601. Any integer composed of 3n identical digits is divisible by

Discrete Structures and Optimization • Number theory • UGC NET Paper 2 Computer Science JUNE 2011

602. Proposition ¬p ∨ q is equivalent to

Discrete Structures and Optimization • Propositional logic • UGC NET Paper 2 Computer Science JUNE 2011

603. Operation commutative but not associative is?

Discrete Structures and Optimization • Boolean Algebra • UGC NET Paper 2 Computer Science JUNE 2011

604. Chain letter: each forwards to 4; stops after 100 non-senders. Total seen & senders?

Discrete Structures and Optimization • Tree Counting • UGC NET Paper 2 Computer Science JUNE 2011

605. Ways to place n distinct objects into k boxes with n_i in box i is

Discrete Structures and Optimization • Combinatorics • UGC NET Paper 2 Computer Science JUNE 2011

606. The Mandelbrot set uses iteration x_{n+1}=x_n²+z with

Discrete Structures and Optimization • Complex Dynamics • UGC NET Paper 2 Computer Science JUNE 2011

607. Given graphs A (K₃,₃) and B (K₅), which are planar?

Discrete Structures and Optimization • Graph Theory: Planarity • UGC NET Paper 2 Computer Science JUNE 2011

608. Solutions to x1+x2+x3=11 with x1≥1,x2≥2,x3≥3 is

Discrete Structures and Optimization • Integer Partitions • UGC NET Paper 2 Computer Science JUNE 2011

609. ∀x∀y∃z (x+y=z) is true; ∃z∀x∀y (x+y=z) is false.

Discrete Structures and Optimization • Logic & Quantifiers • UGC NET Paper 2 Computer Science JUNE 2011

610. The power set of {∅} is?

Discrete Structures and Optimization • Set Theory • UGC NET Paper 2 Computer Science JUNE 2011

611. Power set size of A∪B for A={2,3,5,7}, B={2,5,8,9} is

Discrete Structures and Optimization • Set Theory • UGC NET Paper 2 Computer Science JUNE 2011

612. Let V1=2i−j+k, V2=i+j−k: the angle between them and a perpendicular vector are

Discrete Structures and Optimization • Vector Algebra • UGC NET Paper 2 Computer Science JUNE 2011

613. Max colors needed for any planar graph = __.

Discrete Structures and Optimization • Graph Coloring • UGC NET Paper 2 Computer Science JUNE 2011

614. Two cosets aH and bH in a group are always _?

Discrete Structures and Optimization • Group Theory • UGC NET Paper 2 Computer Science JUNE 2011

615. Optimal assignment for given cost matrix via Hungarian is:?

Discrete Structures and Optimization • Assignment Problem • UGC NET Paper 2 Computer Science JUNE 2011

616. Time complexity of m-coloring decision problem is:?

Discrete Structures and Optimization • Graph Coloring • UGC NET Paper 2 Computer Science JUNE 2011

617. Feasible region of an LP is:?

Discrete Structures and Optimization • Linear Programming • UGC NET Paper 2 Computer Science JUNE 2011

618. In simplex, if D_j<0 column has all ≤0 ⇒ solution is:?

Discrete Structures and Optimization • Linear Programming • UGC NET Paper 2 Computer Science JUNE 2011

619. Q(x,y): x+y=0. ∃y∀x Q? and ∀x∃y Q? Which valid?

Discrete Structures and Optimization • Logic • UGC NET Paper 2 Computer Science JUNE 2011

620. Number of symmetric relations on n-set and reflexive+sym on n-set =:?

Discrete Structures and Optimization • Relations • UGC NET Paper 2 Computer Science JUNE 2011