GATE CSE 2023

Question 21

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 same process ?

• Page Tabel base register 

• Stack pointer

• Program Counter

• General purpose register

Question 22

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

• Function call

• malloc call

• Page Fault

• System call

Question 23

Which of the following option is/are correct?

• The intersection of two regular languages is REGULAR.

• THE intersection of two context-free languages is CONTEXT-FREE.

• The intersection of two recursive languages is RECURSIVE.

• The intersection of two recursive enumerable languages is recursively language.

Question 24

Which one of the following statements is INCORRECT about the OSPF (Open shortest path ) routing protocol used in the INTERNET?

• OSPF implements the Bellman-Ford algorithm to find the shortest path.

• OSPF uses the Dijkstra algorithm to implement least coach path routing.

• OSPF uses an interdomain routing algorithm.

• OSPF implements hierarchical routing.

Question 25

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) 

Question 26

Which one or more of the following CPU scheduling algorithms can potentially cause starvation?

• First-in First-Out

• Round Robin

• Priority Scheduling

• Shortest Job First

Question 27

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.

Question 28

Let f and g be functions of natural numbers given by f (n) = n and g(n) = n^2. Which of the following statements is/are TRUE?

• f ∈ O(g)

• f ∈ omega(g)

• f ∈ o(g)

• f ∈ Θ(g)

Question 29

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

[caption width="800"]IMG1[/caption]

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 is 

• 1

• 2

• 3

• 5

Question 30

The value of the definite integral

[caption width="800"]IMG[/caption]

is  _________________

• 0

• 1

• 2

• 3