CS and IT GATE 2023 Questions with Answer

Ques 14 Computer Science

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

L_n = (1+√5/2)ⁿ + (1-√5/2)ⁿ

L_n = (1+√5/2)ⁿ - (1-√5/3)ⁿ

L_n = (1+√5/2)ⁿ + (1-√5/3)ⁿ

L_n = (1+√5/2)ⁿ - (1-√5/2)ⁿ

Ques 15 Computer Science

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.

Longer link length and lower transmission rate

Longer link length and higher transmission rate

Shorter link length and lower transmission rate

Shorter link length and higher transmission rate

Ques 16 Computer Science

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?

det(A) = det(B)

det(B) = -det(A)

det(A) = 0

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

Ques 17 Computer Science

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)

Ques 18 Computer Science

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?

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

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

Universal hashing method.

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

Ques 19 Computer Science

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.

D Flip-flop

D Latch

Half-adder

Demultiplexer

Ques 20 Computer Science

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?

Page table base register

Stack pointer

Program counter

General purpose registers

Ques 21 Computer Science

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

Function Call

malloc Call

Page Fault

System Call

Ques 22 Computer Science

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

OSPF implements Bellman-Ford algorithm to find shortest paths.

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

OSPF is used as an inter-domain routing protocol.

OSPF implements hierarchical routing.

Ques 23 Computer Science

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?

∃x(P(x)∧∀yQ(x,y))

∀x∀yQ(x,y)

∃y∀x(P(x)⇒Q(x,y))

∃x(P(x)∧∃yQ(x,y))

Ques 24 Computer Science

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

f(x) does not have a local maximum.

f(x) has a local maximum.

f(x) does not have a local minimum.

f(x) has a local minimum.

Ques 25 Computer Science

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?

f ∈ O(g)

f ∈ Ω(g)

f ∈ o(g)

f ∈ Θ(g)

Ques 26 Computer Science

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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CS and IT GATE 2023 Questions with Answer