UGC NET · PAPER 2
UGC NET Paper 2 Computer Science – Unit 1: Discrete Structures and Optimisation PYQ (September 2022)
Q2. There are three boxes. The first box has 2 white, 3 black and 4 red balls. The second box has 3 white, 2 black and 2 red balls. The third box has 4 white, 1 black and 3 red balls. A box is chosen at random and 2 balls are drawn, of which 1 is white and 1 is red. What is the probability that the balls came from the first box?
- 0.237
- 0.723
- 0.18
- 0.452
Q10. Consider the primal problem:
Maximize z = 5x1 + 12x2 + 4x3
subject to x1 + 2x2 + x3 = 10
2x1 − x2 + 3x3 = 8
x1, x2, x3 ≥ 0
Its dual problem is
Minimize w = 10y1 + 8y2
subject to y1 + 2y2 ≥ 5
2y1 − y2 ≥ 12
y1 + 3y2 ≥ 4
Which of the following is correct?
Maximize z = 5x1 + 12x2 + 4x3
subject to x1 + 2x2 + x3 = 10
2x1 − x2 + 3x3 = 8
x1, x2, x3 ≥ 0
Its dual problem is
Minimize w = 10y1 + 8y2
subject to y1 + 2y2 ≥ 5
2y1 − y2 ≥ 12
y1 + 3y2 ≥ 4
Which of the following is correct?
- y1 ≥ 0, y2 unrestricted
- y1 ≥ 0, y2 ≥ 0
- y1 is unrestricted, y2 ≥ 0
- y1 is unrestricted, y2 restricted
Q11. The logic expression (P′ ∧ Q) ∨ (P ∧ Q′) ∨ (P ∧ Q) is equivalent to
- P′ ∨ Q
- P ∨ Q′
- P ∨ Q
- P′ ∨ Q′
Q71. Consider α, β, γ as logical variables. Which of the following are correct logical equivalences?
(A) α ∧ (β ∨ γ) ≡ (α ∧ β) ∨ (α ∧ γ)
(B) α ∨ β ≡ ¬α ∨ β
(C) (α ⇒ β) ≡ (¬β ⇒ ¬α)
(D) ¬(α ∨ β) ≡ (¬α ⇒ ¬β)
Choose the correct answer from the options given below:
(A) α ∧ (β ∨ γ) ≡ (α ∧ β) ∨ (α ∧ γ)
(B) α ∨ β ≡ ¬α ∨ β
(C) (α ⇒ β) ≡ (¬β ⇒ ¬α)
(D) ¬(α ∨ β) ≡ (¬α ⇒ ¬β)
Choose the correct answer from the options given below:
- (A) and (D) only
- (B) and (C) only
- (A) and (C) only
- (B) and (D) only
Q72. Let ({a, b}, *) be a semigroup where a * a = b. Consider:
(A) a * b = b * a
(B) b * b = b
Choose the most appropriate answer from the options given below:
(A) a * b = b * a
(B) b * b = b
Choose the most appropriate answer from the options given below:
- (A) only true
- (B) only true
- Both (A) and (B) true
- Neither (A) nor (B) true
Q74. Let ε = 0.0005 and let Rε = {(x, y) ∈ ℝ2 : |x − y| < ε}, which can be interpreted as 'approximately equal'. Rε is
(A) Reflexive
(B) Symmetric
(C) Transitive
Choose the correct answer from the options given below:
(A) Reflexive
(B) Symmetric
(C) Transitive
Choose the correct answer from the options given below:
- (A) and (B) only true
- (B) and (C) only true
- (A) and (C) only true
- (A), (B) and (C) true
Q93. Consider the following in Boolean algebra:
X: a ∨ (b ∧ (a ∨ c)) = (a ∨ b) ∧ (a ∨ c)
Y: a ∧ (b ∨ (a ∧ c)) = (a ∧ b) ∨ (a ∧ c)
The identity a ∨ (b ∧ c) = (a ∨ b) ∧ c is satisfied if
X: a ∨ (b ∧ (a ∨ c)) = (a ∨ b) ∧ (a ∨ c)
Y: a ∧ (b ∨ (a ∧ c)) = (a ∧ b) ∨ (a ∧ c)
The identity a ∨ (b ∧ c) = (a ∨ b) ∧ c is satisfied if
- X is true
- Y is true
- Both X and Y are true
- It does not depend on X and Y
Q95. Given below are two statements: Assertion (A) and Reason (R).
Assertion (A): ¬p
Reason (R): (r → ¬q, r ∨ s, s → ¬q, p → q)
In the light of the above statements, choose the correct answer.
Assertion (A): ¬p
Reason (R): (r → ¬q, r ∨ s, s → ¬q, p → q)
In the light of the above statements, choose the correct answer.
- Both (A) and (R) are true and (R) is the correct explanation of (A)
- Both (A) and (R) are true but (R) is NOT the correct explanation of (A)
- (A) is true but (R) is false
- (A) is false but (R) is true