UGC NET · PAPER 2
UGC NET Paper 2 Computer Science – Unit 1: Discrete Structures and Optimisation PYQ (June 2024 Re-Exam)
Q7. Consider the following relations on {1, 2, 3, 4}. Which of the following relations are reflexive?
(A) R₁ = {(1,1),(1,2),(2,1),(2,2),(3,4),(4,1),(4,4)}
(B) R₂ = {(1,1),(1,2),(2,1)}
(C) R₃ = {(1,1),(1,2),(1,4),(2,1),(2,2),(3,3),(4,1),(4,4)}
(D) R₄ = {(2,1),(3,1),(3,2),(4,1),(4,2),(4,3)}
(E) R₅ = {(1,1),(1,2),(1,3),(1,4),(2,2),(2,3),(2,4),(3,3),(3,4),(4,4)}
Choose the correct answer from the options given below:
(A) R₁ = {(1,1),(1,2),(2,1),(2,2),(3,4),(4,1),(4,4)}
(B) R₂ = {(1,1),(1,2),(2,1)}
(C) R₃ = {(1,1),(1,2),(1,4),(2,1),(2,2),(3,3),(4,1),(4,4)}
(D) R₄ = {(2,1),(3,1),(3,2),(4,1),(4,2),(4,3)}
(E) R₅ = {(1,1),(1,2),(1,3),(1,4),(2,2),(2,3),(2,4),(3,3),(3,4),(4,4)}
Choose the correct answer from the options given below:
- (A), (B) and (C) Only
- (A), (D) and (E) Only
- (D) and (E) Only
- (C) and (E) Only
Q24. Let p be "It is a hot day" and q be "The temperature is 48°C". Write in simple sentences the meaning of ¬p ∧ ¬q.
- It is a hot day or the temperature is 48°C
- It is a cold day or the temperature is 48°C
- It is neither a hot day nor is the temperature 48°C
- It is not a hot day
Q34. A graph G with n ≥ 3 vertices is a Hamiltonian graph if the degree of each vertex is greater than or equal to
- the number of vertices
- double the number of vertices
- half the number of vertices
- four times the number of vertices
Q45. A coin is tossed successively three times. For the event E of getting exactly one head or exactly two heads, with sample space S (n denotes the number of outcomes):
(A) n(S) = 8 and n(E) = 4
(B) n(E) = 6 and n(S) = 8
(C) P(E) = 3/4
(D) P(E) = 1/2
Choose the correct answer from the options given below:
(A) n(S) = 8 and n(E) = 4
(B) n(E) = 6 and n(S) = 8
(C) P(E) = 3/4
(D) P(E) = 1/2
Choose the correct answer from the options given below:
- (A), (B), (C) and (D)
- (B) and (C) Only
- (A) and (D) Only
- (C) and (D) Only
Q47. Consider the following, where p and q are two statements.
(A) ~(p ∧ q) ≡ ~p ∨ ~q
(B) ~(p ∨ q) ≡ ~p ∧ ~q
(C) p ∧ ~p ≡ T
(D) ~(p ⇒ q) ≡ p ∧ ~q
(E) p ∨ q ≡ ~p ∨ ~q
Which of these equivalences are correct?
(A) ~(p ∧ q) ≡ ~p ∨ ~q
(B) ~(p ∨ q) ≡ ~p ∧ ~q
(C) p ∧ ~p ≡ T
(D) ~(p ⇒ q) ≡ p ∧ ~q
(E) p ∨ q ≡ ~p ∨ ~q
Which of these equivalences are correct?
- (A), (B) and (D) only
- (A), (C) and (D) only
- (C), (D) and (E) only
- (A), (B) and (C) only
Q61. Let L(x, y) be the statement "x loves y", where the domain for both x and y consists of all people in the world. Use quantifiers to express "Joy is loved by everyone".
- ∀x L(x, Joy)
- ∀y L(Joy, y)
- ∃y ∀x L(x, y)
- ∃x ¬L(Joy, x)
Q72. Match List I (Queries) with List II (Probability)
| List I | List II |
|---|---|
| (A) A bag contains 6 white and 4 red balls. Two balls are drawn at random. What is the chance they will be the same colour? | (I) 3/68 |
| (B) In a pack of 52 cards, one card is drawn at random. What is the probability that it is either a king or a queen? | (II) 14/68 |
| (C) A bag contains 6 red, 4 white and 8 blue balls. If three balls are drawn at random, find the probability of 1 red and 2 white balls. | (III) 2/13 |
| (D) A bag contains 6 red, 4 white and 8 blue balls. If three balls are drawn at random, find the probability of 2 blue and 1 red ball. | (IV) 7/15 |
- (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
- (A)-(III), (B)-(IV), (C)-(II), (D)-(I)
- (A)-(IV), (B)-(III), (C)-(II), (D)-(I)
- (A)-(IV), (B)-(III), (C)-(I), (D)-(II)
Q78. Let G(V, E) be an undirected graph with l edges. Then the sum of the degrees of all vertices is equal to
- 2l
- l/2
- l²
- √l
Q79. 40 software professionals were interviewed for a job. 25 knew PYTHON, 20 knew JAVA and 7 knew neither language. How many knew both languages?
- 12
- 53
- 10
- 88
Q87. Translate ∀x ∃y (x < y) into English, considering the domain as real numbers for both variables.
- For all real numbers x, there exists a real number y such that x is less than y
- For every real number y, there exists a real number x such that x is less than y
- For some real number x, there exists a real number y such that x is less than y
- For each and every real number x and y, x is less than y