one decimal place) is ________.

Answer: (0.5 to 0.5)

44. The determinant of matrix is _________.

Answer: (8 to 8)

45. It is desired to scale-up a fermentation from 1L to 1000L vessel by maintaining a constant power-to-volume ratio. The small fermenter is operated at an agitator speed of 300 rotations per minute (rpm). If the value of scale up factor is 10, agitator speed in rpm (rounded off to the nearest integer) for the large fermenter is ________.

Answer: (64 to 65)

46. The specific growth rate of a mold during exponential phase of its growth in a batch cultivation is 0.15 h⁻¹. If the cell concentration at 30h is 33 gL⁻¹, the cell concentration in g L⁻¹ (rounded off to the nearest integer) at 24h is ________.

Answer: (13 to 14)

47. A sedimentation tank of height 100 cm is used in a conventional activated sludge process to separate a suspension of spherical shaped granular sludge biomass of 0.5 mm diameter. The viscosity of the liquid is 1 cP. The difference in density between the suspended biomass and the liquid is 0.1g cm⁻³. If the biomass reach their terminal velocity instantaneously, the biomass settling time in min (rounded off to two decimal places) is ________.

Answer: (1.20 to 1.30)

48. In a random mating population, Y and y are dominant and recessive alleles, respectively. If the frequency of Y allele in both sperm and egg is 0.70, then the frequency of Y/y heterozygotes (rounded off to two decimal places) is ________.

Answer: (0.41 to 0.43)

49. Calculate the following integral

Answer: (2 to 2)

50. A feed stream (F1) containing components A and B is processed in a system comprising of separation unit and a mixer as shown below in the schematic diagram. The mole fractions of the components A and B are x_A and x_B, respectively. If F₁ + F₂ = 100 kg h⁻¹, the degrees of freedom of the system is ______.

Answer: (6 to 6)

51. A batch cultivation of E. coli follows zeroth order Monod’s growth kinetics. The cell growth is terminated when the residual dissolved oxygen concentration attains 10% of its saturation value and oxygen mass transfer coefficient (k_La) reaches its maximum value (80 h⁻¹). The saturation value of dissolved oxygen concentration is 0.007 kg m⁻³. . If the maximum specific growth rate and yield coefficient (Y_X/O2) are 0.2 h⁻¹ and 1.5(kg cells) (kgO₂)⁻¹, respectively, then the final cell concentration in kg m⁻³ (rounded off to two decimal places) at the end of the batch cultivation is ________.

Answer: (3.70 to 3.80)

52. Milk flowing through a stainless steel inner tube (40 mm inner diameter) of double tube-type heater is to be heated from 10°C to 85°C by saturated steam condensing at 120°C on the outer surface of the inner tube. Total heat transferred (Q) is 146200 kcal h⁻¹ and the overall heat transfer coefficient is 750 kcal h⁻¹ m⁻²°C⁻¹. The total length of the heating tube in m (rounded off to one decimal place) is ________.

Answer: (23.0 to 24.0)

53. A DNA solution of 50μg mL⁻¹ concentration gives an absorbance of 1.0 at 260 nm. An aliquot of 20 μL from a 50μL purified plasmid solution is diluted with distilled water to a total volume of 1000μ The diluted plasmid solution gives an absorbance of 0.550 at 260 nm. The concentration of the purified plasmid in μg μL⁻¹ (rounded off to two decimal places) is ________.

Answer: (1.37 to 1.38)

54. The possible number of SalI restriction sites in a 9 kb double-stranded DNA, with all four bases occurring in equal proportion (rounded off to the nearest integer) is ________.

Answer: (2 to 2)

55. A bacterium produces acetic acid from ethanol as per the following reaction 2CH₃CH₂OH + 2O₂ → 2CH₃COOH + 2H₂O

The thermodynamic maximum yield of acetic acid from ethanol in g g⁻¹ (rounded off to two decimal places) is ________.

Answer: (1.90 to 2.00)

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

Lift curve slope for tail

Tail area S_t = 80 m²

Wing area S = 350 m²

Distance between mean aerodynamic centers of tail and wing-body

Mean aerodynamic chord

Downwash ε = 0. 4α

Axial location of the wing-body mean aerodynamic center

Axial location of the center of gravity

All axial locations are with respect to the leading edge of the root chord

and along the body x-axis. Ignore propulsive effects.

The pitching-moment-coefficient curve slope (C_mα) is ________ /deg (round off to three decimal places).

Answer: (-0.025 to -0.023)

GATE Exam 2020 Life Sciences (XL) Question Paper With Answer Key

June 8, 2023May 6, 2022 by suresh84

GATE-2020

XL: Life Sciences

GA-General Aptitude

Q1 – Q5 carry one mark each.

1. Rajiv Gandhi Khel Ratna Award was conferred _____Mary Kom, a six-time world champion in boxing, recently in a ceremony _____ the Rashtrapati Bhawan (the President’s official residence) in New Delhi.

(A) with, at

(B) on, in

(D) to, at

Answer: (C)

2. Despite a string of a poor performances, the changes of K. L. Rahul’s selection in the team are ______.

(A) slim

(B) bright

(D) uncertain

Answer: (B)

3. Select the word that fits the analogy:

Cover : Uncover :: Associate : _______

(A) Unassociate

(B) Inassociate

(D) Dissociate

Answer: (D)

4. Hig by floods, he kharif (summer sown) crops in various parts of the county have been affected. Officials believe that the loss in production of the kharif crops can be recovered in the output of the rabi (winter sown) crops so that the country can achieve its food-grain production target of 291 million tons in the crop year 2019-20 (July-June). They are hopeful that good rains in July-August will help the soil retain moisture for a longer period, helping winter sown crops such as wheat and pulses during the November-February period.

Which of the following statements can be inferred from the given passage?

(A) Officials declared that the food-grain production target will be met due to good rains.

(B) Officials want the food-grain production target to be met by the November-February period.

(D) Officials hope that the food-grain production target will be met due to a good rabi produce.

Answer: (D)

5. The difference between the sum of the first 2n natural numbers and the sum of the first n odd natural numbers is ______.

(A) n² – n

(B) n² + n

(D) 2n² + n

Answer: (B)

Q6 – Q10 carry two marks each.

6. Repo rate is the at which Reserve Bank of India (RBI) lends commercial banks, and reverse repo rate is the rate at which RBI borrows money from commercial banks.

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

(A) Decrease in repo rate will increase cost of borrowing and decrease lending by commercial banks.

(B) Increase in repo rate will decrease cost of borrowing and increase lending by commercial banks.

(D) Decrease in repo rate will decrease cost of borrowing and increase lending by commercial banks.

Answer: (D)

7. P, Q, R, S, T, U, V, and W are seated around a circular table.

(I) S is seated opposite to W.

(II) U is seated at the second place to the right of R.

(III) T is seated at the third place to the left of R.

(IV) V is a neighbor of S.

Which of the following must be true?

(A) P is a neighbor of R.

(B) Q is a neighbor of R.

(D) R is the left neighbor of S.

Answer: (C)

8. The distance between Delhi and Agra is 233 km. A car P started travelling from Delhi to Agra and another car Q started from Agra to Delhi along the same road 1 hour after the car P started. The two cars crossed each other 75 minutes after the car Q started. Both cars were travelling at constant speed. The speed of car P was 10 km/hr more than the speed of car Q. How many kilometers the car Q had travelled when the cars crossed each other?

(A) 66.6

(B) 75.2

(D) 116.5

Answer: (B)

9. For a matrix M = [m_ij], i. j= 1, 2, 3, 4, the diagonal elements are all zero and m_ij = −m_ij. The minimum number of elements required to fully specify the matrix is_______.

(A) 0

(B) 6

(D) 16

Answer: (B)

10. The profit shares of two companies P and Q are shown in the figure. If the two companies have invested a fixed and equal amount every year, then the ratio of the total revenue of company P to the total revenue of company Q, during 2013-2018 is ______.

(A) 15 : 17

(B) 16 : 17

(D) 17 : 16

Answer: (B)

XL: Life Sciences – P : Chemistry (Compulsory)

Q1 – Q5 carry one mark each.

1. An aqueous solution contains a mixture of 10⁻⁸ M NaCl and 10⁻⁸ M HCl.

Choose the correct statement about this solution.

(A) The solution is a buffer with pH less than 7.00

(B) The solution is a buffer with pH greater than 7.00

(D) The solution is not a buffer but has its pH greater than 7.00

Answer: (C)

2. The coordination complex which has a distorted octahedral structure is

(Given: Atomic numbers of V: 23; Mn: 25; Ni: 28; Cu: 29)

(A) [Ni(H₂O)₆]²⁺

(B) [Mn(H₂O)₆]²⁺

(D) [Cu(H₂O)₆]²⁺

Answer: (D)

3. In naphthalene, the value of the integer “n” according to Huckel’s rule of aromaticity is ______.

Answer: (2 to 2)

4. The azimuthal quantum number (l) of an electron in the orbital of a copper atom (atomic number: 29) is ______.

Answer: (2 to 2)

5. The standard enthalpy of reaction (in kJ mol⁻¹) for obtaining three moles of H₂(g) from atomic hydrogen in gas phase is ______. (Given: Standard enthalpy of formation of atomic hydrogen is gas phase is 218 kJ mol⁻¹)

Answer: (-1308 to -1308)

Q6 – Q15 carry two marks each.

6. The correct order of the first ionization energies of He, B, N and O in their corresponding ground state is

(A) He > N > O > B

(B) O > N > B > He

(D) N > O > B > He

Answer: (A)

7. Based on the molecular orbital theory, which one of the following statements with respect to N₂, N₂⁺, O₂ and O₂⁺ is correct?

(A) Bond orders of N₂ and O₂ are higher than their corresponding cations.

(B) Bond energy of N₂⁺ is higher than that of N₂, whereas bond energy of O₂⁺ is lower than that of O₂.

(D) The bond in N₂⁺ is shorter than that is N₂, whereas bond in O₂ is shorter than that in O₂⁺.

Answer: (C)

8. Which one of the following statements is incorrect about the diborane molecule?

(A) B-H^t bond is 2-centre-2-electron bond (H^t : terminal hydrogen).

(B) BH^bB bond is a 3-centre-2-electron bond (H^b: bridged hydrogen).

(D) The B-H^t bond distance is longer than B-H^b bond distance (H^t : terminal hydrogen, H^b: bridged hydrogen).

Answer: (D)

9. Given below are Newman projections of ethylene glycol and 1, 2-difluoroethane about their respective C-C bonds. The most stable conformations (lowest energy) of ethylene glycol and 1, 2-difluoroethane are

(A) I and III respectively.

(B) I and IV respectively.

(D) II and IV respectively.

Answer: (A)

10. In the reaction given below, choose the condition that gives an anti-Markovnikov’s product.

(A) Peroxide/HCl

(B) Aqueous mercuric acetate treatment

(D) Sulfuric acid addition

Answer: (C)

11. Which one of the following hexoses will give an osazone that has a different melting point from that of the osazone obtained from D (+) glucose?

Answer: (C)

12. A molecule in solution crystallizes into two different crystal forms with rate constants of 0.02 s⁻¹ and 0.13 s⁻¹. If the crystallization is assumed to be under kinetic control, then the half-life (in seconds, rounded off to one decimal place) of the molecular is ________.

Answer: (4.5 to 4.7)

13. The standard potential (E^θ_cell) for a cell reaction given below is +0.7 V. The standard reactions free energy (∆_rG^θ) for this cell is _____ kJ mol⁻¹ (correct up to two decimal places). (Given: Faraday constant, F = 96500 C mol⁻¹)

Au³⁺ (aq) + 3 Ag(s) → Au(s) + 3Ag⁺ (aq)

Answer: (-202.66 to -202.64)

14. The activation energy (E_a) estimated for a reaction from the Arrhenius equation is 21 kJ mol⁻¹. If the frequency factor is assumed to be independent of temperature, then the ratio of the rate constants determined at 298 K and 260 K is ______ (rounded off to two decimal places). (Given: Gas constant, R = 8.315 J K⁻¹ mol⁻¹)

Answer: (3.44 to 3.46)

15. At a given pressure, a substance is heated from 2000 K to 2600 K. If the entropy of the substance is 60 J K⁻¹ mol⁻¹, and is assumed to be constant over the given temperature range, then the change in the chemical potential (in kJ mol⁻¹) of the substance is _________.

Answer: (-36 to -36)

XL: Life Sciences – Q : Biochemistry

Q1 – Q10 carry one mark each.

1. Which one of the following hormones initiates a signaling cascade by directly binding to an intra-cellular receptor?

(A) Insulin

(B) Gonadotropin

(D) Epinephrine

Answer: (C)

2. Which one of the following bonds is NOT present in ATP ?

(A) Phosphoester

(B) Phosphoanhydride

(D) α-Glycosidic

Answer: (D)

3. The reaction involved in the direct conversion of L-phenylalanine of L-tyrosine is

(A) Hydroxylation

(B) Decarboxylation

(D) Reduction

Answer: (A)

4. The humn major histocompatibility complex (MHC) is

(A) Polygenic and monomorphic

(B) Polygenic and polymorphic

(D) Monogenic and monomorphic

Answer: (B)

5. Har Gobind Khorana and Marshall Nirenberg elucidated the genetic code by using a cell-free protein synthesizing system. It was found that poly(U) and poly(C) result in the synthesis of poly(L-Phe) and poly(L-pro), respectively. Based on these observations, which one of the following conclusions is correct?

(A) Codon GGG specifies L-Phe and codon AAA specifies L-Pro

(B) Codon CCC specifies L-Phe and codon UUU specifies L-pro

(D) Codon UUU specifies L-Phe and codon CCC specifies L-Pro

Answer: (D)

6. Binding of an antibody to its cognate antigen does NOT involve

(A) Covalent bonds

(B) Electrostatic foces

(D) Hydrogen bonds

Answer: (A)

7. A globular protein of molecular weight 50 kDa exists as a mixture of monomers and dimmers in solution. The most appropriate technique for the separation of these two forms of the protein is

(A) Thin layer chromatography

(B) Ion exchange chromatography

(D) Paper chromatography

Answer: (C)

8. Choose the correct order of molecules according to their ability to diffuse across as lipid bilayer.

(A) CO₂ > H₂O > Glucose > RNA

(B) CO₂ > Glucose > H₂O > RNA

(D) H₂O > CO₂ > RNA > Glucose

Answer: (A)

9. When one glucose unit from glycogen gets converted to lactate in the muscle, the ne number of ATP molecules produced is _______.

Answer: (3 to 3)

10. Considering that the three pK_as of histidine are pK₁ = 1.8, pK₂ = 9.2 and pK_R = 6.0, its isoelectric point will be ______ (rounded off to one decimal place).

Answer: (7.5 to 7.7)

Q11- Q20 carry two marks each.

11. One mole of a native protein upon N-terminal analysis yielded one mole each of Asp and Val. Therefore, the protein in its native state exists as a

(A) Monomer

(B) Homo-dimer

(D) Tetramer

Answer: (C)

12. The prosthetic groups/cofactors involved in both 1e⁻ and 2e⁻ transfer in the mitochondrial electron transport chain are

(A) NAD and NADP

(B) NAD and FAD

(D) Coenzyme Q and FMN

Answer: (D)

13. Match the items in Group I with the most appropriate items in Group II and choose the correct option.

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

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

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

Answer: (B)

14. The correct combination of glycosidic linkages present in glycogen is

(A) α 1 → 4 and α 1 → 6

(B) α 1 → 4 and β 1 → 6

(D) α 1 → 6 and β 1 → 6

Answer: (A)

15. Polypeptides are either biosynthesized on the ribosomes using an mRNA template or chemically synthesized by the Merrifield’s solid phase method. The correct directions of peptide synthesis are

(A) C→ N direction on the ribosomes and N → C direction on the solid phase

(B) N → C direction on the ribosomes and C → N direction on the solid phase

(D) C → N direction in both cases

Answer: (B)

16. A solution absorbs 20% of the incident light in a cuvette of path length 1.0 cm. The amount of light transmitted by the same solution in a curvette of 3.0 cm path length is _______% (rounded off to one decimal place).

Answer: (51.1 to 51.3)

17. The second pKa of phosphoric acid is 6.8. The ratio of Na₂HPO₄ to NaH₂PO₄ required to obtain a buffer of pH 7.0 is _______ (rounded off to two decimal places).

Answer: (1.58 to 1.60)

18. A PCR in a 100 μL reaction volume, containing two primers at a concentration of 0.2 μM each, is set up to amplify a 250 base pair DNA fragment. Consider the average molecular weight of one base pair as 660 Da. If the primers are fully consumed by the end of the reaction, the amount of the final PCR product formed is ________μg (rounded off to one decimal place).

Answer: (3.2 to 3.4)

19. An enzyme obeying Michaelis-Menten kinetics shows as reaction velocity (v) of 10 μmol/min when the substrate concentration [S] equals its K_M. The maximal velocity V_max for this enzyme is _______ μmol/min (correct to integer number). (K_M is Michaelis-Menten constant)

Answer: (20 to 20)

20. The enzyme glucose isomerase catalyzes the inter-conversion of glucose and fructose as shown.

The ∆G’₀ for this reaction is zero kcal/mol. After adding glucose isomerase to a 0.12 M glucose solution and allowing the reaction to attain equilibrium, the final concentration of fructose in the reaction mixture will be _____ mM.

Answer: (60 to 60)

XL: Life Sciences – R: Botany

Q1 – Q10 carry one mark each.

1. Indefinite stamen is a characteristic feature of which of the following plant families?

(A) Malvaceae

(B) Apocynaceae

(D) Brassicaceae

Answer: (A)

2. In natural condition, which of the following plants DOES NOT exhibit anomalous secondary growth?

(A) Rice

(B) Aloe

(D) Dracaena

Answer: (A)

3. In a typical angiosperm under natural condition, primary meristems are usually established during

(A) Gametogenesis

(B) Embryogenesis

(D) Secondary growth

Answer: (B)

4. 2-Methoxy-3, 6-dichlorobenzoic acid belongs to which class of plant growth regulators?

(A) Synthetic auxin

(B) Synthetic cytokinin

(D) Brassinosteroid

Answer: (A)

5. In a typical green plant, the first product of Calvin cycle is

(A) Oxaloacetic acid

(B) Succinic acid

(D) 3-Phosphoglyceric acid

Answer: (D)

6. Among the following, which best describes an organism that lives at the expense of other organisms, harmful but usually not killing?

(A) Predator

(B) Symbiotic

(D) Parasite

Answer: (D)

7. The oleo-gum resin asafoetida (hing) is obtained from the cut surface of

(A) Stem

(B) Root

(D) Fruit

Answer: (B)

8. ‘Bakanae’ disease or ‘foolish seedling’ disease is caused by

(A) Fungus

(B) Bacterium

(D) Mycoplasma

Answer: (A)

9. Which of the following chemicals is used for doubling of chromosome numbers during production of ‘doubled haploids’ in crop plants?

(A) Hygromycin

(B) Kanamycin

(D) Glufosinate

Answer: (C)

10. An mRNA of a nuclear encoded plant gene, DSH20 has an ORF of 1353 nucleotides. Provided that average molecular weight of amino acid is 110 Dalton (Da) calculated molecular weight of DSH20 protein in kDa (round off to 1 decimal place) is ______

Answer: (49.5 to 49.5)

Q11 – Q20 carry two marks each.

11. Group I, Group II and Group III represent enzyme, product of the enzymatic reaction, and metabolic process, respectively.

The CORRECT combination fro Group I, Group II and Group III is

(A) P-ii-1, Q-iv-3, R-v-2, S-iii-4

(B) P-ii-1, Q-i-3, R-v-4, S-iii-2

(D) P-iii-1, Q-i-3, R-iv-4, S-ii-2

Answer: (B)

12. Match the following in CORRECT combination between Group I and Group II with reference to the agents that interfere with oxidative phosphorylation

(A) P-iv, Q-i, R-ii, S-iii

(B) P-v, Q-i, R-iii, S-iv

(D) P-v, Q-ii, R-iii, S-iv

Answer: (A)

13. In relation to Agrobacterium mediated genetic engineering in plants, match the following in CORRECT combination

(A) P-iv, Q-iii, R-ii, S-v

(B) P-ii, Q-i, R-iii, S-v

(D) P-iii, Q-i, R-ii, S-iv

Answer: (C)

14. Match the plant part (Group I) with the product obtained (Group II) and the representative plant species (Group III) in CORRECT combination

(A) P-ii-1, Q-i-3, R-iv-2, S-iii-4

(B) P-ii-1, Q-i-2, R-iv-4, S-iii-3

(D) P-iv-3, Q-i-2, R-ii-4, S-iii-1

Answer: (D)

15. Select the CORRECT combination by matching the disease, causal organism and the affected

(A) P-iv-1, Q-iii-3, R-i-2, S-ii-4

(B) P-ii-1, Q-i-6, R-iv-4, S-iii-2

(D) P-iv-1, Q-ii-3, R-iii-2, S-i-5

Answer: (A)

16. Match the following alkaloids with their uses and source plants in CORRECT combination

(A) P-ii-3, Q-iv-1, R-iii-4, S-i-2

(B) P-ii-1, Q-i-3, R-iv-4, S-iii-2

(D) P-iii-4, Q-ii-1, R-iv-3, S-i-2

Answer: (A)

17. Match the following ecological terms with their appropriate definitions

(A) P-i, Q-ii, R-iv, S-iii

(B) P-ii, Q-iv, R-i, S-iii

(D) P-iii, Q-i, R-ii, S-iv

Answer: (B)

18. Arrange the following ‘water reservoirs of earth’ in decreasing order of water volume

P-Streams

Q-Groundwater

R-Glaciers

S-Lakes and inland seas

(A) R-Q-S-P

(B) P-Q-R-S

(D) R-P-Q-S

Answer: (A)

19. Selection markers and the corresponding genes used in plant genetic engineering are given below

Choose the CORRECT combination

(A) P-ii, Q-i, R-iv, S-iii

(B) P-iv, Q-ii, R-i, S-iii

(D) P-iii, Q-iv, R-ii, S-i

Answer: (C)

20. A double homozygous mutant develops green and wrinkled seeds. When it was crossed with true-breeding plant having yellow and round seeds, all the F1 plants developed yellow and round seeds. After self-fertilization of F1, the calculated percentage probability of plants with green and wrinkled seeds in the F2 population (round off to 2 decimal places) is ________

Answer: (6.25 to 6.25)

XL: Life Sciences – S: Microbiology

Q1 – Q10 carry one mark each.

1. The technique of microbial “pure culture” was pioneered by

(A) Edward Jenner

(B) Louis Pasteur

(D) Robert Koch

Answer: (D)

2. The antibacterial trimethoprim is an inhibitor of

(A) dihydrofolate reductase

(B) dihydropteroate synthetase

(D) serine hydroxymethyl transferase

Answer: (A)

3. Choose the correct taxonomical hierarchy among the following:

(A) Species, Genus, Family, Order, Class, Phylum, Domain

(B) Species, Genus, Order, Class, Family, Phylum, Domain

(D) Species, Genus, Family, Class, Order, Phylum, Domain

Answer: (A)

4. Shifting a Sacharomyces cerevisiae culture from fermentative to aerobic respiratory mode will

(A) decrease carbon dioxide production

(B) increase alcohol production

(D) decrease ATP generation per mole of glucose

Answer: (A)

5. Which one of the following diseases is treated by a neuraminidase inhibitor?

(A) Chickenpox

(B) Polio

(D) Japanese encephalitis

Answer: (C)

6. Which one of the following does NOT provide three-dimensional images?

(A) Atomic force microscopy

(B) Confocal scanning laser microscopy

(D) Phase-contrast microscopy

Answer: (D)

7. Which one of the following will increase the resolution of a light microscope ?

(A) Decreasing the numerical aperture of the objective lens

(B) Using an objective lens with a longer working distance

(D) Increasing the wavelength of light

Answer: (C)

8. Which one of the following conditions favors maximum expression of lac operon genes in coli?

(A) Glucose-low, lactose-law, cAMP-high

(B) Glucose-high, lactose-low, cAMP-high

(D) Glucose-high, lactose-high, cAMP-low

Answer: (C)

9. Match the cellular organelle in Group I with its function in Group II

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

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

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

Answer: (B)

10. A 250 μl of bacteriophage stock containing 8 × 10⁸ phages/ml is added to 500 μl of coli culture containing 4 × 10⁸ cells/ml. The multiplicity of infection is _______.

Answer: (1 to 1)

Q11 – Q20 carry two marks each.

11. Digestion of an immunoglobulin G (IgG) molecule with pepsin will NOT

(A) generate a bivalent antigen binding fragment

(B) generate monovalent antigen binding fragments

(D) cleave the heavy chain of IgG molecule

Answer: (B)

12. Match the process involved in nitrogen or sulfur cycle in Group I with the corresponding microbe in Group II.

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

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

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

Answer: (D)

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

Assertion [a]: Diphtheria exotoxin is an example of A-B type toxin.

Reason [r]: The A component of the toxin is released from the host cell while the B component inhibits protein synthesis and kills the host cell.

(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)

14. Which one of the following statements about control of microbial growth is NOT correct?

(A) Nonionizing radiation leads to thymine dimmers formation in DNA

(B) Spirochetes and mycoplasma can pass through membrane filters (0.22-0.45 μm)

(D) Thermoduric bacteria can survive pasteurization

Answer: (C)

15. An example of a differential and selective medium in which colonies of Gram-negative bacteria produce large amounts of acidic products and appear green with a metallic sheen is

(A) Blood agar

(B) EMB agar

(D) Mannitol salt agar

Answer: (B)

16. Which one of the following is an example of substrate level phosphorylation?

(A) Glucose to Glucose 6-phosphate

(B) Fructose 6-phosphate to Fructose 1, 6-biphosphate

(D) 2-phosphoglycerate to Phosphoenolpyruvate

Answer: (C)

17. A bacterial culture containing 3 × 10⁵ live cells was exposed to a newly developed sterilizing agent. After 30 minutes of exposure, 3 live cells remained in culture. The decimal reduction time (in minutes) for the new agent is ______.

Answer: (6 to 6)

18. A bacterial culture has a generation time of 34 minutes. The time taken (in minutes, rounded off to two decimal places) for the OD₅₅₀ of this exponentially growing culture to increase from 0.25 to 0.85 is ______.

Assume that OD₅₅₀ has a linear relationship with the cell density.

Answer: (58.50 to 61.50)

19. A 100 μl aliquot (10⁻⁴ dilution) of the bacterial culture plated on the nutrient agar gave 4 colonies. The bacterial stock concentration (in million cells/ml, rounded off to one decimal place) is _____.

Answer: (0.4 to 0.4)

20. A continuous bacterial culture carried out in a chemostat is set to a flow rate of 40 ml/hr. The culture volume is equivalent to that of a cubical container having 10 cm sides. The dilution rate (in hr⁻¹, rounded off to two decimal places) of this system is ________.

Answer: (0.04 to 0.04)

XL: Life Sciences – T: Zoology

Q1 – Q10 carry one mark each.

1. Which ONE of following leucocytes is phagocytic and has clear cytoplasm?

(A) Eosinophil

(B) Monocyte

(D) Basophil

Answer: (B)

2. Which ONE of the following techniques can be used for detecting the subcellular localization of serotonin receptor in intact cells?

(A) Immunoelectron microscopy

(B) SDS-PAGE

(D) Differential centrifugation

Answer: (A)

3. Which ONE of the following is NOT a site for in situ conservation?

(A) Biosphere reserve

(B) Wild life sanctuary

(D) Biodiversity hotspot

Answer: (C)

4. Which ONE of the following is the precursor molecule for corticosteroids?

(A) Androgen

(B) Estrogen

(D) Mineralocorticoids

Answer: (C)

5. Transitional epithelia is found in which ONE of the following organs?

(A) Liver

(B) Lung

(D) Urinary bladder

Answer: (D)

6. Visual signal transduction cascade is activated by rhodopsin and involves degradation rather than synthesis of which ONE of the following second messenger molecules?

(A) cAMP

(B) IP3

(D) DAG

Answer: (C)

7. The genomes of both human and Drosophila code for an amylase that acts on the same substrate. However, the sequence of nucleotides in the genes encoding the two is dissimilar. This is an example of which ONE of the following types of evolution?

(A) Neutral

(B) Directional

(D) Divergent

Answer: (C)

8. “Round dance” is performed by forager bees to indicate the distance between a food source and their colony. Which ONE of the following best represents this distance?

(A) 45 meters

(B) 450 meters

(D) More than 2000 meters

Answer: (A)

9. Which ONE of the following phyla have choanocytes?

(A) Ctenophora

(B) Nematoda

(D) Porifera

Answer: (D)

10. Which ONE of the following glial cells is NOT derived from the ectoderm?

(A) Astrocytes

(B) Microglial cells

(D) Ependyma

Answer: (B)

Q11 – Q20 carry two marks each.

11. Tarantulas and mosquitoes both belong to the phylum Arthropoda. Which ONE of the following represents the correct number of legs in them respectively?

(A) 6 and 6

(B) 6 and 8

(D) 8 and 6

Answer: (D)

12. Match the following subcellular organelles in Column I with associated functions in Column II

(A) P-(iii), Q-(ii), R-(i), S-(iv)

(B) P-(i), Q-(ii), R-(iii), S-(iv)

(D) P-(ii), Q-(iii), R-(i), S-(iv)

Answer: (C)

13. Match the following genetic disorders in Column I with associated typical chromosomal changes mentioned in Column II

(A) P-(iv), Q-(iii), R-(ii), S-(i)

(B) P-(iv), Q-(ii), R-(i), S-(iii)

(D) P-(iii), Q-(iv), R-(i), S-(ii)

Answer: (D)

14. Match the following components listed in Column I with their respective organs in Column II

(A) P-(ii), Q-(iv), R-(i), S-(iii)

(B) P-(ii), Q-(i), R-(iv), S-(iii)

(D) P-(iii), Q-(iv), R-(ii), S-(i)

Answer: (A)

15. Match the following digestive enzymes in Column I with their respective functions in Column II.

(A) P-(iv), Q-(iii), R-(ii), S-(i)

(B) P-(iv), Q-(iii), R-(i), S-(ii)

(D) P-(iii), Q-(iv), R-(ii), S-(i)

Answer: (B)

16. Which ONE of the following graphs represents the relationship between ventricular end-diastolic volume and cardiac output in a healthy adult individual at rest (solid line) and upon exercise (dotted line)?

Answer: (A)

17. Match the household insect vectors in Column I with their associated diseases in Column II.

(A) P-(iv), Q-(iii), R-(ii), S-(i)

(B) P-(iii), Q-(ii), R-(i), S-(iv)

(D) P-(iii), Q-(iv), R-(ii), S-(i)

Answer: (D)

18. Match the proteins in Column I with the organs in which they are maximally expressed in Column II.

(A) P-(iv), Q-(i), R-(iii), S-(ii)

(B) P-(iii), Q-(iv), R-(ii), S-(i)

(D) P-(i), Q-(ii), R-(iii), S-(iv)

Answer: (C)

19. The graph below shows the activity of enzyme pepsin in the presence of inhibitors aliphatic alcohols (P) or N-acetyl-1-phenylalanine (Q). Which ONE of the following represents the nature of inhibition by P and Q, respectively?

(A) Non-competitive and competitive

(B) Competitive and non-competitive

(D) Competitive and uncompetitive

Answer: (B)

20. In Drosophila, the red eye phenotype (W) is dominant over the recessive white eye mutant (w). In a mixed population of red and white eye flies of 10,000 individuals, 3,600 flies were white eyed. The percentage of the heterozygous red eye flies in this population is ________.

Answer: (48 to 48)

XL: Life Sciences – U : Food Technology

Q1 – Q10 carry one mark each.

1. The enzyme majorly involved in postmortem degradation of muscle proteins is

(A) Trypsin

(B) Calpin

(D) Pepsin

Answer: (B)

2. Which of the following is the correct pair of essential fatty acid?

(A) Oleic acid and Lenoleic acid

(B) Lenoleic acid and Linolenic acid

(D) Linolenic acid and Oleic acid

Answer: (B)

3. Nisin A is produced by

(A) Aspergillus niger

(B) Acttobacter aceti

(D) Clostridium perfringens

Answer: (C)

4. Which of the following bacteria will stain purple color after Gram staining?

(A) Bacillus subtilis

(B) Escherichia coli

(D) Yersinia pestis

Answer: (A)

5. The enzyme system used for removal of glucose from egg white prior to its drying consists of

(A) Glucose oxidase and Catalase

(B) Glucosidase and Glucoisomerase

(D) Gluccoamylase and Glucose oxidase

Answer: (A)

6. The INCORRECT pair of food borne illness and its causative microorganism is

(A) Brucellosis-Brucella Sp.

(B) Peptic ulcers-Bacillus subtilis

(D) Q fever-Coxiella burnatii

Answer: (B)

7. Which of the following is commonly used as preservative in the tomato sauce?

(A) Sodium sulphite

(B) Potassium sorbate

(D) Sodium benzoate

Answer: (D)

8. A fluid with flow behvaviour index less than one (n < 1) is

(A) Dilatant

(B) Pseudoplastic

(D) Newtonian

Answer: (B)

9. The velocity of 2.2 μm diameter fat particles inside a cetribfuge, running at 6000 rpm and 20°C, is 0.25 mm s⁻¹. The velocity of 1.5 μm diameter fat particles inside the same centrifuge running at 7500 rpm and same temperature (round off to 2 decimal places) will be ____ mm s⁻¹.

Answer: (0.15 to 0.21)

10. The initial population of a bacterial strain increases from 1 × 10⁴ cells per mL to 1 × 10⁶ cells per mL in 120 minutes. The generation time for this strain (round off to 2 decimal places) is ______ minutes.

Answer: (17.00 to 19.00)

Q11 – Q20 carry two marks each.

11. Match the protein in Column I with its food source in Column II.

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

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

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

Answer: (D)

12. Match the carbohydrate in Column I with corresponding enzyme used for its hydrolysis in Column II.

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

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

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

Answer: (A)

13. Match the edible oil refining stage in Column I with its purpose in Column II.

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

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

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

Answer: (D)

14. Match the food material in Column I with its related term in Column II.

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

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

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

Answer: (B)

15. Match the components/system in Column I with the peeling method for fruits and vegetables in Column II.

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

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

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

Answer: (C)

16. Which among the given options correctly explains the nature of the microbial culture represented by lines 1, 2 and 3 in the following figure?

Answer: (B)

17. Match the equation/law in Column I with its application in Column II.

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

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

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

Answer: (C)

18. Match the absorber used in modified atmosphere packaging and storage in Column I with the scavenger in Column II.

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

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

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

Answer: (A)

19. During extrusion cooking, food materials are generally subjected to a combination of

(A) high shear and low pressure

(B) high temperature and high shear

(D) low shear and low pressure

Answer: (B)

20. An orange juice flowing at 0.80 kg s⁻¹ enters a counter current double pipe heat exchanger at 20°C and leaves at 72° Inlet and outlet temperatures of the hot water used as heating medium in the exchanger are 81°C and 74°C, respectively. The specific heat of the orange juice is 3.74 kJ kg⁻¹ K⁻¹ and overall heat transfer coefficient is 492 W m⁻² K⁻¹. The heat transfer surface area (round off to 2 decimal places) will be ______ m².

Answer: (11.00 to 14.00)

GATE Exam 2020 Engineering Sciences (XE) Question Paper With Answer Key

June 8, 2023May 6, 2022 by suresh84

GATE-2020

XE: Engineering Sciences

GA-General Aptitude

Q1 – Q5 carry one mark each.

(A) with, at

(B) on, in

(D) to, at

Answer: (C)

2. Despite a string of a poor performances, the changes of K. L. Rahul’s selection in the team are ______.

(A) slim

(B) bright

(D) uncertain

Answer: (B)

3. Select the word that fits the analogy:

Cover : Uncover :: Associate : _______

(A) Unassociate

(B) Inassociate

(D) Dissociate

Answer: (D)

Which of the following statements can be inferred from the given passage?

(A) Officials declared that the food-grain production target will be met due to good rains.

(B) Officials want the food-grain production target to be met by the November-February period.

(D) Officials hope that the food-grain production target will be met due to a good rabi produce.

Answer: (D)

5. The difference between the sum of the first 2n natural numbers and the sum of the first n odd natural numbers is ______.

(A) n² – n

(B) n² + n

(D) 2n² + n

Answer: (B)

Q6 – Q10 carry two marks each.

6. Repo rate is the at which Reserve Bank of India (RBI) lends commercial banks, and reverse repo rate is the rate at which RBI borrows money from commercial banks.

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

(A) Decrease in repo rate will increase cost of borrowing and decrease lending by commercial banks.

(B) Increase in repo rate will decrease cost of borrowing and increase lending by commercial banks.

(D) Decrease in repo rate will decrease cost of borrowing and increase lending by commercial banks.

Answer: (D)

7. P, Q, R, S, T, U, V, and W are seated around a circular table.

(I) S is seated opposite to W.

(II) U is seated at the second place to the right of R.

(III) T is seated at the third place to the left of R.

(IV) V is a neighbor of S.

Which of the following must be true?

(A) P is a neighbor of R.

(B) Q is a neighbor of R.

(D) R is the left neighbor of S.

Answer: (C)

(A) 66.6

(B) 75.2

(D) 116.5

Answer: (B)

9. For a matrix M = [m_ij], i. j= 1, 2, 3, 4, the diagonal elements are all zero and m_ij = −m_ij. The minimum number of elements required to fully specify the matrix is_______.

(A) 0

(B) 6

(D) 16

Answer: (B)

(A) 15 : 17

(B) 16 : 17

(D) 17 : 16

Answer: (B)

XE: Engineering Sciences – A: Engineering Mathematics (compulsory)

Q1 – Q7 carry one mark.

1. Let A be a 4 × 3 non-zero matrix and let b be a 4 × 1 column vector. Then Ax = b has

(A) a solution for every b.

(B) no solution for some b.

(D) a solution if b and the columns of A form a linearly independent set.

Answer: (B)

2. Let x₀, x_1,x₂, … be the sequence generated by the Newton-Raphson method applied to the function f(x) = x³ – 2x + 2 with x₀ = 1 . Then the sequence

(A) converges to 0.

(B) becomes unbounded.

(D) does not converge.

Answer: (D)

3. Let z(t) be the solution of the initial value problem

If the planar curve parameterized by t having x-coordinate z(t) and y-coordinate is closed, then necessarily

(A) b > 0.

(B) b < 0.

(D) b is a non-zero rational number.

Answer: (B)

4. Let z be a complex number. Then the series

(A) converges for all z.

(B) converges for |z| ≤ 1 and diverges for |z| > 1.

(D) converges for |z| < 1 diverges for |z| ≥ 1.

Answer: (A)

5. Let be a vector field whose curl is zero. Then necessarily

(A) a = b c.

(B) a = −b = c.

(D) b = −c.

Answer: (D)

6. Let f(x) be a continuous function on the real line such that for any x, Then f(2) is ______.

Answer: (5 to 5)

7. The number of points at which the function has local minima is _____.

Answer: (2 to 2)

8. Let f(t) be a real-valued differentiable function on (−1, 1) such that f(0) = 0 and

Then the series

(A) converges but not absolutely.

(B) is unbounded.

(D) is bounded but does not converge.

Answer: (C)

9. Let X be a random variable with probability density function

Let 0 < a < b. Then the probability P(X ≤ b \ X ≥ a) depends only on

(A) b – a.

(B) b

(D) a + b.

Answer: (A)

10. Let A be a 3 × 3 matrix such that A² = A. Then it is necessary that

(A) A is the identity matrix or the zero matrix.

(B) the determinant of A⁴ is either 0 or 1.

(D) A has one imaginary eigenvalue.

Answer: (B)

11. Players A and B take turns to throw a fair dice with six faces. If A is the first player to throw, then the probability of B being the first one to get a six is _____ (round off to two decimal places).

Answer: (0.43 to 0.47)

XE: Engineering Sciences – B: Fluid Mechanics

Q1 – Q9 carry one mark each.

1. Figures given below show the velocity and shear stress profiles for the flow in a duct. In each option, ‘1’ represents velocity profile and ‘2’ represents shear stress profile.

Choose the correct option that closely represents the turbulent flow condition.

Answer: (A)

2. The variation of shear stress (r) against strain rate (du/dy) is given in the Figure. identify the line/curve among P, Q, R and S, that represents an ideal fluid.

(A) S

(B) P

(D) R

Answer: (B)

3. A body is under stable equilibrium in a homogeneous fluid, where CG and CB are center of gravity and center of buoyancy, respectively.

Two statements ‘P’ and ‘Q’ are given below:

P: For a fully submerged condition, CG should always be below CB

Q: For a floating body, CG need not be below CB

Choose the option that is valid for the present situation.

(A) P is false; Q is True when metacentre is below CG

(B) P is false; Q is True when metacentre is above CG

(D) P is True; Q is true when metacentre is above CG

Answer: (D)

4. A laminar hydrodynamics boundary layer over a smooth flat plate is shown in the Figure. The shear stress at the wall is denoted by τ_w. Which one of the following conditions is correct.

(A) Pressure is varying along ‘x’ and (τ_w)_x1 > (τ_w)_x2

(B) Pressure is constant along ‘x’ and (τ_w)_x2 > (τ_w)_x1

(D) Pressure is varying along ‘x’ and (τ_w)_x2 > (τ_w)_x1

Answer: (C)

5. A non-dimensional number known as Weber number is used to characterize which one of the following flows.

(A) Motion of fluid in open channel

(B) Motion of fluid droplets

(D) Motion of fluid through a pipe

Answer: (B)

6. A uniform approach flow is subjected to an unsteady and periodic flapping plate as shown in the Figure. Tracer is released to obtain flow visualization lines, which are marked as ‘P’, ‘Q’ and ‘R’.

Choose the correct option that the line ‘R’ represents

(A) Streakline

(B) Streamline

(D) Timeline

Answer: (A)

7. The volume flow between any two points not lying on the same streamline in a flow field is equal to

(A) Change in strain rate between the points

(B) Change in vorticity between the points

(D) Change in stream function between the points

Answer: (D)

8. A liquid flow through a horizontal smooth pipe the diameter 5 cm and discharges into a collection tank of dimension 50 cm × 50 cm × 50 cm. Time taken for a 10 cm rise of liquid level in the collection tank is 40 s.

The flow velocity in the pipe is ——– m/s (rounded off to two decimal places).

Answer: (0.30 to 0.33)

9. The potential function for a two dimensional incompressible flow filed is given as:

Magnitude of the velocity vector at point (2, 1) is ______m/s

Answer: (5 to 5)

Q10 – Q22 carry two marks each.

10. Column I represents a list of elementary plane flows and Column II represents flow past geometry obtained by superposition of these elementary plane flows.

The correct match between Columns I and II is,

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

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

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

Answer: (C)

11. The velocity field for a flow is where t is time. Choose the correct option representing the total acceleration at (x, y, z, t)

Answer: (B)

12. An incompressible viscous fluid is placed between two infinite horizontal parallel plates as shown in the Figure. The plates move in opposite direction with constant velocities U₁ and U₂. The pressure gradient in the x-direction is zero and the only body force is due to the fluid weight. The flow is steady, laminar and two-dimensional. Assume velocity component in ‘y’ direction to be zero.

The correct expression for the velocity distribution between the plates is:

Answer: (A)

13. The stream function of a flow field is Ψ = k(x² – y²x) where k is a constant. Which one of the following represents the voriticity?

(A) -2k

(B) 2k(x + 1)

(D) -2k(x + 1)

Answer: (C)

14. Consider a two dimensional, incompressible steady flow of a Newtonian fluid in which the velocity field is u = −2xy, v = y² – x². Pressure gradients in the x-and y-directions are

Answer: (A)

15. A hydroelectric power plant takes in 30 m³/s of water through its turbine and discharges it to the atmosphere with V₂ = 2 m/s. The total head loss in the turbine and penstock system is 20 m. (Assume turbulent flow with kinetic energy correction factor as 1.1. Density of water is 1000 kg/m³ and acceleration due to gravity, g is 10 m/s²).

The net head available to the turbine for power generation is —————- m.

(rounded off to one decimal place).

Answer: (79.60 to 79.90)

16. Water flows at an average velocity, v of 10 m/s through a horizontal smooth tube of diameter, d 5 cm. The friction actor, f is 0.02. Head loss is obtained using Darcy-Weisbach relation The fluid pressure, p measured at various stations are reported in the table below. The length of the pipe, l between station 0 and station 6 is 6 m.

If acceleration due to gravity, g = 10 m/s² and density of water = 1000 kg/m³, then the fluid pressure at station 6 is ________ kPa (rounded off to one decimal place)

Answer: (183.5 to 184.5)

17. A sphere model of 10 cm diameter is tested in water flowing at 2 m/s. The drag force is measured as 5 N. Prototype of 1.5 m in diameter is tested in air with dynamic similarity conditions. (Density of water is 1000 kg/m³, density of air is 1.2 kg/m³, viscosity of water is 0.001 Ns/m² and viscosity of air is 1.78 × 10⁻⁵ Ns/m²).

Drag force experienced by the prototype is ______ N (rounded off to two decimal places).

Answer: (1.21 to 1.35)

18. A liquid of viscosity 1.74 × 10⁻³ Ns/m² is flowing through a horizontal capillary tube of diameter 0.5 mm. The flow in the tube is steady, incompressible, and fully developed laminar flow. The pressure drop across two locations spaced 1 m apart in the tube is 1.0 MPa.

The flow rate in the tube _______ mm³/s.

Answer: (857 to 924)

19. A venturimeter with 75 mm diameter throat is placed in a 150 mm diameter pipeline carrying water at 25° The pressure drop between the upstream tap and the venture throat is 40 kPa. (Density of water = 1000 kg/m³).

The flow rate is ______ m³/s (rounded off to three decimal places).

Answer: (0.035 to 0.045)

20. A water jet with velocity impinges normal to a moving flat plat with velocity such that the jet splits equally into two halves as shown in Figure. The jet cross-sectional area is 2 cm², is 20 m/s and is 10 m/s and density of water is 1000 kg/m³. Consider steady flow and neglect weight of the jet, weight of the plate and frictional losses.

The absolute value of the force required to keep the plate moving at constant velocity is ____ N.

Answer: (20 to 20)

21. In an inverted manometer (as shown in the Figure), the pressure difference, p_B – p_A is 100 kPa.

Use specific gravity of oil as 08, density of water as 1000 kg/m³, density of mercury as 13600 kg/m³ and acceleration due to gravity as 10 m/s².

The height of the water column, H is _____ cm. (rounded off to one decimal place).

Answer: (30.5 to 34.5)

22. An incompressible, steady flow with uniform velocity condition at the inlet between parallel plates is shown in Figure. The flow develops into a parabolic laminar profile with u = ay(y₀ – y) at the downstream end, where ‘a’ is a constant. Assume unit depth of the plate. For U₀ = 7.5 cm/s, y₀ = 3 cm and the fluid with density, ρ = 800 kg/m³

The value of ‘a’ is _____.

Answer: (5 to 5 OR 500 to 500)

XE: Engineering Sciences – C: Materials Science

Q1 – Q9 carry one mark each.

1. A Pb-Sn sample of eutectic composition, containing α-and β-phases, is examined in a scanning electron microscope. The α-phase contains ~97% Pb (atomic number 82) while β-phase contains ~99 wt% Sn (atomic number 50). The ratio of number of backscattered electrons from α-phase to that from β-phase would be:

(A) Less than 1

(B) Equal to 1

(D) Equal to 0

Answer: (C)

2. Smallest or minimum feature size that can be theoretically resolved in an optical microscope does NOT depend on:

(A) Refractive index of the medium between the lens and the focal point

(B) Intensity of radiation

(D) Numerical aperture of the objective lens

Answer: (B)

3. Following diagram shows a square 2-D lattice with a hexagonal motif(dark colored). The rotational symmetry element that must be present in the system is:

(A) Six-fold rotation

(B) Two-fold rotation

(D) Four-fold rotation

Answer: (B)

4. Density of states, D(E), in a three dimenstional solid varies with energy (E) as

(A) E^1/2

(B) E⁰

(D) E^3/2

Answer: (A)

5. The variation of molar volume (Vm) of a liquid showing glass transition temperature (Tg) while cooling from its melting temperature ™ is depicted by:

(A) I

(B) II

(D) IV

Answer: (A)

6. Find the correct match between polymer name in Column I and the monomer type in Column II.

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

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

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

Answer: (C)

7. A ceramic has a fracture toughness (K_Ic) of 1 MPa.m^1/2. If this ceramic is to be exposed to a maximum stress (σ) of 200 MPa, the maximum value of half crack length ‘a’ (in micrometer, μm), below which the material does not fail, is _____ μm (round off to one decimal place). Loading condition for the sample is shown in the schematic. Assume geometrical factor f = 1.2.

Answer: (5.3 to 5.7)

8. A ceramic material is periodically heated and cooled between 25°C and a higher temperature, T_f. During thermal cycling, the material remains dimensionally constrained. The material can withstand a maximum compressive stress of 200 MPa without failure. Material’s coefficient of thermal expansion is 7.5 × 10⁻⁶ °C⁻¹ and modulus of elasticity (E) is 200 GPa. The lowest value of T_f(in °C) at which material will fails is _______ °C (round-off to the nearest integer). Assume that there is no plastic deformation during thermal cycling.

Answer: (157 to 159)

9. During homogeneous solidification of a liquid metal, the radius of critical nucleus (in nanometer, nm) at a temperature T_S which is below the melting point (T_m), is ______ nm (round-off to one decimal place). Given that γ_sl (solid liquid interfacial energy) is 0.18 J.m⁻² and ∆G_v (change in volume free energy upon transformation from liquid to solid) at T_S is 0.18 × 10⁹m⁻³.

Answer: (1.29 to 2.1)

Q10 – Q22 carry two marks each.

10. Read the two statements related to sintering and select the correct option.

Statement-1: Sintering in vacuum leads to improved densification as compared to sintering under ambient (at atmospheric pressure) condition.

Statement-2: Closed pores formed during sintering inhibit full densification.

(A) Both Statement-1 and Statement-2 are FALSE

(B) Both Statement-1 and Statement-2 are TRUE

(D) Statement-1 is FALSE but Statement-2 is TRUE

Answer: (B)

11. Select the correct option that appropriately matches the process to the material/product that can be fabricated using them.

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

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

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

Answer: (C)

12. Consider a FCC structured metal with lattice parameter a = 3.5 Å. If the material is irradiated using X-rays of wavelength λ = 1.54056 Å, the Bragg angle (2θ) corresponding to the fourth reflection will be:

(A) 88.21°

(B) 76.99°

(D) 93.80°

Answer: (D)

13. The number of Schottky defects per mole of KCl at 300°C under equilibrium condition will be:

Given:

Activation energy for the formation of Schottky defect = 250 kJ.mol⁻¹

Avogadro number = 6.023 × 10²³ mol⁻¹

Universal Gas Constant = 8.314 J.K⁻¹.mol⁻¹

(A) 1.21 × 10¹⁸

(B) 1.52 × 10¹⁶

(D) 2.42 × 10¹²

Answer: (D)

14. In an industry, the probability of an accident occurring in a given month is 1/100. Let P(n) denote the probability that there will be no accident over a period of ‘n’ months. Assume that the events of individual months are independent of each other. The smallest integer value of ‘n’ such that P(n) ≤ 1/2 is _____ (round off to the nearest integer).

Answer: (69 to 69)

15. For a FCC metal, the ratio of surface energy of {111} surface to {100} surface is _____ (round-off to two decimal places). Assume that only the nearest neighbor broken bonds contribute to the surface energy.

Answer: (0.84 to 0.90)

16. Pure silicon (Si) has a band gap (E_g) of 1.1 eV. This Si is doped with 1 ppm (part per million) of phosphorus atoms. Si contains 5 × 10²⁸ atoms per m³ in pure form. At temperature T = 300 K, the shift in Fermi energy upon doping with respect to intrinsic Fermi level of pure Si will be ______ eV (with appropriate sign and round-off to two decimal places).

Intrinsic carrier concentration of Si, n_i, is given as:

Given:

Mass of an electron, m = 9.1 × 10⁻³¹ kg

Charge of an electron, e = 1.6 × 10⁻¹⁹ C

Boltzmann constant, k_B = 1.38 × 10⁻²³ J.K⁻¹

Planck’s constant, h = 6.6 × 10⁻³⁴ J.s⁻¹

Answer: (0.33 to 0.45)

17. The schematic diagram shows the light of intensity I₀ incident on a material (shaded grey) of thickness, x, which has an absorption coefficient, α and reflectance, R. The intensity of transmitted light is I. The reflection of light (of a particular wavelength) occurs at both the surfaces (surfaces indicated in the diagram). The transmittance is estimated to be _______ (round-off to three decimal places).

Given that for the wavelength used, α = 10³ m⁻¹ and R = 0.05.

Answer: (0.330 to 0.334)

18. Fe₃O₄ (also represented as FeO.Fe₂O₃) is a FCC structured inverse spinel (AB₂O₄) material where 1/8 of tetrahedral sites are occupied by half of B cations and 1/2 of the octahedral sites are occupied by remaining B and A cations. The magnetic moments of cations on octahedral sites are antiparalel with respect to those on tetrahedral sites. Atomic number of Fe is 26 and that of O is 8. The saturation magnetic moment of Fe₃O₄ per formula unit in terms of Bohr magnetons (μ_B) will be _____ μ_B. Ignore contribution from orbital magnetic moments.

Answer: (4 to 4)

19. A piezoelectric ceramic with piezoelectric coefficient (d_zz) value of 100 × 10⁻¹²N⁻¹ is subjected to force F_z, of 10 N, applied normal to its x-y face, as shown in the figure. If relative dielectric constant (ε_r) of the material is 1100, the voltage developed along the z-direction of the sample will be _______ Volts (round-off to two decimal places). Ignore any nonlinear effects.

Given: Permittivity of free space (ε₀) is 8.85 × 10⁻¹² F.m⁻¹.

Answer: (0.97 to 1.09)

20. Silicon carbide (SiC) particles are added to Aluminum (Al) matrix to fabricate particle reinforced Al-SiC composite. The resulting composite is required to possess specific modulus (E/ρ; E: elastic modulus, ρ: density) three times that of pure Al. Assuming iso-strain condition, the volume fraction of SiC particles in the composite will be _______ (round-off to two decimal places).

Answer: (0.36 to 0.45)

21. Isothermal weight gain per unit area (∆W/A, where ∆W is the weight gain (in mg) and A is the area (in cm²)) during oxidation of a metal at 600°C follows parabolic rate law, where, ∆W/A = 1.0 mg.cm⁻² after 100 min of oxidation. The ∆W/A after 500 min at 600°C will be _______ mg.cm⁻² (round-off to two decimal places).

Answer: (2.20 to 2.28)

22. A plain carbon steel sample containing 0.1 wt% carbon is undergoing carburization at 1100°C in a carbon rich surroundings with fixed carbon content of 1.0 wt% all the time. The carburization time necessary to achieve a carbon concentration of 0.46 wt% at a depth of 5 mm at 1100°C is ______ hour (round off to the nearest integer).

Given: Diffusivity of carbon in iron at 1100°C is 6.0 × 10⁻¹¹ m².s⁻¹ and

Answer: (77 to 83)

XE: Engineering Sciences – D: Solid Mechanics

Q1 – Q9 carry one mark each.

1. Which among the following statements is true for a body moving on a dry surface under the action of applied forces?

(A) Kinetic-friction force is zero.

(B) Kinetic-friction force is equal to the static-friction force.

(D) Kinetic-friction force is lower than the static-friction force.

Answer: (D)

2. Consider an isotropic material with Young’s modulus E and Poisson’s ratio v. The bulk modulus of this material is given by_____.

Answer: (C)

3. A body subjected to ______ does not undergo change in volume.

(A) uniform tension

(B) pure shear

(D) hydrostatic pressure

Answer: (B)

4. The angular momentum of a particle moving under a central force is

(A) zero

(B) constant in both magnitude and direction.

(D) constant in direction but not magnitude.

Answer: (B)

5. According to Euler-Bernoulli beam theory, which one of the following statements best describes the state of a beam subjected to pure bending?

(A) Transverse shear stress and transverse shear strain are zero.

(B) Transverse shear stress is not zero but transverse shear strain is zero.

(D) Transverse shear stress and transverse shear strain are not zero.

Answer: (A)

6. A rigid square ABCD is subjected to planar forces at the corners as shown.

For this planar force system, the equivalent force couple system at corner A can be represented as

(A) System I

(B) System II

(D) System IV

Answer: (B)

7. A particle of mass 0.1 kg, which is released from rest, falls vertically downward under gravity in a fluid. The fluid offers a resistive force, which is linearly proportional to the particle velocity with 0.1 N.s/m as the constant of proportionality. The uniform gravitational acceleration is 10 m/s² throughout the trajectory of the particle. The magnitude of the particle velocity (in m/s) at time 1 s after release (rounded off to two decimal places) is _______.

Answer: (6.25 to 6.40)

8. The state of two-dimensional plane stress at a point in a body is shown on the triangular element ABC, where cos θ = 3/5 and sin θ = 4/5. The normal stress (in MPa) on the plane AC is ________.

Answer: (90 to 90)

9. Consider two point masses m = 10 kg and M = 30 kg connected by a massless inextensible string passing over a massless and frictionless pulley with radius a = 100 mm as shown. The masses are released from rest and move vertically under the action of gravity. Let acceleration due to gravity, g = 10 m/s². The tension (in N) in the string is_______.

Answer: (150 to 150)

Q10 – Q22 carry two marks each.

10. The cantilever beam AC is composed of two segments AB and BC that are rigidly connected at B. The flexural rigidity of the segment AB is EI, whereas, the flexural rigidity of the segment BC is assumed to be infinite. Determine the magnitude of slope at B due to a force P applied at C.

Answer: (D)

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

Assertion [a]: Efficient columns are designed so that most of the column’s cross-sectional area is located as far away as possible from the principal centroidal axes of the section.

Reason [r]: Load carrying capacity of columns will increase as the moment of inertia of the cross-section increases.

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

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

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

Answer: (A)

12. Consider the structure consisting of two massless elastic bars AB and BC, each of length L, cross-sectional area A, and Young’s modulus E. Connections at A, B, C are all pinned. A horizontal force P acts on the joint B as shown. Calculate the horizontal deflection of the joint B.

Answer: (B)

13. A rigid bar ABC of mass m and length L is hinged at A and has a point mass M attached at C. An elastic spring with linear stiffness k is attached at B as shown. Ignore the effect of gravity and damping. The natural frequency of small oscillations of this system is _______.

Answer: (D)

14. A beam of flexural rigidity EI is fixed at A and supported by a linear spring of stiffness k = EI/L³ at B. Determine the compressive force developed in the spring, when the beam is subjected to a uniformly distributed load of w per unit length.

Answer: (A)

15. The bar AB is fixed at A and is separated by a gap of 0.005 mm from wall at C as shown. The temperature of the bar is increased by 10° If the Young’s modulus of the bar is E = 200 GPa and the coefficient of thermal expansion is α = 10 × 10⁻⁶/°C, then the magnitude of the compressive stress (in MPa) developed in the bar is _________.

Answer: (9.99 to 10.00)

16. A thin walled spherical pressure vessel has mean radius 1000 mm and wall thickness 10 mm. The material has Young’s modulus 200 GPa and Poisson’s ratio 0.25. If the internal pressure is 100 MPa, the radial displacement (in mm) of the spherical pressure vessel ( rounded off to two decimal places) is _____.

Answer: (18.60 to 18.90)

17. A particles of mass m = 100 kg is released from rest and falls under gravity through a height of H = 1 mm directly onto an upright massless elastic bar of length L = 200 mm, Young’s modulus 200 GPa, and cross-sectional area 100 mm². Assume the following during impact : (a) particle mass sticks to the bar, (b) the bar does not buckle, and (c) no energy is lost. Use gravitational acceleration g = 10 m/s². The maximum axial compression (in mm) of the bar due to the impact (rounded off to three decimal places) is _______.

Answer: (4.477 to 4.487)

18. A pin-jointed truss has a pin support at A and a roller support at C. All the members are made of same material and have the same cross-section. Neglect the self-weight of the members. Due to the applied loading shown, the total number of zero force members is _______.

Answer: (7 to 7)

19. Two beams AB and BC having diameter of 100 mm are connected by an internal hinge at B. The structure is fixed at A and roller supported at C. Load of P = 1 kN is applied at B. Ignoring the effect of any transverse shear stress, the tensile stress (in MPa) developed at A due to bending (rounded off to three decimal places) is _______.

Answer: (10.160 to 10.340)

20. The shear force diagram for a beam AD, which is simply supported at A and D, is shown. The magnitude of the maximum bending moment (in kN.m) is ______ (rounded off to three decimal places).

Answer: (5.600 to 5.650)

21. A rectangular thin plate with Young’s modulus 200 GPa and Poisson’s ratio 0.30 is subjected to uniform stress distribution at its edges as shown. However, it is stated the dimension b of the plate does not change under the action of the stress components σ_xx and σ_yy. Considering micro-strains (in 10⁻⁶), the change in the length of dimension a (in mm) is ______ (rounded off to three decimal places).

Answer: (0.175 to 0.190)

22. A solid transmission shaft has length 10 m and diameter 100 mm. The shaft is supported by frictionless bearings at ends that act as simple supports. In addition to its self-weight acting as a uniformly distributed load per unit length, an operational torque of 5πm is applied. The density and yield strength of the material are 8000 kg/m³ and 350 MPa, respectively. Use gravitational acceleration as 10 m/s² and ignore the effect of transverse shear stress. The factor of safety of the shaft as per maximum shear stress failure theory (Tresca criterion) is _________(rounded off to two decimal places).

Answer: (1.90 to 2.05)

XE: Engineering Sciences – E: Thermodynamics

Q1 – Q9 carry one mark each.

1. If x and y are two independent intensive properties of a thermodynamic system, then which relation among the followings fails to identify z as another thermodynamics property?

(A) dz = x dy + y dx

(B) dz = x dy – y dx

(D)

Answer: (B)

2. Internal energy of a thermodynamic system is defined by the

(A) zeroth law of thermodynamics

(B) first law of thermodynamics

(D) third law of thermodynamics

Answer: (B)

3. In a polytropic process described by PVⁿ = constant, if n = 0, the process is called as

(A) isobaric

(B) isochoric

(D) isentropic

Answer: (A)

4. The relation between the coefficient of performance of a refrigerator (COP)_R and the coefficient of performance of a heat pump (COP)_HP is

(A) (COP)_HP = (COP)_R + 1

(B) (COP)_HP = (COP)_R − 1

(D) (COP)_HP × (COP)_R = 1

Answer: (A)

5. If L₁, L₂ and L₃ are the latent heats of vaporization at the critical temperature of nitrogen, water and ammonia, respectively, then which one of the following is true?

(A) L₁ > L₂ > L₃

(B) L₁ > L₂ and L₂ = L₃

(D) L₁ = L₂ = L₃

Answer: (D)

6. A new temperature scale (°N) has been proposed where the normal freezing and normal boiling points of water are marked as 500 °N and 100 °N, respectively. If the temperature of a system is measured to be 0 °N, its temperature according to the Celsius scale (in °C) is ________.

Answer: (125 to 125)

7. Let Z₁ represents the compressibility factor of air at 2 bar and 600 K, and Z₂ represents the compressibility factor of air at 1 bar and 300 K. If air is assumed to be an ideal gas having gas constant of 0.287 kJ/kg.K, then Z₁/Z₂ is _______.

Answer: (1 to 1)

8. The rate of heat received by a heat engine from a source at 900 K is600 kJ/s. The engine rejects heat to the sink of 300 K. The heat engine produces a power of 200 kW. The irreversibility rate (in kW) of the process is _______.

Answer: (198 to 202)

9. A engine working on the air standard Diesel cycle has compression ratio of 18. The cycle has a cut-off of 1.7. If the ratio of specific heats of air is 1.4, then the thermal efficiency (in %) of the cycle (rounded off to 1 decimal place) is ________.

Answer: (63.5 to 65.5)

Q10 – Q22 carry two marks each.

10. A system with rigid wall is initially at a temperature of T₁. It is used as the heat source for a heat engine, which rejects heat to a reservoir maintained at T₀ (T₀ < T₁). The specific heats of the system are constant. If the temperature of the system finally reduces to T₀, then the maximum work recoverable from the heat engine per unit mass of the system is

Answer: (A)

11. A reversible heat engine is operating between two reservoirs maintained at T₁ and T₂, where T₁ > T₂. Which one of the following is the most effective option for increasing its thermal efficiency ?

(A) increasing T₁, while keeping T₂ constant

(B) decreasing T₁, while keeping T₂ constant

(D) decreasing T₂, while keeping T₁ constant

Answer: (D)

12. A 4-m³ reservoir contains 10 kg of a real gas at 200 K. If this gas follows the van der Waal’s equation of state with a = 0.0687 m⁶.kPa/kg², b = 0.00657 m³/kg and R = 0.187 kJ/kg.K, then the reservoir pressure (in kPa) is

(A) 93.5

(B) 94.6

(D) 101.3

Answer: (B)

13. Air at a pressure of 86 kPa and specific volume of 1 m³/kg is heated at constant pressure till it reaches 627 ° Air is assumed to be an ideal gas with constant specific heats. It has the gas constant of 0.287 kJ/kg.K and ratio of specific heats of 1.4. The change in specific entropy of air (in kJ/kg.K) during this process will be

(A) 1.104

(B) 0.740

(D) 0.529

Answer: (A)

14. An air standard Otto cycle has compression ratio of 4. The compression ratio of this cycle is changed to 6. If the ratio of specific heats is 1.4, the percentage increase in its thermal efficiency will be

(A) 20.2

(B) 27.2

(D) 51.2

Answer: (A)

15. In a mixture of gas there are 0.1 kmol of oxygen (O₂), 0.1 kmol of nitrogen (N₂) and 0.8 kmol of methane (CH₄). If the molar mass of O₂, N₂ and CH₄ are 32 kg/mol, 28 kg/mol and 16 kg/mol, respectively, then the mass fraction of N₂ in the gas mixture is

(A) 0.100

(B) 0.170

(D) 0.680

Answer: (C)

16. A particular gas sample is initially maintained at 6000 cm³ and 100 kPa. It is compressed during a quasistatic process following the relation PV² = constant. The compression continues till the volume becomes 2000 cm³. The magnitude of the corresponding work transfer (in kJ) (rounded off to 20 decimal places) is

Answer: (1.15 to 1.25)

17. Carbon dioxide (CO₂) enters an adiabatic rigid nozzle steadily at 1 MPa and 500 °C with a mass flow rate of 1.5 kg/s. The inlet area of the nozzle is 40 cm² and the exit velocity is 10 times of that at the inlet. If CO₂ can be considered as an ideal gas with gas constant of 0.19 kJ/kg.K and the ratio of specific heats of 1.29, the exit temperature (in K) (rounded off to 1 decimal place) is ________.

Answer: (590 to 600)

18. A closed system containing 8 kg of gas undergoes an expansion process following the relation PV² = constant. The initial and final pressures are 1 MPa and 5 kPa, respectively, while the initial volume is 1 m³. If the specific internal energy of the gas decreases by 40 kJ/kg during the process, the heat transfer (in kJ) associated with the process (rounded off to 1 decimal place) is _____.

Answer: (2610 to 2614)

19. Saturation pressure of water at 5 °C is 0.8725 kPa. If the latent heat of vaporization is 2489.1 kJ/kg and gas constant is 0.4615 kJ/kg.K, then the saturation pressure at 10 °C (in kPa) (rounded off to 2 decimal places) is ________.

Answer: (1.20 to 1.26)

20. The turbine inlet conditions of a Rankine cycle are 10 MPa and 500 °C, while the condenser pressure is 10 kPa. The enthalpy and entropy of saturated liquid at 10 kPa are 191.8 kJ/kg and 0.6492 kJ/kg.K, respectively, while the enthalpy and entropy of vapourization at 10 kPa are 2392.1 kJ/kg and 7.4996 kJ/kg.K, respectively. The enthalpy and entropy at the inlet to the turbine are 3375.1 kJ/kg and 6.5995 kJ/kg.K, respectively. The condenser outlet has saturated liquid. Neglecting the pump work, the thermal efficiency (in %) of the cycle (rounded off to 1 decimal place) is _______.

Answer: (39 to 42)

21. The minimum and maximum temperatures of an air standard Brayton cycle are 300 K and 1100 K, respectively. The pressure ratio of this cycle is 6. The ratio of specific heats is 1.4 and the specific heats are constant. For this cycle, the ratio of network output to the turbine work (rounded off to 2 decimal places) is _______.

Answer: (0.52 to 0.57)

22. The specific humidity of air at 100 kPa is 0.015 kg of vapour per kg of dry air. The partial pressure of vapour (in kPa) in the existing state (rounded off to 2 decimal places) is ________.

Answer: (2.30 to 2.40)

XE: Engineering Sciences – F: Polymer Science and Engineering

Q1 – Q9 carry one mark each.

1. The solvent in which chain transfer is maximum in a radical polymerization is

(A) Benzene

(B) Chloroform

(D) Toluene

Answer: (C)

2. The monomer that can NOT be polymerized by anionic polymerization is

(A) Styrene

(B) Ethyl vinyl ether

(D) Methyl methacrylate

Answer: (B)

3. The elastomer retaining flexibility at the lowest temperature is

(A) Styrene butadiene rubber

(B) Nitrile rubber

(D) Butyl rubber

Answer: (C)

4. The polymer with minimum number of branches is

(A) LDPE

(B) LLDPE

(D) VLDPE

Answer: (C)

5. The nearest value of conductivity of Nylon 6 is

(A) 10⁶ S/m

(B) 10⁰ S/m

(D) 10⁻²¹ S/m

Answer: (C)

6. Aramid is a

(A) Polyamide

(B) Polyether

(D) Polyimide

Answer: (A)

7. A miscible blend in 1 : 1 (by weight) composition is formed with

(A) Polystyrene and polybutadiene

(B) Polystyrene and poly(phenylene oxide)

(D) Polystyrene and poly(dimethyl siloxane)

Answer: (B)

8. Dicumyl peroxide is

(A) Plasticizer

(B) Cross-linking agent

(D) Peptizer

Answer: (B)

9. The change in stress of a polymer as a function of time at a fixed strain is known as

(A) Fatigue

(B) Creep

(D) Fracture toughness

Answer: (C)

Q10 – Q22 carry two marks each.

10. Match the polymers in Column A with their corresponding polymerization methods of Column B

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

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

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

Answer: (C)

11. Match the appropriate processing technique in Column A to fabricate the product in Column B

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

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

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

Answer: (D)

12. Match the appropriate characterization technique in Column A used to determine the polymer attributes in Column B

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

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

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

Answer: (D)

13. Match each additive in Column A with its function given in Column B

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

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

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

Answer: (B)

14. Plot of shear stress against rate for various types of fluids is given below. The appropriate assignment for P, Q, R and S is

(A) P-Dilatant, Q-Bingham plastic, R-Pseudoplastic, S-Newtonian

(B) P-Bingham plastic, Q-Pseudoplastic, R-Dilatant, S-Newtonian

(D) P-Newtonian, Q-Diltant, R-Pseudoplastic, S-Bingham plastic

Answer: (B)

15. The number average molecular weight of a polyester formed from equimolar mixture of adipic acid and ethylene glycol at a conversion of 99.5% will be _____ (round off to nearest integer).

Answer: (17150 to 17250)

16. For a freely jointed linear polyethylene chain with molar mass of 1.4 × 10⁵ g mol⁻¹, the value of root mean square end-to-end distance in nanometer is _________(round off to 1 decimal place). [Given: C-C bond length = 0.154 nanometer]

Answer: (15.3 to 15.5)

17. Viscosity measurements were performed for a set of PMMA solutions of different concentrations in toluene at 25° The plot of reduced viscosity against concentration (c) of the PMMA solutions produced an intercept of 21.0 cm³ g⁻¹on the ordinate at c = 0. The value of viscosity average molecular weight of PMMA in toluene at 25 °C is ________ (round off to nearest integer). [Given: Mark-Houwink constants K = 7.5 × 10⁻³ cm³ g⁻¹ and a = 0.72 for PMMA is toluene at 25°C]

Answer: (60000 to 62000)

18. Glass fibre reinforced PP composite is to be prepared with 20 volume % of glass fibre. The densities of glass fibre and PP are 2540 kg m⁻³ and 900 kg m⁻³, respectively. The mass of glass fibre required to produce 1 kg of the composite in kg is ______ (round off to 2 decimal places).

Answer: (0.40 to 0.42)

19. A polymer solution flows through a cylindrical tube with a diameter of 4 mm at a volumetric flow rate of 10⁻⁹ m³ s⁻¹. Under laminar flow condition and assuming the polymer solution to be a Newtonian fluid with viscosity 10² N s m⁻², the value of pressure drop per unit length of the tube in N m⁻³ is _______ (round off the nearest integer). [Consider the value of π as 3.14]

Answer: (15800 to 16000)

20. A molten polymer with a bulk modulus of 1 GPa is pressurized to 200 MPa during injection molding.. The fractional decrease in volume of the molten polymer at this pressurized condition is ________ (round off to 1 decimal place).

Answer: (0.2 to 0.2)

21. Assume that each cross-link produced by vulcanization of polyisoprene contains an average of two sulphur atoms and that the sulphur is present only in the cross-links. If 40% of the isoprene units are cross-linked, the sulphur content in weight percentage is _______ (round off to 2 decimal places)/.

Answer: (15.75 to 15.95)

22. A tensile force of 160 N is applied to a piece of vulcanized rubber of dimension 30 mm × 4 mm × 4 mm. Assuming the vulcanized rubber to be incompressible, if the sample is elongated to 150% of its original length under the same applied force, the true stress in N mm⁻² will be ________ (round off to 1 decimal place).

Answer: (14.9 to 15.1)

XE: Engineering Sciences – G: Food Technology

Q1 – Q9 carry one mark each.

1. The enzyme majorly involved in postmortem degradation of muscle proteins is

(A) Trypsin

(B) Calpin

(D) Pepsin

Answer: (B)

2. Which of the following is the correct pair of essential fatty acids?

(A) Oleic acid and Lenoleic acid

(B) Lenoleic acid and Linolenic acid

(D) Linolenic aci and Oleic acid

Answer: (B)

3. Nisin A is produced by

(A) Aspergillus niger

(B) Acteobacter acetis

(D) Clostridium perfringers

Answer: (C)

4. Which of the following bacteria will stain purple color after Gram staining?

(A) Bacillus subtilis

(B) Escherichia coli

(D) Yersinia pestis

Answer: (A)

5. The enzyme system used for removal of glucose form egg white prior to its drying consists of

(A) Glucose oxidase and Catalase

(B) Glucosidase and Glucoisomerase

(D) Glucoamylase and Glucose oxidase

Answer: (A)

6. The INCORRECT pair of food borne illness and its causative microorganism is

(A) Brucellosis-Brucella Sp.

(B) Peptic ulcers-Bacillus subtilis

(D) Q fever-Coxiella burnatii

Answer: (B)

7. Which of the following is commonly used as a preservative in the tomato sauce?

(A) Sodium sulphite

(B) Potassium sorbate

(D) Sodium benzoate

Answer: (D)

8. The velocity of 2.2 μm diameter fat particles inside a centrifuge, running at 6000 rpm and 20 °C, is 0.25 mm s⁻¹. The velocity of 1.5 μm diameter fat particles inside the same centrifuge running at 7500 rpm and same temperature (round of to 2 decimal places) will be ______ mm s⁻¹.

Answer: (0.15 to 0.21)

9. The initial population of a bacterial strain increases from 1 × 10⁴ cells per mL to 1 × 10⁶ cells per mL in 120 minutes. The generation time for this strain (round off to 2 decimal places) is _______ minutes.

Answer: (17.00 to 19.00)

Q10 – Q22 carry two marks each.

10. Match the protein in Column I with its food source in Column II.

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

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

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

Answer: (D)

11. Match the carbohydrate in Column I with corresponding enzyme used for its hydrolysis in Column II.

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

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

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

Answer: (A)

12. Match the edible oil refining stage in Column I with its purpose in Column II.

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

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

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

Answer: (D)

13. Match the food material in Column I with its related term in Column II.

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

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

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

Answer: (B)

14. Match the component/system in Column I with the peeling method for fruits and vegetables in Column II.

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

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

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

Answer: (C)

15. Which among the given options correctly explains the nature of the microbial culture represented by curves 1, 2 and 3 in the following figure?

Answer: (B)

16. Match the equation/law in Column I with its application in Column II.

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

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

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

Answer: (C)

17. Match the absorber used in modified atmosphere packaging and storage in Column I with the scavenger in Column II.

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

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

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

Answer: (A)

18. During extrusion cooking, food materials are generally subjected to a combination of

(A) high shear and low pressure

(B) high temperature and high shear

(D) low shear and low pressure

Answer: (B)

19. The whole milk at 22°C is pumped through a stainless steel pipe at a flow rate of 3 L s⁻¹. The length and inner diameter of the pipe are 40 m and 4 cm, respectively. If viscosity and density of the milk at the pumping temperature of 0.2 Pa s and 1032 kg m⁻³, respectively, the Revnolds number (rounded off to nearest integer) will be ______.

Answer: (491.00 to 495.00)

20. A hammer mill, operating at a feed rate of 108 ton h⁻¹, consumes 10 kW power for reducing size of wheat gain from 3.92 mm to 1.25 mm. If Bond’s law holds good, the feed rate (round off to 2 decimal places) for reducing the size of the wheat grain to 0.75 mm at the same power consumption level is _______ ton h⁻¹.

Answer: (63.00 to 67.00)

21. During spray drying of a milk sample, inlet and outlet temperatures are maintained at 132°C and 80°C, respectively. If the ambient temperature is 29°C, the thermal efficiency (round of to 2 decimal places) of the dryer will be _______ %.

Answer: (49.00 to 52.00)

22. An orange juice flowing at 0.80 kg s⁻¹ enters a counter current double pipe heat exchanger at 20°C and leaves at 72° Inlet and outlet temperatures of the hot water used as heating medium in the exchanger are 81°C and 74°C, respectively. The specific heat of the orange juice is 3.74 kJ kg⁻¹ K⁻¹ and overall heat transfer coefficient is 492 W m⁻² K⁻¹. The heat transfer surface are (round off to 2 decimal places) will be ______m³.

Answer: (11.00 to 14.00)

XE: Engineering Sciences – H: Atmospheric and Oceanic Sciences

Q1 – Q9 carry one mark each.

1. In the northern hemisphere, the flow in the middle depths of the ocean is geostrophic. As we go down from that level and start approaching the bottom of the ocean, the flow deflects to the left of the geostrophic current because

(A) friction decreases and Coriolis force increases

(B) friction decreases and Coriolis force decreases

(D) friction increases and Coriolis force decreases

Answer: (D)

2. Which one of the following is the definition of a monsoon?

(A) Seasonal reversal of wind direction

(B) High rainfall

(D) Occurs in the tropics

Answer: (A)

3. Anthropogenic emission of ______ is the main contributor to the ongoing ocean acidification.

(A) Methane

(B) Carbon dioxide

(D) Sulpuric acid

Answer: (B)

4. What are phytoplankton?

(A) Microscopic animal life floating on surface of water bodies

(B) Pollen floating freely on surface of water bodies

(D) Microscopic plant life living on the floor of water bodies

Answer: (C)

5. Consider the two atmospheric virtual temperature profiles observed in Delhi given in Figures (i) and (ii) blow.

At what times of the day are you most likely to see such profiles?

(A) (i) Midnight and (ii) noon

(B) (i) 3 pm and (ii) 3 am

(D) (i) 3 am and (ii) 3 pm

Answer: (B)

6. A south-easterly wind is blowing towards which direction?

(A) 135°

(B) 157.5°

(D) 225°

Answer: (C)

7. Consider a dry parcel at 30°C in an isothermal environment at 25° The parcel rises adiabatically by 1 km. Assuming g = 10 ms⁻² and air density = 1 kgm⁻³, the buoyancy force at the new location (rounded off to 2 decimal places) is _______ ms⁻².

Answer: (-0.17 to -0.16)

8. The emissivity of polluted air that reflects and transmits 20% and 60% of the incoming solar radiation, respectively, at a given wavelength (correct up to 1 decimal place) is ______.

Answer: (0.2 to 0.2)

9. Given that the angular velocity of rotation of the Earth = 7.3 × 10⁻⁵ s⁻¹, the period of inertial oscillations generated in the oceans by surface winds at 30° N latitude (rounded off to the nearest integer) is ______ hours.

Answer: (24 to 24)

Q10 – Q22 carry two marks each.

10. Consider a high pressure centre in the northern hemisphere with tangential winds of 10 ms⁻¹ at a distance of 500 km from the centre. Assuming solid body rotation principles, what is the relative vorticity of the flow?

(A) 2 × 10⁻⁵ s⁻¹

(B) −2 × 10⁻⁵ s⁻¹

(D) −4 × 10⁻⁵ s⁻¹

Answer: (D)

11. Which one of the following statements is true for atmospheric and oceanic general circulation models?

(A) Vertical velocity is ignored in oceanic models but not in atmospheric models.

(B) Boussinesq approximation is adequate in oceanic models but not in atmospheric models.

(D) Atmospheric models need parameterizations for subgrid scale processes but oceanic models do not.

Answer: (B)

12. Consider a scenario where air temperature increases by 2 ° We know that saturation vapour pressure for water is increases with temperature. As a result of this effect, the water vapour content of the atmosphere will _____ and the net warming will be ______ than 2°C. The correct pair of words to fill in the blanks (in the right order) is

(A) increase, more

(B) increase, less

(D) decrease, less

Answer: (A)

13. The prevailing Trade winds over the Equator in the Pacific Ocean result in piling up of water in the ______ part of the ocean. As a result, the gradients of the thermocline and the ocean surface have ______ signs. The correct pair of words to fill in the blanks (in the right order) is

(A) western, opposite

(B) western, same

(D) eastern, same

Answer: (A)

14. Consider two different cases, shown in the Figures (i) and (ii) below, with two layers of water of same density on top of each other.

Which one of the following statements is true about convective plumes across the interface of the two layers?

(A) Upward convective plumes in (i) and downward convective plumes in (ii)

(B) Downward convective plumes in (i) and upward convective plumes in (ii)

(D) No convective plume in (i) but upward convective plumes in (ii)

Answer: (B)

15. During the Indian summer monsoon, surface outgoing longwave radiation (OLR) over the Arabian Sea is often observed to be low because

(A) of enhanced convection

(B) monsoon winds advect the OLR away into the Indian subcontinent

(D) surface Bowen ratio is low

Answer: (C)

16. A tsunami wave in the ocean is approaching the coast. Assuming g = 10 ms⁻², the correct group speed of the wave at a depth of 1 km is

(A) 1 ms⁻¹

(B) 10 ms⁻¹

(D) 1000 ms⁻¹

Answer: (C)

17. A tornado is in cyclostrophic balance where the horizontal pressure gradient and centrifugal forces balance each other. Consider a tornado with 100 m radius and a tangential velocity of 100 ms⁻¹ at the edge. Assuming air density = 1 kgm⁻³, the magnitude of the pressure-drop between the centre and the edge of the tornado is ______ kgm⁻¹ s⁻².

Answer: (10000 to 10000)

18. While driving south a distance of 1000 km, the temperature outside your car increases from 10 °C to 20 ° Assuming the air is completely dry, g = 10 ms⁻² and Coriolis parameter = 10⁻⁴ s⁻¹, the vertical gradient of the geostrophic wind (rounded off to 2 decimal places) is _______ ms⁻¹km⁻¹.

Answer: (3.40 to 3.50)

19. A westerly wind of 10 ms⁻¹ is blowing at a location in the Pacific Ocean in the northern hemisphere. Assuming density of sea water = 1000 kgm⁻³, Coriolis parameter = 10⁻⁴ s⁻¹ and drag coefficient for sea water = 10⁻⁶, the Ekman transport due to the wind at that location is ______ kgm⁻¹ s⁻¹.

Answer: (-1000 to -1000)

20. M_x and M_y represent the ocean mass transport in the x and y directions, respectively. L_x and L_y are the corresponding east-west and north-south length scales. For a typical equatorial ocean gyre, if the ratio of zonal to meridional mass transport ≈ 10, then L_x ≈ _______ L_y.

Answer: (10 to 10)

21. Assume the pressure varies exponentially with height: p(z) = p₀e⁻^z/H, where p(z) is the pressure at a height z above the surface, p₀ is the surface pressure, and the scale height H= 7.5 km. Under these conditions, one-fourth of the total mass of the atmosphere lies above a height (rounded off to 1 decimal place) of km above the surface.

Answer: (10.3 to 10.5)

22. Consider an atmospheric column of depth 300 m at the Earth’s surface with an average temperature of 300 K. If the temperature of the layer rises by ∆T = 10 °C, the layer depth h will increase by ∆ Assuming ∆T/T ≈ ∆h/h, air density remains unchanged at 1 kgm⁻³ and g = 10 ms⁻², the change in surface pressure is _______ kgm⁻¹s⁻².

Answer: (-100 to -100 or 100 to 100)

GATE Exam 2020 Textile Engineering and Fibre Science (TF) Question Paper With Answer Key

June 8, 2023May 6, 2022 by suresh84

GATE-2020

TF: Textile Engineering and Fibre Science

GA- General Aptitude

Q1 – Q5 carry one mark each.

1. This book, including all its chapters, ______ interesting. The students as well as the instructor ______ in agreement about it.

(A) is, was

(B) are, are

(D) were, was

Answer: (C)

2. People were prohibited ______ their vehicles near the entrance of the main administrative building.

(A) to park

(B) from parking

(D) to have parked

Answer: (B)

3. Select the word that fits the analogy:

Do : Undo :: Trust : ________

(A) Entrust

(B) Intrust

(D) Untrust

Answer: (C)

4. Stock markets ________ at the news of the coup.

(A) poised

(B) plunged

(D) probed

Answer: (B)

5. If P, Q, R, S are four individuals, how many teams of size exceeding one can be formed, with Q as a member ?

(A) 5

(B) 6

(D) 8

Answer: (C)

Q6 – Q10 carry two marks each.

6. Non-performing Assets (NPAs) of a bank in India is defined as an asset, which remains unpaid by a borrower for a certain period of time in terms of interest, principal, or both. Reserve Bank of India (RBI) has changed the definition of NPA thrice during 1993-2004, in terms of the holding period of loans. The holding period was reduced by one quarter each time. In 1993, the holding period was four quarters (360 days).

Based on the above paragraph, the holding period of loans in 2004 after the third revision was ______ days.

(A) 45

(B) 90

(D) 180

Answer: (B)

7. Select the next element of the series: Z, WV, RQP, ______

(A) LKJI

(B) JIHG

(D) NMLK

Answer: (C)

8. In four-digit integer numbers from 1001 to 9999, the digit group “37” (in the same sequence) appears ______ times.

(A) 270

(B) 279

(D) 299

Answer: (C)

9. Given a semicircle with O as the centre, as shown in the figure, the ratio is ______. where are chords.

(A) √2

(B) √3

(D) 3

Answer: (A)

10. The revenue and expenditure of four different companies P, Q, R and S in 2015 are shown in the figure. If the revenue of company Q in 2015 was 20% more than that in 2014, and company Q had earned a profit of 10% on expenditure in 2014, then its expenditure (in million rupees) in 2014 was _______.

(A) 32.7

(B) 33.7

(D) 35.1

Answer: (C)

TF: Textile Engineering and Fibre Science

Q1 – Q25 carry one mark each.

1. For the matrix the eigenvalues of matrix A² are

(A) 1, 0, 1

(B) 1, 0, 0

(D) 1, 1, 1

Answer: (D)

2. The integrating factor of the differential equation is

(A) e^x

(B) e⁻^x

(D) xe^x

Answer: (A)

3. Laplace transform of cosh(t) is

Answer: (C)

4. In wool, the sulfur containing amino acid is

(A) Alanine

(B) Cystine

(D) Serine

Answer: (B)

5. Viscose rayon is soluble in

(A) Acetone

(B) Chloroform

(D) Sulfuric acid 59% (w/w)

Answer: (D)

6. In carding, the highest draft is kept between

(A) Lap roller and feed roller

(B) Feed roller and licker-in

(D) Cylinder and doffer

Answer: (B)

7. The spinning system in which one revolution of twisting element imparts several turns to the fibre strand is

(A) Ring

(B) Rotor

(D) Wrap

Answer: (C)

8. The technology that does NOT produce a nonwoven fabric is

(A) Spunbonding

(B) Hydroentangling

(D) Braiding

Answer: (D)

9. For the same, yarn and fabric sett, the weave that gives the maximum tearing strength is

(A) Plain

(B) 2 × 2 matt

(D) 2/1 twill

Answer: (C)

10. Two yarns have variance of strength as V₁ and V₂. If V₁ < V₂, the variance ratio ‘F’ would be

(A) V₂/V₁

(B) V₁/V₂

(D) V₂²/V₁²

Answer: (A)

11. Cotton fibre length parameter that CANNOT be obtained from Baer Sorter diagram is

(A) Mean length

(B) Dispersion

(D) Modal length

Answer: (C)

12. The purpose of cabonization of wool fibres is to remove

(A) Waxy matter

(B) Surface scales

(D) Ortho-cortex

Answer: (C)

13. Bio-polishing of cotton fabrics is done using

(A) Cellulase

(B) Amylase

(D) Esterase

Answer: (A)

14. For the given system of linear equations, 2x – z = 1; 5x + y = 7; y + 3z = 5, the sum of x, y and z is_______.

Answer: (4 to 4)

15. If F = xi + yj + zk, then the magnitude of ∇ × F is ______.

Answer: (0 to 0)

16. A polypropylene filament is drawn in two stages with draw ratios of 1.5 and 2 respectively. The overall draw ratio is _______.

Answer: (3 to 3)

17. The refractive indices of a filament in axial and radial directions are 1.58 and 1.52 respectively. The birefringence of the filament (correct up to 2 decimal places) is ______.

Answer: (0.06 to 0.06)

18. A twin-delivery drawframe, running at a delivery speed of 800 m/min with an efficiency of 95%, is producing 5.39 ktex sliver. The rate of production of the drawframe in kg/h (rounded off to 2 decimal places) is _____.

Answer: (537.00 to 539.00)

19. The diameter (mm) of a yarn having twist of 700 turns per meter and surface-twist angle of 20° (rounded off to 2 decimal places) is ______.

Answer: (0.16 to 0.18)

20. A magazine creel has 800 package holders. The effective creel capacity (number) is ______.

Answer: (400 to 400)

21. A shuttle loom is running at 180 picks per minute. The angular velocity of crank shaft (degree/second) is ______.

Answer: (1080 to 1080)

22. The length (km) of 5 kg of 30 Ne yarn (rounded off to the nearest integer) is _____.

Answer: (253 to 255)

23. The limit irregularity and measured irregularity of a yarn are 8.4% and 9.6%, respectively. The index of Irregularity (rounded off to 2 decimal places) is _____.

Answer: (1.10 to 1.15)

24. A padding mangle is processing a fabric at 1320 m/h. The bottom bowl of the mangle is rotating at 25 rpm. Assuming zero slippage at the nip, the diameter (cm) of this bowl is ______.

Answer: (28.00 to 29.00)

25. A Procion H (monochlorotriazine based) reactive dye used for printing of cotton has a molecular weight of 471. Taking the atomic weight of H = 1, C = 12, N = 14, O = 16, Cl = 35.5, the molecular weight of the fully hydrolyzed dye (correct up to 1 decimal place) would be _______.

Answer: (452.5 to 452.5)

Q26 – Q55 carry two marks each.

26. Let The value o L is

(A) 0

(B) 1

(D) ∞

Answer: (B)

27. The solution of the differential equation which satisfies the conditions, y(0) = 0, y’(0) = 3 is

(A) e⁻^x

(B) e^x

(D) e^x – e⁻^2x

Answer: (D)

28. In melt spinning of poly(ethylene terephthalate), pre-drying of polymer chips is essential to avoid

(A) Hydrolytic degradation

(B) Oxidative degradation

(D) Photo-induced degradation

Answer: (A)

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

[a]: Caprolactam is polymerized in the presence of small amount of water of produce fibre grade nylon 6.

[r]: Water reacts as a catalyst and converts caprolactam to aminocaproic acid.

(A) Both [a] and [r] and 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: (A)

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

[a]: Melting point of nylon 66 fibre is much higher that of polyethylene fibre.

[r]: The molecular weight of nylon 66 fibre is significantly higher than that of polyethylene fibre.

(A) Both [a] and [r] and 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)

31. Carding of polyester fibres requires that the values of wire-point density (points/inch²) of

(P) Licker-in (Q) Cylinder (R) Flat

follow the order

(A) P < Q < R

(B) P < R < Q

(D) Q < P < R

Answer: (B)

32. For combing with forward feed, the given parameters are:

Detachment setting = 15 mm, length of feed per combing cycle = 6 mm, Longest fiber length = 30 mm. According to Gegauff’s theory, the noil (%) would be

(A) 9

(B) 16

(D) 49

Answer: (B)

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

[a]: Open-loop autolevelling system needs a signal storage device with time delay function.

[r]: The signal must be stored until the material reaches the adjusting point.

(A) Both [a] and [r] and 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: (A)

34. If both the concentration (%, w/w) of size paste and target add-on are 12%, the total wet pick-up (kg) by 12 kg bone-dry warp sheet is

(A) 6

(B) 12

(D) 24

Answer: (B)

35. At front centre (0°) and a back centre (180°) of a shuttle loom.

(A) The sley velocities are the same but accelerations are different

(B) The sley velocities are different but accelerations are the same

(D) The sley velocities are different and also accelerations are different

Answer: (A)

36. Match the looms listed in Group with the corresponding components given in Group II. The correct option is

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

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

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

Answer: (C)

37. Consider two yarns, one 100% wool and the other 100% cotton, each containing 100 fibres in the yarn cross-section. The respective limit irregularities (%) of wool and cotton yarns will approximately be

(A) 11.2 and 10.6

(B) 10.6 and 11.2

(D) 11.8 and 10.6

Answer: (A)

38. If the numerical value X of yarn linear density, expressed in denier is the same as that expressed in English (Ne) system, then X approximately is

(A) 24.3

(B) 48.6

(D) 97.2

Answer: (C)

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

[a]: Sodium chlorite is a bleaching agent for cotton.

[r]: Sodium chlorite is an effective reducing agent.

(A) Both [a] and [r] and 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)

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

[a]: Acrylic fibres are dyed with basic dyes in acidic medium.

[r]: In acidic medium the acrylic fibre acquires positive charge.

(A) Both [a] and [r] and 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)

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

[a]: Foam finishing significantly reduces the energy consumed in drying.

[r]: The specific heat of air is significantly lower than that of water.

(A) Both [a] and [r] and 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: (B)

42. If the probability density function of a continuous random variable X is given by f(x) = e⁻^x, 0 ≤ x < ∞, the mean of random variable X is _______.

Answer: (1 to 1)

43. Assuming the step size h = 1, the numerical value of the definite integral obtained using Trapezoidal rule (rounded off to 2 decimal places) is ______.

Answer: (0.70 to 0.75)

44. In the production of PET, diglycol terephthalate (DGT) is an intermediate. Taking the atomic weights of H = 1, C = 12, O = 16, the molecular weight of DGT is______.

Answer: (254 to 254)

45. In wet spinning of acrylic filament yarn, the volumetric flow rate of the spinning dope per spinneret hole is 0.1 cm³/min. If the surface speed at the first take up roller is 1.5 m/min and the diameter of spinneret hole is 0.02 cm, then the jet stretch (rounded off to 2 decimal places) is _______.

Answer: (0.46 to 0.48)

46. Two types of polyester staple fibers of fineness 3 and 6 denier and having the same length are mixed in a ratio of 2 : 3 by weight. The mean fibre fineness (denier) of the mix (rounded off to 2 decimal places) is _____.

Answer: (4.25 to 4.35)

47. Two rovings, each with mass CV of 10%, are fed to a ring spinning machine that adds a mass CV of 20%. The mass CV (%) of the yearn (rounded off to 2 decimal places) is _____.

Answer: (21.00 to 22.00)

48. In a drum-driven winder, the grooved drum having a width of 20 cm is rotating at 1000 rpm. If the drum makes 5 revolutions per double traverse, the traverse speed (m/min) is ______.

Answer: (80 to 80)

49. The wale constant and course constant are 4.2 and 5.04 respectively. If the loop length is 4.2 mm, then stitch density (number/cm²) is _______.

Answer: (120 to 120)

50. A cotton fibre has degree of cell wall thickening (θ) of 0.9 and perimeter of 40 μ The actual cross-sectional area of the wall (μm²) of the fibre (rounded off two 1 decimal place) is _______.

Answer: (112.0 to 117.0)

51. A fabric with mass per unit area of 250 g/m² has flexural rigidity of 275 μN-m. The bending length (mm) of the fabric (rounded off to 2 decimal places) is______.

Answer: (46.00 to 50.00)

52. The ‘standard machine rate of loading’ of a tensile tester, working on pendulum lever principle, is 440 N/cm. As the pendulum lever swings from 30° to 45°, the ‘machine rate of loading’ (N/cm), reduces by (rounded off to 2 decimal places) ________.

Answer: (69.00 to 71.00)

53. Under a load of 500 cN, the extension of a yarn of 300 mm length is 10%. If the elastic recovery is 90%, then the length (mm) of the yarn after removal of load is _______.

Answer: (303 to 303)

54. Given that one gram mole of a gas occupies 22.4 L of volume at STP, the atomic weights of H = 1, and that of O = 16, the concentration (g/L) of hydrogen peroxide solution of 25 volume strength (rounded off to 2 decimal places) is _______.

Answer: (75.00 to 77.00)

55. The work of adhesion (W_SL) depends on the surface tension (γ_LV) of the liquid and the contact angle (θ) formed on a surface and is expressed as γ_LV(1 + cos θ). The W_SL for a given fabric and a liquid is reduced to 1/3^rd of the original value after oil repellent treatment. If the measured contact angle of untreated fabric is 60°, the percent change in the contact angle after the treatment is ______.

Answer: (100 to 100)

GATE Exam 2020 Stastics (ST) Question Paper With Answer Key

June 8, 2023May 6, 2022 by suresh84

GATE-2020

ST: Statistics

GA-General Aptitude

Q1 – Q5 carry one mark each.

(A) with, at

(B) on, in

(D) to, at

Answer: (C)

2. Despite a string of a poor performances, the changes of K. L. Rahul’s selection in the team are ______.

(A) slim

(B) bright

(D) uncertain

Answer: (B)

3. Select the word that fits the analogy:

Cover : Uncover :: Associate : _______

(A) Unassociate

(B) Inassociate

(D) Dissociate

Answer: (D)

Which of the following statements can be inferred from the given passage?

(A) Officials declared that the food-grain production target will be met due to good rains.

(B) Officials want the food-grain production target to be met by the November-February period.

(D) Officials hope that the food-grain production target will be met due to a good rabi produce.

Answer: (D)

5. The difference between the sum of the first 2n natural numbers and the sum of the first n odd natural numbers is ______.

(A) n² – n

(B) n² + n

(D) 2n² + n

Answer: (B)

Q6 – Q10 carry two marks each.

6. Repo rate is the at which Reserve Bank of India (RBI) lends commercial banks, and reverse repo rate is the rate at which RBI borrows money from commercial banks.

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

(A) Decrease in repo rate will increase cost of borrowing and decrease lending by commercial banks.

(B) Increase in repo rate will decrease cost of borrowing and increase lending by commercial banks.

(D) Decrease in repo rate will decrease cost of borrowing and increase lending by commercial banks.

Answer: (D)

7. P, Q, R, S, T, U, V, and W are seated around a circular table.

(I) S is seated opposite to W.

(II) U is seated at the second place to the right of R.

(III) T is seated at the third place to the left of R.

(IV) V is a neighbor of S.

Which of the following must be true?

(A) P is a neighbor of R.

(B) Q is a neighbor of R.

(D) R is the left neighbor of S.

Answer: (C)

(A) 66.6

(B) 75.2

(D) 116.5

Answer: (B)

9. For a matrix M = [m_ij], i. j= 1, 2, 3, 4, the diagonal elements are all zero and m_ij = −m_ij. The minimum number of elements required to fully specify the matrix is_______.

(A) 0

(B) 6

(D) 16

Answer: (B)

(A) 15 : 17

(B) 16 : 17

(D) 17 : 16

Answer: (B)

ST: Statistics

Q1 – Q25 carry one mark each.

1. Let M be a 3 × 3 non-zero idempotent matrix and let I₃ denote the 3 × 3 identity matrix. Then which of the following statements is FLASE?

(A) The eigenvalues of M are 0 and 1

(B) Rank(M) = Trace(M)

(D) (I₃ + M)⁻¹ = I₃ – 2M

Answer: (D)

2. Let ℂ denote the set of all complex numbers. Consider the vector space

over the field of real numbers, where for any complex number z, denotes its complex conjugate. If i = √−1, then a basis of V is

(A) {(1, −1, 1), (i, i, i)}

(B) {(1, −1, 1), (i, −i, i)}

(D) {(1, −i, 1), (i, 1, −i)

Answer: (A)

3. Let S = {(x, y) ∈ ℝ × ℝ: x² – y² = 4} and f : S → ℝ be defined by f(x, y) = 6x + y², where ℝ denotes the set of all real numbers. Then

(A) f is bounded of S

(B) the maximum value of f on S is 13

(D) the minimum value of f on S is −13

Answer: (D)

4. Let f : ℝ × ℝ → ℝ be defined by

where ℝ denotes the set of all real numbers and c ∈ ℝ is fixed constant. Then, which of the following statements is TRUE?

(A) There does NOT exists a value of c for which f is continuous at (0, 0)

(B) f is continuous at (0, 0) if c = 0

(D) f is continuous at (0 0) if c = 16

Answer: (D)

5. The moment generating function of a random variable X is given by

Then P(X ≤ 2) equals

(A) 1/3

(B) 1/6

(D) 5/6

Answer: (D)

6. Consider the following two-way fixed effects analysis of variance model

Y_ijk = μ + α_i + β_j + ϵ_ijk, i = 1, 2; j = 1, 2, 3; k = 1, 2, 3;

where ϵ_ijk’s are independently and identically distributed N(0, σ²) random variables, σ ∈ (0, ∞), α₁ + α₂ = 0 and β₁ + β₂ + β₃ = 0. Let SSE denote the sum of squares due to error. For any positive integer v and any α ∈ (0, 1), let χ²_v,α denote the (1 – α)-th quantile of the central chi-square distribution with v degrees of freedom. Then a 95% confidence interval for σ² is given by

Answer: (D)

7. Let X₁, …, X₂₀ be independent and identically distributed random variables with the common probability density function

Then the distribution of the random variableis

(A) central chi-square with 10 degrees of freedom

(B) central chi-square with 20 degrees of freedom

(D) central chi-square with 40 degrees of freedom

Answer: (D)

8. Let X₁, …, X₁₀ be a random sample from a Weibull distribution with the probability density function

where θ ∈ (0, ∞). For any positive integer v and any α ∈ (0, 1), let χ²_v,_α denote the (1 – α)-th quantile of the central chi-square distribution with v degrees of freedom. Then, a 90% confidence interval for θ is

Answer: (A)

9. Let X₁, …, X_n be a random sample of size n (≥2) from a uniform distribution on the interval [−θ, θ], where θ ∈ (0, ∞). A minimal sufficient for θ is

Answer: (C)

10. Let X₁ …, X_n be a random sample of size n(≥2) from N(θ, 2θ²) distribution, where θ ∈ (0, ∞). Which of the following statements is TRUE?

(A) is the unique unbiased estimator of θ² that is a function of minimal sufficient statistic

(B) is an unbiased estimator of θ²

(D) There does NOT exist any unbiased estimator of θ(θ + 1) that is a function of minimal sufficient statistic

Answer: (C)

11. Let {N(t), t ≥ 0} be a Poisson process with rate λ = 2. Given that N(3) = 1, the expected arrival time of the first event of the process is

(A) 1

(B) 3/2

(D) 3

Answer: (B)

12. Consider the regression model

Y_i = β₀ + β₁x_i² + ϵ_i, i = 1, 2, …, n(n ≥ 2);

where β₀ and β₁ are unknown parameters and ϵ_i^’s are random errors. Let y_i be the observed value of Y_i, i = 1, …, n. Using the method of ordinary least squares, the estimate of β₁ is

Answer: (B)

13. Let be a random sample of size n (≥2) from distribution, where 1 ≤ p ≤ n – 1 and ∑ is a positive definite matrix. Define

where for any column vector denotes its transpose. Then the distribution of the statistic is

(A) χ²_p, the central chi-square distribution with p degrees of freedom

(B) F_p,n₋_p, the central F distribution with p and n – p degrees of freedom

(D) where F_p,n₋_p, is the central F distribution with n – p and p degrees of freedom

Answer: (C)

14. Consider a two-way fixed effects analysis of variance model without interaction effect and one observation per cell. If there are 5 factors and 4 columns, then the degrees of freedom for the error sum of squares is

(A) 20

(B) 19

(D) 11

Answer: (C)

15. Let X₁, …, X_n be a random sample of size n (≥ 2) from an exponential distribution with the probability density function

where θ ∈ {1, 2}. Consider the problem of testing H_{0 :}θ = 1 against H₁ : θ = 2, based on X₁, …, X_n. Which of the following statements is TRUE?

(A) Likelihood ratio test at level α (0 < α < 1) leads to the same critical region as the corresponding most powerful test at the same level.

(B) Critical region of level α (0 < α < 1) likelihood ratio test is is the α-th quantile of the central chi-square distribution with 2n degrees of freedom

(D) At any fixed level α (0 < α < 1), the power of the likelihood ratio test is lower than that of the most powerful test

Answer: (A)

16. Te characteristic function of a random variable X is given by

Then P(|X| ≤ 3/2) = _____ (correct up to two decimal places).

Answer: (0.75 to 0.75)

17. Let the random follow distribution, where

Then P(X₁ + X₂ + X₃ + X₄ > 0) = _______ (correct up to one decimal place).

Answer: (0.5 to 0.5)

18. Let {X_n}_n_≥₀ be a homogeneous Markov chain with state space {0, 1} and one-step transition probability matrix If P(X₀ = 0) = 1/3, then 27 × E(X₂) = ______ (correct up to two decimal places).

Answer: (16.25 to 16.25)

19. Let E, F and G be mutually independent events with P(E) = 1/2, P(F) = 1/3 and P(G) = 1/4. Let p be the probability that at least two of the events among E, F and G occur. Then 12 × p = _______ (correct up to one decimal place).

Answer: (3.5 to 3.5)

20. Let the joint probability mass function of (X, Y, Z) be

where k = 10 – x – y – z; x, y, z = 0, 1, … , 10; x + y + z ≤ 10. Then the variance of the random Y + Z equals ______ (correct up to one decimal place).

Answer: (2.1 to 2.1)

21. The total number of standard 4 × 4 Latin squares is _______

Answer: (4 to 4)

22. Let be a 4 × 1 random vector with and variance-covariance matrix

Let be the 4 × 1 random vector of principal components derived from ∑. The proportion of total variation explained by the first two principal components equals ______ (correct up to two decimal places).

Answer: (0.75 to 0.75 OR 75 to 75)

23. Let X₁, …, X_n be a random sample of size n (≥ 2) from an exponential distribution with the probability density function

where θ ∈ (0, ∞). If X₍₁₎ = min{X₁, …, X_n} then the conditional expectation

Answer: (2 to 2)

24. Let Y_i = α + βx_i + ϵ_i, i = 1, 2, …, 7, where x_i’s are fixed covariates and ϵ_i’s are independent and identically distributed random variables with mean zero and finite variance. Suppose that are the least squares estimators of α and β, respectively. Given the following data:

where y_i is the observed value of Y_i, i = 1, …, 7. Then the correlation coefficient between equals_____

Answer: (0 to 0)

25. Let {0, 1, 2, 3} be an observed sample of size from N(θ, 5) distribution, where θ ∈ [2, ∞). Then the maximum likelihood estimate of θ based on the observed sample is ________.

Answer: (2 to 2)

Q26 – Q55 carry two marks each.

26. Let f : ℝ × ℝ → ℝ be defined by

f(x, y) = x⁴ – 2x³y + 16y + 17,

where ℝ denotes the set of all real numbers. Then

(A) f has a local minimum at (2, 4/3)

(B) f has a local maximum at (2, 4/3)

(D) f is bounded

Answer: (C)

27. Consider the linear transformation T : ℂ³ = ℂ × ℂ × ℂ. Which of the following statements is TRUE?

(A) There exists a non-zero vector X such that T(X) = −X

(B) There exist a non-zero vector Y and a real number λ ≠ 1 such that T(Y) = λY

(D) T² = I₃, where I₃ is the 3 × 3 identity matrix

Answer: (C)

28. For real numbers a, b and c, let

Then, which of the following statements is TRUE?

(A) Rank (M) = 3 for every, a, b, c ∈ ℝ

(B) If a + c = 0 then M is diagonalizable for every b ∈ ℝ

(D) If b= 0 and a + c = 1 then M is NOT idempotent

Answer: (C)

29. Let M be a 4 × 4 matrix with (x – 1)² (x – 3)² as its minimal polynomial. Then, which of the following statements is FALSE?

(A) The eigenvalues of M are 1 and 3

(B) The algebraic multiplicity of the eigenvalue 1 is 3

(D) Trace(M) = 8

Answer: (B)

30. Let f : ℝ × ℝ → ℝ be defined by

where ℝ denotes the set of all real numbers. Then which of the following statements is TRUE?

(A) f is differentiable at (1, 2)

(B) f is continuous at (1, 2) but NOT differentiable at (1, 2)

(D) The directional derivative of f at (1, 2) along equals 1

Answer: (A)

31. Which of the following functions is uniformly continuous on the specified domain?

Answer: (C)

32. Let the random vector have the joint probability density function

Which of the following statements is TRUE?

(A) X₁, X₂ and X₃ are mutually independent

(B) X₁, X₂ and X₃ are pairwise independent

(D) Variance of X₁ + X₂ is π²

Answer: (B)

33. Suppose that P₁ and P₂ are two populations having bivariate normal distributions with mean vectors respectively, and the same variance-covariance matrix two new observations. If the prior probabilities for P₁ and P₂ are assumed to be equal and the misclassification costs are also assumed to be equal then, according to linear discriminant rule,

(A) Z₁ is assigned to P₁ and Z₂ is assigned to P₂

(B) Z₁ is assigned to P₂ and Z₂ is assigned to P₁

(D) both Z₁ and Z₂ are assigned to P₂

Answer: (B)

34. Let X₁, …, X_n be a random sample of size n (≥2) from an exponential distribution with the probability density function

where θ ∈ (0, ∞). Which of the following statements is TRUE?

Answer: (D)

35. Let the joint distribution of (X, Y) be bivariate normal with mean vector and variance-covariance matrix where −1 < ρ < 1. Then E[max(X, Y)] equals

(A)

(B)

(D) 1/2

Answer: (B)

36. Let be independent and identically distributed random vectors, where I₃ is the 3 × 3 identity matrix. Let

where J₃ is the 3 × 3 matrix with each entry 1 and for any column vector denotes its transpose. Then the distribution of T is

(A) central chi-square with 5 degrees of freedom

(B) central chi-square with 10 degrees of freedom

(D) central chi-square with 30 degrees of freedom

Answer: (C)

37. Let be independent and identically distributed random vectors, where ∑ is a positive definite matrix. Further, let be a 3 × 4 matrix, where for any matrix M, M^t denotes its transpose. If W_m (n, ∑) denotes a Wishart distribution of order m with n degrees of freedom and variance-covariance matrix ∑, then which of the following statements is TRUE?

(A) ∑⁻^1/2 X^tX∑⁻^1/2 follows W₄(3, I₄) distribution

(B) ∑⁻^1/2X^tX∑⁻^1/2 follows W₃(4, I₃) distribution

(D) X^tX follows W₃(4, ∑) distribution

Answer: (A)

38. Let the joint distribution of the random variables X₁, X₂ and X₃ be where

Then which of the following statements is TRUE?

(A) X₁ – X₂ + X₃ and X₁ are independent

(B) X₁ + X₂ and X₃ – X₁ are independent

(D) X₁ – 2X₂ and 2X₁ + X₂ are independent

Answer: (C)

39. Consider the following one-way fixed effects analysis of variance model

Y_ij = μ + τ_i + ϵ_ij, i = 1, 2, 3; j = 1, 2, 3, 4;

where ϵ_ij’s are independent and identically distributed N(0, σ²) random variables, σ ∈ (0, ∞) and τ₁ + τ₂ + τ₃ = 0. Let MST and MSE denote the mean sum of squares due to treatment and the mean sum of squares due to error, respectively. For testing H₀ : τ₁ = τ₂ = τ₃ = 0 against H₁ : τ_i ≠ 0, for some i = 1, 2, 3, consider the test based on the statistic For positive integers v₁ and v₂, let Fv₁,v₂ be a random variable having the central F-distribution with v₁ and v₂ degrees of freedom. If the observed value of is given to be 104.45, then the p-value of this test equals

(A) P(F_{2, 9} > 104.45)

(B) P(F_{9, 2}< 104.45)

(D) P(F_{2, 6} > 104.45)

Answer: (A)

40. Let X₁, …, X_n be a random sample of size n (≥ 2) from N(θ, 1) distribution, where θ ∈ (−∞, ∞). Consider the problem of testing H₀ : θ ∈ [1, 2] against H₁ : θ < 1 or θ > 2, based on X₁, …, X_n. Which of the following statements is TRUE?

(A) Critical region, of level α (0 < α < 1) of uniformly most powerful test for H₀ against H₁ is of the form where c₁ and c₂ are such that test is of level α

(B) Critical region, of level α(0 < α < 1) of uniformly most powerful test for H₀ against H₁ is of the form {(x₁, …, x_n) : where c and d are such that the test is level α

(D) At any level α ∈ (0, 1), the power of uniformly most powerful test for H₀ against H₁ is less than α

Answer: (C)

41. In a pure birth process with birth rates λ_n = 2ⁿ, n ≥ 0, let the random variable T denote the time taken for the population size to grow from 0 to 5. If Var(T) denotes the variance of the random variable T, then 256 × Var(T) = _______

Answer: (341 to 341)

42. Let {X_n}_n_≥₀ be a homogenous Markov chain whose state space is {0, 1, 2} and whose one-step transition probability matrix is Then _____ (correct up to one decimal place).

Answer: (0.7 to 0.7)

43. Let (X, Y) be a random vector such that, for any y > 0, t he conditional probability density function of X given by Y = y is f_x|Y=y (x) = ye⁻^yx, x > 0.

If the marginal probability density function of Y is g(y) = ye⁻^y, y > 0 then E(Y|X = 1) = ______ (correct up to one decimal place).

Answer: (1.5 to 1.5)

44. Let (X, Y) be a random vector with the joint moment generating function

Let Φ(∙) denote the distribution function of the standard normal distribution and p = P(X + 2Y < 1). If Φ(0) = 0.5, Φ(0.5) = 0.6915, Φ(1) = 0.8413 and Φ(1.5) = 0.9332 then the value of 2p + 1 (round off to two decimal places) equals______

Answer: (1.61 to 1.63)

45. Consider a homogeneous Markov chain {X_n}_n_≥₀ with state space {0, 1, 2, 3} and one-step transition probability matrix

Assume that P(X₀ = 1) = 1. Let p be the probability that state 0 will be visited before state 3. Then 6 × p = ______

Answer: (4 to 4)

46. Let (X, Y) be a random vector with joint probability mass function

where Then the variance of Y equals ______

Answer: (1 to 1)

47. Let X be a discrete random variable with probability mass function f ∈ {f₀, f₁}, where

The power of the most powerful level α = 0.1 test for testing H₀ : X ~ f₀ against H₁:X ~ f₁, based on X, equals _______ (correct up to two decimal places).

Answer: (0.12 to 0.12)

48. Let be a random vector following distribution, where Then the partial correlation coefficient between X₂ and X₃, with fixed X₁, equals _______ (correct up to two decimal places).

Answer: (0.25 to 0.25)

49. Let X₁, X₂, X₃ and X₄ be a random sample from a population having probability density function f_θ(x) = f(x – θ), −∞ < x < ∞, where θ ∈ (−∞, ∞) and f(−x) = f(x), for all x ∈ (−∞, ∞). For testing H₀: θ = 0 against H₁: θ < 0, let T⁺ denote the Wilcoxon Signed-rank statistic. Then under H₀, 32 × P(T⁺ ≤ 5) ______

Answer: (18 to 18)

50. A simple linear regression model with unknown intercept and unknown slope is fitted to the following data

using the method of ordinary least squares. Then the predicted value of y corresponding to x = 5 is _______

Answer: (16 to 16)

51. Let D = {(x, y, z) ∈ ℝ × ℝ × ℝ : 0 ≤ x, y, z ≤ 1, x + y + z ≤ 12}, where ℝ denotes the set of all real numbers. If then 84 × I = _____

Answer: (7 to 7)

52. Let the random vector (X, Y) have the joint distribution function

Let Var(X) and Var(Y) denote the variances of random variables X and Y, respectively. Then 16 Var(X) + 32 Var(Y) = _______

Answer: (22 to 22)

53. Let {X_n}_n_≥₁ be a sequence of independent and identically distributed random variables with E(X₁) = 0, E(X₁²) = 1 and E(X₁⁴) = 3. Further, let

where Φ(∙) denotes the cumulative distribution function of the standard normal distribution, then c² = ______(correct up to one decimal place.

Answer: (1.5 to 1.5)

54. Let the random vector have the joint probability density function

Then the variance of the random variable X₁ + X₂ + X₃ equals ______ (correct up to one decimal place).

Answer: (1.8 to 1.8)

55. Let X₁, …, X₅ be a random sample from a distribution with the probability density function

where θ (−∞, ∞). For testing H₀ : θ = 0 against H₁ : θ, let be the sign test statistic, where

Then the size of the test, which rejects H₀ if and only if equals ______ (correct up to one decimal place).

Answer: (0.5 to 0.5)

GATE Exam 2020 Production and Industrial Engineering (PI) Question Paper With Answer Key

June 8, 2023May 3, 2022 by suresh84

GATE-2020

PI: Production and Industrial Engineering

GA-General Aptitude

Q1 – Q5 carry one mark each.

1. While I agree _____ his proposal this time, I do not often agree _____ him.

(A) to, with

(B) with, to

(D) to, to

Answer: (A)

2. The recent measures to improve the output would _______ the level of production to our satisfaction.

(A) increase

(B) decrease

(D) qualize

Answer: (A)

3. Select the word that fits the analogy:

White : Whitening : Light: ______

(A) Lightning

(B) Lightening

(D) Enlightening

Answer: (B)

4. In one of the greatest innings ever seen in 142 years of Test history, Ben Stokes upped the tempo in a five-and-a-half hour long stay of 219 balls including 11 fours and 8 sixes that saw him finish on a 135 not out as England squared the five-match series.

Based on their connotations in the given passage, which one of the following meanings DOES NOT match?

(A) upped = increased

(B) squared = lost

(D) saw = resulted in

Answer: (B)

5. There are five levels {P, Q, R, S, T} in a linear supply chain before a product reaches customers, as shown in the figure.

At each of the five levels, the price of the product is increased by 25%. If the product is produced at level P at the cost of Rs. 120 per unit, what is the price paid (in rupees) by the customers?

(A) 187.50

(B) 234.38

(D) 366.21

Answer: (D)

Q6 – Q10 carry two marks each.

6. Climate change and resilience deal with two aspects – reduction of sources of non-renewable energy resources and reducing vulnerability of climate change aspects. The terms ‘mitigation’ and ‘adaptation’ are used to refer to these aspects, respectively.

Which of the following assertions is best supported by the above in information?

(A) Mitigation deals with consequences of climate change.

(B) Adaptation deals with causes of climate change.

(D) Adaptation deals with actions taken to combat gree-house gas emissions.

Answer: (C)

7. Find the missing element in the following figure.

(A) d

(B) e

(D) y

Answer: (A)

8. It was estimated that 52 men can complete a strip in a newly constructed highway connecting cities P and Q in 10 days. Due to an emergency, 12 men were sent to another project. How many number of days, more than the original estimate, will be required to complete the strip?

(A) 3 days

(B) 5 days

(D) 13 days

Answer: (A)

9. An engineer measures THREE quantities X, Y and Z in an experiment. She finds that they follow a relationship that is represented in the figure below : (the product of X and Y linearly varies with Z)

Then, which of the following statements is FALSE?

(A) For fixed Z; X is proportional to Y

(B) For fixed Y; X is proportional to Z

(D) XY/Z is constant

Answer: (A)

10. The two pie-charts given below show the data of total students and only girls registered in different streams in a university. If the total number of students registered in the university is 5000, and the total number of the registered girls is 1500; then, the ratio of boys enrolled in Arts to the girls enrolled in Management is ______.

(A) 2:1

(B) 9:22

(D) 22:9

Answer: (D)

PI: Production and Industrial Engineering

Q1 – Q25 carry one mark each.

1. The divergence of the vector is

(A) 2x

(B) 2y

(D) 0

Answer: (D)

2. An integrating factor for the differential equation is

(A) e^m

(B) e⁻^m

(D) e^mx

Answer: (D)

3. For the complex numbers z₁ = 2 + 3i and z₂ = 4 – 5i, the value of (z₁ + z₂)² is

(A) 32 – 24i

(B) −32 – 24i

(D) −32 + 24i

Answer: (A)

4. To solve x² – 2 = 0, the Newton-Raphson method has been employed. If the initial guess x₀ = 1.0, the next estimate of the root, x₁, will be

(A) 0.5

(B) 1.0

(D) 2.0

Answer: (C)

5. If x is a random variable with the expected value of 5 and the variance of 1, then the expected value of x² is

(A) 24

(B) 25

(D) 36

Answer: (C)

6. Group I lists phases of steel and Group II lists crystal structures in the table below.

Match the phase with the corresponding crystal structure.

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

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

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

Answer: (A)

7. The figure shows two bodies P and Q. The body Q is placed on the ground and the body P is placed on top of it. The weights of P and Q are W_P and W_Q, respectively. The bodies are at rest and all the surfaces are assumed to be frictionless. R represents reaction force, if any, between the bodies.

The correct free body diagram of the body P is

Answer: (B)

8. The figure shows as mechanism with 3 revolute pairs (between the links 1 and 2, 2 and 3, and 3 and 4) and a prismatic pair (between the links 1 and 4). Which one of the four links should be fixed to obtain the mechanism that forms the basis of the quick-return mechanism widely used in a shaper?

(A) Link 1

(B) Link 2

(D) Link 4

Answer: (B)

9. The state of stress at a point in the body under plane stress condition is shown in the figure. The positive directions of x and y axes are also shown. The material of the body is homogeneous and isotropic, with modulus of elasticity E and Poisson’s ratio v. The longitudinal strain in the x-direction is

Answer: (C)

10. The figure shows two bodies connected through a riveted joint with one rivet. The diameter of the rivet is d (in m). The joint transmits a load of F(in N) whose line of action is perpendicular to and intersects the vertical axis of the rivet. Neglect any effect of bending of the rivet. If the allowable shear stress for the material of the rivet is τ N/m², the diameter of the rivet required to prevent failure in shear is

Answer: (B)

11. Consider flow of an oil with Reynolds number 1500 in a pipe of diameter 5 cm. The kinematic viscosity of the oil, v = 0.75 cm²/s. The value of average velocity in m/s is

(A) 0.75

(B) 1.50

(D) 4.50

Answer: (C)

12. A Carnot heat engine receives 600 kJ of heat per cycle from a source at 627°C and rejects heat to a sink at 27° The amount of heat rejected to the sink per cycle (rounded off to the nearest integer) in kJ is

(A) 26

(B) 200

(D) 574

Answer: (B)

13. The process used for producing long bars of fiber reinforced plastics (FRP) with uniform cross-section is

(A) Extrusion

(B) Pultrusion

(D) Thermoforming

Answer: (B)

14. The purpose of the ratchet in a micrometer is to

(A) impart smooth movement to the spindle

(B) compensate for the wear of the screw thread

(D) maintain sufficient and uniform measuring pressure

Answer: (D)

15. End mill cutters are mounted on the spindle of a vertical milling machine using

(A) vice

(B) collet

(D) driver plate

Answer: (B)

16. Self-sharpening tendency of a conventional grinding wheel depends upon

(A) wheel structure

(B) wheel grade

(D) grit size

Answer: (B)

17. A non-traditional machining process which utilizes mechanical energy as the principal energy source for removing the material is

(A) Electric discharge machining

(B) Laser beam machining

(D) Plasma arc machining

Answer: (C)

18. In a manufacturing of self-lubricating bearings by powder metallurgy, an important secondary operation that is carried out after sintering is

(A) Cold isostatic pressing

(B) Hot isostatic pressing

(D) Infiltration

Answer: (C)

19. Which of the following is a causal forecasting method?

(A) Naïve approach

(B) Moving average

(D) Linear regression

Answer: (D)

20. An approach used in the product development which combines the efforts of design, manufacturing, and other functions to reduce the total time in introducing a new product in the market is

(A) Concurrent engineering

(B) Lean manufacturing

(D) Break-even anlaysis

Answer: (A)

21. The Bellman’s principle of optimality is related to

(A) Linear programming problem

(B) Transportation problem

(D) Assignment problem

Answer: (C)

22. The process capability ratio C_p is given by

Answer: (A)

23. In a uniaxial tensile test on a specimen of a ductile material, the ultimate tensile strength is found to be 400 MPa and the elongation up to the maximum load is 25%. The true stress at the maximum load in MPa is ______.

Answer: (500 to 500)

24. Suppose the control system of a fighter jet consists of three unrelated components in series, and it is desired to have 98% reliability of the system. If the reliability level of all the components is the same, then the reliability of each component (rounded off to three decimal places) is ________.

Answer: (0.993 to 0.994 OR 99.300 to 99.400)

25. The product structure tree in the figure below shows the components needed to assemble one unit of product P.

The number of units of component D needed to assemble 10 units of product P is ___________.

Answer: (220 to 220)

Q26 – Q55 carry two marks each.

26. General solution of is

Answer: (C)

27. For the matrix the eigenvectors are

Answer: (B)

28. A truss with two bars PR and QR, making angles α and β, respectively, with the vertical, is shown in the figure below. The connections at P, Q and R are hinged connections. The truss supports body of weight W (in N) at R as shown. The tension in the bar QR(in N) is

Answer: (D)

29. The figure shows a beam of length L (in m) with a uniformly distributed transverse load of W (in N/m) acting over it. The width and depth of the beam cross section are b (in m) and t (in m), respectively. The magnitude of the maximum bending stress in the beam in N/m² is

Answer: (A)

30. The vertices of rectangle PQRS are as follows in a 2-D CAD system.

P(-4, -2); Q(-2, -3); R(-3, -5); S(-5, -4)

The coordinates of the corresponding new vertices, P’, Q’, R’, S’ after translation of the rectangle along x-axis in the positive direction by 6 units and along y-axis in the positive direction by 3 units are

(A) P’(-10, -5); Q’(-8, -6); R’(-9, -8); S’(-11, -7)

(B) P’(2, 1); Q’(4, 0); R’(3, -2); S’ (1, -1)

(D) P’(-10, 1); Q’(-8, 0); R’(-9, -2); S’(-11, -1)

Answer: (B)

31. The statement that best describes the function of a GO gauge in the context of Taylor’s principle of gauging is

(A) GO gauge checks the Maximum Material Condition and is designed to check as many dimensions as possible

(B) GO gauge checks the Least Material Condition and is designed to check as many dimensions as possible

(D) GO gauge checks the Least Material Condition and is designed to check only one dimension

Answer: (A)

32. The figures shows revenue generated over different product life cycle stages marked as P, Q, R and S. Group I lists these product life cycle stages. Group II lists typical efforts leading to revenue maximizing during a stage.

Match the stage with the efforts.

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

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

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

Answer: (D)

33. A company manufactures products P and Q in quantities x₁ and x₂, respectively, using two resources. The following Linear Programming Problem (LPP) is Maximize Z = 3x₁ + 2x₂

subject to x₁ + 2x₂ ≤ 2 (for Resource 1)

2x₁ + x₂ ≤ 2 (for Resource 2)

and x₁, x₂ ≥ 0.

The shadow price for Resource 2 is

(A) 0

(B) 2/3

(D) 4/3

Answer: (D)

34. A rectifying inspection is performed on a lot of size W = 1000 using a Single-Sampling Plant with the sample size n = 60 and the acceptance number c = 1. If t he Acceptable Quality Level is 1.0%, the producer’s risk associated with the sampling plan (rounded off to the nearest integer) in % is

(A) 12

(B) 33

(D) 88

Answer: (A)

35. For y = −x² + 9x – 2, the value of using Simpson’s 1/3 rule with two intervals (rounded off to two decimal places) is ______.

Answer: (58.00 to 59.00)

36. If the probability density function of a random variable x is given by

the value of k is ______.

Answer: (3 to 3)

37. A solid shaft has to transmit 50 kW of power at a speed of 1910 RPM. Ignore any possible bending of the shaft. The maximum allowable shear stress for the material of the shaft is 80 MPa. The minimum diameter of the shaft required to prevent failure due to shear (rounded off to one decimal place) in cm is _______.

Answer: (2.0 to 3.0)

38. A flywheel is to be used in an IC engine to limit fluctuation of angular speed. The average of the maximum and the minimum angular speed is 500 RPM, and the maximum fluctuation of energy is 10,000 N-m. Neglecting rotary inertia of any other components, the moment of inertia of the flywheel about its axis of rotation required to limit the maximum fluctuation of speed of 30 RPM (rounded off to one decimal place) in kg-m² is ________.

Answer: (59.0 to 62.0)

39. A tank of large cross-sectional area contains water up to a height of 5 m as shown in the figure. The top water surface is under a pressure of p₁ = 0.2 MPa. A small, smooth and round tap at the bottom of the tank is opened to the atmosphere (p₂ = 0.1 MPa).

Use the acceleration due to gravity, g = 9.81 m/s² and the density of water, ρ = 1000 kg/m³. The velocity with which the water will exit from the tap under the conditions shown in the figure (rounded off to one decimal place) is m/s is _______.

Answer: (17.2 to 17.4)

40. A steel ball of 12 mm diameter is heated to 1225 K. It is then slowly cooled in air to a temperature of 475 K. During the cooling process, the ambient temperature is 325 K and the heat transfer coefficient is 30 W/m²-k. Assume the density of steel is 7800 kg/m³ and the specific heat is 600 J/kg-K. Using the lumped capacitance method of analysis, the calculated time for the required cooling (rounded off to one decimal place) in second is _______.

Answer: (557.0 to 561.0)

41. A mass of 3 kg of Argon gas at 3 bar, 27°C is contained in a rigid, insulated vessel. Paddle wheel work is done on the gas for 30 minutes at the rate of 0.015 kW. Specific heat at constant volume, C_v, for Argon is 0.3122 kJ/kg-K. The final temperature of the gas (rounded off to one decimal place) in Kelvin is ________.

Answer: (327.0 to 331.0)

42. The figure shows drawing of a part with dimensions and tolerances, both in mm. The permissible tolerance for slot A (rounded off to one decimal place) in mm is ±_______.

Answer: (0.6 to 0.6)

43. To manufacture a product by casting, molten metal is poured in a cavity of rectangular cross section in a sand mold with a side blind riser as shown in the figure. The dimensions of the mold cavity are 60 cm × 40 cm × 20 cm.

The riser is cylindrical in shape with diameter equal to height. It is required that the solidification time of the riser should be 25% greater than that of the mold. Using Chvorinov’s rule, the diameter of the riser (rounded off to one decimal place) in cm should be ______.

Answer: (36.0 to 37.0)

44. A cylindrical billet of 90 mm diameter is extruded to produce an I-section as shown in the figure (all dimensions in mm).

The total extrusion pressure (p_e) in MPa required for the above process is given by

where, σ_m is the mean flow stress of the material, and A₀ and A_f are the initial and the final cross-sectional areas, respectively. If the mean flow stress of the extruded material is 80 MPa, the force required for the above extrusion (rounded off to one decimal place) in kN is _________.

Answer: (1672.0 to 1675.0)

45. The heat generated in resistance spot welding operation for joining two metal sheets with a certain set of process parameters is 2000 J. For a second spot welding operation on the same sheets without any change in the overall resistance of the system, the current is increased by 25% and the time for which the current is applied is reduced to half. The heat generated in the second operation (rounded off to one decimal place) in J is _______.

Answer: (1560.0 to 1563.0)

46. A vertical boring operation is performed in a cast iron plate to enlarge a blind hole to a diameter of 25 mm up to a depth of 100 mm in a single pass. The cutting speed and the feed used in the process are 100 m/min and 0.1 mm/rev, respectively. Considering the allowance for tool approach as 2 mm, the actual machining time (rounded off to two decimal places) in minutes is ________.

Answer: (0.78 to 0.82)

47. For a particular tool-workpiece combination, the value of exponent n in Taylor’s tool life equation is 0.5. If the cutting speed is reduced by 50% keeping all the other machining conditions same, the increase in tool life in % is _______.

Answer: (300 to 300)

48. In a waterjet machining process, the water pressure used is 500 MPa. The diameter of orifice of the nozzle through which the waterjet comes out is 0.25 mm. Neglecting frictional and other losses, and using the density of water as 1000 kg/m³, the mass flow rate of the waterjet (rounded off to two decimal places) in kg/min is _________.

Answer: (2.85 to 3.00)

49. The movement along the z-axis of a CNC drilling machine is controlled by using a servo motor, a lead screw and an incremental encoder. The lead screw has 2 threads/cm and it is directly coupled to the servo motor. The incremental encoder attached to the lead screw emits 100 pulses/revolution. The control resolution in microns is _______.

Answer: (50 to 50)

50. A project consists of seven activities as listed in the table. The time required for each activity and its immediate predecessor(s) are also given.

The project completion time using Critical Path Method (CPM) in weeks is _______.

Answer: (20 to 20)

51. A company is planning to procure a machine to produce a component. There are two alternatives available – machine A and machine B. The cost of producing x units of the component (in Rs.) using machine A is given as C_A(x) = 10000 + 170x + x². The cost of producing x units of the component (in Rs.) using machine B is given as C_B(x) = 15000 + 400x. If machine B is to be preferred, then the minimum number of units to be produced should be ________.

Answer: (250 to 250)

52. The availability of an old photocopier was 90% and the Mean Time between Failure (MTBF) was 200 days. It has been replaced with a new photocopier having an availability of 95%. Now, the Mean Time to Repair (the time during which the photocopier is unavailable for service) has increased by 5 days. The MTBF of the new photocopier (rounded off to the nearest integer) in days is _______.

Answer: (500 to 523)

53. A car company manufactures 200 units of a component per day. The component is installed in different car models at a rate of 15000 units per year. The company operates its production facility 300 days per year to manufacture the component. The setup cost for each production run is Rs. 200 and the inventory holding cost per year is Rs. 2 per The Economic Production Quantity (EPQ) is ________.

Answer: (2000 to 2000)

54. A company has to perform five tasks (P, Q, R, S and T) to make an assembly. Task times and immediate predecessors of the tasks are listed below. If an assembly line is designed to obtain the maximum output rate, the efficiency of the line in % is ______.

Answer: (95 to 95)

55. In a work study experiment, it is observed that a worker completes a job in an average time of 15 minutes with a performance rating of 120%. The time required for another worker having a performance rating of 80% to complete the same job (rounded off to one decimal place) in minutes is ______.

Answer: (22.5 to 22.5)

GATE Exam 2020 Physics (PH) Question Paper With Answer Key

June 8, 2023May 3, 2022 by suresh84

GATE-2020

PH: Physics

GA – General Aptitude

Q1 – Q5 carry one mark each.

1. He is known for his unscrupulous ways. He always sheds______ tears to deceive people.

(A) fox’s

(B) crocodile’s

(D) fox

Answer: (C)

2. Jofra Archer, the England fast bowler, is ____ than accurate.

(A) more fast

(B) faster

(D) more faster

Answer: (A)

3. Select the word that fits the analogy:

Build : Building :: Grow : ______

(A) Grown

(B) Grew

(D) Growed

Answer: (C)

4. I do not think you know the case well enough to have opinions. Having said that, I agree with your other point.

What does the phrase “having said that” mean in the given text?

(A) as opposed to what I have said

(B) despite what I have said

(D) contrary to what I have said

Answer: (B)

5. Define [x] as the greatest integer less than or equal to x, for each x ∈ (−∞, ∞). If y = [x], then area under y for x ∈ [1, 4] is _______.

(A) 1

(B) 3

(D) 6

Answer: (D)

Q6 – Q10 carry two marks each.

6. Crowd funding deals with mobilization of funds for a project from a large number of people, who would be willing to invest smaller amounts through web-based platforms in the project.

Based on the above paragraph, which of the following is correct about crowd funding?

(A) Funds raised through unwilling contributions on web-based platforms.

(B) Funds raised through large contributions on web-based platforms.

(D) Funds raised through voluntary contributions on web-based platforms.

Answer: (D)

7. P, Q, R and S are to be uniquely coded using α and β. If P is coded as αα and Q as αβ, then R and S, respectively, can be coded as ______.

(A) βα and αβ

(B) ββ and αα

(D) βα and ββ

Answer: (D)

8. The sum of the first n terms in the sequence 8, 88, 888, 8888, … is ______.

(A)

(B)

(C)

(D)

Answer: (D)

9. Select the graph that schematically represents BOTH y = x_m and y = x^1/m properly in the interval 0 ≤ x ≤ 1, for integer values of m, where m > 1.

Answer: (A)

10. The bar graph shows the data of the students who appeared and passed in an examination for four schools P, Q, R and S. The average of success rates (in percentage) of these four schools is ________.

(A) 58.5%

(B) 58.8%

(D) 59.3%

Answer: (C)

PH: Physics

Q1 – Q25 carry one mark each.

1. Which one of the following is a solution of for k real?

(A) e⁻^kx

(B) sin kx

(D) sin hx

Answer: (A)

2. A real, invertible 3 × 3 matrix M has eigenvalues λ_i, (i = 1, 2, 3) and the corresponding eigenvectors are Which one of the following is correct?

Answer: (B)

3. A quantum particle is subjected to the potential

The ground state wave function of the particle is proportional to

Answer: (D)

4. Let respectively denote the lowering and raising operators of a one-dimensional simple harmonic oscillator. Let be the energy eigenstate of the simple harmonic oscillator. Given that is also an eigenstate of the corresponding eigenvalue is

(A) n(n – 1)

(B) n(n + 1)

(D) n²

Answer: (A)

5. Which one of the following is a universal logic gate?

(A) AND

(B) NOT

(D) NAND

Answer: (D)

6. Which one of the following is the correct binary equivalent of the hexadecimal F6C?

(A) 0110 1111 1100

(B) 1111 0110 1100

(D) 0110 1100 0111

Answer: (B)

7. The total angular momentum j of the ground state of the nucleus is

(A) 1/2

(B) 1

(D) 5/2

Answer: (D)

8. A particle X is produced in the process π⁺ + p → K⁺ + X via the strong interaction. If the quark content of the K⁺ is , the quark content of X is

(A)

(B) u u d

(D)

Answer: (C)

9. A medium (ε_r > 1, μ_r = 1, σ > 0) is semi-transparent to an electromagnetic wave when

(A) Conduction current >> Displacement current

(B) Conduction current << Displacement current

(D) Both Conduction current and Displacement current are zero

Answer: (B)

10. A particle is moving in a central force field given by is the unit vector pointing away from the center of the field. The potential energy of the particle is given by

(A) k/r²

(B) k/2r²

(D) −k/2r²

Answer: (D)

11. Choose the correct statement related to the Fermi energy (E_F) and the chemical potential (μ) of a metal.

(A) μ = E_F only at 0 K

(B) μ = E_F at finite temperature

(D) μ > E_F at finite temperature

Answer: (A)

12. Consider a diatomic molecule formed by identical atoms. If E_V and E_e represent the energy of the vibrational nuclear motion and electronic motion respectively, then in terms of the electronic mass m and nuclear mass M, E_V/E_e is proportional to

(A) (m/M)^1/2

(B) m/M

(D) (m/M)²

Answer: (A)

13. Which one of the following relations determines the manner in which the electric field lines are refracted across the interface between two dielectric media having dielectric constants ε₁ and ε₂ (see figure) ?

(A) ε₁ sinθ₁ = ε₂ sinθ₂

(B) ε₁ cosθ₁ = ε₂ cosθ₂

(D) ε₁ cotθ₁ = ε₂ cotθ₂

Answer: (D)

14. If are the electric and magnetic fields respectively, then is

(A) odd under parity and even under time reversal

(B) even under parity and odd under time reversal

(D) even under parity and even under time reversal

Answer: (C)

15. A small disc is suspended by a fiber such that it is free to rotate about the fiber axis (see figure). For small angular deflections, the Hamiltonian for the disc is given by

where I is the moment of inertia and α is the restoring torque per unit deflection. The disc is subjected to angular deflections (θ) due to thermal collisions from the surrounding gas at temperature T and p₀ is the momentum conjugate to θ. The average and t he root-mean-square angular deflection, θ_avg and θ_rms, respectively are

Answer: (B)

16. As shown in the figure, an ideal gas is confined to chamber A of an insulated container, with vacuum in chamber B. When the plug in the wall separating the chambers A and B is removed, the gas fills both the chambers. Which one of the following statements is true?

(A) The temperature of the gas remains unchanged

(B) Internal energy of the gas decreases

(D) Internal energy of the gas increases as its atoms have more space to move around

Answer: (A)

17. Particle A with angular momentum j = 3/2 decays into two particles B and C with angular momenta j₁ and j₂, respectively. If the value of α is ______.

Answer: (1 to 1)

18. Far from the Earth, the Earth’s magnetic field can be approximated as due to bar magnet of magnetic pole strength 4 × 10¹⁴ Assume this magnetic field is generated by a current carrying loop encircling the magnetic equator. The current required to do so is about 4 × 10ⁿ A, where n is an integer. The value of n is _____.

(Earth’s circumference: 4 × 10⁷ m)

Answer: (7 to 7)

19. The number of distinct ways the primitive unit cell can be constructed for the two dimensional lattice as shown in the figure is_____.

Answer: (5 to 5)

20. A hydrogenic atom is subjected to a strong magnetic field. In the absence of spin-orbit coupling, the number of doubly degenerated states created out of the d-level is _______.

Answer: (3 to 3)

21. A particle Y undergoes strong decay Y → π⁻ + π⁻. The isospin of Y is ______.

Answer: (2 to 2)

22. For a complex variable z and the contour c: |z| = 1 taken in the counter clockwise direction, _______.

Answer: (-2 to -2)

23. Let p be the momentum conjugate to the generalized coordinate q. If the transformation

Q = √2q^m cos p

P = √2q^m sin p

is canonical, then m = ______.

Answer: (0.5 to 0.5)

24. A conducting sphere of radius 1 m is placed in air. The maximum number of electrons that can be put on the sphere to avoid electrical breakdown is about 7 × 10ⁿ, where n is integer. The value of n is ______.

Assume:

Breakdown electric field strength in air is

Permittivity of free space ε₀ = 8.85 × 10⁻¹² F/m

Electron charge e = 1.60 × 10⁻¹⁹ C

Answer: (14 to 15)

25. If a particle is moving along a sinusoidal curve, the number of degrees of freedom of the particle is ______.

Answer: (1 to 1)

Q26 – Q55 carry two marks each.

26. The product of eigenvalues of is

(A) −1

(B) 1

(D) 2

Answer: (A)

27. Let Let ℝ³ denote the three-dimensional real vector space. Which one of the following is correct?

(A) S is an orthonormal set

(B) S is a linearly dependent set

(D)

Answer: (C)

28. denotes the spin operator defined as Which one of the following is correct?

(A) The eigenstates of spin operator

(B) The eigenstates of spin operator

(D) In the spin state upon the measurement of , the probability for obtaining

Answer: (D)

29. The input voltage (V_in) to the circuit shown in the figure is 2cos(100t) V. The output voltage (V_out) is If R = 1 kΩ, the value of C (in μF) is

(A) 0.1

(B) 1

(D) 100

Answer: (C)

30. Consider a 4-bit counter constructed out of four flip-flops. It is formed by connecting the J and K inputs to logic high and feeding the Q output to the clock input of the following flip-flop (see the figure). The input signal to the counter is series of square pulses and the change of state is triggered by the falling edge. At time t = t₀ the outputs are in logic low state (Q₀ = Q₁ = Q₂ = Q₃ = 0). Then at t = t₁, the logic state of the outputs is

(A) Q₀ = 1, Q₁ = 0, Q₂ = 0 and Q₃ = 0

(B) Q₀ = 0, Q₁ = 0, Q₂ = 0 and Q₃ = 1

(D) Q₀ = 0, Q₁ = 1, Q₂ = 1 and Q₃ = 1

Answer: (B)

31. Consider the Lagrangian where a, b and c are constants. If p_x and p_y are the momenta conjugate to the coordinates x and y respectively, then the Hamiltonian is

Answer: (A)

32. Which one of the following matrices does NOT represent a proper rotation in a plane?

Answer: (D)

33. A uniform magnetic field exists in an inertial frame K. A perfect conducting sphere moves with a constant velocity with respect to this inertial frame. The rest frame of the sphere is K’ (see figure). The electric and magnetic fields in K and K’ are related as

The induced surface charge density on the sphere (to the lowest order in v/c) in the frame K’ is

(A) maximum along z’

(B) maximum along y’

(D) uniform over the sphere

Answer: (A)

34. A charge q moving with uniform speed enters a cylindrical region in free space at t = 0 and exits the region at t = τ (see figure). Which one of the following options best describes the time dependence of the total electric flux φ(t), through the entire surface of the cylinder?

Answer: (D)

35. Consider a one-dimensional non-magnetic crystal with one atom per unit cell. Assume that the valence electrons (i) dot not interact with each other and (ii) interact weakly with the ions. If n is the number of valence electrons per unit cell, then at 0 K,

(A) the crystal is metallic for any value of n

(B) the crystal is non-metallic for any value of n

(D) the crystal is metallic for odd values of n

Answer: (D)

36. According to the Fermi gas model of the nucleus, the nucleons move in a spherical volume of radius R(=R₀A^1/3, where A is the mass number and R₀ is an empirical constant with the dimensions of length). The Fermi energy of the nucleus E_F is proportional to

(A) R₀²

(B) 1/R₀

(D) 1/R₀³

Answer: (C)

37. Consider a two dimensional crystal with 3 atoms in the basis. The number of allowed optical branches (n) and acoustic branches (m) due to the lattice vibrations are

(A) (n, m) = (2, 4)

(B) (n, m) = (3, 3)

(D) (n, m) = (1, 5)

Answer: (C)

38. The internal energy U of a system is given by U(S, V) = λV⁻^2/3S², where λ is a constant of appropriate dimensions; V and S denote the volume and entropy, respectively. Which one of the following gives the correct equation of state of the system?

Answer: (A)

39. The potential energy of a particle of mass m is given by U(x) = a sin(k²x – π/2), a > 0, k² > 0. The angular frequency of small oscillations of the particle about x = 0 is

Answer: (B)

40. The radial wave function of a particle in a central potential is given by where A is the normalization constant and a is positive constant of suitable dimensions. If γa is the most probable distance of the particle from the force center, the value of γ is _________.

Answer: (4 to 4)

41. A free particle of mass M is located in a three-dimensional cubic potential well with impenetrable walls. The degeneracy of the fifth excited state of the particle is __________.

Answer: (6 to 6)

42. Consider the circuit given in the figure. Let the forward voltage drop across each diode be 0.7 V. The current I (in mA) through the resistor is ____________.

Answer: (8 to 8)

43. Let u^u denote the 4-velocity of a relativistic particle whose squre u^uu_μ = 1. If ε_μ_v_ρσ is the Levi-Civita tensor then the value of ε_μ_v_ρσu^μu^vu^ρu^σ is ______.

Answer: (0 to 0)

44. Consider a simple cubic monoatomic Bravias lattice which has a basis with vectors a is the lattice parameter. The Bragg reflection is observed due to t he change in the wave vector between the incident and the scattered beam as given by where are primitive reciprocal lattice vectors. For n₁ = 3, n₂ = 3 and n₃ = 2, the geometrical structure factor is _______.

Answer: (2 to 2)

45. A plane electromagnetic wave of wavelength λ is incident on a circular loop of conducting wire. The loop radius is a(a << λ). The angle (in degrees), made by the Poynting vector with t he normal to the plane of the loop to generate a maximum induced electrical signal, is _______.

Answer: (-270 to -270 or -90 to -90 or 90 to 90 or 270 to 270)

46. An electron in a hydrogen atom is in the state n = 3, l = 2, m = − Let denote the y-component of the orbital angular momentum operator. If the value of α is ________.

Answer: (1 to 1)

47. A sinusoidal voltage of the form V(t) = V₀ cos(ωt) is applied across a parallel plate capacitor placed in vacuum. Ignoring the edge effects, the induced emf within the region between the capacitor plates can be expressed as a power series in ω. The lowest non-vanishing exponent in ω is ________.

Answer: (2 to 2)

48. If for –π ≤ x ≤ π, the value of a₂ is ______.

Answer: (-1 to -1)

49. Let

The value of is _______.

Answer: (0 to 0)

50. Consider the Hamiltonian where

is the time independent penturbation given by

where k > 0. If the maximum energy eigenvalue of is 3 eV corresponding to E = 2 eV, the value of k (rounded off to three decimal places) in eV is ______.

Answer: (0.706 to 0.708)

51. A hydrogen atom is in an orbital angular momentum state lies on a cone which makes a half angle 30° with respect to the z-axis, the value of l is _______.

Answer: (3 to 3)

52. In the center of mass frame, two protons each having energy 7000 GeV, collide to produce protons and anti-protons. The maximum number of anti-protons produced is_______.

(Assume the proton mass to be 1 GeV/c²)

Answer: (6999 to 6999)

53. Consider a gas of hydrogen atoms in the atmosphere of the Sun where the temperature is 5800 K. If a sample from this atmosphere contains 6.023 × 10²³ of hydrogen atoms in the ground state, the number of hydrogen atoms in the first excited state is approximately 8 × 10ⁿ, where n is an integer. The value of n is ______.

(Boltzmann constant: 8.617 × 10⁻⁵ eV/K)

Answer: (14 to 15)

54. For a gas of non-interacting particles, the probability that a particle has a speed v in the interval v to v + dv is given by

If E is the energy of a particle, then the maximum in the corresponding energy distribution in units of E/k_BT occurs at _______ (rounded off to one decimal place).

Answer: (0.5 to 0.5)

55. The Planck’s energy density distribution is given by At long wavelengths, the energy density of photons in thermal equilibrium with a cavity at temperature T varies as T^α, where α is _______.

Answer: (1 to 1)

GATE Exam 2020 Petroleum Engineering (PE) Question Paper With Answer Key

June 8, 2023May 3, 2022 by suresh84

GATE-2020

PE-Petroleum Engineering

GA – General Aptitude

Q1 – Q5 carry one mark each.

1. He is known for his unscrupulous ways. He always sheds______ tears to deceive people.

(A) fox’s

(B) crocodile’s

(D) fox

Answer: (C)

2. Jofra Archer, the England fast bowler, is ____ than accurate.

(A) more fast

(B) faster

(D) more faster

Answer: (A)

3. Select the word that fits the analogy:

Build : Building :: Grow : ______

(A) Grown

(B) Grew

(D) Growed

Answer: (C)

4. I do not think you know the case well enough to have opinions. Having said that, I agree with your other point.

What does the phrase “having said that” mean in the given text?

(A) as opposed to what I have said

(B) despite what I have said

(D) contrary to what I have said

Answer: (B)

5. Define [x] as the greatest integer less than or equal to x, for each x ∈ (−∞, ∞). If y = [x], then area under y for x ∈ [1, 4] is _______.

(A) 1

(B) 3

(D) 6

Answer: (D)

Q6 – Q10 carry two marks each.

6. Crowd funding deals with mobilization of funds for a project from a large number of people, who would be willing to invest smaller amounts through web-based platforms in the project.

Based on the above paragraph, which of the following is correct about crowd funding?

(A) Funds raised through unwilling contributions on web-based platforms.

(B) Funds raised through large contributions on web-based platforms.

(D) Funds raised through voluntary contributions on web-based platforms.

Answer: (D)

7. P, Q, R and S are to be uniquely coded using α and β. If P is coded as αα and Q as αβ, then R and S, respectively, can be coded as ______.

(A) βα and αβ

(B) ββ and αα

(D) βα and ββ

Answer: (D)

8. The sum of the first n terms in the sequence 8, 88, 888, 8888, … is ______.

(A)

(B)

(C)

(D)

Answer: (D)

9. Select the graph that schematically represents BOTH y = x_m and y = x^1/m properly in the interval 0 ≤ x ≤ 1, for integer values of m, where m > 1.

Answer: (A)

(A) 58.5%

(B) 58.8%

(D) 59.3%

Answer: (C)

PE: Petroleum Engineering

Q1 – Q25 carry one mark each.

1. Consider a vector field, are the unit vectors along the x, y, and z directions, respectively. The divergence of A at the point (1, 1, 1) is equal to

(A) 0

(B) 2

(D) 4

Answer: (D)

2. Inverse Laplace transform of the function, is given by

(A) 1 – e^t

(B) 1 + e^t

(D) 1 + e⁻^t

Answer: (C)

3. The solution of the differential equation, with the condition y = 1 at x = 1, is given by

Answer: (D)

4. Two complex numbers are given as, where, I = √−1, and θ₁ and θ₂ are the principal arguments, Given, θ₁ ≠ θ₂ and |θ₁ – θ₂| ≠ π. If which one of the following conditions is correct?

(A) 2 < m < 3

(B) 0 < m < 2

(D) m = 0

Answer: (B)

5. Match the following

(A) P-I, Q-II, R-III

(B) P-II, Q-I, R-III

(D) P-III, Q-I, R-II

Answer: (D)

6. Shear stress versus shear rate plots for four different fluids are given in the Figure. Which curve represents a pseudoplastic fluid?

(A) I

(B) II

(D) IV

Answer: (C)

7. Which one of the following is NOT a desired function of a hydraulic fracturing fluid additive?

(A) Oxygen scavenging to prevent attack on polymers.

(B) Increasing viscosity of fracturing fluid during flow back.

(D) Work as surfactant to facilitate post treatment clean-up.

Answer: (B)

8. Formation damage could be a result of

(i) scale formation near the wellbore

(ii) coke formation due to in-situ combustion

(iii) precipitation of asphaltene

(iv) condensate banking

Which one of the following options is correct?

(A) (i) and (iv) only

(B) (i) and (iii) only

(D) (i), (ii), (iii) and (iv)

Answer: (D)

9. Which of the following statement(s) about gas and water coning in the reservoir is/are correct?

(i) Gas and water coning is characterized by downward movement of water and upward movement of gas near the producing wellbore.

(ii) Gas and water coning is characterized by downward movement of gas and upward movement of water near the producing wellbore.

(iv) Gas and water coning is caused when gravitational forces dominate over viscous forces.

(A) (i) and (iv) only

(B) (ii) only

(D) (iv) only

Answer: (B)

10. Given the figure

Which one of the following options represents the correct combination of the trajectory number and the corresponding drilling type?

(A) i → Build and Hold, ii → S-Type, iii → Modified S-Type, iv → Continuous Build

(B) i → Continuous Build, ii → Build and Hold, iii → Modified S-Type, iv → S-Type

(D) i → Build and Hold, ii → Modified S-Type, iii → S-Type, iv → Continuous Build

Answer: (B)

11. A stable geothermal gradient (approx. 25°C/km) in the earth’s crust will suddenly increase to a higher gradient value, when

(A) there is excessive erosion or upliftment

(B) there is excessive subsidence or deposition

(D) there is excessive subsidence and erosion simultaneously

Answer: (A)

12. A drawdown test is conducted at a constant flow rate in an oil well for a reservoir with constant compressibility. Which one of the following is valid for semi steady state condition?

(A) Rate of pressure change at the wellbore is less than that at the boundary.

(B) The effect of the outer boundary of the reservoir is felt at the wellbore.

(D) Pressure in the reservoir does not change with time.

Answer: (B)

13. Formation volume factor (B₀) versus Pressure (P) plot for an oil is given in the Figure.

Match the following with the corresponding pressure given in the Figure.

(I) Bubble point

(II) Saturated oil

(III) Under-saturated oil

(A) I-P₁, II-P₂, III-P₃

(B) I-P₁, II-P₃, III-P₂

(D) I-P₂, II-P₃, III-P₁

Answer: (C)

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

(A) Flash point of gasoline is lower than that of diesel.

(B) Pour point is the temperature at which oil creases to flow.

(D) Higher the aromatic content of diesel, higher is its aniline point.

Answer: (D)

15. Which one of the following additives is commonly added to drilling fluids to remove hydrogen sulfide?

(A) Sodium chloride

(B) Calcium chloride

(D) Bentonite

Answer: (C)

16. Two rigid spherical particles of the same density, with a diameter ratio D₁ : D₂ = 1:2, settle freely through a pool of liquid. The terminal settling velocity is given by the Stoke’s law. What is the ratio of their terminal settling velocities, V₁ : V₂ ?

(A) 1:2

(B) 2:1

(D) 4:1

Answer: (C)

17. Which one of the following options best represents the correct order of increasing thermal conductivity of the subsurface formations?

(A) Coal < Shale < Dolomite < Evaporite

(B) Evaporite < Shale < Coal < Dolomite

(D) Shale < Coal < Evaporite < Dolomite

Answer: (A)

18. Which one of the following options is the correct combination of kerogen Type and the source from which it is derived?

(A) Type I-Lacustrine, Type II-Terrestrial, Type III-Marine, Type IV-Varied

(B) Type I-Lacustrine, Type II- Marine, Type III- Terrestrial, Type IV-Varied

(D) Type I- Marine, Type II- Terrestrial, Type III- Varied, Type IV- Lacustrine

Answer: (B)

19. The number of power outages in a city in a given time interval is a Poisson random variable with a mean of 2 power outages per month. The Poisson distribution is given by,

The probability of exactly 2 power outages in 2 months (rounded off to two decimal places) is _______.

Answer: (0.12 to 0.18)

20. Anhydrous sodium hydroxide is added to 10 litre of water to raise its pH from 7.0 to 9.0. The molar mass of sodium hydroxide is 40 g/mol. Assuming complete dissociation of sodium hydroxide and zero volume change of mixing, the amount of sodium hydroxide added (rounded off to two decimal places) is ______ mg.

Answer: (3.85 to 4.10)

21. Consider unidirectional, laminar flow of water through a homogeneous porous media as shown in the Figure. Here, H = 100 m, W = 500 m, L = 500 m, permeability of the porous media is 10⁻¹² m², and the driving pressure drop (across length L) is 10⁶ Use the viscosity of water as 10⁻³ Pa.s.

At steady state, the volumetric flow rate of water (rounded off to two decimal places) is given by __________ m³/s.

Answer: (0.09 to 0.12)

22. A dry gas well is producing a gas stream of the following molar composition: 95% methane and 5% carbon dioxide. The molar mass of methane is 16 g/mol and that of carbon dioxide is 44 g/mol. Assuming ideal gas behavior, gas constant R = 8.31 J mol⁻¹ K⁻¹, the gas stream density at 10⁷ Pa and 350 K (rounded off to one decimal place) is _______ kg/m³.

Answer: (59.00 to 61.00)

23. Consider fluid flow through the annular space between two cylindrical tubes. The outer diameter of the inner tube is 40 mm and the inner diameter of the outer tube is 50 mm. The hydraulic mean diameter for fluid flow calculations (rounded off to one decimal place) is _______ mm.

Answer: (9.0 to 10.5)

24. A build up test was performed on a well after 1000 hours of oil production. During the shut-in period, the Horner’s approximation is valid which results in the following equation relating the shut-in well pressure (P_ws) to the shut-in time:

Here, k is the reservoir permeability, h is the reservoir thickness, P_i is the initial reservoir pressure, q is the flow rate during production, μ is the oil viscosity, t_D is the dimensionless production time, P_D(t_D) is the dimensionless pressure at t_D, γ is a constant, and X is dependent on the shut-in time and the production time.

The value of X after 5 hours of the shut-in (rounded off to one decimal place) is _______.

Answer: (200.5 to 201.5)

25. The initial oil production from on offshore well is 1000 STB/day, which decreased to 960 STB/day in 30 days. Using the ‘exponential decline model’, the daily production rate after 360 days from the start (rounded off to one decimal place) will be ________ STB/day.

Answer: (610.0 to 615.0)

Q26 – Q55 carry two marks each.

26. An incompressible fluid flows through a network of pipes as shown in the given Figure. The total pressure drop across points a and b is 2 kPa. The flow rates (in m³/s)in sections 1, 2, and 3 are q₁, q₂ and q₃ The pressure drops (in kPa) are 4q₁, 3q₂, and 2q₃ across sections 1, 2, and 3 respectively.

For a steady-state flow operation, the system of equations for flow rates is given by,

The correct option for the numeric value of X is

(A) −0.50

(B) −1.75

(D) −2.00

Answer: (B)

27. Match the following for Enhanced Oil Recovery operations

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

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

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

Answer: (B)

28. An compressible fluid is flowing through a tube of radius, R and length, L. The shear rate dependence of the fluid viscosity is given by the power law, is the scalar shear rate, k is a constant, and n is the flow behavior index. Assuming the flow to be steady, laminar, and fully developed, the velocity profile inside the tube for a pressure drop of ∆p applied across the tube is

Answer: (A)

29. The apparent permeability of a core measured using air is K_a, and its absolute permeability measured using an incompressible liquid is K_L. If, P_m is the mean air pressure in the core during permeability measurement, and c is a positive constant linked to the pore geometry, then K_a and K_L are related as

Answer: (C)

30. The plot of volume (V) versus pressure (P) for two reservoir fluids (I and II) obtained in a constant composition expansion (CCE) is shown in the Figure, Here, V_sat is saturation volume and P_sat is saturation pressure. The measurements were carried out at constant temperature (the measured reservoir temperature) throughout the experiment. Which one of the following statements for the type of reservoir is correct ?

(A) I is a gas condensate reservoir and II is an oil reservoir.

(B) I is an oil reservoir and II is a gas condensate reservoir,

(D) I is a dry gas reservoir and II is gas condensate reservoir.

Answer: (B)

31. The following primary and secondary porosity types are prevalent in the subsurface formations:

(1) Interparticle

(2) Intraparticle

(3) Fracture

(4) Solution

(5) Bedding plane voids

(6) Channel

Which one of the following options represents the correct combination?

(A) Primary (1, 2, 3); Secondary (4, 5, 6)

(B) Primary (1, 2, 5); Secondary (3, 4, 6)

(D) Primary (2, 4, 6); Secondary (1, 3, 5)

Answer: (B)

32. In the given Figure, which one of the following options represents the correct combination of drainage and imbibitions processes for a water wet rock in the subsurface, as indicated by number 1 to 4?

(A) 1-oil displacing water, 2-spontaneous brine imbibitions, 3-water displacing oil, 4-spontaneous oil imbibition

(B) 1- water displacing oil, 2- spontaneous oil imbibition, 3- spontaneous brine imbibition, 4- oil displacing water

(D) 1- water displacing oil, 2- spontaneous brine imbibition, 3- oil displacing water, 4- spontaneous oil imbibition

Answer: (A)

33. The following notations are defined for a porous medium:

φ = porosity,

S_p = surface area of the pore per unit bulk volume of the core,

τ = tortuosity factor for the interconnected porous channel,

C = geometric factor of the pore.

The correct combination for the hydraulic radius (r_h) and absolute permeability (k) of a porous medium is

Answer: (C)

34. Match the following

(A) I-P, II-Q, III-R

(B) I-R, II-Q, III-P

(D) I-R, II-P, III-Q

Answer: (D)

35. Select the correct combination of a floating vessel motion in a horizontal plane (P) and a vertical plane (Q)

(A) P: (Surge, Sway, Yaw) and Q: (Heave, Roll, Pitch)

(B) P: (Heave, Roll, Pitch) and Q: (Surge, Sway, Yaw)

(D) P: (Surge, Sway, Pitch) and Q: (Heave, Roll, Yaw)

Answer: (A)

36. The equation x³ – 3x – 5 = 0 is to be solved using the Newton-Raphson method. Starting with an initial guess of 2, the value of x after three iterations ( rounded off to three decimal places) is ______.

Answer: (2.276 to 2.281)

37. The axis of a cylinder of radius a and length L is along the z-axis with center of the flat surface at (0, 0, 0). An inextensible string of negligible thickness is wound tightly as a right-handed helix around the curved surface of the cylinder. The two ends of the string are at (a, 0, 0) and (a, 0, L).

The parametric equation of the right-handed helix is given by,

r(θ) = [a cos θ, a sin θ, cθ],

where r, is the position vector and θ is in radian.

Given the total length of the string (rounded off to two decimal places) is ________ cm.

Answer: (8.80 to 9.20)

38. A data set containing n ( = 10) independent measurements (x_i, y_i) is to be fitted by a simple linear regression model. The last square estimates of regression coefficients are obtained and the regression estimate is given by

where, Cov(x, y) is the sample covariance and Var(x) is the sample variance.

The values are given below:

For the given data set, the unbiased variance for the error (round off to two decimal places) is ________.

Answer: (0.16 to 0.20)

39. A porous medium of 10 cm length is made of three horizontal, cylindrical capillaries of inside diameters 2 μm, 4 μm, and 6 μm as shown in the Figure (not to scale).

Oil is being injected in this porous medium that was initially filled completely with water. The interfacial tension between oil and water is 0.025 N/m. Consider water as the completely wetting phase, i.e., contact angle is 0°. When the pressure drop across the porous medium is 20 kPa, the maximum saturation of oil in the porous medium is 0.643.

When the pressure drop is increased to 30 kPa, the maximum oil saturation (rounded off to two decimal places) will be ________ (in fraction).

Answer: (0.90 to 0.95)

40. A unidirectional, immiscible displacement of an oil is carried out with water in a cylindrical reservoir core sample (Buckley-Leverett theory is applicable). The connate water saturation is 0.25. A fractional flow of water (f_w) vs. water saturation (S_w) curve is drawn for the process. A line drawn from a point (S_w = 0.25, f_w = 0) on the fractional flow curve is tangent at the point (S_w = 0.8, f_w = 0.8) on the curve.

The average water saturation in the core at the time of breakthrough (rounded off to two decimal places) is _______ (in fraction).

Answer: (0.90 to 0.96)

41. In a hydrate reservoir, the porosity of the porous medium is 0.3 and the solid hydrate saturation is 0.5. Assume that the permeability (in mD) in a porous medium is given by where, ϕ_e is the effective porosity available for the fluids. The permeability of the hydrate bearing porous medium (rounded off to two decimal places) is ______ mD.

Answer: (23.00 to 28.00)

42. The slip velocity for a gas-liquid flow in a vertical production well is 0.1 m/s. The superficial velocity of each of the phases is 0.1 m/s. The fractional hold-up of the gas phase (rounded off to two decimal places) is ______.

Answer: (0.36 to 0.40)

43. A three stage reciprocating compressor is to compress 4 mol/s of methane from 1 bar absolute to 60 bar absolute pressure. The gas temperature is 303 K at the suction. The compression ratio in each stage is equal and the compression is isentropic. The gas behaves as an ideal gas and the ratio of specific heat capacities (C_p/C_v) is 1.4. Take gas constant, R = 8.31 J mol⁻¹ K⁻¹.

The minimum work rate of compression required for the gas (rounded off to two decimal places) is _______ kJ/s.

Answer: (48.00 to 52.00)

44. In a 1-1 counter flow shell and tube heat exchanger, a liquid process stream (C_p = 2.1 kJ kg⁻¹ K⁻¹) is cooled from 430 K to 330 K using water (C_p = 4.2 kJ kg⁻¹ K⁻¹) having an inlet temperature of 280 K. The process stream flows on the shell side at a rate of 1 kg/s and the water on the tube side at a rate of 2.5 kg/s. The overall heat transfer coefficient is 600 W m⁻² K⁻¹. Neglecting the heat loss to the surroundings, the required heat transfer area (rounded off to two decimal places) is ______ m².

Answer: (3.80 to 4.50)

45. A pre-flush of 15 wt% HCl solution (density = 1070 kg/m³) is used to dissolve dolomite in a sandstone reservoir. The molecular formula, molar mass, and density of dolomite are CaMG(CO₃)₂, 184.3 g/mol, and 2840 kg/m³, respectively. The molar mass of HCl is 36.5 g/mol.

If the pre-flush has to remove all the dolomite, the volumetric dissolving power of the pre-flush (rounded off to three decimal places) is _______ (m³ of dolomite/m³ of 15 wt% HCl solution).

Answer: (0.068 to 0.074)

46. A cuboidal wooden block of density 750 kg/m³, with horizontal dimensions of 2.0 m ×0 m and vertical height of 0.8 m, floats in water (density = 1000 kg/m³). The acceleration due to gravity is 9.81 m/s². The distance between center of gravity and metacenter of the block (rounded off to two decimal places) is _______ m.

Answer: (0.03 to 0.05)

47. It is desired to determine the radius of investigation (r_inv) of a low-permeability and low-pressure gas reservoir which produces under a constant flow rate. Use the following data:

Absolute permeability (k) = 0.01 mD,

Porosity (φ) = 0.05,

Total isothermal compressibility (C_t) = 200 × 10⁻⁶ psia⁻¹, and

Viscosity (μ) = 0.05 cP.

Assuming transient flow conditions are valid, the radius of investigation (r_inv) after 200 hours of gas production (rounded off to one decimal place) is ______ ft.

Answer: (55.0 to 67.0)

48. Well stimulation is carried out in a homogeneous formation. The well is stimulated up to a radial of 54 inch from the surface of the wellbore. The diameter of the wellbore is 12 inch. The permeability enhancement in the stimulated region is found to be 10 times that of the unstimulated region. Assuming steady-state radial flow, the skin factor after stimulation (rounded off to two decimal places) is _______.

Answer: (-2.20 to -1.95)

49. A gas reservoir has a permeability of 1.0 mD, which is to be fractured hydraulically to create a 600 m long and 0.30 cm wide fracture of 2 × 10⁵ mD permeability around the center of damage area. The fracture conductivity for the well (rounded off to two decimal places) is _______.

Answer: (1.80 to 2.20)

50. A producing oil well with the drainage to wellbore radius ratio of 2981 is found to have a skin factor of 8. Assume steady state operation and negligible pressure drop in the tubing.

The ratio of production rate of the ‘damaged’ to the ‘undamabged’ well (rounded off to two decimal places) is _______.

Answer: (0.45 to 0.55)

51. It is desired to prepare a Class H cement slurry having a density of 2100 kg/m³ using hematite as an additive. The water requirement for the Class H cement is 20 litre/50 kg cement and that for hematite is 3 litre/1000 kg hematite.

Given:

Density of class H cement = 3125 kg/m³

Density of hematite = 5000 kg/m³

Density of water = 1000 kg/m³

Weight of one sack of cement = 50.0 kg

Assuming zero volume change of mixing, the amount of hematite that should be blended with one sack of cement (rounded off to two decimal places) is _______ kg.

Answer: (9.00 to 10.50)

52. A gas reservoir without aquifer is at 300 bar (absolute) and 90° The GIIP (gas initial in place) is 10⁷ m³ (at surface conditions). Neglect formation and water compressibility.

Given:

Surface pressure = 1 bar (absolute)

Surface temperature = 25°C

Gas compressibility factor, Z (at surface condition) = 1

Z (at 300 bar (absolute) and 90°C) = 0.88

Z (at 100 bar (absolute) and 90°C) = 0.83

If the reservoir pressure reduces to 100 bar (absolute) under isothermal conditions, the total volume of gas (at surface conditions) produced from the reservoir (rounded off to two decimal places) is _______ × 10⁶ m³.

Answer: (6.00 to 7.00)

53. Given the following data of a shale gas formation:

W_TOC (weight fraction of total organic carbon (TOC)) = 0.10

S_wT (total water saturation) = 0.25

ρ_TOC (density of TOC) = 1.10 g/cm³

ρ_m(density of matrix) = 2.65 g/cm³

ρ_g (density of gas) = 0.35 g/cm³

ρ_w (density of water) = 1.00 g/cm³

ρ_b (formation bulk density) = 2.00 g/cm³

Consider that only water and gas are present in the formation and the following equations apply,

where, ρ_f is the fluid density, φ_T is the total porosity, and V_TOC is the volume fraction of TOC.

The volume fraction of TOC (rounded of to two decimal places) is _______.

Answer: (0.15 to 0.20)

54. It is desired to drill a deviated well with ‘build and hold type’ trajectory. The kickoff point is at a vertical depth of 1500 ft from the surface and the rate of build is 2°/100 ft. At a true vertical depth (TVD) of 7500 ft, the net horizontal departure to the target is 2500 ft. The total measured depth is ______ ft.

Answer: (8000 to 8050)

55. A cylindrical core sample of 4 inch diameter and 20 inch length is obtained from a consolidated reservoir sand. At the reservoir temperature, the formation water resistivity (R_w) is 0.15 ohm-m whereas, the resistance of the core, which is 100% saturated with brine, is 100 ohm. Use the generalized form of the Archie’s formula relating Formation Resistivity Factor (F_R) and the porosity (φ). Assume, a(tortuosity factor) = 1, and m (cementation factor) = 2.

The porosity (in fraction) of the core (rounded off to two decimal places) is _______.

Answer: (0.28 to 0.34)

GATE Exam 2020 Metallurgical Engineering (MT) Question Paper With Answer Key

June 8, 2023May 3, 2022 by suresh84

GATE-2020

MT-Metallurgical Engineering

GA – General Aptitude

Q1 – Q5 carry one mark each.

1. He is known for his unscrupulous ways. He always sheds______ tears to deceive people.

(A) fox’s

(B) crocodile’s

(D) fox

Answer: (C)

2. Jofra Archer, the England fast bowler, is ____ than accurate.

(A) more fast

(B) faster

(D) more faster

Answer: (A)

3. Select the word that fits the analogy:

Build : Building :: Grow : ______

(A) Grown

(B) Grew

(D) Growed

Answer: (C)

4. I do not think you know the case well enough to have opinions. Having said that, I agree with your other point.

What does the phrase “having said that” mean in the given text?

(A) as opposed to what I have said

(B) despite what I have said

(D) contrary to what I have said

Answer: (B)

5. Define [x] as the greatest integer less than or equal to x, for each x ∈ (−∞, ∞). If y = [x], then area under y for x ∈ [1, 4] is _______.

(A) 1

(B) 3

(D) 6

Answer: (D)

Q6 – Q10 carry two marks each.

6. Crowd funding deals with mobilization of funds for a project from a large number of people, who would be willing to invest smaller amounts through web-based platforms in the project.

Based on the above paragraph, which of the following is correct about crowd funding?

(A) Funds raised through unwilling contributions on web-based platforms.

(B) Funds raised through large contributions on web-based platforms.

(D) Funds raised through voluntary contributions on web-based platforms.

Answer: (D)

7. P, Q, R and S are to be uniquely coded using α and β. If P is coded as αα and Q as αβ, then R and S, respectively, can be coded as ______.

(A) βα and αβ

(B) ββ and αα

(D) βα and ββ

Answer: (D)

8. The sum of the first n terms in the sequence 8, 88, 888, 8888, … is ______.

(A)

(B)

(C)

(D)

Answer: (D)

9. Select the graph that schematically represents BOTH y = x_m and y = x^1/m properly in the interval 0 ≤ x ≤ 1, for integer values of m, where m > 1.

Answer: (A)

(A) 58.5%

(B) 58.8%

(D) 59.3%

Answer: (C)

MT: Metallurgical Engineering

Q1 – Q25 carry one mark each.

1. The general solution to the following homogeneous ODE, is The values of λ₁ and λ₂ are:

(A) −1 and −3

(B) −3 and −3

(D) 1 and 3

Answer: (A)

2. The number of independent elastic constants of an isotropic material is:

(A) 1

(B) 2

(D) 4

Answer: (B)

3. A slip system consist of a slip plane and a slip direction. Which one of the following is NOT a valid slip system in a FCC copper crystal?

Answer: (B)

4. A dielectric material is:

(A) Electrical conductor

(B) Metallic magnet

(D) Electrical insulator

Answer: (D)

5. Which one of the following processes is an example of an electrolytic cell?

(A) Corrosion of a metal rod in ambient atmosphere

(B) Charging of a rechargeable battery

(D) Sacrificial cathodic protection system

Answer: (B)

6. Which one of the following statements regarding selective leaching of a binary alloy is TRUE?

(A) The lower atomic weight element is leached.

(B) The element having higher diffusivity is leached.

(D) The element with lower density is leached.

Answer: (C)

7. In green sand casting, which one of the following is NOT a part of the gating system?

(A) Runner

(B) Sprue

(D) Pouring basin

Answer: (MTA)

8. For a material to exhibit superplasticity, one of the requirements is:

(A) Coarse-grained microstructure

(B) High strain-rate sensitivity

(D) High modulus of elasticity

Answer: (B)

9. The dye penetrant test for detecting flaws is based on:

(A) Magnetism

(B) Sound propagation

(D) Capillary action

Answer: (D)

10. When 1 mole of C₃H₈ at 300 K is burnt with stoichiometric amount of oxygen at 300 K to form CO₂ and H₂O, the adiabatic flame temperature is 5975 K. If C₃H₈ is burnt under the same conditions but with excess oxygen, the adiabatic flame temperature will be

(A) equal to 5975 K irrespective of the amount of excess oxygen.

(B) higher than 5975 K irrespective of the amount of excess oxygen.

(D) higher or lower than 5975 K depending on the amount of excess oxygen.

Answer: (C)

11. Two solid spheres X and Y of identical diameter are made of different materials having thermal diffusivities 100 × 10⁻⁶ m²s⁻¹ and 25 × 10⁻⁶ m²s⁻¹ Both spheres are heated in a furnace maintained at 1000 K. If the center of the sphere X reaches 800 K in 1 hour, time required for the center of sphere Y to reach 800 K is

(A) 1 hour.

(B) 2 hours.

(D) 16 hours.

Answer: (C)

12. Select the correct spectra (shown on a log-log scale in the figures) for emission from a gray surface and a black body, both maintained at 1000 K.

Answer: (D)

13. Given the three vectors X = −i – j + k, Y = −i + 2j + k and Z = i + k, which one of the following statements is TRUE?

(A) X, Y and Z are mutually perpendicular.

(B) X, Y and Z are coplanar.

(D) Z makes an angle of 60° with the normal to the plane containing X and Y.

Answer: (A)

14. Angle between two neighboring tetrahedral bonds is Si having a diamond cubic structure is:

(A) 102.5°

(B) 109.5°

(D) 135.5°

Answer: (B)

15. The sequence of precipitation during aging of Al – 4 wt.% Cu alloy is:

(A) GP zone → θ” → θ’ → θ

(B) GP zone → θ → θ’ → θ”

(D) θ” → θ’ → GP zone → θ

Answer: (A)

16. The indenter used in Rockwell hardness measurements on C scale is

(A) diamond cone.

(B) 10 mm steel ball.

(D) 1/16-in. steel ball

Answer: (A)

17. For the function y = a^x, the derivative at x = 1 is:

(A) 1

(B) a

(D) a ln a

Answer: (D)

18. Cupola is a furnace used to produce

(A) cast irons.

(B) plain carbon steels.

(D) aluminium alloys.

Answer: (A)

19. The function y = e^x and y = e⁻^x intersect at the point:

(A) (1, 3)

(B) (−2, 2)

(D) (−1, −1)

Answer: (C)

20. A heavily cold-worked metal will

(A) yield a coarser recrystalized grain size.

(B) possess a lower driving force for recrystallization.

(D) recrystallize at lower temperatures.

Answer: (D)

21. For the function f(x) given in the figure, the value of is _______ (round off to one decimal place).

Answer: (0.5 to 0.5)

22. A component subjected to tensile stress in a mechanical device is monitored periodically for cracks by NDT. The NDT technique can only detect cracks (both surface and internal) which are larger than 1 mm. Keeping a 10% margin of safety, the maximum allowed tensile stress on the component will be ______ MPa (round off to the nearest integer).

Given, fracture toughness K_IC = 30 MPa m^1/2 and assume crack geometry factor of unity.

Answer: (480 to 494)

23. An iron plate with a total exposed surface area of 50 cm² undergoes atmospheric corrosion. If 200 g of weight is lost over a period of 10 years, then the corrosion rate is _______ kg.m⁻².year⁻¹ (round off to the nearest integer).

Answer: (4 to 4)

24. In cold-rolling, for the sheet to be drawn into rolls, the angle of contact (or angle of bite) should be less than or equal to _______ degree (round off to one decimal place).

Given, the coefficient of friction between sheet and roll is 0.1

Answer: (5.6 to 5.8)

25. The number of atoms per unit area in (100) plane of Pb is _______ nm⁻² (round off to the nearest integer).

Given, crystal structure and atomic radius of Pb are FCC and 0.175 nm respectively.

Answer: (7 to 9)

Q26 – Q55 carry two marks each.

26. In the edge dislocation configuration given in the figure, dislocations X and Y are fixed and separated by a distance 2h on the same slip plane. Dislocation Z is free to glide on a parallel slip plane. The two slip planes are separated by distance h. Which one of the following statements is TRUE regarding the stability of dislocation Z at positions 1, 2 and 3?

(A) Position 1: unstable equilibrium; Position 2: unstable; Position 3: unstable

(B) Position 1: stable equilibrium; Position 2: unstable; Position 3: unstable

(D) Position 1: stable equilibrium; Position 2: unstable; Position 3: stable

Answer: (A)

27. Which one of the following dislocation reactions is NOT feasible in a FCC crystal?

Answer: (B)

28. A galvanic cell is formed by connecting and wires immersed in their respective ion solutions. The cell discharges spontaneously with a voltage of 0.5 V. The ratio of the concentration of [Fe²⁺] to [Zn²⁺] ions in the cell is of the order of:

Given, R = 8.314 J.mol⁻¹.K⁻¹, F = 96500 C.mol⁻¹, T = 298 K

(A) 10⁻⁶

(B) 10⁻⁵

(D) 10⁷

Answer: (C)

29. The divergence of the vector field (x³ + y³)i + 3xy²j + 3zy²k is;

(A) 3y² + 6xy + 6x²

(B) 3x² + 6y² + 9xy + 6yz

(D) 3(x + y)²

Answer: (D)

30. Match the products in Column I with the manufacturing processes in Column II.

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

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

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

Answer: (D)

31. f(x) = x ln(x) + (1 – x) ln(1 – x) + 3x(1 – x) has _______ at x = 0.5

(A) a local minimum

(B) a local maximum

(D) a non-zero slope

Answer: (B)

32. Match the process in Column I with the most appropriate mechanisms in Column II.

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

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

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

Answer: (C)

33. Match the reactors in column I with the corresponding products in Column II.

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

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

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

Answer: (C)

34. X-ray diffraction pattern from an elemental metal with a FCC crystal structure shows the first peak at a Bragg angle θ = 24.65°. The lattice parameter of this metal is _____nm.

Given, wavelength of the X-ray used is 0.1543 nm.

(A) 0.185

(B) 0.262

(D) 0.370

Answer: (C)

35. Match the materials in Column I with their common applications in Column II.

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

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

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

Answer: (D)

36. The Mg-Sn phase diagram exhibits two eutectics on either side of the high melting intermetallic line compound, Mg₂Sn, as given below.

At 561°C: L (36.9 wt.% Sn) → α (14.48 wt.% Sn) + Mg₂Sn

At 203°C: L(97.87 wt.% Sn) → β-Sn (almost 100 wt. % Sn) + Mg₂Sn

After the eutectic reaction has gone to completion and equilibrium has been attained at a temperature just below 561°C, the amount of eutectic constituent present in the alloy, Mg-50 wt.% Sn, is approximately_______(in wt.%).

Given, atomic weight of Sn is 118.7 and Mg is 24.3

(A) 25

(B) 38

(D) 75

Answer: (C)

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

Assertion [a]: Low-alloy steels used for medium-temperature creep resistance often have additions of strong carbide-forming elements.

Reason [r]: During creep deformation, the particles with higher misfit with the matrix, lose coherency.

(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: (B)

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

Assertion [a]: The rate of homogenization in a dilute substitutional solid solution of B in A is controlled by the diffusivity of B.

Reason [r]: Atomic migration cannot occur along dislocations and grain boundaries.

(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)

39. Match the elements in Column I with their electronic behaviour given in Column II.

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

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

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

Answer: (C)

40. Radius of the largest interstitial atom that can be accommodated in an octahedral void in BCC iron without distorting the lattice is _______nm (round off to three decimal places).

Assume hard sphere model and radius of Fe atom as 0.124 nm.

Answer: (0.018 to 0.020)

41. The production process of cylindrical pipes results in a statistical scatter in their diameter which is modeled by a normal distribution with a mean value of 10 mm. If the area under the normal curve between 9 mm and 10 mm is 0.35, then the probability of producing pipes of diameter greater than 11 mm is __________ (round off to two decimal

Answer: (0.14 to 0.16 or 14 to 16)

42. The solution (using trapezoidal rule) of the integral by dividing the range 0 to 1 into two equal intervals is _______ (round off to two decimal places).

Answer: (0.71 to 0.75)

43. Iron is corroding in fresh water which has dissolved oxygen concentration of 15 mM. The anodic current density at an overpotential of 120 mV is _____ A.cm⁻² (round off to three decimal places).

Given:

(1) Anodic Tafel slope is 0.06 V.

(2) Diffusion coefficient of oxygen is 2.42 × 10⁻⁵ cm².s⁻¹.

(3) Diffusion layer thickness is 0.06 cm.

Answer: (0.190 to 0.238)

44. A metal oxidizes at 1200 K with a parabolic rate constant of 3 × 10⁻⁶ g².cm⁻⁴.s⁻¹. Time taken for the oxide film to grow to thickness of 2 μm is ________ s (round off to two decimal places).

Given, density of oxide is 6.5 g.cm⁻³.

Answer: (0.54 to 0.58)

45. Two plates of composition, Fe−10 wt.% Ni and Fe−20 wt.% Ni are fusion-welded using a filler rod of composition 20 wt.% Ni-80 wt.% Cr. Contribution to dilution of the weld pool is 20% from each plate. The Ni content in the weld pool is ______wt.% (round off to the nearest integer).

Answer: (15 to 15)

46. Figure shows schematic of a venturimeter. The cross sectional area is 100 mm² at A and is 50 mm² at B. If air is flowing through the venturimeter at a flow rate of 10⁻³m³.s⁻¹, the height H in the air-over-water manometer is ________ mm (round off to the nearest integer).

Assume.

(1) Incompressible flow with no friction losses.

(2) Density of air is 1 kg m⁻³.

(3) Density of water is 1000 kg m⁻³.

(4) Acceleration due to gravity is 9.8 ms⁻².

Answer: (14 to 16)

47. For effective communition in a ball mill, it is desired that the balls travelling along the mill wall leave the wall at point C and travel freely in air along the path CDA, as shown in the figure. If ∠BOC is 120°, the rotational speed of the mill is ________ rpm (rounded off to one decimal place) by performing suitable force balance at point C.

Assume:

(1) There is no slip between the ball and mill wall.

(2) O is the rotational axis of the mill and OB is parallel to the vector g.

(3) Inner diameter of ball mill is 3.26 m.

(4) Acceleration due to gravity g is 9.8 m s⁻².

Answer: (15.6 to 17.6)

48. If liquid copper is cooled to 1353 K, magnitude of the driving force for liquid to transform to solid is _______ J. mol⁻¹ (round off to one decimal place).

Given, melting temperature and enthalpy of melting of copper are 1356 K and 13 kJ.mol⁻¹ resepctively.

Answer: (28.6 to 29.0)

49. 1000 kg of liquid steel containing 0.03 wt.% S needs to be desulphurized using a slag to bring the sulphur content down to 0.015 wt.%. The quantity of slag needed is _______ kg(round off to the nearest integer).

Assume:

(1) Thermodynamic equilibrium

(2) No sulphur in the slag prior to desulphurization treatment

Given the equilibrium sulphur partition ratio between slag and steel, is 50.

Answer: (19 to 21)

50. Zone refining of Si results in residual P content of 0.1 parts per billion by weight. The electrical conductivity of this zone refined Si is ________ Ω⁻¹ .m⁻¹ (round off to two decimal places.)

Given:

(1) Avogadro number is 6.02 × 10²³.

(2) Density of Si is 2.33 g.cm⁻³.

(3) Atomic weight of P is 30.97.

(4) Charge of electron is 1.6 × 10⁻¹⁹ A.s

(5) Mobility of electron is 0.2 m².V⁻¹.s⁻¹

Answer: (0.14 to 0.16)

51. The steady state creep rate of a material increases by a factor of 20 when the temperature is increased from 890 K to 980 K. The creep rate at a temperature of ________ K (round off to the nearest integer) will be 5 times the creep rate at 890 K.

Answer: (933 to 939)

52. Crack growth is being continuously measured in test specimen subjected to constant amplitude cyclic stress with a mean stress of zero. The crack growth rate is related to the stress intensity range, ∆K as where, a is the crack length and N is the number of cycles. When the crack length increases by a factor of two, the crack growth rate will increase by a factor of _______ (round off to one decimal place).

Answer: (2.6 to 3.0)

53. In a top gated mold, liquid metal enters the mold cavity as a freely falling steam under gravity from a height of 0.5 m. Ignore the fluid friction due to viscosity and the drag due to changes in the direction of flow. If the volume of the mold cavity is 10 m³, then the time required to fill the mold is ________ s (round off to nearest integer).

Given:

(1) Acceleration due to gravity is 9.8 m.s⁻².

(2) Cross-sectional area of gate is 0.2 m².

Answer: (14 to 18)

54. A Basic Oxygen Furnace operator, at the end of oxygen blow, measures the dissolved oxygen content in the steel as 0.03 wt.% and the steel temperature as 1800 K. The carbon content [C] in the steel is ________ wt.% (round off to two decimal places).

Assume:

(1) Equilibrium between dissolved carbon [C], dissolved oxygen [O], and CO (gas) at 1 atmosphere.

(2) Henry’s law is valid for both [C] and [O]

Given:

Answer: (0.06 to 0.08)

55. M and N are 3 × 3 matrices. If the det(M) is −9 and the det(N) is −14, then the det(NM) is _______ (round off to the nearest integer).

Answer: (126 to 126)

GATE Exam 2020 Mining Engineering (MN) Question Paper With Answer Key

June 8, 2023May 3, 2022 by suresh84

GATE-2020

MN-Mining Engineering

GA-General Aptitude

Q1-Q5 carry one mark each.

(A) with, at

(B) on, in

(D) to, at

Answer: (C)

2. Despite a string of a poor performances, the changes of K. L. Rahul’s selection in the team are ______.

(A) slim

(B) bright

(D) uncertain

Answer: (B)

3. Select the word that fits the analogy:

Cover : Uncover :: Associate : _______

(A) Unassociate

(B) Inassociate

(D) Dissociate

Answer: (D)

Which of the following statements can be inferred from the given passage?

(A) Officials declared that the food-grain production target will be met due to good rains.

(B) Officials want the food-grain production target to be met by the November-February period.

(D) Officials hope that the food-grain production target will be met due to a good rabi produce.

Answer: (D)

5. The difference between the sum of the first 2n natural numbers and the sum of the first n odd natural numbers is ______.

(A) n² – n

(B) n² + n

(D) 2n² + n

Answer: (B)

Q6 – Q10 carry two marks each.

6. Repo rate is the at which Reserve Bank of India (RBI) lends commercial banks, and reverse repo rate is the rate at which RBI borrows money from commercial banks.

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

(A) Decrease in repo rate will increase cost of borrowing and decrease lending by commercial banks.

(B) Increase in repo rate will decrease cost of borrowing and increase lending by commercial banks.

(D) Decrease in repo rate will decrease cost of borrowing and increase lending by commercial banks.

Answer: (D)

7. P, Q, R, S, T, U, V, and W are seated around a circular table.

(I) S is seated opposite to W.

(II) U is seated at the second place to the right of R.

(III) T is seated at the third place to the left of R.

(IV) V is a neighbor of S.

Which of the following must be true?

(A) P is a neighbor of R.

(B) Q is a neighbor of R.

(D) R is the left neighbor of S.

Answer: (C)

(A) 66.6

(B) 75.2

(D) 116.5

Answer: (B)

9. For a matrix M = [m_ij], i. j= 1, 2, 3, 4, the diagonal elements are all zero and m_ij = −m_ij. The minimum number of elements required to fully specify the matrix is_______.

(A) 0

(B) 6

(D) 16

Answer: (B)

(A) 15 : 17

(B) 16 : 17

(D) 17 : 16

Answer: (B)

MN: Mining Engineering

Q1 – Q25 carry one mark each.

1. The eigenvalues of the matrix are

(A) 6, 4

(B) 4, 5

(D) −4, 5

Answer: (C)

2. For the electric delay detonator shown in the figure. the components P, Q and R, respectively, are

(A) fuse head, delay element, priming charge

(B) fuse head, priming charge, delay element

(D) delay element, fuse head, priming charge

Answer: (A)

3. Match the following safety arrangement for a surface-to-underground shaft hoist with their corresponding safety functions.

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

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

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

Answer: (D)

4. The fore bearings and back bearings of the lines of an open compass traverse are given below.

The stations that are free from local attraction are

(A) P and Q

(B) Q and R

(D) S and T

Answer: (B)

5. The plane stress condition is given by

(A) ε_zz = 0, γ_yz = 0, γ_zx = 0

(B) σ_zz = 0, τ_yz = 0, τ_zx = 0

(D) ε_zz ≠ 0, γ_yz ≠ 0, γ_zx ≠ 0

Answer: (B)

6. Match the following metals with their corresponding minerals.

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

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

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

Answer: (C)

7. Match the wire rope types with their corresponding cross-sectional diagrams.

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

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

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

Answer: (A)

8. The ‘ratchet and pawl’ mechanism in a jack hammer drill

(A) forces down the piston

(B) provides a twisting force to the drill steel

(D) prevents reverse rotation of rifle bar

Answer: (D)

9. Post-pillar method of stoping is a variant of

(A) cut and fill stoping

(B) sublevel stoping

(D) sublevel caving

Answer: (A)

10. ‘Cross-measure borehole method’ is used for

(A) rock slope monitoring

(B) methane drainage

(D) subsidence monitoring

Answer: (B)

11. The dry and wet bulb temperatures at the inlet of the airstream are 30°C and 25°C, respectively. The corresponding values at the outlet of the airstream are 26°C and 25°C, respectively. The psychrometric process that occurs in the airstream is described as

(A) latent cooling

(B) sensible cooling

(D) evaporative cooling

Answer: (D)

12. For a mixture of inflammable gases, the lower and upper explosibility limits can be computed using

(A) Dalton’s law

(B) Graham’s law

(D) Boyle’s law

Answer: (C)

13. The code for the lowest category of mineral resources under United Nations Framework Classification (UNFC) system is

(A) 444

(B) 123

(D) 111

Answer: (C)

14. Match the following sampling patterns with the corresponding sampling types.

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

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

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

Answer: (B)

15. In the context of gas testing using flame safety lamp, the correct statement is

(A) Each accumulation test has to be necessarily followed by percentage test

(B) Accumulation test is always done after percentage test

(D) Percentage test is done only in the event of accumulation test giving negative result

Answer: (D)

16. For x in the range of [−3, 3], the maximum value for the function f(x) = x³ – 6x² + 9x + 15 is _________ (round off to 1 decimal place).

Answer: (18.0 to 20.0)

17. A rock sample has coefficient of thermal diffusivity 1.282 × 10⁻⁶ m²/s specific heat 900 J/(kg°C) and density 2600 kg/m³. The coefficient of thermal conductivity of the rock sample in W/(m°C) is ________ (round off to 1 decimal place).

Answer: (2.9 to 3.1)

18. A random variable X has the following probability mass function.

The expected value of the variable X is _______ (round off to 1 decimal place).

Answer: (5.4 to 5.6)

/bg_collapse]

19. A random sample has five observations as shown below.

The coefficient of variation of the sample is ________ (round off to 3 decimal places).

Answer: (0.120 to 0.125)

20. Rock strata has unit weight of 25 kN/m³ and Poisson’s ratio 1/3. At a depth of 200 m, the horizontal stress in MPa is _______(round off to 1 decimal place).

Answer: (2.4 to 2.6)

21. A shovel of bucket capacity 4.2 m³ makes 900 passes per day with a fill factor of 0.8. If the swell factor of the rock is 1.4, then in-situ volume handled b the shovel in a month of 24 working days in m³ is ________ (round off to 1 decimal place).

Answer: (51830.0 to 51850.0)

22. A cylindrical sample of granular material has the following measurements:

Length: 10 cm

Diameter: 5 cm

Weight: 350 g

Assume the sample is completely dry with specific gravity of solid grains 2.8. The void ratio of the sample is ________ (round off to 3 decimal places).

Answer: (0.560 to 0.580)

23. The following consecutive readings were taken at uniform intervals with a level and a leveling staff on continuously sloping ground.

0.405, 1.035, 1.654, 0.240, 0.615, 1.125, 0.800, 1.125

The number of change points is _______.

Answer: (2 to 2)

24. The cost of a slurry pump is Rs. 50,000 and it has an estimated life of 7 years. If the salvage value is Rs. 8,000, the annual depreciation following straight-line depreciation method, in Rupees, is ________(round of to 1 decimal place).

Answer: (5990.0 to 6010.0)

25. In a mine bench, the shovel loading time follows exponential distribution with a mean loading time of 5 min per dumper. The arrival rate of dumpers that are identical in capacity, follows Poisson distribution with a mean arrival rate of 8 per hour. The probability that the shovel remains idle is _______ (round off to 2 decimal places).

Answer: (0.32 to 0.34)

Q26 – Q55 two marks each.

26. For the value of is

Answer: (B)

27. For the differential equation assuming the constant of integration to be C, the general solution is

Answer: (D)

28. A belt-drive used for power transmission between two parallel shafts has a belt of mass 1.2 kg/m, and the maximum allowable belt tension is 2250 N. If the centrifugal tension is one third of the maximum allowable belt tension, the speed at which maximum power is transmitted by the belt, in m/s, is

(A) 46.48

(B) 37.73

(D) 35.36

Answer: (C)

29. An air receiver of a compressor, having volume 0.5 m³, supplies air for charging ANFO in drill holes. During the charging process the absolute pressure of the air receiver falls from 900 kPa to 700 kPa. Assuming the entire process is isothermal, the volume of air supplied by the receiver at 100 kPa ambient pressure, in m³ is

(A) 1.00

(B) 0.39

(D) 4.48

Answer: (A)

30. A conveyor belt consumes 60 kW power while running at a speed of 3.0 m/s. The angle of lap is 180° and the coefficient of friction between belt and pulley is 0.2. The maximum tension (kN) in the belt is

(A) 21.7

(B) 61.7

(D) 42.9

Answer: (D)

31. A linear programming problem is stated below.

Maximize Z = 3x₁ + 5x₂

subject to, 2x₁ + x₂ ≤ 8

6x₁ + 8x₂ ≤ 30

x_1,x₂ ≥ 0

The objective function has

(A) infinite number of solutions

(B) unbounded solution

(D) infeasible solution

Answer: (C)

32. An explosive mixture has 80 g of ammonium nitrate (NH₄NO₃) and 14 g of fuel oil (C₁₀H₂₀). The oxygen balance in the mixture is

(A) surplus by 32 g

(B) deficient by 24 g

(D) deficient by 32 g

Answer: (D)

33. A cylindrical sample of cross-sectional area A, length L, and Young’s Modulus E, is subjected to a constant uniaxial load P. Within the elastic limit of loading, the total strain energy stored is

Answer: (D)

34. A surface mine production system long with reliability of the individual components is shown below. The system reliability is ________ (round off to 3 decimal places).

Answer: (0.530 to 0.550)

35. The selling price of one rock bolt (in Rs.) is given as, S = (200 – 10n⁻⁵), where n is the number of bolts produced. The manufacturing cost of rock bolts has a fixed components of Rs. 15000, and a variable components of Rs. 100 per bolt. The minimum break-even production, in number of rock bolts, is _______ (round off to 1 decimal place).

Answer: (148.0 to 154.0)

36. Two underground mines are separated by a horizontal coal barrier of 60 m thickness. One mine is inundated, whereas the other mine as a blind heading of dimensions 4.0 m wide and 2.5 m height terminating at the barrier. The overall in-situ shear strength of the coal mass is 500 kPa. Assume that the failure mode is in shear. At a factor of safety of 10, the maximum water head that can be withstood by the coal barrier, in m, is ________ (round off to 1 decimal place).

Answer: (385.0 to 410.0)

37. Air enters from ambient atmosphere into a level duct of uniform cross-section area 0.2 m² at a flow rate of 2.0 m³/s and density of 1.2 kg/m³. The entry shock loss factor is 1.0 and the resistance of the duct per meter length is 1.0 Ns²/m⁸. The static pressure measured at a distance of 20 m from the duct entrance in Pa, is ______ (round off to 1 decimal place).

Answer: (-205.0 to -195.0)

38. A sealed-off area air sample consists of 16.0%O₂, 3.0%CO₂, and the rest is N₂. Assume that the standard composition of atmospheric air is 21.0% O₂ and 79.0% N₂. The percentage of blackdamp in the air sample is ________ (round off to 2 decimal places).

Answer: (22.00 to 25.00)

39. A diesel loader produces 60 l/s of exhaust fumes containing 5000 ppm of CO. The incoming air has 10 ppm of CO. The minimum amount air flow in m³/s that is needed at the loader to dilute CO to a permissible level of 50 ppm is ________ (round off to 1 decimal place).

Answer: (7.2 to 7.7)

40. The equation for peak particle velocity (PPV) from blast induced ground vibration is given by

where k and B are site constants.

In a field study, the following readings are recorded.

The value of B is _______ (round off to 3 decimal places).

Answer: (-1.255 to -1.165)

41. An underground copper mine sends 2500 tonnes of ore per day to the concentrator plant having an average grade of 1.2% Cu. The plant produces concentrate of 25.0% Cu with a recovery of 93.0%. The solids portion of tailings generated from the plant per day in tonnes is________ (round of to 1 decimal place).

Answer: (2380.0 to 2396.0)

42. A mine gallery is supported by regularly placed roof bolts of 100 kN allowable pull force per bolt, as shown below. Assuming unit weight of the immediate roof is 25 kN/m³, the factor of safety of the support system is _________ (round off to 2 decimal places).

Answer: (2.10 to 2.45)

43. The slip circle of radius 30.0 m in an overburden slope is shown with the centre of slip circle at point O. The tension crack is completely filled with water. For one meter width of the slope, the moment exerted by the force of water about O in kN-m is _______ (round off to 1 decimal place).

Answer: (3360.0 to 3480.0)

44. The function values at four points of x are shown in the table. The area under the function, using trapezoidal method, is _______ (round off to 1 decimal place).

Answer: (71.0 to 72.0)

45. A particle starting from rest moves in a straight line such that after time, t (seconds), the acceleration becomes (6 – t/4) cm/s². When the acceleration becomes zero, the velocity of the particle in cm/s is _______ (round off to 1 decimal place).

Answer: (71.0 to 73.0)

46. A parallelepiped has edge vectors as shown below.

The volume of the parallelepiped is ______ round off to 1 decimal place).

Answer: (87.0 to 89.0)

47. For a development heading, the blasting parameters are

Cross-section: 6.0 m × 5.0 m

Total number of holes: 72

Number of trimmer holes: 30

Depth of each hole: 3.5 m

Charge per hole (except trimmers): 3.5 kg

Charge per trimmer hole: 1.8 kg

Pull per round: 90% of hole depth

The powder factor for the development round in m³/kg is _______ (round off to 2 decimal places).

Answer: (0.44 to 0.50)

48. The following figure represents the observations from the level survey of an underground gallery.

If the reduced level of station A is 100.0 m, the reduced level of station D in m is ______ (round off to 1 decimal place).

Answer: (100.4 to 100.6)

49. A tracheometer was setup at station P and the following readings were taken at two stations A and B with the staff held vertical and the line of sight horizontal.

The additive and multiplying constants of the tracheometer are 0 and 100, respectively. The length of AB in m is ________ (round off to 1 decimal place).

Answer: (157.0 to 161.0)

50. The geometry of a simple planar curve (ADB) is shown below. The value of the mid-ordinate of the curve in m is ________ (round off to 1 decimal place).

Answer: (248.0 to 252.0)

51. A steel cube of side 50 mm is subjected to a uniform pressure of 200 MPa acting on each face. The Young’s modulus and Poisson’s ratio of the material are 200 GPa and 0.25, respectively. The decrease in the side of the cube in mm is _______ (round off to 3 decimal places).

Answer: (0.020 to 0.030)

52. In the figure shown below, the friction coefficient between the block and the inclined plane is 0.2, and all the pulleys are weightless. The weight of the block is 10 N. The minimum force P in Newtons that is needed to slide the block up the inclined plane is _______ (round off to 2 decimal places).

Answer: (67.00 to 69.00)

53. An assignment problem is given below with the cost of assignment as shown.

If only one task can be assigned to one group, the minimum cost of assignment is _______.

Answer: (18 to 18)

54. A vertical stopping bock of length 60.0 m, height 40.0 m, and average width 1.5 m has sharp boundary walls. However, the mining width of the stopping block is 2.0 m. The tonnage factors are 3.0 tonne/m³ for ore and 2.5 tonne/m³ for wall rocks. The average grade of ore is 10.0%. The overall grade of ore mined on account of dilution in percentage is _________ (round off to 2 decimal places).

Answer: (7.70 to 7.95)

55. A bauxite ore body has four boreholes as shown below. For each borehole, the grade of alumina, the thickness of the ore body, and the triangular area of influence are as shown.

The average grade of ore body in the region ABCD in percentage is ________ (round off to 1 decimal place).

Answer: (30.8 to 31.6)

GATE Exam 2020 Mechanical Engineering (ME-2) Question Paper With Answer Key

June 8, 2023May 3, 2022 by suresh84

GATE-2020

ME-2: Mechanical Engineering

GA-General Aptitude

Q1 – Q5 carry one mark each.

1. While I agree _____ his proposal this time, I do not often agree ____him.

(A) to, with

(B) with, to

(D) to, to

Answer: (A)

2. The recent measures to improve the output would ______ the level of production satisfaction.

(A) increase

(B) decrease

(D) equalise

Answer: (A)

3. Select the word that fits the analogy:

White : Whitening :: Light :______

(A) Lightning

(B) Lightening

(D) Enlightening

Answer: (B)

Based on their connotations in the given passage, which one of the following meanings DOES NOT match?

(A) upped = increased

(B) squared = lost

(D) saw = resulted in

Answer: (B)

5. There are five levels {P, Q, R, S, T} in a linear supply chain before a product reaches customers, as shown in the figure.

At each of the five levels, the price of the product is increased by 25%. If the product is produced at level P at the cost of Rs. 120 per unit, what is the price paid (in rupees) by the customers?

(A) 187.50

(B) 234.38

(D) 366.21

Answer: (D)

Q6 – Q10 carry two marks each.

Which of the following assertions is best supported by the above information?

(A) Mitigation deals with consequences of climate change.

(B) Adaptation deals with causes of climate change.

(D) Adaptation deals with actions taken to combat green-house gas emissions.

Answer: (C)

7. Find the missing element in the following figure.

(A) d

(B) e

(D) y

Answer: (A)

8. It was estimated that 52 men can complete a strip in a newly constructed highway connecting cities P and Q in 10 days. Due to an emergency, 12 men were sent to another project. How many number of days, more than original estimate, will be required to complete the strip?

(A) 3 days

(B) 5 days

(D) 13 days

Answer: (A)

Then, which of the following statements is FALSE?

(A) For fixed Z; X is proportional to Y

(B) For fixed Y; X is proportional to Z

(D) XY/Z is constant

Answer: (A)

(A) 2 : 1

(B) 9 : 22

(D) 22 : 9

Answer: (D)

ME2: Mechanical Engineering

Q1 – Q25 carry one mark each.

1. The sum of two normally distributed random variables X and Y is

(A) always normally distributed

(B) normally distributed, only if X and Y are independent

(D) normally distributed, only if X and Y have the same mean

Answer: (MTA)

2. A matrix P is decomposed into its symmetric part S and skew symmetric part V. If then matrix P is

Answer: (B)

3. Let Then, I may also be expressed as

Answer: (C)

4. The solution of which additionally satisfies in the Laplace s-domain is

Answer: (A)

5. An attempt is made to pull a roller of weight W over a curb (step) by applying a horizontal force F as shown in the figure.

The coefficient of static friction between the roller and the ground (including the edge of the step) is μ. Identify the correct free body diagram (FBD) of the roller when the roller is just about to climb over the step.

Answer: (B)

6. A circular disk of radius r is confined to roll without slipping at P and Q as shown in the figure.

(A) v/r

(B) r/2r

(D) 3v/2r

Answer: (D)

7. The equation of motion of a spring-mass-damper system is given by

The damping factor for the system is

(A) 0.25

(B) 0.5

(D) 3

Answer: (B)

8. The number of qualitatively distinct kinematic inversions possible for a Grashof chain with four revolute pairs is

(A) 1

(B) 2

(D) 4

Answer: (C)

9. The process, that uses a tapered horn to amplify and focus the mechanical energy for machining of glass, is

(A) electrochemical machining

(B) electrical discharge machining

(D) abrasive jet machining

Answer: (C)

10. Two plates, each of 6 mm thickness, are to be butt-welded. Consider the following processes and select the correct sequence in increasing order of size of the heat affected zone.

(1) Arc welding

(2) MIG welding

(3) Laser beam welding

(4) Submerged are welding

(A) 1-4-2-3

(B) 3-4-2-1

(D) 3-2-4-1

Answer: (D)

11. Which one of the following statements about a phase diagram is INCORRECT?

(A) It indicates the temperature at which different phases start to melt

(B) Relative amount of different phases can be found under given equilibrium conditions

(D) Solid solubility limits are depicted by it

Answer: (C)

12. The figure below shows a symbolic representation of the surface texture in a perpendicular lay orientation with indicative values (I through VI) marking the various specifications whose definitions are listed below.

P: Maximum Waviness Height (mm); Q: Maximum Roughness Height (mm);

Q: Minimum Roughness Height (mm); S: Maximum Waviness Width (mm);

T: Maximum Roughness Width (mm); U: Roughness Width Cutoff (mm).

The correct match between the specifications and the symbols (I to VI) is

(A) I-R, II-Q, III-P, IV-S, V-U, VI-T

(B) I-R, II-P, III-U, IV-S, V-T, VI-Q

(D) I-Q, II-U, III-R, IV-T, V-S, VI-P

Answer: (A)

13. In materials Requirement Planning, if the inventory holding cost is very high and the setup cost is zero, which one of the following lot sizing approaches should be used?

(A) Economic Order Quantity

(B) Lot-for-Lot

(D) Fixed Period Quantity, for 2 periods

Answer: (B)

14. Which of the following conditions is used to determine the stable equilibrium of all partially submerged floating bodies?

(A) Centre of buoyancy must be above the centre of gravity

(B) Centre of buoyancy must be below the centre of gravity

(D) Metacentre must be at a lower level than the centre of gravity

Answer: (C)

15. In the space above the mercury column in a barometer tube, the gauge pressure of the vapour is

(A) positive, but more than one atmosphere

(B) negative

(D) positive, but less than one atmosphere

Answer: (B)

16. A closed vessel contains pure water, in thermal equilibrium with its vapour at 25°C (Stage # 1), as shown.

The vessel in this stage is then kept inside an isothermal over which is having an atmosphere of hot air maintained at 80°C. The vessel exchanges heat with the oven atmosphere and attains a new thermal equilibrium (Stage # 2). If the Valve A is now opened inside the oven, what will happen immediately after opening the valve?

(A) Water vapor inside the vessel will come out of the Valve A

(B) Hot air will go inside the vessel through Valve A

(D) All the vapor inside the vessel will immediately condense

Answer: (B)

17. For an air-standard Diesel cycle,

(A) heat addition is at constant volume and heat rejection is at constant pressure

(B) heat addition is at constant pressure and heat rejection is at constant pressure

(D) heat addition is at constant volume and heat rejection is at constant volume

Answer: (C)

18. The values of enthalpies at t he stator inlet and rotor outlet of a hydraulic turbomachine stage are h₁ and h₃ The enthalpy at t he stator outlet (or, rotor inlet) is h₂. The condition (h₂ – h₁) = (h₃ – h₂) indicates that the degree of reaction of this stage is

(A) zero

(B) 50%

(D) 100%

Answer: (B)

19. Let I be a 100 dimensional identity matrix and E be the set of its distinct (no value appears more than once in E) real eigenvalues. The number of elements in E is _______.

Answer: (1 to 1)

20. A beam of negligible mass is hinged at support P and has a roller support Q as shown in the figure.

A point load of 1200 N is applied at point R. The magnitude of the reaction force at support Q is ______ N.

Answer: (1500 to 1500)

21. A machine member is subjected to fluctuating stress σ = σ₀ cos(8πt). The endurance limit of the material is 350 MPa. If the factor of safety used in the design is 3.5 then the maximum allowable value of σ₀ is ________MPa (round off to 2 decimal places).

Answer: (99.98 to 100.02)

22. A bolt head has to be made at the end of a rod of diameter d = 12 mm by localized forging (upsetting) operation. The length of the unsupported portion of the rod is 40 mm. To avoid buckling of the rod, a closed forging operation has to be performed with a maximum die diameter of _____ mm.

Answer: (18 to 19.5)

23. Consider the following network of activities, with each activity named A-L, illustrated in the nodes of the network.

The number of hours required for each activity is shown alongside the nodes. The slack on the activity L, is _______ hours.

Answer: (2 to 2)

24. In a furnace, the inner and outer sides of the brick wall (k₁ = 2.5 W/m.K) are maintained at 1100°C and 700°C, respectively as shown in figure.

The brick wall is covered by an insulating material of thermal conductivity k₂. The thickness of the insulation is 1/4^th of the thickness of the brick wall. The outer surface of the insulation is at 200°C. The heat flux through the composite walls is 2500 W/m².

The value of k₂ is _____W/m.K (round off to one decimal place).

Answer: (0.5 to 0.5)

25. If a reversed Carnot cycle operates between the temperature limits of 27°C and −3°C, then the ratio of the COP of a refrigerator to that of a heat pump (COP of refrigerator / COP of heat pump) based on the cycle is________ (round off to 2 decimal places).

Answer: (0.89 to 0.91)

Q26 – Q55 carry two marks each.

26. The directional derivative of f(x, y, z) = xyz at point (−1, 1, 3) in the direction of vector is

(A)

(B) −7/3

(D) 7

Answer: (C)

27. The function f(z) of complex variable z = x + iy, where i = √−1, is given as f(z) = (x³ – 3xy²) + i v(x, y). For this function to be analytic, v(x, y) should be

(A) (3xy² – y³) + constant

(B) (3x²y² – y³) + constant

(D) (3x²y – y³) + constant

Answer: (D)

28. A cantilever of length l, and flexural rigidity EI, stiffened by a spring of stiffness k, is loaded by a transverse force P, as shown.

The transverse deflection under the load is

Answer: (D)

29. The sun (S) and the planet (P) of an epicyclic gear train shown in the figure have identical number of teeth.

If the sun (S) and the outer ring (R) gears are rotated in the same direction with angular speed ω_S and ω_R. Respectively, then the angular speed of the arm AB is

Answer: (A)

30. A thin-walled cylinder of radius r and thickness t is open at both ends, and fits snugly between two rigid walls under ambient conditions, as shown in the figure.

The material of the cylinder has Young’s modulus E, Poisson’s ratio v, and coefficient of thermal expansion α. What is the minimum rise in temperature ∆T of the cylinder (assume uniform cylinder temperature with no buckling of the cylinder) required to prevent gas leakage if the cylinder has to store the gas at an internal pressure of p above the atmosphere?

Answer: (C)

31. A helical spring has spring constant k. If the wire diameter, spring diameter and the number of coils are all doubled then the spring constant of the new spring becomes

(A) k/2

(B) k

(D) 16k

Answer: (B)

32. Two rollers of diameters D₁(in mm) and D₂ (in mm) are used to measure the internal taper angle in the V-groove of a machined component. The heights H₁ (in mm) and H₂ (in mm) are measured by using a height gauge after inserting the rollers into the same V-groove as shown in the figure.

Which one of the following is the correct relationship to evaluate the angle α as shown in the figure?

Answer: (A)

33. The forecast for the monthly demand of a product is given in the table below.

The forecast is made by using the exponential smoothing method. The exponential smoothing coefficient used in the forecasting the demand is

(A) 0.10

(B) 0.40

(D) 1.00

Answer: (A)

34. One kg of air in a closed system undergoes an irreversible process from an initial state of p₁ = 1 bar (absolute) and T₁ = 27°C, to a final state of p₂ = 3 bar (absolute) and T₂ = 127° If the gas constant of air is 287 J/kg.K and the ratio of the specific heats γ = 1.4, then the change in the specific entropy (in J/kg.K) of the air in the process is

(A) −26.3

(B) 28.4

(D) indeterminate, as the process is irreversible

Answer: (A)

35. For the integral the absolute percentage error in numerical evaluation with the Trapezoidal rule, using only the end points, is ________ (round off to one decimal place).

Answer: (5.1 to 5.5)

36. A fair coin is tossed 20 times. The probability that ‘head’ will appear exactly 4 times in the first ten tosses, and ‘tail’ will appear exactly 4 times in the next ten tosses is ________ (round off to 3 decimal places).

Answer: (0.041 to 0.043)

37. A hollow spherical ball of radius 20 cm floats in still water, with half of its volume submerged. Taking the density of water as 1000 kg/m³, and the acceleration due to gravity as 10 m/s², the natural frequency of small oscillations of the ball, normal to the water surface is ________ radian/s (round off to 2 decimal places).

Answer: (8.60 to 8.70)

38. Uniaxial compression test data for a solid metal bar of length 1 m is shown in the figure.

The bar material has a linear elastic response from O to P followed by a nonlinear response. The point P represents the yield point of the material. The rod is pinned at both the ends. The minimum diameter of the bar so that it does not buckle under axial loading before reaching the yield point is _______mm (round off to one decimal place).

Answer: (55.0 to 58.0)

39. The turning moment diagram of a flywheel fitted to a fictitious engines is shown in the figure.

The mean turning moment is 2000 Nm. The average engine speed is 1000 rpm. for fluctuation in the speed to be within ±2% of the average speed, the mass moment o inertia of the flywheel is ______ kg.m².

Answer: (3.55 to 3.65)

40. A rigid block of mass m₁ = 10 kg having velocity v₀ = 2 m/s strikes a stationary block of mass m₂ = 30 kg after traveling 1 m along a frictionless horizontal surface as shown in the figure.

The two masses stick together and jointly move by a distance of 0.25 m further along the same frictionless surface, before they touch the mass-less buffer that is connected to the rigid vertical wall by means of a linear spring having a spring constant k = 10⁵ N/m. The maximum deflection of the spring is _________ cm (round off to 2 decimal places).

Answer: (0.98 to 1.02)

41. A steel spur pinion has a module (m) of 1.25 mm, 20 teeth and 20° pressure angle. The pinion rotates at 1200 rpm and transmits power to a 60 teeth gear. The face width (F) is 50 mm, Lewis form factor Y = 0.322 and a dynamic factor K_v = 1.26. The bending stress (σ) induced in a tooth can be calculated by using the Lewis formula given below.

If the maximum bending stress experienced by the pinion is 400 MPa, the power transmitted is _______ kW (round off to one decimal place).

Lewis formula: where W^t is the tangential load acting on the pinion.

Answer: (9.8 to 10.8)

42. A mould cavity of 1200 cm³ volume has to be filled through a sprue of 10 cm length feeding a horizontal runner. Cross-sectional area at the base of the sprue is 2 cm². Consider acceleration due to gravity as 9.81 m/s². Neglecting frictional losses due to molten metal flow, the time taken to fill the mould cavity is ________ seconds (round of to 2 decimal places).

Answer: (4 to 9)

43. A cylindrical bar with 200 mm diameter is being turned with a tool having geometry 0° – 9° – 7° – 8° – 15°- 30° – 0.05 inch (Coordinate system, ASA) resulting in a cutting force F_c1. If the tool geometry is changed to 0° – 9° – 7° – 8° – 15° – 0° – 0.05 inch (Coordinate system, ASA) and all the other parameters remain unchanged, the cutting force changes to F_c2. Specific cutting energy (in J/mm³) is U_c = U₀(t₁)⁻⁴, where U₀ is the specific energy coefficient, and t₁ is the uncut thickness in mm. The value of percentage change in cutting force F_c2, i.e. is ________ (round off to one decimal place).

Answer: (-5.8 to -5.5)

44. There are two identical shaping machines S₁ and S₂. In machine S₂, the width of the workpiece is increased by 10% and the feed is decreased by 10%, with respect to that of S₁. If all other conditions remain the same then the ratio of total time per pass in S₁ and S₂ will be ________ (round of to one decimal place).

Answer: (0.7 to 0.9)

45. Bars of 250 mm length and 25 mm diameter are to be turned on a lathe with a feed of 0.2 mm/rev. Each regrinding of the tool costs Rs. 20. The time required for each tool change is 1 min. Tool life equation is given as VT² = 24 (where cutting speed V is in m/min and tool life T is in min). The optimum tool cost per piece for maximum production rate is Rs. _______ (round off to 2 decimal places).

Answer: (26.00 to 28.00)

46. A point ‘P’ on a CNC controlled XY-stage is moved to another point ‘Q’ using the coordinate system shown in the figure below and rapid positioning command (G00).

A pair of stepping motors with maximum sped of 800 rpm, controlling both the X and Y motion of the stage, are directly coupled to a pair of lead screws, each with a uniform pitch of 0.5 mm. The time needed to position the point ‘P’ to the point ‘Q’ is _________ minutes (round off to 2 decimal places).

Answer: (1.40 to 1.60)

47. For a single item inventory system, the demand is continuous, which is 10000 per year. The replenishment is instantaneous and backorders (S units) per cycle are allowed as shown in the figure.

As soon as the quantity (Q units) ordered from the supplier is received, the backordered quantity is issued to the customers. The ordering cost is Rs. 300 per order. The carrying cost is Rs. 4 per unit per year. The cost of backordering is Rs. 25 per unit per year. Based on the total cost minimization criteria, the maximum inventory reached in the system is __________ (round off to nearest integer).

Answer: (1130 to 1140)

48. Consider a flow through a nozzle, as shown in the figure below.

The air flow is steady, incompressible and inviscid. The density of air is 1.23 kg/m³. The pressure difference (p₁ – p_atm) is _______ kPa (round off to 2 decimal places).

Answer: (1.50 to 1.55)

49. Water (density 1000 kg/m³) flows through an inclined pipe of uniform diameter. The velocity, pressure and elevation at section A are V_A = 3.2 m/s, p_A = 186 kPa and z_A = 24.5 m, respectively, and those at section B are V_B = 3.2 m/s, p_B = 260 kPa and z_B = 9.1 m, respectively. If acceleration due to gravity is 10 m/s² then the head lost due to friction is _________ m (round off to one decimal place).

Answer: (7.9 to 8.1)

50. The spectral distribution of radiation from a black body at T₁ = 3000 K has a maximum at wavelength λ_max. The body cools down to a temperature T₂. If the wavelength corresponding to the maximum of the spectral distribution at T₂ is 1.2 times of the original wavelength λ_max, then the temperature T₂ is ________ K (round off to the nearest integer).

Answer: (2499 to 2501)

51. Water flows through a tube of 3 cm internal diameter and length 20 m. The outside surface of the tube is heated electrically so that it is subjected to uniform heat flux circumferentially and axially. The mean inlet and exit temperatures of the water are 10°C and 70°C, respectively. The mass flow rate of the water is 720 kg/h. Disregard the thermal resistance of the tube wall. The internal heat transfer coefficient is 1697 W/m².K. Take specific heat C_p of water as 4.179 kJ/kg.K. The inner surface temperature at the exit section of the tube is ________ °C (round off to one decimal place).

Answer: (85.1 to 86.1)

52. Air is contained in a frictionless piston-cylinder arrangement as shown in the figure.

The atmospheric pressure is 100 kPa and the initial pressure of air in the cylinder is 105 kPa. The area of piston is 300 cm². Heat is now added and the piston moves slowly from its initially position until it reaches the stops. The spring constant of the linear spring is 12.5 N/mm. Considering the air inside the cylinder as the system, the work interaction is _________ J (round off to the nearest integer).

Answer: (543 to 545)

53. Moist air at 105 kPa, 30°C and 80% relative humidity flows over a cooling coil in an insulated air-conditioning duct. Saturated air exits the duct at 100 kPa and 15° The saturation pressures of water at 30°C and 15°C are 4.24 kPa and 1.7 kPa respectively. Molecular weight of water is 18 g/mol and that of air is 28.94 g/mol. The mass of water condensing out from the duct is ______ g/kg of dry air (round off to the nearest integer).

Answer: (10 to 10)

54. In a stream power plant, superheated steam at 10 MPa and 500°C, is expanded isentropically in a turbine until it becomes a saturated vapour. It is then reheated at constant pressure to 500° The steam is next expanded isentropically in another turbine until it reaches the condenser pressure of 20 kPa. Relevant properties of steam are given in the following two tables. The work done by both the turbines together is _______ kJ/kg (round off to the nearest integer).

Answer: (1500 to 1525)

55. Keeping all other parameters identical, the Compression Ratio (CR) of an air standard diesel cycle is increased from 15 to 21. Take ratio of specific heats = 1.3 and cut-off ratio of the cycle r_c = 2.

The difference between the new and the old efficiency values, in percentage.

(η_new|_CR=21) – (η_old|_CR=15) = __________% (round off to one decimal place).

Answer: (4.6 to 4.9)