UGC NET · PAPER 2
UGC NET Paper 2 Computer Science – Unit 1: Discrete Structures and Optimisation PYQ (December 2022 Shift 1)
Q1. Which of the following is NOT logically equivalent to P → Q?
- ~P ∨ Q
- ~Q → ~P
- ~(P ∧ ~Q)
- ~Q → P
Q2. Seven people enter a lift. The lift stops at only three (unspecified) floors. At each of the three floors no one enters, but at least one person leaves. After the three stops the lift is empty. In how many ways can this happen?
- 1844
- 2187
- 1806
- 343
Q3. The coefficient of x²y³z² in the expansion of (x + y + z)⁷ is
- C(7, 3) × C(5, 2)
- C(7, 2) × C(5, 3)
- C(7, 3) × C(7, 2)
- C(5, 3) × C(5, 2)
Q4. What is the minimum number of students in a discrete mathematics class to be sure that at least six will receive the same grade, if there are seven possible grades: S, A, B, C, D, P and F?
- 7
- 13
- 36
- 14
Q41. Consider the following statements:
A. A group can have zero elements.
B. A group cannot have any idempotent element except the identity element.
C. An isomorphism from a group ⟨G, *⟩ to ⟨G, *⟩ is called an automorphism.
D. If every element in a group is its own inverse, then the group must be abelian.
Choose the correct answer about the four statements given above.
A. A group can have zero elements.
B. A group cannot have any idempotent element except the identity element.
C. An isomorphism from a group ⟨G, *⟩ to ⟨G, *⟩ is called an automorphism.
D. If every element in a group is its own inverse, then the group must be abelian.
Choose the correct answer about the four statements given above.
- B, C and D are correct
- Only A and C are correct
- Only B and C are correct
- All A, B, C and D are correct
Q42. Consider the following statements:
A. The number of labelled binary trees possible with n nodes is (2n)!/(n+1)!
B. The number of binary search trees possible with n (distinct) keys is (2n)!/((n+1)! n!)
C. The number of unlabelled binary trees possible with n nodes is C(2n, n)/(n+1)!
D. The number of simple, undirected, labelled graphs possible with n vertices is 2^(n(n−1)/2)
Choose the correct answer from the options given below:
A. The number of labelled binary trees possible with n nodes is (2n)!/(n+1)!
B. The number of binary search trees possible with n (distinct) keys is (2n)!/((n+1)! n!)
C. The number of unlabelled binary trees possible with n nodes is C(2n, n)/(n+1)!
D. The number of simple, undirected, labelled graphs possible with n vertices is 2^(n(n−1)/2)
Choose the correct answer from the options given below:
- A, B and C are only correct
- A, B and D are only correct
- B, C and D are only correct
- A, C and D are only correct
Q43. The relation R = {(1, 3), (1, 1), (3, 1), (1, 2), (3, 3), (4, 4)} defined on {1, 2, 3, 4} is ____
- Reflexive, symmetric but not transitive
- Symmetric, anti-symmetric and transitive
- Asymmetric, anti-symmetric and not transitive
- Not reflexive, not symmetric and not transitive
Q76. Let G be a simple undirected graph with n (n > 10) vertices and k connected components. What is the minimum possible number of edges of G?
- k(n − 1)
- n(k − 1)
- n + k − 2
- n − k