GATE 2025 Question Paper Computer Science and Information Technology (CS-2) (Afternoon)

GATE
2025
Question Paper | Answer Key
Graduate Aptitude Test in Engineering
(GATE) is a prestigious national-level exam
that assesses candidates for
comprehensive understanding in various
undergraduate-level subjects in
Engineering, Technology, Science,
Architecture, and Humanities.

General Aptitude
Q.1 – Q.5 Carry ONE mark Each

Q.1 Despite his initial hesitation, Rehman’s _________ to contribute to the success of
the project never wavered.

Select the most appropriate option to complete the above sentence.

(A) ambivalence

(B) satisfaction

(C) resolve

(D) revolve

Organising Institute: IIT Roorkee Page 1 of 48

Q.2 Bird : Nest :: Bee : _______

Select the correct option to complete the analogy.

(A) Kennel

(B) Hammock

(C) Hive

(D) Lair

Organising Institute: IIT Roorkee Page 2 of 48

Q.3 If 𝑃𝑒 𝑥 = 𝑄𝑒 −𝑥 for all real values of 𝑥, which one of the following statements is
true?

(A) 𝑃=𝑄=0

(B) 𝑃=𝑄=1

(C) 𝑃 = 1; 𝑄 = −1

(D) 𝑃
=0
𝑄

Organising Institute: IIT Roorkee Page 3 of 48

Q.4 The paper as shown in the figure is folded to make a cube where each square
corresponds to a particular face of the cube. Which one of the following options
correctly represents the cube?

Note: The figures shown are representative.

(A)

(B)

(C)

(D)

Organising Institute: IIT Roorkee Page 4 of 48

Q.5 Let 𝑝1 and 𝑝2 denote two arbitrary prime numbers. Which one of the following
statements is correct for all values of 𝑝1 and 𝑝2 ?

(A) 𝑝1 + 𝑝2 is not a prime number.

(B) 𝑝1 𝑝2 is not a prime number.

(C) 𝑝1 + 𝑝2 + 1 is a prime number.

(D) 𝑝1 𝑝2 + 1 is a prime number.

Organising Institute: IIT Roorkee Page 5 of 48

Q.6 – Q.10 Carry TWO marks Each

Q.6 Based only on the conversation below, identify the logically correct inference:

“Even if I had known that you were in the hospital, I would not have gone there to
see you”, Ramya told Josephine.

(A) Ramya knew that Josephine was in the hospital.

(B) Ramya did not know that Josephine was in the hospital.

(C) Ramya and Josephine were once close friends; but now, they are not.

(D) Josephine was in the hospital due to an injury to her leg.

Organising Institute: IIT Roorkee Page 6 of 48

Q.7 If IMAGE and FIELD are coded as FHBNJ and EMFJG respectively then, which
one among the given options is the most appropriate code for BEACH ?

(A) CEADP

(B) IDBFC

(C) JGIBC

(D) IBCEC

Organising Institute: IIT Roorkee Page 7 of 48

Q.8 Which one of the following options is correct for the given data in the table?

Iteration (i) 0 1 2 3

Input (I) 20 −4 10 15

Output (X) 20 16 26 41

Output (Y) 20 −80 −800 −12000

(A) 𝑋(𝑖) = 𝑋(𝑖 − 1) + 𝐼(𝑖); 𝑌(𝑖) = 𝑌(𝑖 − 1)𝐼(𝑖); 𝑖>0

(B) 𝑋(𝑖) = 𝑋(𝑖 − 1)𝐼(𝑖); 𝑌(𝑖) = 𝑌(𝑖 − 1) + 𝐼(𝑖); 𝑖>0

(C) 𝑋(𝑖) = 𝑋(𝑖 − 1)𝐼(𝑖); 𝑌(𝑖) = 𝑌(𝑖 − 1)𝐼(𝑖); 𝑖>0

(D) 𝑋(𝑖) = 𝑋(𝑖 − 1) + 𝐼(𝑖); 𝑌(𝑖) = 𝑌(𝑖 − 1)𝐼(𝑖 − 1); 𝑖>0

Organising Institute: IIT Roorkee Page 8 of 48

Q.9 In the given figure, PQRS is a square of side 2 cm and PLMN is a rectangle. The
corner L of the rectangle is on the side QR. Side MN of the rectangle passes through
the corner S of the square.

What is the area (in cm2) of the rectangle PLMN?

Note: The figure shown is representative.

N

P S

M

Q L R

(A) 2√2

(B) 2

(C) 8

(D) 4

Organising Institute: IIT Roorkee Page 9 of 48

Q.10 The diagram below shows a river system consisting of 7 segments, marked P, Q, R,
S, T, U, and V. It splits the land into 5 zones, marked Z1, Z2, Z3, Z4, and Z5. We
need to connect these zones using the least number of bridges. Out of the following
options, which one is correct?

Note: The figure shown is representative.

Z2 Z3
R
V

P T
Q Z4

Z1 U
S Z5

(A) Bridges on P, Q, and T

(B) Bridges on P, Q, S, and T

(C) Bridges on Q, R, T, and V

(D) Bridges on P, Q, S, U, and V

Organising Institute: IIT Roorkee Page 10 of 48

Q.11 – Q.35 Carry ONE mark Each

Q.11 1 2
If 𝐴 = ( ), then which ONE of the following is 𝐴8 ?
2 −1

(A) 25 0
( )
0 25

(B) 125 0
( )
0 125

(C) 625 0
( )
0 625

(D) 3125 0
( )
0 3125

𝑥 1
Q.12 The value of 𝑥 such that 𝑥 > 1, satisfying the equation ∫1 𝑡 ln 𝑡 𝑑𝑡 = 4 is

(A) √𝑒

(B) 𝑒

(C) 𝑒2

(D) 𝑒−1

Organising Institute: IIT Roorkee Page 11 of 48

Q.13 Consider a binary tree 𝑇 in which every node has either zero or two children.
Let 𝑛 > 0 be the number of nodes in 𝑇.

Which ONE of the following is the number of nodes in 𝑇 that have exactly two
children?

(A) 𝑛−2
2

(B) 𝑛−1
2

(C) 𝑛
2

(D) 𝑛+1
2

Organising Institute: IIT Roorkee Page 12 of 48

Q.14 Let 𝐿, 𝑀, and 𝑁 be non-singular matrices of order 3 satisfying the equations

𝐿2 = 𝐿−1 , 𝑀 = 𝐿8 and 𝑁 = 𝐿2 .

Which ONE of the following is the value of the determinant of (𝑀 − 𝑁)?

(A) 0

(B) 1

(C) 2

(D) 3

Q.15 Let 𝑃(𝑥) be an arbitrary predicate over the domain of natural numbers.

Which ONE of the following statements is TRUE?

(A) (𝑃(0) ∧ (∀𝑥 [𝑃(𝑥) ⇒ 𝑃(𝑥 + 1)])) ⇒ (∀𝑥 𝑃(𝑥))

(B) (𝑃(0) ∧ (∀𝑥 [𝑃(𝑥) ⇒ 𝑃(𝑥 − 1)])) ⇒ (∀𝑥 𝑃(𝑥))

(C) (𝑃(1000) ∧ (∀𝑥 [𝑃(𝑥) ⇒ 𝑃(𝑥 − 1)])) ⇒ (∀𝑥 𝑃(𝑥))

(D) (𝑃(1000) ∧ (∀𝑥 [𝑃(𝑥) ⇒ 𝑃(𝑥 + 1)])) ⇒ (∀𝑥 𝑃(𝑥))

Organising Institute: IIT Roorkee Page 13 of 48

Q.16 Consider the following statements:

(i) Address Resolution Protocol (ARP) provides a mapping from an IP
address to the corresponding hardware (link-layer) address.
(ii) A single TCP segment from a sender S to a receiver R cannot carry both
data from S to R and acknowledgement for a segment from R to S.

Which ONE of the following is CORRECT?

(A) Both (i) and (ii) are TRUE

(B) (i) is TRUE and (ii) is FALSE

(C) (i) is FALSE and (ii) is TRUE

(D) Both (i) and (ii) are FALSE

Organising Institute: IIT Roorkee Page 14 of 48

Q.17 Consider the routing protocols given in List I and the names given in List II:

List I List II

(i) Distance vector routing (a) Bellman-Ford

(ii) Link state routing (b) Dijkstra

For matching of items in List I with those in List II, which ONE of the following
options is CORRECT?

(A) (i) – (a) and (ii) – (b)

(B) (i) – (a) and (ii) – (a)

(C) (i) – (b) and (ii) – (a)

(D) (i) – (b) and (ii) – (b)

Organising Institute: IIT Roorkee Page 15 of 48

Q.18 A machine receives an IPv4 datagram. The protocol field of the IPv4 header has the
protocol number of a protocol X.

Which ONE of the following is NOT a possible candidate for X?

(A) Internet Control Message Protocol (ICMP)

(B) Internet Group Management Protocol (IGMP)

(C) Open Shortest Path First (OSPF)

(D) Routing Information Protocol (RIP)

Organising Institute: IIT Roorkee Page 16 of 48

Q.19 Consider the following C program:

#include <stdio.h>

void stringcopy(char *, char *);

int main(){

char a[30] = "@#Hello World!";

stringcopy(a, a + 2);

printf("%s\n", a);

return 0;

}

void stringcopy(char *s, char *t) {

while(*t)

*s++ = *t++;

}

Which ONE of the following will be the output of the program?

(A) @#Hello World!

(B) Hello World!

(C) ello World!

(D) Hello World!d!

Organising Institute: IIT Roorkee Page 17 of 48

Q.20 Consider an unordered list of 𝑁 distinct integers.

What is the minimum number of element comparisons required to find an integer
in the list that is NOT the largest in the list?

(A) 1

(B) 𝑁−1

(C) 𝑁

(D) 2𝑁 − 1

Q.21 Consider the following statements about the use of backpatching in a compiler for
intermediate code generation:

(I) Backpatching can be used to generate code for Boolean expression in
one pass.
(II) Backpatching can be used to generate code for flow-of-control
statements in one pass.

Which ONE of the following options is CORRECT?

(A) Only (I) is correct.

(B) Only (II) is correct.

(C) Both (I) and (II) are correct.

(D) Neither (I) nor (II) is correct.

Organising Institute: IIT Roorkee Page 18 of 48

Q.22 Given the following syntax directed translation rules:

Rule 1: 𝑅 → 𝐴𝐵 {𝐵. 𝑖 = 𝑅. 𝑖 − 1; 𝐴. 𝑖 = 𝐵. 𝑖; 𝑅. 𝑖 = 𝐴. 𝑖 + 1; }
Rule 2: 𝑃 → 𝐶𝐷 {𝑃. 𝑖 = 𝐶. 𝑖 + 𝐷. 𝑖; 𝐷. 𝑖 = 𝐶. 𝑖 + 2; }
Rule 3: 𝑄 → 𝐸𝐹 {𝑄. 𝑖 = 𝐸. 𝑖 + 𝐹. 𝑖; }

Which ONE is the CORRECT option among the following?

(A) Rule 1 is S-attributed and L-attributed; Rule 2 is S-attributed and not L-attributed;
Rule 3 is neither S-attributed nor L-attributed

(B) Rule 1 is neither S-attributed nor L-attributed; Rule 2 is S-attributed and L-
attributed; Rule 3 is S-attributed and L-attributed

(C) Rule 1 is neither S-attributed nor L-attributed; Rule 2 is not S-attributed and
is L-attributed; Rule 3 is S-attributed and L-attributed

(D) Rule 1 is S-attributed and not L-attributed; Rule 2 is not S-attributed and
is L-attributed; Rule 3 is S-attributed and L-attributed

Organising Institute: IIT Roorkee Page 19 of 48

Q.23 Consider a network that uses Ethernet and IPv4. Assume that IPv4 headers do not
use any options field. Each Ethernet frame can carry a maximum of 1500 bytes in
its data field. A UDP segment is transmitted. The payload (data) in the UDP
segment is 7488 bytes.

Which ONE of the following choices has the CORRECT total number of fragments
transmitted and the size of the last fragment including IPv4 header?

(A) 5 fragments, 1488 bytes

(B) 6 fragments, 88 bytes

(C) 6 fragments, 108 bytes

(D) 6 fragments, 116 bytes

Q.24 Which ONE of the following languages is accepted by a deterministic pushdown
automaton?

(A) Any regular language.

(B) Any context-free language.

(C) Any language accepted by a non-deterministic pushdown automaton.

(D) Any decidable language.

Organising Institute: IIT Roorkee Page 20 of 48

Q.25 Let 𝐺1 , 𝐺2 be Context Free Grammars (CFGs) and 𝑅 be a regular expression. For a
grammar 𝐺, let 𝐿(𝐺) denote the language generated by 𝐺.

Which ONE among the following questions is decidable?

(A) Is 𝐿(𝐺1 ) = 𝐿(𝐺2 )?

(B) Is 𝐿(𝐺1 ) ∩ 𝐿(𝐺2 ) = ∅?

(C) Is 𝐿(𝐺1 ) = 𝐿(𝑅)?

(D) Is 𝐿(𝐺1 ) = ∅?

Q.26 Processes 𝑃1, 𝑃2, 𝑃3, 𝑃4 arrive in that order at times 0, 1, 2, and 8 milliseconds
respectively, and have execution times of 10, 13, 6, and 9 milliseconds respectively.
Shortest Remaining Time First (SRTF) algorithm is used as the CPU scheduling
policy. Ignore context switching times.

Which ONE of the following correctly gives the average turnaround time of the four
processes in milliseconds?

(A) 22

(B) 15

(C) 37

(D) 19

Organising Institute: IIT Roorkee Page 21 of 48

Q.27 An audit of a banking transactions system has found that on an earlier occasion, two
joint holders of account 𝐴 attempted simultaneous transfers of Rs. 10000 each from
account 𝐴 to account 𝐵. Both transactions read the same value, Rs. 11000, as the
initial balance in 𝐴 and were allowed to go through. 𝐵 was credited Rs. 10000 twice.
𝐴 was debited only once and ended up with a balance of Rs. 1000.

Which of the following properties is/are certain to have been violated by the
system?

(A) Atomicity

(B) Consistency

(C) Isolation

(D) Durability

Q.28 Which of the following is/are part of an Instruction Set Architecture of a processor?

(A) The size of the cache memory

(B) The clock frequency of the processor

(C) The number of cache memory levels

(D) The total number of registers

Organising Institute: IIT Roorkee Page 22 of 48

Q.29 Which of the following statements regarding Breadth First Search (BFS) and
Depth First Search (DFS) on an undirected simple graph G is/are TRUE?

(A) A DFS tree of 𝐺 is a Shortest Path tree of 𝐺.

(B) Every non-tree edge of G with respect to a DFS tree is a forward/back edge.

(C) If (𝑢, 𝑣) is a non-tree edge of G with respect to a BFS tree, then the distances from
the source vertex 𝑠 to 𝑢 and 𝑣 in the BFS tree are within ±1 of each other.

(D) Both BFS and DFS can be used to find the connected components of G.

Organising Institute: IIT Roorkee Page 23 of 48

Q.30 Consider the two lists List I and List II given below:

List I List II

(i) Context free languages (a) Closed under union

(ii) Recursive languages (b) Not closed under complementation

(iii) Regular languages (c) Closed under intersection

For matching of items in List I with those in List II, which of the following
option(s) is/are CORRECT?

(A) (i) – (a), (ii) – (b), and (iii) – (c)

(B) (i) – (b), (ii) – (a), and (iii) – (c)

(C) (i) – (b), (ii) – (c), and (iii) – (a)

(D) (i) – (a), (ii) – (c), and (iii) – (b)

Organising Institute: IIT Roorkee Page 24 of 48

Q.31 Consider the following logic circuit diagram.

Which is/are the CORRECT option(s) for the output function 𝐹?

(A) ̅̅̅̅̅
𝑋𝑌

(B) 𝑋̅ + 𝑌̅ + 𝑋𝑌̅

(C) ̅̅̅̅̅
𝑋 𝑌 + 𝑋̅ + 𝑋𝑌̅

(D) 𝑋 + 𝑌̅

Q.32 The following two signed 2’s complement numbers (multiplicand M and
multiplier Q) are being multiplied using Booth’s algorithm:

M: 1100 1101 1110 1101 and Q: 1010 0100 1010 1010

The total number of addition and subtraction operations to be performed is
___________. (Answer in integer)

Organising Institute: IIT Roorkee Page 25 of 48

Q.33 int x=126,y=105;
do {
if(x>y) x=x-y;
else y=y-x;
} while(x!=y);

printf("%d",x);

The output of the given C code segment is ________. (Answer in integer)

Q.34 In a 4-bit ripple counter, if the period of the waveform at the last flip-flop is 64
microseconds, then the frequency of the ripple counter in kHz is ________. (Answer
in integer)

Q.35 Suppose the values 10, −4, 15, 30, 20, 5, 60, 19 are inserted in that order into an
initially empty binary search tree. Let 𝑇 be the resulting binary search tree.
The number of edges in the path from the node containing 19 to the root node of 𝑇
is ___________. (Answer in integer)

Organising Institute: IIT Roorkee Page 26 of 48

Q.36 – Q.65 Carry TWO marks Each

Q.36 Suppose we are transmitting frames between two nodes using Stop-and-Wait
protocol. The frame size is 3000 bits. The transmission rate of the channel is 2000
bps (bits/second) and the propagation delay between the two nodes is 100
milliseconds. Assume that the processing times at the source and destination are
negligible. Also, assume that the size of the acknowledgement packet is negligible.
Which ONE of the following most accurately gives the channel utilization for the
above scenario in percentage?

(A) 88.23

(B) 93.75

(C) 85.44

(D) 66.67

Organising Institute: IIT Roorkee Page 27 of 48

Q.37 Let 𝐺 be an edge-weighted undirected graph with positive edge weights. Suppose a
positive constant 𝛼 is added to the weight of every edge.

Which ONE of the following statements is TRUE about the minimum spanning
trees (MSTs) and shortest paths (SPs) in 𝐺 before and after the edge weight update?

(A) Every MST remains an MST, and every SP remains an SP.

(B) MSTs need not remain MSTs, and every SP remains an SP.

(C) Every MST remains an MST, and SPs need not remain SPs.

(D) MSTs need not remain MSTs, and SPs need not remain SPs.

Organising Institute: IIT Roorkee Page 28 of 48

Q.38 A meld operation on two instances of a data structure combines them into one single
instance of the same data structure. Consider the following data structures:

P: Unsorted doubly linked list with pointers to the head node and tail node
of the list.

Q: Min-heap implemented using an array.

R: Binary Search Tree.

Which ONE of the following options gives the worst-case time complexities for
meld operation on instances of size 𝑛 of these data structures?

(A) P: Θ(1), Q: Θ(𝑛), R: Θ(𝑛)

(B) P: Θ(1), Q: Θ(𝑛 log 𝑛), R: Θ(𝑛)

(C) P: Θ(𝑛), Q: Θ(𝑛 log 𝑛), R: Θ(𝑛2 )

(D) P: Θ(1), Q: Θ(𝑛), R: Θ(𝑛 log 𝑛)

Organising Institute: IIT Roorkee Page 29 of 48

Q.39 For a direct-mapped cache, 4 bits are used for the tag field and 12 bits are used to
index into a cache block. The size of each cache block is one byte. Assume that
there is no other information stored for each cache block.

Which ONE of the following is the CORRECT option for the sizes of the main
memory and the cache memory in this system (byte addressable), respectively?

(A) 64 KB and 4 KB

(B) 128 KB and 16 KB

(C) 64 KB and 8 KB

(D) 128 KB and 6 KB

Q.40 Given a Context-Free Grammar 𝐺 as follows:

𝑆 → 𝐴𝑎 | 𝑏𝐴𝑐 | 𝑑𝑐 | 𝑏𝑑𝑎

𝐴→𝑑

Which ONE of the following statements is TRUE?

(A) 𝐺 is neither LALR(1) nor SLR(1)

(B) 𝐺 is CLR(1), not LALR(1)

(C) 𝐺 is LALR(1), not SLR(1)

(D) 𝐺 is LALR(1), also SLR(1)

Organising Institute: IIT Roorkee Page 30 of 48

Q.41 An array 𝐴 of length 𝑛 with distinct elements is said to be bitonic if there is an index
1 ≤ 𝑖 ≤ 𝑛 such that 𝐴[1. . 𝑖] is sorted in the non-decreasing order and 𝐴[𝑖 + 1 . . 𝑛]
is sorted in the non-increasing order.

Which ONE of the following represents the best possible asymptotic bound for the
worst-case number of comparisons by an algorithm that searches for an element in
a bitonic array 𝐴?

(A) Θ(𝑛)

(B) Θ(1)

(C) Θ(log 2 𝑛)

(D) Θ(log 𝑛)

Q.42 Let ℱ be the set of all functions from {1, … , 𝑛} to {0,1}. Define
the binary relation ≼ on ℱ as follows:

∀𝑓, 𝑔 ∈ ℱ, 𝑓 ≼ 𝑔 if and only if ∀𝑥 ∈ {1, … , 𝑛}, 𝑓(𝑥) ≤ 𝑔(𝑥), where 0 ≤ 1.

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

(A) ≼ is a symmetric relation

(B) (ℱ, ≼ ) is a partial order

(C) (ℱ, ≼ ) is a lattice

(D) ≼ is an equivalence relation

Organising Institute: IIT Roorkee Page 31 of 48

Q.43 Given the following Karnaugh Map for a Boolean function 𝐹(𝑤, 𝑥, 𝑦, 𝑧):

Which one or more of the following Boolean expression(s) represent(s) 𝐹?

(A) 𝑤
̅𝑥̅ 𝑦̅𝑧̅ + 𝑤𝑥̅ 𝑦̅𝑧̅ + 𝑤
̅𝑥̅ 𝑦𝑧̅ + 𝑤𝑥̅ 𝑦𝑧̅ + 𝑥𝑧

(B) 𝑤
̅𝑥̅ 𝑦̅𝑧̅ + 𝑤
̅𝑥̅ 𝑦𝑧̅ + 𝑤𝑥̅ 𝑦𝑧 + 𝑥𝑧

(C) 𝑤
̅𝑥̅ 𝑦̅𝑧̅ + 𝑤𝑥̅ 𝑦̅𝑧̅ + 𝑤𝑥̅ 𝑦̅𝑧 + 𝑥𝑧

(D) 𝑥̅ 𝑧̅ + 𝑥𝑧

Organising Institute: IIT Roorkee Page 32 of 48

Q.44 Consider a system of linear equations 𝑃𝑋 = 𝑄 where 𝑃 ∈ ℝ3×3 and Q ∈ ℝ3×1 .
Suppose 𝑃 has an LU decomposition, 𝑃 = 𝐿𝑈, where

1 0 0 𝑢11 𝑢12 𝑢13
𝑙
𝐿 = [ 21 1 0] and 𝑈 = [ 0 𝑢22 𝑢23 ].
𝑙31 𝑙32 1 0 0 𝑢33

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

(A) The system 𝑃𝑋 = 𝑄 can be solved by first solving 𝐿𝑌 = 𝑄 and then 𝑈𝑋 = 𝑌.

(B) If 𝑃 is invertible, then both 𝐿 and 𝑈 are invertible.

(C) If 𝑃 is singular, then at least one of the diagonal elements of 𝑈 is zero.

(D) If 𝑃 is symmetric, then both 𝐿 and 𝑈 are symmetric.

Organising Institute: IIT Roorkee Page 33 of 48

Q.45 Consider a stack data structure into which we can PUSH and POP records. Assume
that each record pushed in the stack has a positive integer key and that all keys are
distinct.

We wish to augment the stack data structure with an 𝑂(1) time MIN operation that
returns a pointer to the record with smallest key present in the stack

1) without deleting the corresponding record, and
2) without increasing the complexities of the standard stack operations.

Which one or more of the following approach(es) can achieve it?

(A) Keep with every record in the stack, a pointer to the record with the smallest key
below it.

(B) Keep a pointer to the record with the smallest key in the stack.

(C) Keep an auxiliary array in which the key values of the records in the stack are
maintained in sorted order.

(D) Keep a Min-Heap in which the key values of the records in the stack are maintained.

Organising Institute: IIT Roorkee Page 34 of 48

Q.46 Consider the following relational schema along with all the functional dependencies
that hold on them.

R1(A, B, C, D, E): { 𝐷 → 𝐸, 𝐸𝐴 → 𝐵, 𝐸𝐵 → 𝐶}

R2(A, B, C, D): { 𝐴 → 𝐷, 𝐴 → 𝐵, 𝐶 → 𝐴}

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

(A) R1 is in 3NF

(B) R2 is in 3NF

(C) R1 is NOT in 3NF

(D) R2 is NOT in 3NF

Organising Institute: IIT Roorkee Page 35 of 48

Q.47 Consider a demand paging system with three frames, and the following page
reference string: 1 2 3 4 5 4 1 6 4 5 1 3 2. The contents of the frames are as follows
initially and after each reference (from left to right):

initially after
- 1* 2* 3* 4* 5* 4 1 6* 4 5 1* 3* 2*
- 1 1 1 1 1 1 1 6 6 6 6 6 2
- - 2 2 4 4 4 4 4 4 4 1 1 1
- - - 3 3 5 5 5 5 5 5 5 3 3

The *-marked references cause page replacements.

Which one or more of the following could be the page replacement policy/policies
in use?

(A) Least Recently Used page replacement policy

(B) Least Frequently Used page replacement policy

(C) Most Frequently Used page replacement policy

(D) Optimal page replacement policy

Organising Institute: IIT Roorkee Page 36 of 48

Q.48 𝑃 = {𝑃1 , 𝑃2 , 𝑃3 , 𝑃4 } consists of all active processes in an operating system.
𝑅 = {𝑅1 , 𝑅2 , 𝑅3 , 𝑅4 } consists of single instances of distinct types of resources in the
system.

The resource allocation graph has the following assignment and claim edges.

Assignment edges: 𝑅1 → 𝑃1 , 𝑅2 → 𝑃2 , 𝑅3 → 𝑃3 , 𝑅4 → 𝑃4 (the assignment edge
𝑅1 → 𝑃1 means resource 𝑅1 is assigned to process 𝑃1 , and so on for others)

Claim edges: 𝑃1 → 𝑅2 , 𝑃2 → 𝑅3 , 𝑃3 → 𝑅1 , 𝑃2 → 𝑅4 , 𝑃4 → 𝑅2 (the claim edge
𝑃1 → 𝑅2 means process 𝑃1 is waiting for resource 𝑅2 , and so on for others)

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

(A) Aborting 𝑃1 makes the system deadlock free.

(B) Aborting 𝑃3 makes the system deadlock free.

(C) Aborting 𝑃2 makes the system deadlock free.

(D) Aborting 𝑃1 and 𝑃4 makes the system deadlock free.

Organising Institute: IIT Roorkee Page 37 of 48

Q.49 Three floating point numbers 𝑋, 𝑌, and 𝑍 are stored in three registers RX, RY, and
RZ, respectively in IEEE 754 single precision format as given below in
hexadecimal:

RX = 0xC1100000, RY = 0x40C00000, and RZ = 0x41400000

Which of the following option(s) is/are CORRECT?

(A) 4(𝑋 + 𝑌) + 𝑍 = 0

(B) 2𝑌 – 𝑍 = 0

(C) 4𝑋 + 3𝑍 = 0

(D) 𝑋+𝑌+𝑍 = 0

Q.50 Which of the following Boolean algebraic equation(s) is/are CORRECT?

(A) 𝐴̅ 𝐵 𝐶 + 𝐴 𝐵̅ 𝐶̅ + 𝐴̅ 𝐵̅ 𝐶̅ + 𝐴 𝐵̅ 𝐶 + 𝐴 𝐵 𝐶 = 𝐵 𝐶 + 𝐵̅ 𝐶̅ + 𝐴̅ 𝐵̅

(B) 𝐴 𝐵 + 𝐴̅ 𝐶 + 𝐵 𝐶 = 𝐴 𝐵 + 𝐴̅ 𝐶

(C) (𝐴 + 𝐶) (𝐴̅ + 𝐵) = 𝐴 𝐵 + 𝐴̅ 𝐶

(D) ̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
(𝐴 + 𝐵̅ + 𝐷 ̅ ) (𝐶 + 𝐷) (𝐴̅ + 𝐶 + 𝐷 ) (𝐴 + 𝐵 + 𝐷 ̅ ) = 𝐴̅ 𝐷 + 𝐶̅ 𝐷
̅

Organising Institute: IIT Roorkee Page 38 of 48

Q.51 Consider two grammars 𝐺1 and 𝐺2 with the production rules given below:

𝐺1 : 𝑆 → 𝑖𝑓 𝐸 𝑡ℎ𝑒𝑛 𝑆 | 𝑖𝑓 𝐸 𝑡ℎ𝑒𝑛 𝑆 𝑒𝑙𝑠𝑒 𝑆 | 𝑎

𝐸→𝑏

𝐺2 : 𝑆 → 𝑖𝑓 𝐸 𝑡ℎ𝑒𝑛 𝑆 | 𝑀

𝑀 → 𝑖𝑓 𝐸 𝑡ℎ𝑒𝑛 𝑀 𝑒𝑙𝑠𝑒 𝑆 | 𝑐

𝐸→𝑏

where 𝑖𝑓, 𝑡ℎ𝑒𝑛, 𝑒𝑙𝑠𝑒, 𝑎, 𝑏, 𝑐 are the terminals.

Which of the following option(s) is/are CORRECT?

(A) 𝐺1 is not 𝐿𝐿(1) and 𝐺2 is 𝐿𝐿(1).

(B) 𝐺1 is 𝐿𝐿(1) and 𝐺2 is not 𝐿𝐿(1).

(C) 𝐺1 and 𝐺2 are not 𝐿𝐿(1).

(D) 𝐺1 and 𝐺2 are ambiguous.

Organising Institute: IIT Roorkee Page 39 of 48

Q.52 Let Σ = {𝑎, 𝑏, 𝑐}. For 𝑥 ∈ Σ ∗ , and 𝛼 ∈ Σ, let #𝛼 (𝑥) denote the number of
occurrences of 𝛼 in 𝑥.

Which one or more of the following option(s) define(s) regular language(s)?

(A) {𝑎𝑚 𝑏 𝑛 | 𝑚, 𝑛 ≥ 0}

(B) {𝑎, 𝑏}∗ ∩ {𝑎𝑚 𝑏 𝑛 𝑐 𝑚−𝑛 | 𝑚 ≥ 𝑛 ≥ 0}

(C) {𝑤 | 𝑤 ∈ {𝑎, 𝑏}∗ , #𝑎 (𝑤) ≡ 2 (mod 7), and #𝑏 (𝑤) ≡ 3 (mod 9)}

(D) {𝑤 | 𝑤 ∈ {𝑎, 𝑏}∗ , #𝑎 (𝑤) ≡ 2 (mod 7), and #𝑎 (𝑤) = #𝑏 (𝑤)}

Organising Institute: IIT Roorkee Page 40 of 48

Q.53 Consider the database transactions T1 and T2, and data items X and Y. Which of
the schedule(s) is/are conflict serializable?

Transaction T1
Transaction T2
R1(X)
W2(X)
W1(Y)
W2(Y)
R1(X)
COMMIT(T2)
W1(X)
COMMIT(T1)

(A) R1(X), W2(X), W1(Y), W2(Y), R1(X), W1(X), COMMIT(T2), COMMIT(T1)

(B) W2(X), R1(X), W2(Y), W1(Y), R1(X), COMMIT(T2), W1(X), COMMIT(T1)

(C) R1(X), W1(Y), W2(X), W2(Y), R1(X), W1(X), COMMIT(T1), COMMIT(T2)

(D) W2(X), R1(X), W1(Y), W2(Y), R1(X), COMMIT(T2), W1(X), COMMIT(T1)

Organising Institute: IIT Roorkee Page 41 of 48

Q.54 Consider the following relational schema:

Students (rollno: integer, name: string, age: integer, cgpa: real)

Courses (courseno: integer, cname: string, credits: integer)

Enrolled (rollno: integer, courseno: integer, grade: string)

Which of the following options is/are correct SQL query/queries to retrieve the
names of the students enrolled in course number (i.e., courseno) 1470?

(A) SELECT S.name
FROM Students S
WHERE EXISTS (SELECT * FROM Enrolled E
WHERE E.courseno = 1470
AND E.rollno = S.rollno);

(B) SELECT S.name
FROM Students S
WHERE SIZEOF (SELECT * FROM Enrolled E
WHERE E.courseno = 1470
AND E.rollno = S.rollno) > 0;

(C) SELECT S.name
FROM Students S
WHERE 0 < (SELECT COUNT(*)
FROM Enrolled E
WHERE E.courseno = 1470
AND E.rollno = S.rollno);

(D) SELECT S.name
FROM Students S NATURAL JOIN Enrolled E
WHERE E.courseno = 1470;

Organising Institute: IIT Roorkee Page 42 of 48

Q.55 Given a computing system with two levels of cache (L1 and L2) and a main
memory. The first level (L1) cache access time is 1 nanosecond (ns) and the “hit
rate” for L1 cache is 90% while the processor is accessing the data from L1 cache.
Whereas, for the second level (L2) cache, the “hit rate” is 80% and the “miss
penalty” for transferring data from L2 cache to L1 cache is 10 ns. The “miss
penalty” for the data to be transferred from main memory to L2 cache is 100 ns.

Then the average memory access time in this system in nanoseconds is
___________ . (rounded off to one decimal place)

A 5-stage instruction pipeline has stage delays of 180, 250, 150, 170, and 250,
respectively, in nanoseconds. The delay of an inter-stage latch is 10 nanoseconds.
Q.56 Assume that there are no pipeline stalls due to branches and other hazards. The time
taken to process 1000 instructions in microseconds is __________ . (rounded off to
two decimal places)

Q.57 In a B+- tree where each node can hold at most four key values, a root to leaf path
consists of the following nodes:

A = (49, 77, 83, -), B = (7, 19, 33, 44), C = (20*, 22*, 25*, 26*)

The *-marked keys signify that these are data entries in a leaf.

Assume that a pointer between keys 𝑘1 and 𝑘2 points to a subtree containing keys
in [𝑘1 , 𝑘2 ), and that when a leaf is created, the smallest key in it is copied up into
its parent.

A record with key value 23 is inserted into the B+- tree.

The smallest key value in the parent of the leaf that contains 25* is __________.
(Answer in integer)

Organising Institute: IIT Roorkee Page 43 of 48

Q.58 A computer system supports a logical address space of 232 bytes. It uses two-level
hierarchical paging with a page size of 4096 bytes. A logical address is divided into
a 𝑏-bit index to the outer page table, an offset within the page of the inner page
table, and an offset within the desired page. Each entry of the inner page table uses
eight bytes. All the pages in the system have the same size.

The value of 𝑏 is ___________ . (Answer in integer)

Q.59 Consider the following algorithm someAlgo that takes an undirected graph 𝐺 as
input.

someAlgo(𝐺)

1. Let 𝑣 be any vertex in 𝐺. Run BFS on 𝐺 starting at
𝑣. Let 𝑢 be a vertex in 𝐺 at maximum distance from
𝑣 as given by the BFS.
2. Run BFS on 𝐺 again with 𝑢 as the starting vertex.
Let 𝑧 be the vertex at maximum distance from 𝑢 as
given by the BFS.
3. Output the distance between 𝑢 and 𝑧 in 𝐺.

The output of someAlgo(𝑇) for the tree shown in the given figure is
___________. (Answer in integer)

Organising Institute: IIT Roorkee Page 44 of 48

Q.60 Let Σ = {1,2,3,4}. For 𝑥 ∈ Σ ∗ , let 𝑝𝑟𝑜𝑑(𝑥) be the product of symbols in
𝑥 modulo 7. We take 𝑝𝑟𝑜𝑑(𝜖) = 1, where 𝜖 is the null string.

For example, 𝑝𝑟𝑜𝑑(124) = (1 × 2 × 4) mod 7 = 1.

Define 𝐿 = {𝑥 ∈ Σ ∗ | 𝑝𝑟𝑜𝑑(𝑥) = 2}.

The number of states in a minimum state DFA for 𝐿 is ___________. (Answer in
integer)

Q.61 An application executes 6.4 × 108 number of instructions in 6.3 seconds. There are
four types of instructions, the details of which are given in the table. The duration
of a clock cycle in nanoseconds is _________. (rounded off to one decimal place)
Instruction type Clock cycles required per Number of instructions
instruction (CPI) executed
Branch 2 2.25 × 108
Load 5 1.20 × 108
Store 4 1.65 × 108
Arithmetic 3 1.30 × 108

Organising Institute: IIT Roorkee Page 45 of 48

Q.62 Consider the following C program:

#include <stdio.h>

int main(){

int a;

int arr[5] = {30,50,10};

int *ptr;

ptr = &arr[0] + 1;

a = *ptr;

(*ptr)++;

ptr++;

printf("%d", a + (*ptr) + arr[1]);

return 0;

}

The output of the above program is ___________. (Answer in integer)

Organising Institute: IIT Roorkee Page 46 of 48

Q.63 Consider the following C program:

#include <stdio.h>

int g(int n) {
return (n+10);
}

int f(int n) {
return g(n*2);
}

int main() {
int sum, n;
sum=0;
for (n=1; n<3; n++)
sum += g(f(n));
printf ("%d", sum);
return 0;

}

The output of the given C program is ________. (Answer in integer)

Q.64 A quadratic polynomial (𝑥 − 𝛼)(𝑥 − 𝛽) over complex numbers is said to be square
invariant if (𝑥 − 𝛼)(𝑥 − 𝛽) = (𝑥 − 𝛼 2 )(𝑥 − 𝛽 2 ). Suppose from the set of all
square invariant quadratic polynomials we choose one at random.

The probability that the roots of the chosen polynomial are equal is __________.
(rounded off to one decimal place)

Organising Institute: IIT Roorkee Page 47 of 48

Q.65 The unit interval (0,1) is divided at a point chosen uniformly distributed over (0,1)
in ℝ into two disjoint subintervals.

The expected length of the subinterval that contains 0.4 is ___________. (rounded
off to two decimal places)

Organising Institute: IIT Roorkee Page 48 of 48

Entrance Exams
Agricultural Entrance Exams
Architecture Entrance Exam
Arts and Humanities Entrance Exams
Commerce Entrance Examinations
Common Entrance Examinations
Computer Application Entrance Exams
Design Entrance Exams
Education Entrance Exams
Engineering Entrance Exams
Hotel Management Entrance Exams
Law Entrance Exams
MBA Entrance Exams
Media & Journalism Entrance Exams
Medical Entrance Exams
Nursing Entrance Exams
Pharmacy Entrance Exams
Science Entrance Exams
Diploma & Polytechnic
Lateral Entry