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.
- A warehouse has 50 aisles, 85 horizontal locations in each aisle, and 5 shelves. Storage bins are specified by aisle, location and shelf. What is the least number of products so that at least two must be stored in the s…
- A person climbing stairs can take one or two stairs at a time. How many ways can the person climb a flight of eight stairs?
- For which value of n is the wheel graph Wₙ regular?
- Which of the following Graphs is(are) planar?
- Match List I (identity) with List II (name). List I: A. x + x = x, B. x + 0 = x, C. x + 1 = 1, D. x + xy = x. List II: I. Identity law, II. Absorption law, III. Idempotent law, IV. Domination law.
- Let (X, *) be a semigroup in which, for every a, b in X, a ≠ b implies a * b ≠ b * a. Which equalities hold? A. a * a = a for every a. B. a * b * a = a for all a, b. C. a * b * c = a * c for all a, b, c.
- Maximize Z = 6x + 5y subject to 2x − 3y ≤ 5, x + 3y ≤ 11, 4x + y ≤ 15, x, y ≥ 0. The optimal value is
- Given below are two statements Statement I: In an undirected graph, number of odd degree vertices is even. Statement II: In an undirected graph, sum of degrees of all vertices is even. In light of the above statements,…
- The number of positive integers not exceeding 100 that are either odd or the square of an integer is ____
- How many ways are there to pack six copies of the same book into four identical boxes, where a box contains six books?
- Which of the following pairs of propositions are not logically equivalent?
- Maximize z = 2x₁ + 3x₂ subject to 2x₁ + x₂ ≤ 4, x₁ + 2x₂ ≤ 5, x₁, x₂ ≥ 0. The optimum value is
- If f(x)=x is my friend, and p(x)=x is perfect, then the correct logical translation of the statement "some of my friends are not perfect" is:
- Consider the following properties: A. Reflexive B. Antisymmetric C. Symmetric A = {a, b, c, d, e, f, g} Let and R = {(a, a), (b, b), (c, d), (c, g), (d, g), (e, e), (f, f), (g, g)} be a relation on (A). Which of the fol…
- Consider the argument with premise ∀x(P(x) ∨ Q(x)) and conclusion (∀x P(x)) ∧ (∀x Q(x)): (A) ∀x(P(x) ∨ Q(x)) premise; (B) P(c) ∨ Q(c) universal instantiation from A; (C) P(c) simplification from B; (D) ∀x P(x) universal…
- Consider the following statements: (A) Any tree is 2-colorable (B) A graph G has no cycles of even length if it is bipartite. (C) A graph G is 2-colorable if it is bipartite. (D) A graph G can be colored with d+1 colors…
- Consider the statement: A person who is radical (R) is electable (E) if he/she is conservative (C), but otherwise is not electable. Which of these assertions are correct? (A) (R ∧ E) ⇔ C (B) R ⇒ (E ⇔ C) (C) R ⇒ ((C ⇒ E)…
- Let R1 = {(1,1), (2,2), (3,3)} and R2 = {(1,1), (1,2), (1,3), (1,4)}. Match List I with List II. List I: A. R1 ∪ R2, B. R1 − R2, C. R1 ∩ R2, D. R2 − R1. List II: I. {(1,1), (1,2), (1,3), (1,4), (2,2), (3,3)}, II. {(1,1)…
- Find the lexicographic ordering of the bit strings 0 < 1 given below based on the ordering . (A) 001 (B) 010 (C) 011 (D) 0001 (E) 0101 Choose the correct answer from the options given below:
- Statement I: 5 divides n⁵ − n whenever n is a non-negative integer. Statement II: 6 divides n³ − n whenever n is a non-negative integer.
- A basic feasible solution of an transportation problem is said to be non- degenerate, if basic feasible solution contains exactly------------- number of individual allocation in-------------- positions.
- Maximize z = x₁ + x₂ subject to x₁ + 2x₂ ≤ 2000, x₁ + x₂ ≤ 1500, x₂ ≤ 600, x₁, x₂ ≥ 0. The solution is
- What are the GLB and LUB of the sets A = {3, 9, 12} and B = {1, 2, 4, 5, 10}, if they exist, in the poset (Z⁺, /)?
- Let (P) be the set of all people. Let (R) be a binary relation on (P) such that (a, b) is in R if a is a brother of b. Is (R) symmetric transitive, an equivalence relation, a partial order relation?
- A tree has 2 n vertices of degree 1,3 n vertices of degree 2, n vertices of degree 3 . Determine the number of vertices and edges in tree.
- How many reflexive relations are there on a set with 4 elements?
- Using a^(2c) mod n = (a^c)² mod n and a^(2c+1) mod n = a·(a^c)² mod n, for a = 7, b = 17 and n = 561, what is a^b mod n?
- A clique in an undirected graph is a V ′ ⊆ V subset of vertices, such that u, v) ∈ E u ∈ V ′ v ∈ V ′
- Consider the following statements: S : ∀xP(x) ∨ ∀xQ(x) 1 and ∀x(P(x) ∨ Q(x)) are not logically equivalent. S : ∃xP(x) ∧ ∃xQ(x) 2 and ∃x(P(x) ∧ Q(x)) are not logically equivalent Which of the following statements is/are…
- Consider the following statements : S (G, *) a ∈ G 1 : If a group is of order n, and is am = e m ≤ n such that for some integer , then m must divide n. S (G, *) 2 : If a group is of even order, then there a ∈ G a ≠ e mu…