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.
- 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…
- How many solution does the equation x + y + z = 11 have, where x, y, z are non-negative integers?
- Match the LIST-I with LIST-II. 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. Antisym…
- How many edges are there in a graph with 10 vertices each of degree six?
- 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:
- Which of the following additional properties is supposed to be satisfied by a group (G, *) to be an abelian group?
- 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(…
- Match the LIST-I with LIST-II. Match the equivalent propositions in List-I and List-II 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) Choose the c…
- Match the LIST-I with LIST-II.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 Choose the correct answer…
- Let and be subgroups of group . Which of the following is False?
- 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 fro…
- Consider the following List-I and List-II in context of graph & model.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 Met…
- The number of vertices of odd degree in any graph of 'n' vertices with 'e' edges is :
- 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 :
- 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 pl…
- Consider a linear program {max cᵀx | Ax ≤ b}. Which of the following statements is true?
- In a pack of 42 cards, 3 cards are chosen one after the other. Find the number of ways this can be done without replacement:
- A positive integer is selected at random from the set of positive integers not exceeding 200. What is the probability that the selected number is divisible by either 2 or 5?
- Match List I with List IIList I List II A. If the Indian team wins, then it is raining I. Inverse B. If the Indian team does not win, then it is not raining II. Converse C. If it is raining, then the Indian team wins II…
- Let P denote "She is intelligent" and let Q denote "She is happy." Given below are the statements: (a) If she is intelligent, then she is unhappy. (b) She is neither intelligent nor happy. (c) It is necessary to be not…
- In a group of 120 people: 65 eat Rice, 45 eat bread, 42 eat curd, 20 eat both Rice and bread, 25 eat both Rice and curd, 15 eat both bread and curd, and 8 eat all three items. Which of the following is the number of peo…
- Choose the correct statement for a group G:
- Let m and n be positive integers. Consider: (A) If n ≠ 1, then m < mn. (B) If k is composite, then k = mn where 1 < m, n > k. (C) If mn = 1, then m = 1 and n = 1. (D) If k is composite, then k = mn where 1 < m, n < k. W…
- Which one of the following is NOT a basic solution of the system of linear equations x₁ + 2x₂ + x₃ = 4 2x₁ + x₂ + 5x₃ = 5
- Match List I with List II: match the logically equivalent propositionsList I List II A. p → q I. (p ∧ q) ∨ (¬p ∧ ¬q) B. ¬(p ∨ (¬p ∧ q)) II. ¬p ∨ q C. p ↔ q III. ¬(p ∨ q) D. ¬(p ↔ q) IV. ¬p ↔ q
- The probability that A hits a target is 1/4, and the probability that B hits the target is 2/5. Both shoot at the target. What is the probability that at least one of them hits the target, i.e., that A or B (or both) hi…
- If x and y are elements in a group G and if x⁵ = y³ = e, where e is the identity of G, then the inverse of x²yx⁴y² must be
- Arrange the following graphs on the basis of number of edges in increasing order (for large n): A. Kₙ (Complete Graph) B. Cₙ (Cycle graph) C. Wₙ (Wheel graph) D. Kₙ,ₙ (Complete Bipartite Graph) E. Qₙ (n-cube graph) Choo…
- A linear programming problem (LPP) is as follows: Min z = 30x − 18y, subject to the constraints 3x + 4y ≤ 60, 5x − 3y ≥ 20 and x, y ≥ 0. In this feasible region, the solution(s) of the LPP is/are A. (4, 0) B. (2, 0) C.…
- Which of the following graphs is/are planar? Graph A (vertices a–f): edges ab, ac, bd, cf, de, ef, bf, cd. Graph B (vertices a–f): edges af, ae, ad, ac, bf, bc, bd, ef, df, ce. Graph C (vertices a–i): edges hi, hg, he,…