CS/IT Gate Yearwise 


CS and IT Gate 2023 Questions with Answer

Ques 14 GATE 2023

The Lucas sequence Ln is defined by the recurrence relation:
Ln = Ln-1 + Ln-2, for n ≥ 3, with L1 = 1 and L2 = 3.
Which one of the options given is TRUE?

A

Ln = (1+√5/2)n + (1-√5/2)n

B

Ln = (1+√5/2)n - (1-√5/3)n

C

Ln = (1+√5/2)n + (1-√5/3)n

D

Ln = (1+√5/2)n - (1-√5/2)n


(a) is the correct answer.

Ques 15 GATE 2023

Suppose two hosts are connected by a point-to-point link and they are configured to use Stop-and-Wait protocol for reliable data transfer. Identify in which one of the following scenarios, the utilization of the link is the lowest.

A

Longer link length and lower transmission rate

B

Longer link length and higher transmission rate

C

Shorter link length and lower transmission rate

D

Shorter link length and higher transmission rate


(a) is the correct answer.

Ques 16 GATE 2023

Let det(A) and det(B) denote the determinants of the matrices A and B, respectively. Which one of the options given below is TRUE?

A

det(A) = det(B)

B

det(B) = -det(A)

C

det(A) = 0

D

det(AB) = det(A) + det(B)


(a) is the correct answer.

Ques 17 GATE 2023

Consider the following definition of a lexical token id for an identifier in a programming language, using extended regular expressions:

Which one of the following Non-deterministic Finite-state Automata with e-transitions accepts the set of valid identifiers? (A double-circle denotes a final state)

A

B

C

D


(b) is the correct answer.

Ques 18 GATE 2023

An algorithm has to store several keys generated by an adversary in a hash table. The adversary is malicious who tries to maximize the number of collisions. Let k be the number of keys, m be the number of slots in the hash table, and k > m. Which one of the following is the best hashing strategy to counteract the adversary?

A

Division method, i.e., use the hash function h(k) = k mod m.

B

Multiplication method, i.e., use the hash function h(k) = [m(kA - [kA])], where A is a carefully chosen constant.

C

Universal hashing method.

D

If k is a prime number, use Division method. Otherwise, use Multiplication method.


(c) is the correct answer.

Ques 19 GATE 2023

The output of a 2-input multiplexer is connected back to one of its inputs as shown in the figure.

Match the functional equivalence of this circuit to one of the following options.

A

D Flip-flop

B

D Latch

C

Half-adder

D

Demultiplexer


(b) is the correct answer.

Ques 20 GATE 2023

Which one or more of the following need to be saved on a context switch from one thread (T1) of a process to another thread (T2) of the same process?

A

Page table base register

B

Stack pointer

C

Program counter

D

General purpose registers


(b,c,d) is the correct answer.

Ques 21 GATE 2023

Which one or more of the following options guarantee that a computer system will transition from user mode to kernel mode?

A

Function Call

B

malloc Call

C

Page Fault

D

System Call


(c,d) is the correct answer.

Ques 22 GATE 2023

Which of the following statements is/are INCORRECT about the OSPF (Open Shortest Path First) routing protocol used in the Internet?

A

OSPF implements Bellman-Ford algorithm to find shortest paths.

B

OSPF uses Dijkstra's shortest path algorithm to implement least-cost path routing.

C

OSPF is used as an inter-domain routing protocol.

D

OSPF implements hierarchical routing.


(a,c) is the correct answer.

Ques 23 GATE 2023

Geetha has a conjecture about integers, which is of the form
∀x(P(x)⇒∃yQ(x,y)),
where P is a statement about integers, and Q is a statement about pairs of integers. Which of the following (one or more) option(s) would imply Geetha's conjecture?

A

∃x(P(x)∧∀yQ(x,y))

B

∀x∀yQ(x,y)

C

∃y∀x(P(x)⇒Q(x,y))

D

∃x(P(x)∧∃yQ(x,y))


(b,c) is the correct answer.

Ques 24 GATE 2023

Let f(x) = x3 + 15x2 - 33x - 36 be a real-valued function. Which of the following statements is/are TRUE?

A

f(x) does not have a local maximum.

B

f(x) has a local maximum.

C

f(x) does not have a local minimum.

D

f(x) has a local minimum.


(b,d) is the correct answer.

Ques 25 GATE 2023

Let f and g be functions of natural numbers given by f(n) = n and g(n) = n2. Which of the following statements is/are TRUE?

A

f ∈ O(g)

B

f ∈ Ω(g)

C

f ∈ o(g)

D

f ∈ Θ(g)


(a,c) is the correct answer.

Ques 26 GATE 2023

Let A be the adjacency matrix of the graph with vertices {1, 2, 3, 4, 5}.

Let λ1, λ2, λ3, λ4, and λ5 be the five eigenvalues of A. Note that these eigenvalues need not be distinct. The value of λ1 + λ2 + λ3 + λ4 + λ5 = _______.


(1) is the correct answer.

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