UGC NET Paper 2 Computer Science – Unit 1: Discrete Structures and Optimization PYQ (December 2024)

Q7. Which one of the following is NOT a basic solution of the system of linear equations
x₁ + 2x₂ + x₃ = 4
2x₁ + x₂ + 5x₃ = 5

Q14. Match List I with List II: match the logically equivalent propositions

List 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

Q22. 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) hit the target?

Q40. 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

Q58. 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)
Choose the correct answer from the options given below:

Q62. 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. (7, 5)
D. (0, 15)
E. (8, 5)
Choose the correct answer from the options given below:

Q69. 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, ia, if, ag, ae, ad, ab, bf, be, cf, cd, de, fg.
Choose the most appropriate answer from the options given below:

Q89. Which of the following statements are true about sets?
A. 0 ∈ ∅
B. ∅ ∈ {0}
C. ∅ ∈ {∅}
D. {∅} ∈ {∅}
E. {∅} ⊂ {∅, {∅}}
Choose the correct answer from the options given below: