UGC NET · PAPER 2
UGC NET Paper 2 Computer Science – Unit 1: Discrete Structures and Optimization PYQ (June 2025)
Q1. In a pack of 42 cards, 3 cards are chosen one after the other. Find the number of ways this can be done without replacement:
- 1722
- 1752
- 68880
- 6880
Q27. A positive integer is selected at random from the set of positive integers not exceeding 200. What is the probability that the selected number is divisible by either 2 or 5?
- 2/5
- 3/5
- 4/5
- 1/5
Q28. Match List I with List II
| List I | List II |
|---|---|
| A. If the Indian team wins, then it is raining | I. Inverse |
| B. If the Indian team does not win, then it is not raining | II. Converse |
| C. If it is raining, then the Indian team wins | III. Contrapositive |
| D. If it is not raining, then the Indian team does not win | IV. Conditional |
- A-II, B-I, C-IV, D-III
- A-III, B-I, C-II, D-IV
- A-IV, B-I, C-II, D-III
- A-III, B-II, C-IV, D-I
Q34. Let P denote "She is intelligent" and let Q denote "She is happy." Given below are the statements:
(a) If she is intelligent, then she is unhappy.
(b) She is neither intelligent nor happy.
(c) It is necessary to be not intelligent in order to be happy.
(d) To be not intelligent is to be unhappy.
Which of the following is the correct propositional expression for the above statements?
(a) If she is intelligent, then she is unhappy.
(b) She is neither intelligent nor happy.
(c) It is necessary to be not intelligent in order to be happy.
(d) To be not intelligent is to be unhappy.
Which of the following is the correct propositional expression for the above statements?
- (a) P → ¬Q; (b) P ∧ ¬Q; (c) Q → ¬P; (d) P → ¬Q
- (a) P → Q; (b) ¬P ∧ ¬Q; (c) ¬Q → P; (d) ¬P → ¬Q
- (a) P → ¬Q; (b) ¬P ∧ ¬Q; (c) Q → ¬P; (d) ¬P → ¬Q
- (a) P → ¬Q; (b) P ∧ ¬Q; (c) Q → P; (d) ¬P → ¬Q
Q35. In a group of 120 people: 65 eat Rice, 45 eat bread, 42 eat curd, 20 eat both Rice and bread, 25 eat both Rice and curd, 15 eat both bread and curd, and 8 eat all three items. Which of the following is the number of people who eat at least one of the three items?
- 56
- 100
- 92
- 65
Q53. Choose the correct statement for a group G:
- If for all x, y ∈ G, (xy)² = x²y², then G is commutative.
- If for all x ∈ G, x³ = 1, then G is commutative (1 is the identity element of G).
- If for all x ∈ G, x⁵ = 1, then G is commutative (1 is the identity element of G).
- If G is commutative, a subgroup of G need not be commutative.
Q87. Let m and n be positive integers. Consider:
(A) If n ≠ 1, then m < mn.
(B) If k is composite, then k = mn where 1 < m, n > k.
(C) If mn = 1, then m = 1 and n = 1.
(D) If k is composite, then k = mn where 1 < m, n < k.
Which of the following is correct?
(A) If n ≠ 1, then m < mn.
(B) If k is composite, then k = mn where 1 < m, n > k.
(C) If mn = 1, then m = 1 and n = 1.
(D) If k is composite, then k = mn where 1 < m, n < k.
Which of the following is correct?
- (A), (C), (D)
- (B), (C), (D)
- (A), (B)
- (A), (B), (C)