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General Aptitude(10)Engineering Mathematics(11)CS Core(44)

General Aptitude

10 Questions

GATE→2024→General Aptitude→Verbal Ability

Q1

MCQ[1 Mark]

If '->' denotes increasing order of intensity, then the meaning of the words [dry -> arid -> parched] is analogous to [diet -> fast -> _]. Which one of the given options is appropriate to fill the blank?

(A)

starve

(B)

reject

(C)

feast

(D)

deny

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q2

MCQ[1 Mark]

If two distinct non-zero real variables x and y are such that (x+y) is proportional to (x-y) then the value of y/x is a constant.

(A)

depends on xy

(B)

depends only on x and not on y

(C)

depends only on y and not on x

(D)

is a constant

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q3

MCQ[1 Mark]

Consider the following sample of numbers: 9, 18, 11, 14, 15, 17, 10, 69, 11, 13. The median of the sample is

(A)

13.5

(B)

14

(C)

11

(D)

18.7

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q4

MCQ[1 Mark]

The number of coins of ₹1, 25 paise, and 10 paise denominations that a person has are in the ratio 5:3:13. Of the total amount, the percentage of money in 25 paise coins is

(A)

21%

(B)

14 2/7 %

(C)

10%

(D)

30%

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q5

MCQ[1 Mark]

For positive non-zero real variables p and q, if log(p^2 + q^2) = log p + log q + 2 log 3, then, the value of (p^4 + q^4)/(p^2 q^2) is

(A)

79

(B)

81

(C)

9

(D)

83

Explanation

GATE→2024→General Aptitude→Verbal Ability

Q6

MCQ[2 Marks]

In the given text, the blanks are numbered (i)-(iv). Select the best match for all the blanks.

(A)

(i) down, (ii) down, (iii) on

(B)

(i) on, (ii) down, (iii) for

(C)

(i) down, (ii) out, ...

(D)

(i) on, ...

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q7

MCQ[2 Marks]

A rectangular paper sheet of dimensions 54 cm x 4 cm is taken. The two longer edges of the sheet are joined together to create a cylindrical tube. A cube whose surface area is equal to the area of the sheet is also taken. Then, the ratio of the volume of the cylindrical tube to the volume of the cube is

(A)

1/\pi

(B)

2/\pi

(C)

3/\pi

(D)

4/\pi

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q8

MCQ[2 Marks]

The pie chart presents the percentage contribution of different macronutrients to a typical 2,000 kcal diet of a person. The total fat (all three types), in grams, this person consumes is

(A)

44.4

(B)

77.8

(C)

100

(D)

3,600

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q9

MCQ[2 Marks]

A rectangular paper of 20 cm x 8 cm is folded 3 times. Each fold is made along the line of symmetry, which is perpendicular to its long edge. The perimeter of the final folded sheet (in cm) is

(A)

18

(B)

24

(C)

20

(D)

21

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q10

MCQ[2 Marks]

The least number of squares to be added in the figure to make AB a line of symmetry is

(A)

6

(B)

4

(C)

5

(D)

7

Explanation

Engineering Mathematics

11 Questions

GATE→2024→Engineering Mathematics→Calculus

Q11

MCQ[1 Mark]

Let f: R -> R be a function such that f(x) = max{x, x^3}, x in R. The set of all points where f(x) is NOT differentiable is

(A)

{-1, 1, 2}

(B)

{-2, -1, 1}

(C)

{0, 1}

(D)

{-1, 0, 1}

Explanation

GATE→2024→Engineering Mathematics→Linear Algebra

Q12

MCQ[1 Mark]

The product of all eigenvalues of the matrix [[1, 2, 3], [4, 5, 6], [7, 8, 9]] is

(A)

0

(B)

0 [Wait, option B is 1, let's check determinant]

(C)

2

(D)

3

Explanation

GATE→2024→Engineering Mathematics→Probability and Statistics

Q13

MCQ[1 Mark]

Consider a permutation sampled uniformly at random from {1, 2, ..., n} for some n >= 4. Let X be the event that 1 occurs before 2, and Y that 3 occurs before 4. Which one of the following is TRUE?

(A)

X must occur

(B)

Events X and Y are independent

(C)

Y must occur

(D)

Event X is more likely than Y

Explanation

GATE→2024→Engineering Mathematics→Discrete Mathematics

Q14

MSQ[1 Mark]

Which of the following statements is/are TRUE?

(A)

(B)

(C)

(D)

Explanation

GATE→2024→Engineering Mathematics→Probability and Statistics

Q15

MSQ[1 Mark]

Let A and B be two events in a probability space with P(A)=0.3, P(B)=0.5, and P(A intersect B)=0.1. Which of the following statements is/are TRUE?

(A)

The two events A and B are independent

(B)

P(A \cup B) = 0.7

(C)

P(A \cap B^c) = 0.2

(D)

P(A^c \cap B^c) = 0.4

Explanation

GATE→2024→Engineering Mathematics→Discrete Mathematics

Q16

NAT[1 Mark]

Let A and B be non-empty finite sets such that there exist one-to-one and onto functions (i) from A to B and (ii) from A to A union B. Number of possible values of |A| is

Explanation

GATE→2024→Engineering Mathematics→Discrete Mathematics

Q17

NAT[1 Mark]

Number of spanning trees in a complete graph of 4 vertices labelled A, B, C, and D is

Explanation

GATE→2024→Engineering Mathematics→Linear Algebra

Q18

MSQ[2 Marks]

Let A be n x m matrix with m > n. Which of the following statements is/are TRUE for Ax = 0?

(A)

There exist at least m-n linearly independent solutions to this system

(B)

There exist m-n linearly independent vectors such that every solution is a linear combination...

(C)

There exists a non-zero solution in which at least m-n variables are 0

(D)

There exists a solution in which at least n variables are non-zero

Explanation

GATE→2024→Engineering Mathematics→Discrete Mathematics

Q19

MSQ[2 Marks]

The chromatic number of a graph is the minimum number of colours used in a proper colouring. Let G be any graph with n vertices and chromatic number k. Which of the following statements is/are always TRUE?

(A)

G contains a complete subgraph with k vertices

(B)

G contains an independent set of size at least n/k

(C)

G contains at least k(k-1)/2 edges

(D)

G contains a vertex of degree at least k

Explanation

GATE→2024→Engineering Mathematics→Discrete Mathematics

Q20

MSQ[2 Marks]

Consider the operators o and [] defined by a o b = ab, a [] b = a + 2b, for positive integers. Which of the following properties hold?

(A)

(B)

(C)

(D)

Explanation

GATE→2024→Engineering Mathematics→Probability and Statistics

Q21

NAT[2 Marks]

A bag contains ... balls. Two balls are drawn randomly without replacement. Given that the first ball drawn is red, the probability both drawn are red is

Explanation

CS Core

44 Questions

GATE→2024→CS Core→Digital Logic

Q22

MCQ[1 Mark]

Consider a system that uses 5 bits for representing signed integers in 2's complement format. A = 01010 and B = 11010. Which operation results in an arithmetic overflow or underflow?

(A)

A + B

(B)

A - B

(C)

B - A

(D)

2 * B

Explanation

GATE→2024→CS Core→Computer Organization and Architecture

Q23

MCQ[1 Mark]

Which one of the following statements is FALSE?

(A)

In the cycle stealing mode of DMA, one word of data is transferred between an I/O device and main memory in a stolen cycle

(B)

For bulk data transfer, the burst mode of DMA has a higher throughput than the cycle stealing mode

(C)

Programmed I/O mechanism has a better CPU utilization than the interrupt driven I/O mechanism

(D)

The CPU can start executing an interrupt service routine faster with vectored interrupts than with non-vectored interrupts

Explanation

GATE→2024→CS Core→Computer Networks

Q24

MCQ[1 Mark]

User browsing webpage. Packets: (i) HTTP GET index, (ii) DNS request, (iii) HTTP GET image, (iv) TCP SYN. Correct chronological order?

(A)

(iv), (ii), (iii), (i)

(B)

(ii), (iv), (iii), (i)

(C)

(ii), (iv), (i), (iii)

(D)

(iv), (ii), (i), (iii)

Explanation

GATE→2024→CS Core→Algorithms

Q25

MCQ[1 Mark]

Given array of N elements, check if sorted in single pass comparing adjacent elements. Worst-case time complexity?

(A)

both O(N) and \Omega(N)

(B)

O(N) but not \Omega(N)

(C)

\Omega(N) but not O(N)

(D)

neither O(N) nor \Omega(N)

Explanation

GATE→2024→CS Core→Programming and Data Structures

Q26

MCQ[1 Mark]

Consider the following C program... Output of printf('%d', a)?

(A)

(B)

(C)

1

(D)

Explanation

GATE→2024→CS Core→Programming and Data Structures

Q27

MCQ[1 Mark]

Consider the following recursive C program with getchar() and putchar(). Input: 1234 followed by newline.

(A)

(B)

(C)

4321 as output

(D)

Explanation

GATE→2024→CS Core→Databases

Q28

MCQ[1 Mark]

Let S be the specification: 'Instructors teach courses. Students register for courses. Courses are allocated classrooms. Instructors guide students.' Which ER diagram correctly represents S?

(A)

(i)

(B)

(ii)

(C)

(iii)

(D)

(iv)

Explanation

GATE→2024→CS Core→Databases

Q29

MCQ[1 Mark]

In a B+ tree, the requirement of at least half-full (50%) node occupancy is relaxed for which one of the following cases?

(A)

Only the root node

(B)

All leaf nodes

(C)

All internal nodes

(D)

Only the leftmost leaf node

Explanation

GATE→2024→CS Core→Theory of Computation

Q30

MSQ[1 Mark]

Let L1, L2 be two regular languages and L3 a language which is not regular. Which of the following statements is/are always TRUE?

(A)

$L_{1}=L_{2}$ if and only if $L_{1}\cap\overline{L_{2}}=\phi$

(B)

$L_{1}\cup L_{3}$ is not regular

(C)

$L_{3}$ is not regular

(D)

$\overline{L_{1}}\cup\overline{L_{2}}$ is regular

Explanation

GATE→2024→CS Core→Operating System

Q31

MSQ[1 Mark]

Which of the following statements about threads is/are TRUE?

(A)

Threads can only be implemented in kernel space

(B)

Each thread has its own file descriptor table for open files

(C)

All the threads belonging to a process share a common stack

(D)

Threads belonging to a process are by default not protected from each other

Explanation

GATE→2024→CS Core→Operating System

Q32

MSQ[1 Mark]

Which of the following process state transitions is/are NOT possible?

(A)

Running to Ready

(B)

Waiting to Running

(C)

Ready to Waiting

(D)

Running to Terminated

Explanation

GATE→2024→CS Core→Compiler Design

Q33

MSQ[1 Mark]

Which of the following is/are Bottom-Up Parser(s)?

(A)

Shift-reduce Parser

(B)

Predictive Parser

(C)

LL(1) Parser

(D)

LR Parser

Explanation

GATE→2024→CS Core→Digital Logic

Q34

MSQ[1 Mark]

Consider the circuit shown below where the gates may have propagation delays. Which of the following statements about the circuit is/are CORRECT?

(A)

With no propagation delays, the output Y is always logic Zero

(B)

With no propagation delays, the output Y is always logic One

(C)

With propagation delays, the output Y can have a transient logic One after X transitions from logic Zero to logic One

(D)

With propagation delays, the output Y can have a transient logic Zero after X transitions from logic One to logic Zero

Explanation

GATE→2024→CS Core→Computer Networks

Q35

MSQ[1 Mark]

TCP client P successfully establishes a connection to TCP server Q. Let N_P denote the sequence number in SYN, N_Q denote acknowledgement number in SYN ACK. Which of the following statements is/are CORRECT?

(A)

The sequence number N_P is chosen randomly by P

(B)

The sequence number N_P is always 0 for a new connection

(C)

The acknowledgement number N_Q is equal to N_P

(D)

The acknowledgement number N_Q is equal to N_P + 1

Explanation

GATE→2024→CS Core→Computer Organization and Architecture

Q36

MSQ[1 Mark]

Consider a 5-stage pipelined processor. Which of the following statements about forwarding is/are CORRECT?

(A)

In a pipelined execution, forwarding means the result from a source stage of an earlier instruction is passed on to the destination stage of a later instruction

(B)

In forwarding, data from the output of the MEM stage can be passed on to the EX stage

(C)

Forwarding helps in reducing data hazard stalls

(D)

Forwarding does not require any extra hardware...

Explanation

GATE→2024→CS Core→Computer Networks

Q37

MSQ[1 Mark]

Which of the following fields is/are modified in the IP header of a packet going out of a network address translation (NAT) device from an internal network to an external network?

(A)

Source IP

(B)

Destination IP

(C)

Header Checksum

(D)

Total Length

Explanation

GATE→2024→CS Core→Programming and Data Structures

Q38

NAT[1 Mark]

Evaluate expression 3 + 1 + 5 * 2 / 7 + 2 - 4 - 7 - 6 / 2 as per given operator precedence and associativity rules.

Explanation

GATE→2024→CS Core→Databases

Q39

NAT[1 Mark]

Consider relations R(A,B) and S(A,C). Total number of tuples obtained by evaluating sigma_{B<C}(R join_{R.A=S.A} S) is

Explanation

GATE→2024→CS Core→Computer Networks

Q40

MCQ[2 Marks]

Consider a network path P-Q-R between nodes P and R via router Q. Node P sends a file of size 10^6 bytes... Which one of the following options gives the time (in seconds, rounded off to 3 decimal places) at which R receives all the chunks of the file?

(A)

8.000

(B)

8.008

(C)

15.992

(D)

16.000

Explanation

GATE→2024→CS Core→Compiler Design

Q41

MCQ[2 Marks]

Consider the following syntax-directed definition (SDD)... Given 'MMLK' as the input, which one of the following options is the CORRECT value computed by the SDD (in the attribute S.val)?

(A)

45

(B)

50

(C)

(D)

Explanation

GATE→2024→CS Core→Compiler Design

Q42

MCQ[2 Marks]

Consider the following grammar G, with S as the start symbol. The grammar G has three incomplete productions denoted by (1), (2), and (3)... Which one of the following options CORRECTLY fills in the incomplete productions?

(A)

(1) S->Rf (2) T->\epsilon (3) R->cTR

(B)

(C)

(D)

Explanation

GATE→2024→CS Core→Compiler Design

Q43

MCQ[2 Marks]

Consider the following pseudo-code. Which one of the following options CORRECTLY specifies the number of basic blocks and the number of instructions in the largest basic block, respectively?

(A)

(B)

(C)

(D)

7 and 6

Explanation

GATE→2024→CS Core→Operating System

Q44

MCQ[2 Marks]

Consider the following two threads T1 and T2 that update two shared variables a and b. Assume that initially a=b=1... Which one of the following options lists all the possible combinations of values of a and b after both T1 and T2 finish execution?

(A)

(a=4, b=4); (a=3, b=3); (a=4, b=3)

(B)

(C)

(D)

Explanation

GATE→2024→CS Core→Programming and Data Structures

Q45

MCQ[2 Marks]

An array [82, 101, 90, 11, 111, 75, 33, 131, 44, 93] is heapified. Which one of the following options represents the first three elements in the heapified array?

(A)

(B)

(C)

131, 11, 93

(D)

131, 111, 90

Explanation

GATE→2024→CS Core→Algorithms

Q46

MCQ[2 Marks]

Consider the following recurrence relation: T(n) = T(sqrt(n)) + n for n >= 1, T(1) = 1. Which one of the following options is CORRECT?

(A)

T(n) = \Theta(n \log \log n)

(B)

T(n) = \Theta(n \log n)

(C)

T(n) = \Theta(n^2 \log n)

(D)

T(n) = \Theta(n^2 \log \log n)

Explanation

GATE→2024→CS Core→Programming and Data Structures

Q47

MCQ[2 Marks]

Consider a binary min-heap containing 10^5 distinct elements. Let k be the index (in the underlying array) of the maximum element stored in the heap. The number of ancestors of max element...

(A)

(B)

52

(C)

27

(D)

1

Explanation

GATE→2024→CS Core→Databases

Q48

MSQ[2 Marks]

Which of the following options is/are TRUE?

(A)

$(X,Y)\rightarrow(Z,W)$ implies $X\rightarrow(Z,W)$

(B)

$(X,Y)\rightarrow(Z,W)$ implies $(X,Y)\rightarrow Z$

(C)

$((X,Y)\rightarrow Z$ and $W\rightarrow Y)$ implies $(X,W)\rightarrow Z$

(D)

$(X\rightarrow Y$ and $Y\rightarrow Z)$ implies $X\rightarrow Z$

Explanation

GATE→2024→CS Core→Algorithms

Q49

MSQ[2 Marks]

Let G be a directed graph and T a depth first search (DFS) spanning tree in G rooted at v. Suppose T is also a breadth first search (BFS) tree in G. Which of the following statements is/are TRUE?

(A)

There are no back-edges in G with respect to the tree T

(B)

There are no cross-edges in G with respect to the tree T

(C)

There are no forward-edges in G with respect to the tree T

(D)

The only edges in G are the edges in T

Explanation

GATE→2024→CS Core→Databases

Q50

MSQ[2 Marks]

Consider the following read-write schedule S over three transactions T1, T2, and T3... Which of the following transaction schedules is/are conflict equivalent to S?

(A)

T1 T2 T3

(B)

T1 T3 T2

(C)

T3 T2 T1

(D)

T3 T1 T2

Explanation

GATE→2024→CS Core→Digital Logic

Q51

MSQ[2 Marks]

Consider F(X,Y,Z) = sum m(3,5,6,7). Which of the following is/are CORRECT?

(A)

(B)

$F(X,Y,Z)=XY+YZ+XZ$

(C)

$F(X,Y,Z)$ is independent of input Y

(D)

$F(X,Y,Z)$ is independent of input X

Explanation

GATE→2024→CS Core→Programming and Data Structures

Q52

MSQ[2 Marks]

Consider the following C function definition. Which of the following statements is/are TRUE about the above function?

(A)

If the inputs are x=20, y=10, then the return value is greater than 220

(B)

If the inputs are x=20, y=20, then the return value is greater than 2^20

(C)

If the inputs are x=20, y=10, then the return value is greater than 2^10

(D)

If the inputs are x=10, y=20, then the return value is greater than 2^20

Explanation

GATE→2024→CS Core→Theory of Computation

Q53

MSQ[2 Marks]

Consider the 5-state DFA M accepting the language L(M) over {0,1}*. Which of the following statements is/are FALSE?

(A)

States 2 and 4 are distinguishable in M

(B)

States 3 and 4 are distinguishable in M

(C)

States 2 and 5 are distinguishable in M

(D)

Any string w with n_0(w) = n_1(w) is in L(M)

Explanation

GATE→2024→CS Core→Computer Organization and Architecture

Q54

MSQ[2 Marks]

Consider two set-associative cache memory architectures: WBC (write back) and WTC (write through). Which of the following statements is/are TRUE?

(A)

A read miss in WBC never evicts a dirty block

(B)

A read miss in WTC never triggers a write back operation of a cache block to main memory

(C)

A write hit in WBC can modify the value of the dirty bit of a cache block

(D)

A write miss in WTC always writes the victim cache block to main memory before loading the missed block...

Explanation

GATE→2024→CS Core→Computer Organization and Architecture

Q55

NAT[2 Marks]

Consider a 512 GB hard disk with 32 storage surfaces. There are 4096 sectors per track and each sector holds 1024 bytes of data. The number of cylinders in the hard disk is

Explanation

GATE→2024→CS Core→Computer Organization and Architecture

Q56

NAT[2 Marks]

The baseline execution time of a program on a 2 GHz single core machine is 100 ns. 90% parallelizable. Overhead 10 ns per core. Number of cores that minimize execution time?

Explanation

GATE→2024→CS Core→Computer Organization and Architecture

Q57

NAT[2 Marks]

A given program has 25% load/store instructions. Ideal CPI = 2. 2% instruction miss rate, 8% data miss rate. Miss penalty = 100 cycles. Speedup (rounded off to two decimal places) achieved with a perfect cache is

Explanation

GATE→2024→CS Core→Operating System

Q58

NAT[2 Marks]

Consider the following code snippet using fork() and wait(). Total number of times the printf statement is executed is

Explanation

GATE→2024→CS Core→Computer Networks

Q59

NAT[2 Marks]

Consider the entries shown below in the forwarding table of an IP router... Number of packets forwarded via the next hop router R2 is

Explanation

GATE→2024→CS Core→Theory of Computation

Q60

NAT[2 Marks]

Let G be a CFG in Chomsky Normal Form with 3 terminals and 10 variables. String w = a^30 b^30 c^30 is derivable from S. Number of steps in derivation S ->* w is

Explanation

GATE→2024→CS Core→Algorithms

Q61

NAT[2 Marks]

The number of edges present in the forest generated by the DFS traversal of an undirected graph G with 100 vertices is 40. The number of connected components in G is

Explanation

GATE→2024→CS Core→Theory of Computation

Q62

NAT[2 Marks]

Consider two regular expressions over {0,1}: r = 0* + 1*, s = 01* + 10*. Total number of strings of length <= 5, which are neither in r nor in s, is

Explanation

GATE→2024→CS Core→Operating System

Q63

NAT[2 Marks]

Consider a memory management system... Physical address corresponding to virtual address 2500 is

Explanation

GATE→2024→CS Core→Digital Logic

Q64

NAT[2 Marks]

Consider a digital logic circuit consisting of three 2-to-1 multiplexers M1, M2, and M3... For inputs X1=1, X2=1, X3=0, X4=0, the number of combinations of A, B, C that give output Y=1 is

Explanation

GATE→2024→CS Core→Computer Networks

Q65

NAT[2 Marks]

Consider sending an IP datagram of size 1420 bytes... Number of fragments that would be delivered at the receiver is

Explanation