Discrete Structures and Optimization – Previous Year Questions
272 questions from past UGC NET Paper 2 – Computer Science papers, each with the correct answer. Open any question for its explanation.
- Match List - I with List - II.
- Arrange the following in ascending order: (a) remainder of 49¹⁶ divided by 17 (b) remainder of 24⁴⁶ divided by 9 (c) remainder of 155¹⁷ divided by 17 (d) last digit of 7⁴⁵
- Given below are two statements : Statement (I): If H is a nonempty finite subset of ∈ ∀ ∈ a group G and ab H a,b H then H is also a group Statement (II): There is no homomorphism existing from (Z,+) to (Q,+); where Z is…
- The cost function of total food is:
- Which of the following constraints when formulating the LPP?
- Which of the following are quantities (in grams) of food X and Y respectively when the cost of food is minimum:
- The dual of the formulated LPP is :
- The minimum cost of food is:
- Let R = {x ∈ N : x is a multiple of 3 and x ≤ 100} and S = {x ∈ N : x is a multiple of 5 and x < 100}. What is the number of elements in (R ∩ S) × (S ∩ R)?
- How many integral solutions are there to x + y + z + w = 29, where x ≥ 1, y ≥ 2, z ≥ 3 and w ≥ 0?
- Let G = ℝ − {0} and H = {−1, 1} be groups under multiplication. Then the map φ : G → H defined by φ(x) = x/|x| is
- Find the sum of all four digit numbers formed using the digits 1,2,4 and 6 .
- Match List I with List II. List I: A. A △ B, B. A − (B ∪ C), C. A − (B ∩ C), D. A ∩ (B − C). List II: I. (A − B) ∪ (A − C), II. (A − B) ∩ (A − C), III. (A − B) ∪ (B − A), IV. (A ∩ B) − (A ∩ C).
- Consider the following statements. A. The identity is unique in any monoid. B. A monoid is a group if there exists inverse of each element of monoid. C. Semi group has closure, associative and identity properties. D. Qu…
- Seven people enter a lift. The lift stops only at three floors (which are unspecified). At each of the three floors, no one enters the lift, but at least one person leaves the lift. After the three floor stops, the lift…
- Consider: A. A group can have zero elements. B. A group cannot have any idempotent element except the identity. C. An isomorphism from a group ⟨G, *⟩ to ⟨G, *⟩ is called an automorphism. D. If every element in a group i…
- The relation R = {(1, 3), (1, 1), (3, 1), (1, 2), (3, 3), (4, 4)} {1, 2, 3, 4} defined in is ____
- The negation of "Some students like hockey" is:
- A relation ' R ' is defined on ordered pairs of integers as (x, y) R(u, v) if x<u and y>v. Then R is
- Consider the Graph below: How many spanning trees can be found?
- Match the List-I and List-II
- Four persons: P, Q, R and S are in police custody and one of them has committed a crime. They confess as follows: A. Person P: Q did it. B. Person Q: S did it. C. Person R: I did not do it. D. Person S: Q lied. If exact…
- 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 is: minimize w = 10y1 + 8y2 subject to y1 + 2y2 ≥ 5, 2y1 − y2 ≥ 12, y1 + 3y2 ≥ 4. Wh…
- Considering α, β, γ as logical variables, which represent correct equivalences? (A) (α ∧ (β ∨ γ)) ≡ ((α ∧ β) ∨ (α ∧ γ)) (B) (α ∨ β) ≡ ¬α ∨ β (C) (α ⇒ β) ≡ (¬β ⇒ ¬α) (D) ¬(α ∨ β) ≡ (¬α ⇒ ¬β)
- Let ({a, b}, *) be a semigroup where a * a = b. Which hold? (A) a * b = b * a (B) b * b = b
- Let ε = 0.0005 and R_ε be the relation {(x, y) ∈ ℝ² : |x − y| < ε}, interpreted as 'approximately equal'. R_ε is (A) reflexive (B) symmetric (C) transitive.
- Assertion (A): p̄. Reason (R): (r → q̄, r ∨ s, s → q̄, p → q). Choose the correct answer.
- Which of the following are logically equivalent? A. ¬p → (q → r) and q → (p ∨ r) B. (p → q) → r and p → (q → r) C. (p → q) → (r → s) and (p → r) → (q → s)
- Statement I: ⌊2x⌋ = ⌊x⌋ + ⌊x + 1/2⌋ for every real x. Statement II: ⌈x + y⌉ = ⌈x⌉ + ⌈y⌉ for all real x and y.
- How many ways are there to assign 5 different jobs to 4 different employees if every employee is assigned at least 1 job?