641. Conversion ∃u∀v∀x∃y P→Q to ∀v∀x(P(f(a),v,x,g(v,x))→Q(a,v,g(v,x))) is called

Discrete Structures and Optimization • Logic • UGC NET Paper 2 Computer Science JUNE 2013

642. Truth values of ∃!x P(x)→∃x P(x) and ∃!x ¬P(x)→¬∀x P(x) are

Discrete Structures and Optimization • Predicate logic • UGC NET Paper 2 Computer Science JUNE 2013

643. Compound proposition true exactly when two of p,q,r are true is

Discrete Structures and Optimization • Propositional logic • UGC NET Paper 2 Computer Science JUNE 2013

644. Relation “divides” on positive integers is

Discrete Structures and Optimization • Relations • UGC NET Paper 2 Computer Science JUNE 2013

645. In the simplex method, if Δⱼ=0 for a nonbasic variable, the solution is

Discrete Structures and Optimization • Simplex method • UGC NET Paper 2 Computer Science JUNE 2013

646. A BFS to m×n transportation problem is degenerate if positive allocations < m+n–1.

Discrete Structures and Optimization • Transportation problem • UGC NET Paper 2 Computer Science JUNE 2013

647. Transportation problem cost by Vogel’s method on matrix (given) is

Discrete Structures and Optimization • Transportation problem • UGC NET Paper 2 Computer Science JUNE 2013

648. If F and G are n-variable Boolean functions, which holds?

Discrete Structures and Optimization • Boolean Algebra • UGC NET Paper 2 Computer Science JUNE 2013

649. Match identities to names: (a) idempotent; (b) identity; (c) dominance; (d) absorption. Order a–d → iii, ii, iv, i.

Discrete Structures and Optimization • Boolean Identities • UGC NET Paper 2 Computer Science JUNE 2013

650. Number of 8-bit strings beginning with either 111 or 101 = _____.

Discrete Structures and Optimization • Combinatorics • UGC NET Paper 2 Computer Science JUNE 2013

651. Count triples (i,j,k) from 1..30 where (i+j+k)%3==0. Output?

Discrete Structures and Optimization • Counting Techniques • UGC NET Paper 2 Computer Science JUNE 2013

652. A simple graph on n vertices is guaranteed connected if it has how many edges?

Discrete Structures and Optimization • Extremal Graph Theory • UGC NET Paper 2 Computer Science JUNE 2013

653. Ways to paint 12 offices with 3 green,2 pink,2 yellow, rest white = ___.

Discrete Structures and Optimization • Permutations with Repetition • UGC NET Paper 2 Computer Science JUNE 2013

654. Express ∃!x P(x) using ∀,∃, logical ops.

Discrete Structures and Optimization • Predicate Logic • UGC NET Paper 2 Computer Science JUNE 2013

655. Which logic circuit is shown by an XOR gate symbol with a bubble?

Discrete Structures and Optimization • Boolean algebra • UGC NET Paper 2 Computer Science JUNE 2013

656. Correct predicate for “Every natural number has one successor”?

Discrete Structures and Optimization • Predicate logic • UGC NET Paper 2 Computer Science JUNE 2013

657. Minimum people for ≥50% chance two share a birthday is at least ________

Discrete Structures and Optimization • Probability • UGC NET Paper 2 Computer Science JUNE 2013

658. If an artificial variable remains in basic column of optimal simplex, solution is ________

Discrete Structures and Optimization • Simplex method • UGC NET Paper 2 Computer Science JUNE 2013

659. Consider A={1…1000}. How many divisible by 3 or 5 or both?

Discrete Structures and Optimization • Counting • UGC NET Paper 2 Computer Science JUNE 2013

660. If f(x)=x⁴, g(x)=x²+1, h(x)=x²+72, find h∘(g∘f)(x) and (h∘g)∘f(x).

Discrete Structures and Optimization • Functions • UGC NET Paper 2 Computer Science JUNE 2013