Turing Prep | Previous Year Questions | GATE CS/IT - 2024 SET

Question : 1

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?

starve

reject

feast

deny

Correct Answer : A

Question Type : MCQ

Max Marks : 1

Negative Marks : 0.33

Question : 2

If two distinct non-zero real variables 𝑥 and 𝑦 are such that (𝑥 + 𝑦) is proportional to (𝑥 − 𝑦) then the value of $\frac{x}{y}$

depends on 𝑥𝑦

depends only on 𝑥 and not on 𝑦

depends only on 𝑦 and not on 𝑥

is a constant

Correct Answer : D

Question Type : MCQ

Max Marks : 1

Negative Marks : 0.33

Question : 3

Consider the following sample of numbers:

9, 18, 11, 14, 15, 17, 10, 69, 11, 13

The median of the sample is

13.5

14

11

18.7

Correct Answer : A

Question Type : MCQ

Max Marks : 1

Negative Marks : 0.33

Question : 4

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

21%

$14 \frac{2}{7}\% $

10%

30%

Correct Answer : C

Question Type : MCQ

Max Marks : 1

Negative Marks : 0.33

Question : 5

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 $\frac{{p^4 + q^4}}{{p^2q^2}} $ is

79

81

9

83

Correct Answer : A

Question Type : MCQ

Max Marks : 1

Negative Marks : 0.33

Question : 6

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

Steve was advised to keep his head ___(i)___before heading ___(ii)___to bat; for, while he had a head ___(iii)___batting, he could only do so with a cool head ___(iv)___his shoulders.

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

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

(i) down (ii) out (iii) for (iv) on

(i) on (ii) out (iii) on (iv) for

Correct Answer : C

Question Type : MCQ

Max Marks : 2

Negative Marks : 0.67

Question : 7

A rectangular paper sheet of dimensions 54 cm × 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

1/π

2/π

3/π

4/π

Correct Answer : A

Question Type : MCQ

Max Marks : 2

Negative Marks : 0.67

Question : 8

The pie chart presents the percentage contribution of different macronutrients to a typical 2,000 kcal diet of a person.

The typical energy density (kcal/g) of these macronutrients is given in the table.

Macronutrient	Energy density (kcal/g)
Carbohydrates	4
Proteins	4
Unsaturated fat	9
Saturated fat	9
Trans fat	9

The total fat (all three types), in grams, this person consumes is

44.4

78.4

100

3,600

Correct Answer : C

Question Type : MCQ

Max Marks : 2

Negative Marks : 0.67

Question : 9

A rectangular paper of 20 cm × 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

18

24

20

21

Correct Answer : A

Question Type : MCQ

Max Marks : 2

Negative Marks : 0.67

Question : 10

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

6

4

5

7

Correct Answer : A

Question Type : MCQ

Max Marks : 2

Negative Marks : 0.67

Question : 11

Let 𝑓: ℝ → ℝ be a function such that 𝑓(𝑥) = max{𝑥, $x^3$ }, 𝑥 ∈ ℝ , where ℝ is the set of all real numbers. The set of all points where 𝑓(𝑥) is NOT differentiable is

{−1, 1, 2}

{−2, −1, 1}

{0, 1}

{−1, 0, 1}

Correct Answer : D

Question Type : MCQ

Max Marks : 1

Negative Marks : 0.33

Question : 12

The product of all eigenvalues of the matrix $\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \\ \end{bmatrix} $ is

−1

0

1

2

Correct Answer : B

Question Type : MCQ

Max Marks : 1

Negative Marks : 0.33

Question : 13

Consider a system that uses 5 bits for representing signed integers in 2’s complement format. In this system, two integers 𝐴 and 𝐵 are represented as 𝐴=01010 and 𝐵=11010. Which one of the following operations will result in either an arithmetic overflow or an arithmetic underflow?

A + B

A - B

B - A

2 * B

Correct Answer : B

Question Type : MCQ

Max Marks : 1

Negative Marks : 0.33

Question : 14

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

The events 𝑋 and 𝑌 are mutually exclusive

The events 𝑋 and 𝑌 are independent

Either event 𝑋 or 𝑌 must occur

Event 𝑋 is more likely than event 𝑌

Correct Answer : B

Question Type : MCQ

Max Marks : 1

Negative Marks : 0.33

Question : 15

Which one of the following statements is FALSE?

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

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

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

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

Correct Answer : C

Question Type : MCQ

Max Marks : 1

Negative Marks : 0.33

Question : 16

A user starts browsing a webpage hosted at a remote server. The browser opens a single TCP connection to fetch the entire webpage from the server. The webpage consists of a top-level index page with multiple embedded image objects. Assume that all caches (e.g., DNS cache, browser cache) are all initially empty. The following packets leave the user’s computer in some order.

(i) HTTP GET request for the index page

(ii) DNS request to resolve the web server’s name to its IP address

(iii) HTTP GET request for an image object

(iv) TCP SYN to open a connection to the web server

Which one of the following is the CORRECT chronological order (earliest in time to latest) of the packets leaving the computer ?

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

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

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

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

Correct Answer : C

Question Type : MCQ

Max Marks : 1

Negative Marks : 0.33

Question : 17

Given an integer array of size N, we want to check if the array is sorted (in either ascending or descending order). An algorithm solves this problem by making a single pass through the array and comparing each element of the array only with its adjacent elements. The worst-case time complexity of this algorithm is

both Ο(𝑁) and Ω(𝑁)

Ο(𝑁) but not Ω(𝑁)

Ω(𝑁) but not Ο(𝑁)

neither Ο(𝑁) nor Ω(𝑁)

Correct Answer : A

Question Type : MCQ

Max Marks : 1

Negative Marks : 0.33

Question : 18

Consider the following C program:

#include <stdio.h>

int main() {
int a = 6;
int b = 0;

while (a < 10) {
a = a / 12 + 1;
a += b;
}

printf("%d", a);

return 0;
}

Which one of the following statements is CORRECT?

The program prints 9 as output

The program prints 10 as output

The program gets stuck in an infinite loop

The program prints 6 as output

Correct Answer : C

Question Type : MCQ

Max Marks : 1

Negative Marks : 0.33

Question : 19

Consider the following C program:

Assume that the input to the program from the command line is 1234 followed by a newline character. Which one of the following statements is CORRECT?

The program will not terminate

The program will terminate with no output

The program will terminate with 4321 as output

The program will terminate with 1234 as output

Correct Answer : C

Question Type : MCQ

Max Marks : 1

Negative Marks : 0.33

Question : 20

Let S be the specification: "Instructors teach courses. Students register for courses. Courses are allocated classrooms. Instructors guide students." Which one of the following ER diagrams CORRECTLY represents S?

(i)

(ii)

(iii)

(iv)

Correct Answer : D

Question Type : MCQ

Max Marks : 1

Negative Marks : 0.33

Question : 21

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

Only the root node

All leaf nodes

All internal nodes

Only the leftmost leaf node

Correct Answer : A

Question Type : MCQ

Max Marks : 1

Negative Marks : 0.33

Question : 22

Which of the following statements about a relation R in first normal form (1NF) is/are TRUE ?

R can have a multi-attribute key

R cannot have a foreign key

R cannot have a composite attribute

R cannot have more than one candidate key

Correct Answer : AC

Question Type : MSQ

Max Marks : 1

Negative Marks : 0

Question : 23

Let $L_1 $, $L_2 $ be two regular languages and $L_3 $a language which is not regular. Which of the following statements is/are always TRUE?

$L_1 = L_2 $ if and only if $ {L_1 \cap \overline{L_2}} = \text{𝜙}$

𝐿1 ∪ 𝐿3 is not regular

$\overline{L_3}$ is not regular

$\overline{L_1} ∪ \overline{L_2}$ is regular

Correct Answer : CD

Question Type : MSQ

Max Marks : 1

Negative Marks : 0

Question : 24

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

Threads can only be implemented in kernel space

Each thread has its own file descriptor table for open files

All the threads belonging to a process share a common stack

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

Correct Answer : D

Question Type : MSQ

Max Marks : 1

Negative Marks : 0

Question : 25

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

Running to Ready

Waiting to Running

Ready to Waiting

Running to Terminated

Correct Answer : BC

Question Type : MSQ

Max Marks : 1

Negative Marks : 0

Question : 26

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

Shift-reduce Parser

Predictive Parser

LL(1) Parser

LR Parser

Correct Answer : AD

Question Type : MSQ

Max Marks : 1

Negative Marks : 0

Question : 27

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

The two events 𝐴 and 𝐵 are independent

𝑃(𝐴 ∪ 𝐵) = 0.7

$P(A \cap B^c) $ = 0.2, where $B^c$ is the complement of the event B

$P(A^c \cap B^c) $ = 0.4, where $A^c$ and $B^c$ are the complements of the events 𝐴 and 𝐵, respectively

Correct Answer : BC

Question Type : MSQ

Max Marks : 1

Negative Marks : 0

Question : 28

Consider the circuit shown below where the gates may have propagation delays. Assume that all signal transitions occur instantaneously and that wires have no delays. Which of the following statements about the circuit is/are CORRECT?.

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

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

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

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

Correct Answer : AC

Question Type : MSQ

Max Marks : 1

Negative Marks : 0

Question : 29

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

The sequence number $N_P$ is chosen randomly by P

The sequence number $N_P$ is always 0 for a new connection

The acknowledgement number $N_Q$ is equal to $N_P $

The acknowledgement number $N_Q$ is equal to $N_P$ + 1

Correct Answer : AD

Question Type : MSQ

Max Marks : 1

Negative Marks : 0

Question : 30

Consider a 5-stage pipelined processor with Instruction Fetch (IF), Instruction Decode (ID), Execute (EX), Memory Access (MEM), and Register Writeback (WB) stages. Which of the following statements about forwarding is/are CORRECT?

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

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

Forwarding cannot prevent all pipeline stalls

Forwarding does not require any extra hardware to retrieve the data from the pipeline stages

Correct Answer : ABC

Question Type : MSQ

Max Marks : 1

Negative Marks : 0

Question : 31

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?

Source IP

Destination IP

Header Checksum

Total Length

Correct Answer : AC

Question Type : MSQ

Max Marks : 1

Negative Marks : 0

Question : 32

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 × 𝐴 to 𝐴 ∪ 𝐵. The number of possible values of |𝐴| is __________

Correct Answer : 2

Question Type : NAT

Max Marks : 1

Negative Marks : 0

Question : 33

Consider the operator precedence and associativity rules for the integer arithmetic operators given in the table below.

Operator	Precedence	Associativity
+	Highest	Left
-	High	Right
*	Medium	Right
/	Low	Right

The value of the expression 3 + 1 + 5 ∗ 2 / 7 + 2 − 4 − 7 − 6 / 2 as per the above rules is __________

Correct Answer : 6

Question Type : NAT

Max Marks : 1

Negative Marks : 0

Question : 34

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

Correct Answer : 16

Question Type : NAT

Max Marks : 1

Negative Marks : 0

Question : 35

Consider the following two relations, R(A,B) and S(A,C):

R
A	B
10	20
20	30
30	40
30	50
30	95

S
A	C
10	90
30	45
40	80

The total number of tuples obtained by evaluating the following expression

$\sigma_{B < C}(R \bowtie_{R.A = S.A} S) $

is _________

Correct Answer : 2

Question Type : NAT

Max Marks : 1

Negative Marks : 0

Question : 36

Consider a network path P—Q—R between nodes P and R via router Q. Node P sends a file of size 106 bytes to R via this path by splitting the file into chunks of 103 bytes each. Node P sends these chunks one after the other without any wait time between the successive chunk transmissions. Assume that the size of extra headers added to these chunks is negligible, and that the chunk size is less than the MTU.

Each of the links P—Q and Q—R has a bandwidth of 106 bits/sec, and negligible propagation latency. Router Q immediately transmits every packet it receives from P to R, with negligible processing and queueing delays. Router Q can simultaneously receive on link P—Q and transmit on link Q—R.

Assume P starts transmitting the chunks at time 𝑡 = 0. 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?

8.000

8.008

15.992

16.000

Correct Answer : B

Question Type : MCQ

Max Marks : 2

Negative Marks : 0.67

Question : 37

Consider the following syntax-directed definition (SDD).

𝑆 → 𝐷𝐻𝑇U	{ 𝑆. 𝑣𝑎𝑙 = 𝐷. 𝑣𝑎𝑙 + 𝐻. 𝑣𝑎𝑙 + 𝑇. 𝑣𝑎𝑙 + 𝑈. 𝑣𝑎𝑙; }
𝐷 → "M"$D_1$	{ 𝐷. 𝑣𝑎𝑙 = 5 + $D_1$. 𝑣𝑎𝑙; }
𝐷 → 𝜖	{ 𝐷. 𝑣𝑎𝑙 = −5; }
𝐻 → "L"$H_1$	{ 𝐻. 𝑣𝑎𝑙 = 5 ∗ 10 +$H_1$. 𝑣𝑎𝑙; }
𝐻 → 𝜖	{ 𝐻. 𝑣𝑎𝑙 = −10; }
𝑇 → "C"$T_1$	{ 𝑇. 𝑣𝑎𝑙 = 5 ∗ 100 + $T_1$. 𝑣𝑎𝑙; }
𝑇 → 𝜖	{ 𝑇. 𝑣𝑎𝑙 = −5; }
𝑈 → "K"	{ 𝑈. 𝑣𝑎𝑙 = 5; }

Given "MMLK" as the input, which one of the following options is the CORRECT value computed by the SDD (in the attribute 𝑆. 𝑣𝑎𝑙)?

45

50

55

65

Correct Answer : A

Question Type : MCQ

Max Marks : 2

Negative Marks : 0.67

Question : 38

Consider the following grammar 𝐺, with 𝑆 as the start symbol. The grammar 𝐺 has three incomplete productions denoted by (1), (2), and (3).

𝑆 → 𝑑𝑎𝑇 | (1)

𝑇 → 𝑎𝑆 | 𝑏𝑇 | (2)

𝑅 → (3) | 𝜖

The set of terminals is {𝑎, 𝑏, 𝑐, 𝑑, 𝑓}. The FIRST and FOLLOW sets of the different non-terminals are as follows

FIRST(𝑆) = {𝑐, 𝑑, 𝑓}, FIRST(𝑇) = {𝑎, 𝑏, 𝜖}, FIRST(𝑅) = {𝑐, 𝜖}

FOLLOW(𝑆) = FOLLOW(𝑇) = {𝑐, 𝑓, $}, FOLLOW(𝑅) = {𝑓}

Which one of the following options CORRECTLY fills in the incomplete productions?

(1) 𝑆 → 𝑅𝑓 (2) 𝑇 → 𝜖 (3) 𝑅 → 𝑐𝑇𝑅

(1) 𝑆 → 𝑓𝑅 (2) 𝑇 → 𝜖 (3) 𝑅 → 𝑐𝑇𝑅

(1) 𝑆 → 𝑓𝑅 (2) 𝑇 → 𝑐𝑇 (3) 𝑅 → 𝑐𝑅

(1) 𝑆 → 𝑅𝑓 (2) 𝑇 → 𝑐𝑇 (3) 𝑅 → 𝑐𝑅

Correct Answer : A

Question Type : MCQ

Max Marks : 2

Negative Marks : 0.67

Question : 39

Consider the following pseudo-code.

𝐿1: 𝑡1 = −1

𝐿2: 𝑡2 = 0

𝐿3: 𝑡3 = 0

𝐿4: 𝑡4 = 4 ∗ 𝑡3

𝐿5: 𝑡5 = 4 ∗ 𝑡2

𝐿6: 𝑡6 = 𝑡5 ∗ 𝑀

𝐿7: 𝑡7 = 𝑡4 + 𝑡6

𝐿8: 𝑡8 = 𝑎[𝑡7]

𝐿9: if 𝑡8 <= 𝑚𝑎𝑥 goto 𝐿11

𝐿10: 𝑡1 = 𝑡8

𝐿11: 𝑡3 = 𝑡3 + 1

𝐿12: if 𝑡3 < 𝑀 goto 𝐿4

𝐿13: 𝑡2 = 𝑡2 + 1

𝐿14: if 𝑡2 < 𝑁 goto 𝐿3

𝐿15: 𝑚𝑎𝑥 = 𝑡1

Which one of the following options CORRECTLY specifies the number of basic

blocks and the number of instructions in the largest basic block, respectively ?

6 and 6

6 and 7

7 and 7

7 and 6

Correct Answer : D

Question Type : MCQ

Max Marks : 2

Negative Marks : 0.67

Question : 40

Consider the following two threads T1 and T2 that update two shared variables a and b. Assume that initially a = b = 1. Though context switching between threads can happen at any time, each statement of T1 or T2 is executed atomically without interruption. T1 T2 a = a + 1; b = 2 * b; b = b + 1; a = 2 * a; Which one of the following options lists all the possible combinations of values of a and b after both T1 and T2 finish execution?

T1 T2

a = a + 1; b = 2 * b;

b = b + 1; a = 2 * a;

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

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

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

(a = 2, b = 2); (a = 2, b = 3); (a = 3, b = 4)

Correct Answer : A

Question Type : MCQ

Max Marks : 2

Negative Marks : 0.67

Question : 41

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?

82, 90, 101

82, 11, 93

131, 11, 93

131, 111, 90

Correct Answer : D

Question Type : MCQ

Max Marks : 2

Negative Marks : 0.67

Question : 42

Consider the following recurrence relation:

$T(n) = \begin{cases} \sqrt{n} \cdot T(\sqrt{n}) + n & \text{for } n \geq 1 \\ 1 & \text{for } n = 1 \end{cases} $

Which one of the following options is CORRECT?

𝑇(𝑛) = Θ(𝑛 log log 𝑛)

𝑇(𝑛) = Θ(𝑛 log 𝑛)

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

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

Correct Answer : A

Question Type : MCQ

Max Marks : 2

Negative Marks : 0.67

Question : 43

Consider a binary min-heap containing 105 distinct elements. Let 𝑘 be the index (in the underlying array) of the maximum element stored in the heap. The number of possible values of 𝑘 is

53

52

27

1

Correct Answer : A

Question Type : MCQ

Max Marks : 2

Negative Marks : 0.67

Question : 44

The symbol → indicates functional dependency in the context of a relational database. Which of the following options is/are TRUE?

(𝑋, 𝑌) → (𝑍, 𝑊) implies 𝑋 → (𝑍, 𝑊)

(𝑋, 𝑌) → (𝑍, 𝑊) implies (𝑋, 𝑌) → 𝑍

((𝑋, 𝑌) → 𝑍 and 𝑊 → 𝑌) implies (𝑋, 𝑊) → 𝑍

(𝑋 → 𝑌 and 𝑌 → 𝑍) implies 𝑋 → 𝑍

Correct Answer : BCD

Question Type : MSQ

Max Marks : 2

Negative Marks : 0

Question : 45

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

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

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

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

The only edges in 𝐺 are the edges in 𝑇

Correct Answer : C

Question Type : MSQ

Max Marks : 2

Negative Marks : 0

Question : 46

Consider the following read-write schedule 𝑆 over three transactions 𝑇1, 𝑇2, and 𝑇3, where the subscripts in the schedule indicate transaction IDs:

𝑆: 𝑟1(𝑧); 𝑤1(𝑧); 𝑟2(𝑥); 𝑟3(𝑦); 𝑤3(𝑦); 𝑟2(𝑦); 𝑤2(𝑥); 𝑤2(𝑦);

Which of the following transaction schedules is/are conflict equivalent to 𝑆 ?

$T_1 T_2 T_3$

$T_1 T_3 T_2$

$T_3 T_2 T_1$

$T_3 T_1 T_2$

Correct Answer : BCD

Question Type : MSQ

Max Marks : 2

Negative Marks : 0

Question : 47

Consider a Boolean expression given by 𝐹(𝑋, 𝑌, 𝑍) = ∑(3,5,6,7).

Which of the following statements is/are CORRECT?

𝐹(𝑋, 𝑌, 𝑍) = Π(0,1,2,4)

𝐹(𝑋, 𝑌, 𝑍) = 𝑋𝑌 + 𝑌𝑍 +𝑋𝑍

𝐹(𝑋, 𝑌, 𝑍) is independent of input 𝑌

𝐹(𝑋, 𝑌, 𝑍) is independent of input 𝑋

Correct Answer : AB

Question Type : MSQ

Max Marks : 2

Negative Marks : 0

Question : 48

Consider the following C function definition.

                int f(int x, int y) {
                for (int i = 0; i < y; i++) {
                x = x + x + y;
                }
                return x;
                }

Which of the following statements is/are TRUE about the above function?

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

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

If the inputs are x=20, y=10, then the return value is less than 2¹⁰

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

Correct Answer : BD

Question Type : MSQ

Max Marks : 2

Negative Marks : 0

Question : 49

Let 𝐴 be any 𝑛 × 𝑚 matrix, where 𝑚 > 𝑛. Which of the following statements is/are TRUE about the system of linear equations 𝐴𝑥 = 0 ?

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

There exist 𝑚 − 𝑛 linearly independent vectors such that every solution is a linear combination of these vectors

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

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

Correct Answer : A

Question Type : MSQ

Max Marks : 2

Negative Marks : 0

Question : 50

Consider the 5-state DFA 𝑀 accepting the language 𝐿(𝑀) ⊂ (0 + 1)^∗shown below. For any string 𝑤 ∈ (0 + 1)^∗ let $n_0$(𝑤) be the number of 0 ′ 𝑠 in 𝑤 and $n_1$(𝑤) be the number of 1′𝑠 in 𝑤.

Which of the following statements is/are FALSE?

States 2 and 4 are distinguishable in 𝑀

States 3 and 4 are distinguishable in 𝑀

States 2 and 5 are distinguishable in 𝑀

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

Correct Answer : BC

Question Type : MSQ

Max Marks : 2

Negative Marks : 0

Question : 51

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

𝐺 contains a complete subgraph with 𝑘 vertices

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

𝐺 contains at least 𝑘(𝑘 − 1)/2 edges

𝐺 contains a vertex of degree at least 𝑘

Correct Answer : BC

Question Type : MSQ

Max Marks : 2

Negative Marks : 0

Question : 52

Consider the operators ◊ and □ defined by 𝑎 ◊ 𝑏 = 𝑎 + 2𝑏, 𝑎□𝑏 = 𝑎𝑏, for positive integers. Which of the following statements is/are TRUE?

Operator ◊ obeys the associative law

Operator □ obeys the associative law

Operator ◊ over the operator □ obeys the distributive law

Operator □ over the operator ◊ obeys the distributive law

Correct Answer : BD

Question Type : MSQ

Max Marks : 2

Negative Marks : 0

Question : 53

Consider two set-associative cache memory architectures: WBC, which uses the write back policy, and WTC, which uses the write through policy. Both of them use the LRU (Least Recently Used) block replacement policy. The cache memory is connected to the main memory. Which of the following statements is/are TRUE?

A read miss in WBC never evicts a dirty block

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

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

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

Correct Answer : BC

Question Type : MSQ

Max Marks : 2

Negative Marks : 0

Question : 54

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 _________

Correct Answer : 4096

Question Type : NAT

Max Marks : 2

Negative Marks : 0

Question : 55

The baseline execution time of a program on a 2 GHz single core machine is 100 nanoseconds (ns). The code corresponding to 90% of the execution time can be fully parallelized. The overhead for using an additional core is 10 ns when running on a multicore system. Assume that all cores in the multicore system run their share of the parallelized code for an equal amount of time.

The number of cores that minimize the execution time of the program is ________

Correct Answer : 3

Question Type : NAT

Max Marks : 2

Negative Marks : 0

Question : 56

A given program has 25% load/store instructions. Suppose the ideal CPI (cycles per instruction) without any memory stalls is 2. The program exhibits 2% miss rate on instruction cache and 8% miss rate on data cache. The miss penalty is 100 cycles. The speedup (rounded off to two decimal places) achieved with a perfect cache (i.e., with NO data or instruction cache misses) is _________

Correct Answer : 3.00 to 3.00

Question Type : NAT

Max Marks : 2

Negative Marks : 0

Question : 57

Consider the following code snippet using the fork() and wait() system calls. Assume that the code compiles and runs correctly, and that the system calls run successfully without any errors.

int x = 3;

while(x > 0) {

fork();

printf("hello");

wait(NULL);

x--;

}

The total number of times the printf statement is executed is _______

Correct Answer : 14

Question Type : NAT

Max Marks : 2

Negative Marks : 0

Question : 58

Consider the entries shown below in the forwarding table of an IP router. Each entry consists of an IP prefix and the corresponding next hop router for packets whose destination IP address matches the prefix. The notation “/N” in a prefix indicates a subnet mask with the most significant N bits set to 1.

Prefix	Next hop router
10.1.1.0/24	R1
10.1.1.128/25	R2
10.1.1.64/26	R3
10.1.1.192/26	R4

This router forwards 20 packets each to 5 hosts. The IP addresses of the hosts are 10.1.1.16, 10.1.1.72, 10.1.1.132, 10.1.1.191, and 10.1.1.205 . The number of packets forwarded via the next hop router R2 is _______

Correct Answer : 40

Question Type : NAT

Max Marks : 2

Negative Marks : 0

Question : 59

Let 𝐺 = (𝑉, Σ, 𝑆, 𝑃) be a context-free grammar in Chomsky Normal Form with Σ = {𝑎, 𝑏, 𝑐} and 𝑉 containing 10 variable symbols including the start symbol 𝑆. The string 𝑤 = 𝑎³⁰𝑏³⁰𝑐³⁰ is derivable from 𝑆. The number of steps (application of rules) in the derivation 𝑆 →^∗𝑤 is _________

Correct Answer : 179

Question Type : NAT

Max Marks : 2

Negative Marks : 0

Question : 60

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 _________

Correct Answer : 60

Question Type : NAT

Max Marks : 2

Negative Marks : 0

Question : 61

Consider the following two regular expressions over the alphabet {0,1}:

𝑟 = 0^∗ + 1^∗

𝑠 = 01^∗ + 10^∗

The total number of strings of length less than or equal to 5, which are neither in 𝑟 nor in 𝑠, is _________

Correct Answer : 44

Question Type : NAT

Max Marks : 2

Negative Marks : 0

Question : 62

Consider a memory management system that uses a page size of 2 KB. Assume that both the physical and virtual addresses start from 0. Assume that the pages 0, 1, 2, and 3 are stored in the page frames 1, 3, 2, and 0, respectively. The physical address (in decimal format) corresponding to the virtual address 2500 (in decimal format) is _________

Correct Answer : 6596

Question Type : NAT

Max Marks : 2

Negative Marks : 0

Question : 63

A bag contains 10 red balls and 15 blue balls. Two balls are drawn randomly without replacement. Given that the first ball drawn is red, the probability (rounded off to 3 decimal places) that both balls drawn are red is _________

Correct Answer : 0.370 to 0.380

Question Type : NAT

Max Marks : 2

Negative Marks : 0

Question : 64

Consider a digital logic circuit consisting of three 2-to-1 multiplexers M1, M2, and M3 as shown below. X1 and X2 are inputs of M1. X3 and X4 are inputs of M2. A, B, and C are select lines of M1, M2, and M3, respectively.

For an instance of inputs X1=1, X2=1, X3=0, and X4=0, the number of combinations of A, B, C that give the output Y=1 is _________

Correct Answer : 4

Question Type : NAT

Max Marks : 2

Negative Marks : 0

Question : 65

Consider sending an IP datagram of size 1420 bytes (including 20 bytes of IP header) from a sender to a receiver over a path of two links with a router between them. The first link (sender to router) has an MTU (Maximum Transmission Unit) size of 542 bytes, while the second link (router to receiver) has an MTU size of 360 bytes. The number of fragments that would be delivered at the receiver is ________

Correct Answer : 6

Question Type : NAT

Max Marks : 2

Negative Marks : 0

𝑆 → 𝐷𝐻𝑇U	{ 𝑆. 𝑣𝑎𝑙 = 𝐷. 𝑣𝑎𝑙 + 𝐻. 𝑣𝑎𝑙 + 𝑇. 𝑣𝑎𝑙 + 𝑈. 𝑣𝑎𝑙; }
𝐷 → "M"\(D_1\)	{ 𝐷. 𝑣𝑎𝑙 = 5 + \(D_1\). 𝑣𝑎𝑙; }
𝐷 → 𝜖	{ 𝐷. 𝑣𝑎𝑙 = −5; }
𝐻 → "L"\(H_1\)	{ 𝐻. 𝑣𝑎𝑙 = 5 ∗ 10 +\(H_1\). 𝑣𝑎𝑙; }
𝐻 → 𝜖	{ 𝐻. 𝑣𝑎𝑙 = −10; }
𝑇 → "C"\(T_1\)	{ 𝑇. 𝑣𝑎𝑙 = 5 ∗ 100 + \(T_1\). 𝑣𝑎𝑙; }
𝑇 → 𝜖	{ 𝑇. 𝑣𝑎𝑙 = −5; }
𝑈 → "K"	{ 𝑈. 𝑣𝑎𝑙 = 5; }

GATE CS/IT - 2024 SET - 1

Prefix

Next hop router