681. Match (Controlled Inverter, Full adder, Half adder, Binary adder) to codes a b c d.

Discrete Structures and Optimization • Digital Logic • UGC NET Paper 2 Computer Science AUG 2016

682. Evaluate prefix `* + 3 + 3 – 3 + 3 3 3`.

Discrete Structures and Optimization • Expression Evaluation • UGC NET Paper 2 Computer Science AUG 2016

683. Given the compound proposition ¬(p∧q) ↔ (¬p∨¬q), what are its prefix and postfix forms?

Discrete Structures and Optimization • Expression Trees • UGC NET Paper 2 Computer Science AUG 2016

684. Number of length-4 strings by regex `(0+1+2+3+)*`?

Discrete Structures and Optimization • Formal Languages • UGC NET Paper 2 Computer Science AUG 2016

685. Given graphs G₁ and G₂, which has an Euler circuit?

Discrete Structures and Optimization • Graph Theory • UGC NET Paper 2 Computer Science AUG 2016

686. The Karnaugh map simplifies to which Boolean sum?

Discrete Structures and Optimization • K-Map Simplification • UGC NET Paper 2 Computer Science AUG 2016

687. Inferences: I1: If Sunday→no school; school was open→not Sunday. I2: If Sunday→no school; not Sunday→school open. Which?

Discrete Structures and Optimization • Logic • UGC NET Paper 2 Computer Science AUG 2016

688. Let n(x)=vegetarian, m(y)=meat, e(x,y)=x eats y. Which formulas are equivalent? I ∀x[n(x)↔∀y(e(x,y)→¬m(y))] II ∀x[n(x)↔¬∃y(m(y)∧e(x,y))] III ∀x[∃y(m(y)∧e(x,y))↔¬n(x)].

Discrete Structures and Optimization • Predicate Logic • UGC NET Paper 2 Computer Science AUG 2016

689. Which of the following XOR identities is incorrect?

Discrete Structures and Optimization • Boolean Algebra – XOR • UGC NET Paper 2 Computer Science AUG 2016

690. Simplify F(x,y,z) given 000→0,001→1,010→0,011→1,100→1,101→0,110→1,111→0.

Discrete Structures and Optimization • Boolean Simplification • UGC NET Paper 2 Computer Science AUG 2016

691. The simplified form of (ĀB + ĀBC + AC)(ĀC + B̄) is?

Discrete Structures and Optimization • Boolean Simplification • UGC NET Paper 2 Computer Science AUG 2016

692. How many full parenthesizations for `A ∩ B – A ∩ B – A`?

Discrete Structures and Optimization • Combinatorics – Parenthesizations • UGC NET Paper 2 Computer Science AUG 2016

693. n-vertex convex polygon triangulation uses T chords and yields triangles. T=?, triangles=?

Discrete Structures and Optimization • Computational Geometry • UGC NET Paper 2 Computer Science AUG 2016

694. Number of spanning trees in K₄ and K₂,₂ respectively?

Discrete Structures and Optimization • Graph Theory • UGC NET Paper 2 Computer Science AUG 2016

695. A clique in a simple undirected graph is a complete subgraph not contained in any larger one. How many cliques are there in the graph shown?

Discrete Structures and Optimization • Graph Theory – Cliques • UGC NET Paper 2 Computer Science AUG 2016

696. Feasible region of LP has _____ property.

Discrete Structures and Optimization • Linear programming • UGC NET Paper 2 Computer Science AUG 2016

697. Number of equivalence relations with exactly 3 classes on 5 elements?

Discrete Structures and Optimization • Partitions • UGC NET Paper 2 Computer Science AUG 2016

698. Three cards: BB, RR, BR. You draw one, see a color. What’s P(opposite side same)?

Discrete Structures and Optimization • Probability • UGC NET Paper 2 Computer Science AUG 2016

699. If R₁,R₂ reflexive on A, which is correct?

Discrete Structures and Optimization • Relations • UGC NET Paper 2 Computer Science AUG 2016

700. Revised vs. standard simplex: (a) needs less compute (b) auto inverse basis (c) fewer entries. Correct?

Discrete Structures and Optimization • Simplex method • UGC NET Paper 2 Computer Science AUG 2016