661. Tree with degrees 4,4,3,2 and rest 1. Total vertices?

Discrete Structures and Optimization • Graph theory • UGC NET Paper 2 Computer Science DEC 2014

662. Consider the graph shown below. This graph is a ________.

Discrete Structures and Optimization • Graph theory • UGC NET Paper 2 Computer Science DEC 2014

663. Negation of “−2≤x≤−1 or 1≤x≤2” is ?

Discrete Structures and Optimization • Predicate logic • UGC NET Paper 2 Computer Science DEC 2014

664. A program picks k∈{1…10^6} 10^6 times. P(k=1 at least once)?

Discrete Structures and Optimization • Probability • UGC NET Paper 2 Computer Science DEC 2014

665. To convert a max-assignment problem to a min-assignment, you ___.

Discrete Structures and Optimization • Assignment Problem • UGC NET Paper 2 Computer Science DEC 2014

666. Big-O of n! and log(n!) is ___.

Discrete Structures and Optimization • Asymptotic Analysis • UGC NET Paper 2 Computer Science DEC 2014

667. How many distinct truth-tables exist for compound propositions in p and q?

Discrete Structures and Optimization • Boolean Functions • UGC NET Paper 2 Computer Science DEC 2014

668. Which of Graphs A–D is isomorphic to the given graph?

Discrete Structures and Optimization • Graph Isomorphism • UGC NET Paper 2 Computer Science DEC 2014

669. K_{m,n} has a Hamiltonian circuit when ___.

Discrete Structures and Optimization • Graph Theory • UGC NET Paper 2 Computer Science DEC 2014

670. Fractional knapsack n=4, profits=(10,10,12,18), weights=(2,4,6,9), capacity=15. Max profit = ___.

Discrete Structures and Optimization • Greedy Algorithms • UGC NET Paper 2 Computer Science DEC 2014

671. Which special case in the simplex method does NOT require reformulation? Alternate optimality; infeasibility; unboundedness.

Discrete Structures and Optimization • Linear Programming • UGC NET Paper 2 Computer Science DEC 2014

672. Which statements are NOT correct? i. 2’s-complement of 0 is 0. ii. MSB cannot express magnitude. iii. n-bit 2’s-comp has 2ⁿ⁻¹ positives, 2ⁿ⁻¹ negatives, 1 zero. iv. Significant bits are 1’s for positive and 0’s for negative.

Discrete Structures and Optimization • Number Representations • UGC NET Paper 2 Computer Science DEC 2014

673. Cards to guarantee: i.two aces of two suits, ii.two aces, iii.two same rank, iv.two different ranks.

Discrete Structures and Optimization • Pigeonhole Principle • UGC NET Paper 2 Computer Science DEC 2014

674. Evaluate truth of: I. (∃!x P(x))→∃xP(x); II. (∃!x ¬P(x))→¬∀xP(x).

Discrete Structures and Optimization • Predicate Logic • UGC NET Paper 2 Computer Science DEC 2014

675. If F is self-dual (F(x)=¬F(¬x)), how many Boolean functions of n variables are self-dual?

Discrete Structures and Optimization • Self-Dual Functions • UGC NET Paper 2 Computer Science DEC 2014

676. Initial BFS for the given transportation table (not shown) yields minimum cost = ___.

Discrete Structures and Optimization • Transportation Problem • UGC NET Paper 2 Computer Science DEC 2014

677. The Boolean function ¬(¬p∧q)∧¬(¬p∧¬q) ∨ (p∧r) simplifies to which?

Discrete Structures and Optimization • Boolean Algebra • UGC NET Paper 2 Computer Science DEC 2014

678. Which logic operation does this combinational circuit perform?

Discrete Structures and Optimization • Combinational Circuits • UGC NET Paper 2 Computer Science DEC 2014

679. The output of the following combinational circuit is :

Discrete Structures and Optimization • Combinational circuits • UGC NET Paper 2 Computer Science DEC 2014

680. What is the probability that a random bit-string of length 10 is a palindrome?

Discrete Structures and Optimization • Combinatorics • UGC NET Paper 2 Computer Science DEC 2014