UGC NET · PAPER 2
UGC NET Paper 2 Computer Science – Unit 1: Discrete Structures and Optimisation PYQ (22 June 2026)
Q55. Which of the following have true value if universe of discourse consist of all integers:
A. ∃n (2n = 3n)
B. ∀n (n² ≥ n)
C. ∀n (2n > n)
D. ∃n (n² = 2)
E. ∀x∀y ∃z (xy = z)
Choose the correct answer from the options given below:
A. ∃n (2n = 3n)
B. ∀n (n² ≥ n)
C. ∀n (2n > n)
D. ∃n (n² = 2)
E. ∀x∀y ∃z (xy = z)
Choose the correct answer from the options given below:
- B, C and E only
- A, B and E only
- A, B, C and D only
- B, C, D and E only
Q57. How many solution does the equation x + y + z = 11 have, where x, y, z are non-negative integers?
- 33
- 66
- 68
- 78
Q80. Match the LIST-I with LIST-II.
Each of the following relations is defined on set {1, 2, 3, 4}. Match the relation types.
Choose the correct answer from the options given below:
Each of the following relations is defined on set {1, 2, 3, 4}. Match the relation types.
| LIST-I (Relation) | LIST-II (Relation type) |
|---|---|
| A. {(2,2), (2,3), (2,4), (3,2), (3,3), (3,4)} | I. Antisymmetric |
| B. {(2,4), (4,2)} | II. Only transitive |
| C. {(1,2), (2,3), (3,4)} | III. Only symmetric |
| D. {(1,3), (1,4), (2,3), (2,4), (3,1), (3,4)} | IV. neither symmetric, nor transitive |
- A-II, B-III, C-I, D-IV
- A-II, B-III, C-IV, D-I
- A-IV, B-III, C-I, D-II
- A-I, B-III, C-IV, D-II
Q84. How many edges are there in a graph with 10 vertices each of degree six?
- 60
- 15
- 20
- 30
Q85. Arrange the following in ascending order on the basis of number of distinct prime numbers in their prime factorization.
A. 729
B. 1001
C. 1111
D. 420
Choose the correct answer from the options given below:
A. 729
B. 1001
C. 1111
D. 420
Choose the correct answer from the options given below:
- A, C, B, D
- D, A, B, C
- A, B, C, D
- D, A, C, B
Q89. Which of the following additional properties is supposed to be satisfied by a group (G, *) to be an abelian group?
- Commutative
- Identity
- Inverse
- Associativity
Q90. Suppose P(·) is used for power set and ∅ is the usual notation of empty set. Arrange the following on the basis of their cardinality in non-decreasing order:
A. P({a, b, {a,b}})
B. P({∅, a, {a}, {{a}}})
C. P(P(∅))
D. P(P({a}))
E. P({{a,b}, c})
Choose the correct answer from the options given below:
A. P({a, b, {a,b}})
B. P({∅, a, {a}, {{a}}})
C. P(P(∅))
D. P(P({a}))
E. P({{a,b}, c})
Choose the correct answer from the options given below:
- C, D, A, B, E
- D, C, E, A, B
- C, D, E, A, B
- D, C, B, A, E
Q98. Match the LIST-I with LIST-II. Match the equivalent propositions in List-I and List-II
Choose the correct answer from the options given below:
| LIST-I | LIST-II |
|---|---|
| A. P→(Q→P) | I. (P∨Q)∧¬(P∧Q) |
| B. P→(Q∨R) | II. (P∨R)→Q |
| C. (P→Q)∧(R→Q) | III. (P→Q)∨(P→R) |
| D. ¬(P⇔Q) | IV. ¬P→(P→Q) |
- A-IV, B-II, C-III, D-I
- A-IV, B-III, C-II, D-I
- A-I, B-II, C-III, D-IV
- A-I, B-III, C-II, D-IV
Q102. Match the LIST-I with LIST-II.
Choose the correct answer from the options given below:
| LIST-I | LIST-II |
|---|---|
| A. Commutative law | I. P∧(Q∨R) = (P∧Q)∨(P∧R) |
| B. Distributive law | II. P∧(P∨Q) = P |
| C. Demorgan law | III. P∧Q = Q∧P |
| D. Adsorption law | IV. ¬(P∨Q) = ¬P∧¬Q |
- A-III, B-IV, C-II, D-I
- A-II, B-I, C-IV, D-III
- A-III, B-I, C-IV, D-II
- A-IV, B-II, C-III, D-I
Q103. Let and
be subgroups of group . Which of the following is False?
- H1.H2 = {h1*h2 : h1 ∈ H1 and h2 ∈ H2} is a subgroup.
- H1.H2 = {h1*h2 : h1 ∈ H1 and h2 ∈ H2} is a normal subgroup given that H1 and H2 are normal subgroups.
- is a subgroup.
- is a subgroup.
Q105. A tree is :
A. a circuitless connected graph
B. a connected graph of 'n' vertices with (n − 1) edges
C. a circuitless graph of 'n' vertices with (n − 1) edges
D. a minimally connected graph
Choose the correct answer from the options given below :
A. a circuitless connected graph
B. a connected graph of 'n' vertices with (n − 1) edges
C. a circuitless graph of 'n' vertices with (n − 1) edges
D. a minimally connected graph
Choose the correct answer from the options given below :
- A, B and C only
- B, C and D only
- A, B, C and D
- A and B only
Q106. Consider the following List-I and List-II in context of graph & model.
Choose the correct answer from the options given below:
| LIST-I | LIST-II |
|---|---|
| A. Planar Graph | I. Probabilistic Model |
| B. Bipartite Graph | II. Deterministic Model |
| C. PERT | III. 4 - Colorable |
| D. CPM (Critical Path Method) | IV. 2 - Colorable |
- A-III, B-IV, C-I, D-II
- A-IV, B-III, C-I, D-II
- A-II, B-IV, C-I, D-III
- A-III, B-IV, C-II, D-I
Q112. The number of vertices of odd degree in any graph of 'n' vertices with 'e' edges is :
- odd
- even
- (n − e)
- prime
Q116. Let R = {(1, 2), (3, 4), (2, 2)} and S = {(4, 2), (2, 5), (3, 1), (1, 3)} be two relations. The composite relation R∘S of R and S is :
- (4, 2), (3, 2), (2, 5)
- (1, 5), (3, 2), (2, 5)
- (1, 3), (3, 1), (2, 5)
- (2, 5), (3, 1), (2, 3), (3, 3)
Q120. Out of 32 people, 30 save paper and 14 people save plastic bottles. What is the total number of people who save both paper and plastic bottles? Assume all people save either paper or plastic bottles or both paper and plastic bottles.
- 12
- 14
- 16
- 18
Q122. Consider a linear program {max cᵀx | Ax ≤ b}. Which of the following statements is true?
- the dual program is {min bᵀy | Aᵀy ≤ c, y ≥ 0}
- the dual program is {min bᵀy | Aᵀy ≥ c, y ≥ 0}
- the dual program is {min bᵀy | Aᵀy = c, y ≥ 0}
- the dual program is {max bᵀY | AᵀY = c}