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.
- 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.…
- 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…
- The relation R = {(1, 3), (1, 1), (3, 1), (1, 2), (3, 3), (4, 4)} defined on {1, 2, 3, 4} is ____
- 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?
- 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
- Suppose you are married and you and your partner attend a party with three other married couples. Several handshakes took place. No one shook hands with himself (or herself) or with their partner, and no one shook hands…
- Consider the following graph with vertices A, B, C, D and edges: A – B, B – C, A – D, B – D, C – D (A, B, C lie in a row; D is below and joined to all three.) How many spanning trees can be found?
- Consider the following statements: P: There exists no simple, undirected and connected graph with 80 vertices and 77 edges. Q: All vertices of an Euler graph are of even degree. R: Every simple, undirected, connected an…
- Consider the following statements: A. There exists a Boolean algebra with 5 elements. B. Every element of a Boolean algebra has a unique complement. C. If a lattice L is a Boolean algebra then L is not relatively comple…
- Match List I with List II. 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-colourable d. CPM IV. 2-c…
- Consider the statements: I. There does not exist a polynomial-time algorithm to solve integer linear programming problems. II. The main focus of PERT is 'minimising time'. Choose the correct option about statements I an…
- Four persons P, Q, R and S are in custody and one of them has committed a crime. They say: P: Q did it. Q: S did it. R: I did not do it. S: Q lied. If exactly one of the statements is false, who is guilty?
- 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 a…
- 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 W…
- The logic expression (P′ ∧ Q) ∨ (P ∧ Q′) ∨ (P ∧ Q) is equivalent to
- 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…
- 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:
- 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:
- 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
- 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.
- The prototyping model has the sequence: (A) Customer Evaluation (B) Quick design (C) Requirements (D) Implement (E) Design
- The selection of Spiral Model based on characteristics of requirements: (A) Are requirements easily understandable and defined? (B) Do we change requirements quite often? (C) Can we define requirements early in the cycl…
- Statement (I): In Reuse Oriented Model, Modification of the old system parts appropriate to the new requirements. Statement (II): In Reuse Oriented Model, Integration of the modified parts are not possible into the new…
- How do you create agile processes to manage unpredictability? (A) Requirements gathering must be conducted very carefully (B) Risk analysis must be conducted before planning takes place (C) Software increments must be d…
- RAD software process model stands for
- The model in which the requirements are implemented by its category is
- Match List-I with List-II: List-I (Software process model) (a) Waterfall model (b) Incremental development (c) Prototyping (d) RAD List-II (Software system) (i) An e-business that starts with only the basic functionalit…
- Which of the following statements is/are false? P: The clean-room strategy to software engineering is based on the incremental software process model. Q: The clean-room strategy to software engineering is one of the way…
- Which of the following is not one of the principles of agile software development method?