GATE CS 2024 Set 1 mock test

Question 1 of 65

MCQMultiple choice: one correct option1 markWrong answer: −1/3

If ' $\rightarrow$ ' denotes increasing order of intensity, then the meaning of the words

[dry $\rightarrow$ arid $\rightarrow$ parched] is analogous to [diet $\rightarrow$ fast $\rightarrow$ ________ ].

Which one of the given options is appropriate to fill the blank?

A

starve

B

reject

C

feast

D

deny

Question 2 of 65

MCQMultiple choice: one correct option1 markWrong answer: −1/3

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

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

Question 3 of 65

MCQMultiple choice: one correct option1 markWrong answer: −1/3

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

Question 4 of 65

MCQMultiple choice: one correct option1 markWrong answer: −1/3

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

A

21%

B

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

C

10%

D

30%

Question 5 of 65

MCQMultiple choice: one correct option1 markWrong answer: −1/3

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

A

79

B

81

C

9

D

83

Question 6 of 65

MCQMultiple choice: one correct option2 marksWrong answer: −2/3

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.

A

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

B

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

C

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

D

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

Question 7 of 65

MCQMultiple choice: one correct option2 marksWrong answer: −2/3

A rectangular paper sheet of dimensions $54\text{ cm} \times 4\text{ cm}$ 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

$4/\pi$

Question 8 of 65

MCQMultiple choice: one correct option2 marksWrong answer: −2/3

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

Pie chart of Macronutrient energy contribution: Carbohydrates 35%, Proteins 20%, Unsaturated fat 20%, Saturated fat 20%, Trans fat 5%.

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

A

44.4

B

77.8

C

100

D

3,600

Question 9 of 65

MCQMultiple choice: one correct option2 marksWrong answer: −2/3

A rectangular paper of $20\text{ cm} \times 8\text{ cm}$ 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

Question 10 of 65

MCQMultiple choice: one correct option2 marksWrong answer: −2/3

The least number of squares to be added in the figure to make $\text{AB}$ a line of symmetry is

Horizontal dashed line AB with 6 unit squares: on the left, one square above AB at column 2, one below AB at column 1, and one two rows below AB at column 2; on the right, two adjacent squares below AB and one square below the rightmost of those two.

A

6

B

4

C

5

D

7

Question 11 of 65

MCQMultiple choice: one correct option1 markWrong answer: −1/3

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

A

$\{-1, 1, 2\}$

B

$\{-2, -1, 1\}$

C

$\{0, 1\}$

D

$\{-1, 0, 1\}$

Question 12 of 65

MCQMultiple choice: one correct option1 markWrong answer: −1/3

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

A

$-1$

B

$0$

C

$1$

D

$2$

Question 13 of 65

MCQMultiple choice: one correct option1 markWrong answer: −1/3

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

$A + B$

B

$A - B$

C

$B - A$

D

$2 * B$

Question 14 of 65

MCQMultiple choice: one correct option1 markWrong answer: −1/3

Consider a permutation sampled uniformly at random from the set of all permutations of $\{1, 2, 3, \cdots, n\}$ for some $n \ge 4$ . 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?

A

The events $X$ and $Y$ are mutually exclusive

B

The events $X$ and $Y$ are independent

C

Either event $X$ or $Y$ must occur

D

Event $X$ is more likely than event $Y$

Question 15 of 65

MCQMultiple choice: one correct option1 markWrong answer: −1/3

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

Question 16 of 65

MCQMultiple choice: one correct option1 markWrong answer: −1/3

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 ?

A

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

B

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

C

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

D

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

Question 17 of 65

MCQMultiple choice: one correct option1 markWrong answer: −1/3

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

A

both $\text{O}(N)$ and $\Omega(N)$

B

$\text{O}(N)$ but not $\Omega(N)$

C

$\Omega(N)$ but not $\text{O}(N)$

D

neither $\text{O}(N)$ nor $\Omega(N)$

Question 18 of 65

MCQMultiple choice: one correct option1 markWrong answer: −1/3

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?

A

The program prints 9 as output

B

The program prints 10 as output

C

The program gets stuck in an infinite loop

D

The program prints 6 as output

Question 19 of 65

MCQMultiple choice: one correct option1 markWrong answer: −1/3

Consider the following C program:

#include <stdio.h>
void fX();
int main(){
    fX();
    return 0;}

void fX(){
    char a;
    if((a=getchar()) != '\n')
        fX();
    if(a != '\n')
        putchar(a);}

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?

A

The program will not terminate

B

The program will terminate with no output

C

The program will terminate with 4321 as output

D

The program will terminate with 1234 as output

Question 20 of 65

MCQMultiple choice: one correct option1 markWrong answer: −1/3

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?

Four ER diagrams. (i): Instructor-Teaches-Course; Course-Allocation-Classroom; Course linked to an entity Registration and to a relationship Student, and Instructor-Guides-Student (Student drawn as a relationship). (ii): Instructor-Teaches-Course; Course-Allocation-Classroom; Course-Registration (relationship) linked to an entity Projects; Instructor-Guides-Projects. (iii): Instructor-Teaches-Course; Classroom joined directly to Course by a line, with Allocation attached only to Course; Course-Registration-Student; Instructor-Guides-Student. (iv): Instructor-Teaches-Course; Course-Allocation-Classroom; Course-Registration-Student; Instructor-Guides-Student.

A

(i)

B

(ii)

C

(iii)

D

(iv)

Question 21 of 65

MCQMultiple choice: one correct option1 markWrong answer: −1/3

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

Question 22 of 65

MSQMultiple select: one or more correct options1 markNo negative marking

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

A

R can have a multi-attribute key

B

R cannot have a foreign key

C

R cannot have a composite attribute

D

R cannot have more than one candidate key

Question 23 of 65

MSQMultiple select: one or more correct options1 markNo negative marking

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?

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

$\overline{L_3}$ is not regular

D

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

Question 24 of 65

MSQMultiple select: one or more correct options1 markNo negative marking

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

Question 25 of 65

MSQMultiple select: one or more correct options1 markNo negative marking

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

Question 26 of 65

MSQMultiple select: one or more correct options1 markNo negative marking

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

A

Shift-reduce Parser

B

Predictive Parser

C

LL(1) Parser

D

LR Parser

Question 27 of 65

MSQMultiple select: one or more correct options1 markNo negative marking

Let $A$ and $B$ be two events in a probability space with $P(A) = 0.3, P(B) = 0.5$ , and $P(A \cap B) = 0.1$ . 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

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

D

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

Question 28 of 65

MSQMultiple select: one or more correct options1 markNo negative marking

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?

Combinational circuit where input X feeds directly into the top input of a 2-input AND gate and also passes through a NOT gate into the bottom input of the AND gate to produce output Y.

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

Question 29 of 65

MSQMultiple select: one or more correct options1 markNo negative marking

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?

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 $N_P + 1$

Question 30 of 65

MSQMultiple select: one or more correct options1 markNo negative marking

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?

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 input of the EX stage of the next instruction

C

Forwarding cannot prevent all pipeline stalls

D

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

Question 31 of 65

MSQMultiple select: one or more correct options1 markNo negative marking

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

Question 32 of 65

NATNumerical answer1 markNo negative marking

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 $A \times A$ to $A \cup B$ . The number of possible values of $|A|$ is __________

Your answer

A number: digits, one decimal point and an optional minus sign at the start.

Question 33 of 65

NATNumerical answer1 markNo negative marking

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 __________

Your answer

A number: digits, one decimal point and an optional minus sign at the start.

Question 34 of 65

NATNumerical answer1 markNo negative marking

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

Your answer

A number: digits, one decimal point and an optional minus sign at the start.

Question 35 of 65

NATNumerical answer1 markNo negative marking

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

Relation R(A, B)
R.A	R.B
10	20
20	30
30	40
30	50
50	95

Relation S(A, C)
S.A	S.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 _________

Your answer

A number: digits, one decimal point and an optional minus sign at the start.

Question 36 of 65

MCQMultiple choice: one correct option2 marksWrong answer: −2/3

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 to R via this path by splitting the file into chunks of $10^3$ 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 $10^6$ 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?

A

8.000

B

8.008

C

15.992

D

16.000

Question 37 of 65

MCQMultiple choice: one correct option2 marksWrong answer: −2/3

Consider the following syntax-directed definition (SDD).

\begin{aligned} S &\rightarrow DHTU && \{ S.val = D.val + H.val + T.val + U.val; \} \\ D &\rightarrow \text{"M"} D_1 && \{ D.val = 5 + D_1.val; \} \\ D &\rightarrow \epsilon && \{ D.val = -5; \} \\ H &\rightarrow \text{"L"} H_1 && \{ H.val = 5 * 10 + H_1.val; \} \\ H &\rightarrow \epsilon && \{ H.val = -10; \} \\ T &\rightarrow \text{"C"} T_1 && \{ T.val = 5 * 100 + T_1.val; \} \\ T &\rightarrow \epsilon && \{ T.val = -5; \} \\ U &\rightarrow \text{"K"} && \{ U.val = 5; \} \end{aligned}

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

55

D

65

Question 38 of 65

MCQMultiple choice: one correct option2 marksWrong answer: −2/3

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

\begin{aligned} S &\rightarrow daT \mid (1) \\ T &\rightarrow aS \mid bT \mid (2) \\ R &\rightarrow (3) \mid \epsilon \end{aligned}

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

\text{FIRST}(S) = \{c, d, f\},\quad \text{FIRST}(T) = \{a, b, \epsilon\},\quad \text{FIRST}(R) = \{c, \epsilon\}

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

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

A

(1) $S \rightarrow Rf$ (2) $T \rightarrow \epsilon$ (3) $R \rightarrow cTR$

B

(1) $S \rightarrow fR$ (2) $T \rightarrow \epsilon$ (3) $R \rightarrow cTR$

C

(1) $S \rightarrow fR$ (2) $T \rightarrow cT$ (3) $R \rightarrow cR$

D

(1) $S \rightarrow Rf$ (2) $T \rightarrow cT$ (3) $R \rightarrow cR$

Question 39 of 65

MCQMultiple choice: one correct option2 marksWrong answer: −2/3

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 ?

A

6 and 6

B

6 and 7

C

7 and 7

D

7 and 6

Question 40 of 65

MCQMultiple choice: one correct option2 marksWrong answer: −2/3

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?

A

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

B

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

C

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

D

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

Question 41 of 65

MCQMultiple choice: one correct option2 marksWrong answer: −2/3

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

82, 90, 101

B

82, 11, 93

C

131, 11, 93

D

131, 111, 90

Question 42 of 65

MCQMultiple choice: one correct option2 marksWrong answer: −2/3

Consider the following recurrence relation:

T(n) = \begin{cases} \sqrt{n}T(\sqrt{n}) + n & \text{for } n \ge 1, \\ 1 & \text{for } n = 1. \end{cases}

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

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

Question 43 of 65

MCQMultiple choice: one correct option2 marksWrong answer: −2/3

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

A

53

B

52

C

27

D

1

Question 44 of 65

MSQMultiple select: one or more correct options2 marksNo negative marking

The symbol $\rightarrow$ indicates functional dependency in the context of a relational database. 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

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

D

$(X \rightarrow Y \text{ and } Y \rightarrow Z)$ implies $X \rightarrow Z$

Question 45 of 65

MSQMultiple select: one or more correct options2 marksNo negative marking

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 $T$ ?

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 $T$

Question 46 of 65

MSQMultiple select: one or more correct options2 marksNo negative marking

Consider the following read-write schedule $S$ over three transactions $T_1, T_2$ , and $T_3$ , where the subscripts in the schedule indicate transaction IDs:

S: r_1(z);\; w_1(z);\; r_2(x);\; r_3(y);\; w_3(y);\; r_2(y);\; w_2(x);\; w_2(y);

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

A

$T_1 T_2 T_3$

B

$T_1 T_3 T_2$

C

$T_3 T_2 T_1$

D

$T_3 T_1 T_2$

Question 47 of 65

MSQMultiple select: one or more correct options2 marksNo negative marking

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

Which of the following statements is/are CORRECT?

A

$F(X, Y, Z) = \prod(0, 1, 2, 4)$

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 $X$

Question 48 of 65

MSQMultiple select: one or more correct options2 marksNo negative marking

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?

A

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

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 less than $2^{10}$

D

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

Question 49 of 65

MSQMultiple select: one or more correct options2 marksNo negative marking

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

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 of these vectors

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

Question 50 of 65

MSQMultiple select: one or more correct options2 marksNo negative marking

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

5-state DFA M with start and accepting state 1, upper branch states 2 and 3, and lower branch states 4 and 5.

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 $L(M)$

Question 51 of 65

MSQMultiple select: one or more correct options2 marksNo negative marking

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?

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 $k$

Question 52 of 65

MSQMultiple select: one or more correct options2 marksNo negative marking

Consider the operators $\diamond$ and $\square$ defined by $a \diamond b = a + 2b, \; a \square b = ab$ , for positive integers. Which of the following statements is/are TRUE?

A

Operator $\diamond$ obeys the associative law

B

Operator $\square$ obeys the associative law

C

Operator $\diamond$ over the operator $\square$ obeys the distributive law

D

Operator $\square$ over the operator $\diamond$ obeys the distributive law

Question 53 of 65

MSQMultiple select: one or more correct options2 marksNo negative marking

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

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 to the cache

Question 54 of 65

NATNumerical answer2 marksNo negative marking

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 _________

Your answer

A number: digits, one decimal point and an optional minus sign at the start.

Question 55 of 65

NATNumerical answer2 marksNo negative marking

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 ________

Your answer

A number: digits, one decimal point and an optional minus sign at the start.

Question 56 of 65

NATNumerical answer2 marksNo negative marking

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 _________

Your answer

A number: digits, one decimal point and an optional minus sign at the start.

Question 57 of 65

NATNumerical answer2 marksNo negative marking

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 _______

Your answer

A number: digits, one decimal point and an optional minus sign at the start.

Question 58 of 65

NATNumerical answer2 marksNo negative marking

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 _______

Your answer

A number: digits, one decimal point and an optional minus sign at the start.

Question 59 of 65

NATNumerical answer2 marksNo negative marking

Let $G = (V, \Sigma, S, P)$ be a context-free grammar in Chomsky Normal Form with $\Sigma = \{a, b, c\}$ and $V$ containing 10 variable symbols including the start symbol $S$ . The string $w = a^{30}b^{30}c^{30}$ is derivable from $S$ . The number of steps (application of rules) in the derivation $S \rightarrow^* w$ is _________

Your answer

A number: digits, one decimal point and an optional minus sign at the start.

Question 60 of 65

NATNumerical answer2 marksNo negative marking

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 _________

Your answer

A number: digits, one decimal point and an optional minus sign at the start.

Question 61 of 65

NATNumerical answer2 marksNo negative marking

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 _________

Your answer

A number: digits, one decimal point and an optional minus sign at the start.

Question 62 of 65

NATNumerical answer2 marksNo negative marking

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 _________

Your answer

A number: digits, one decimal point and an optional minus sign at the start.

Question 63 of 65

NATNumerical answer2 marksNo negative marking

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 _________

Your answer

A number: digits, one decimal point and an optional minus sign at the start.

Question 64 of 65

NATNumerical answer2 marksNo negative marking

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.

Three 2-to-1 multiplexers M1, M2, and M3. M1 has inputs 0=X1, 1=X2, select S1=A, and output Q1 feeding input 0 of M3. M2 has inputs 0=X3, 1=X4, select S2=B, and output Q2 feeding input 1 of M3. M3 has select S3=C and output Y.

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 _________

Your answer

A number: digits, one decimal point and an optional minus sign at the start.

Question 65 of 65

NATNumerical answer2 marksNo negative marking

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 ________

Your answer

A number: digits, one decimal point and an optional minus sign at the start.

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