621. Graph shortest paths: dist(s,u)=53; dist(s,v)=65 ⇒ edge(u,v) weight is:?

Discrete Structures and Optimization • Shortest Paths • UGC NET Paper 2 Computer Science JUNE 2012

622. The dual of a Boolean expression swaps

Discrete Structures and Optimization • Boolean Algebra: Duality • UGC NET Paper 2 Computer Science JUNE 2012

623. SOP expansion for F(x,y,z)=(x+y)–z is

Discrete Structures and Optimization • Boolean Functions: SOP • UGC NET Paper 2 Computer Science JUNE 2012

624. If p(n,r)=perm(n,r), then p(n+1,r)=p(n,r)*(n+1)/(n+1–r). Which formula?

Discrete Structures and Optimization • Combinatorics: Permutations • UGC NET Paper 2 Computer Science JUNE 2012

625. Regex for complement of L={aⁿbᵐ, n≥4,m≤3} is

Discrete Structures and Optimization • Formal Languages • UGC NET Paper 2 Computer Science JUNE 2012

626. Edges in a forest of t trees with n vertices =

Discrete Structures and Optimization • Graph Theory: Forests • UGC NET Paper 2 Computer Science JUNE 2012

627. A graph is non-planar iff it contains a subgraph homeomorphic to

Discrete Structures and Optimization • Graph Theory: Planarity • UGC NET Paper 2 Computer Science JUNE 2012

628. P(m,n): “m divides n”. I. ∀m∀n P(m,n). II. ∃m∀n P(m,n). Truth?

Discrete Structures and Optimization • Logic & Quantifiers • UGC NET Paper 2 Computer Science JUNE 2012

629. How to express “some person keeps animals as pets”?

Discrete Structures and Optimization • Predicate logic • UGC NET Paper 2 Computer Science JUNE 2012

630. Equivalent of ¬∃x F[x] is

Discrete Structures and Optimization • Predicate logic • UGC NET Paper 2 Computer Science JUNE 2012

631. If an artificial variable is basic in optimal simplex, the solution is

Discrete Structures and Optimization • Simplex method • UGC NET Paper 2 Computer Science JUNE 2012

632. Degeneracy in transportation means

Discrete Structures and Optimization • Transportation problem • UGC NET Paper 2 Computer Science JUNE 2012

633. The golden ratio φ and its conjugate satisfy which equation?

Discrete Structures and Optimization • Algebra • UGC NET Paper 2 Computer Science JUNE 2012

634. Operator s defined by truth table. (x s y) s z = x s (y s z) is

Discrete Structures and Optimization • Algebraic structures • UGC NET Paper 2 Computer Science JUNE 2012

635. Big-O estimates for (n log n+n²)(n³+2) & (n!+2ⁿ)/(n³+log(n²+1)) are

Discrete Structures and Optimization • Asymptotic analysis • UGC NET Paper 2 Computer Science JUNE 2012

636. How many different Boolean functions of degree 4 are there?

Discrete Structures and Optimization • Boolean algebra • UGC NET Paper 2 Computer Science JUNE 2012

637. Test has 100 T/F questions; answers may be blank also. How many ways to answer?

Discrete Structures and Optimization • Counting • UGC NET Paper 2 Computer Science JUNE 2012

638. Which connected simple graph has exactly one spanning tree?

Discrete Structures and Optimization • Graph theory • UGC NET Paper 2 Computer Science JUNE 2012

639. How many edges must be removed to form a spanning forest with N vertices, M edges, C components?

Discrete Structures and Optimization • Graph theory • UGC NET Paper 2 Computer Science JUNE 2012

640. A vertex cover of G(V,E) is a subset V₁⊆V such that for every (u,v)∈E

Discrete Structures and Optimization • Graph theory • UGC NET Paper 2 Computer Science JUNE 2012