Top MCQs on NP Complete Complexity with Answers (original) (raw)

A problem in NP is NP-complete if

It can be reduced to the 3-SAT problem in polynomial time
The 3-SAT problem can be reduced to it in polynomial time
It can be reduced to any other problem in NP in polynomial time
Some problem in NP can be reduced to it in polynomial time

Language L1 is polynomial time reducible to language L2. Language L3 is polynomial time reducible to L2, which in turn is polynomial time reducible to language L4. Which of the following is/are True?

I. If L4 ∈ P, L2 ∈ P
II. If L1 ∈ P or L3 ∈ P, then L2 ∈ P
III. L1 ∈ P, if and only if L3 ∈ P
IV. If L4 ∈ P, then L1 ∈ P and L3 ∈ P

Which of the following is an NP-hard problem that can be approximated using a greedy algorithm?

Traveling salesman problem
Minimum spanning tree problem

Assuming P != NP, which of the following is true ?
(A) NP-complete = NP

(B) NP-complete [Tex]\\cap [/Tex]P = [Tex]\\Phi [/Tex]

(D) P = NP-complete

Which of the following is true about NP-Complete and NP-Hard problems.

If we want to prove that a problem X is NP-Hard, we take a known NP-Hard problem Y and reduce Y to X
The first problem that was proved as NP-complete was the circuit satisfiability problem.
NP-complete is a subset of NP Hard

Let SHAM3 be the problem of finding a Hamiltonian cycle in a graph G = (V,E) with V divisible by 3 and DHAM3 be the problem of determining if a Hamiltonian cycle exists in such graphs. Which one of the following is true?

Both DHAM3 and SHAM3 are NP-hard
SHAM3 is NP-hard, but DHAM3 is not
DHAM3 is NP-hard, but SHAM3 is not
Neither DHAM3 nor SHAM3 is NP-hard

Consider the following two problems of graph. 1) Given a graph, find if the graph has a cycle that visits every vertex exactly once except the first visited vertex which must be visited again to complete the cycle.2) Given a graph, find if the graph has a cycle that visits every edge exactly once. Which of the following is true about above two problems.

Problem 1 belongs NP Complete set and 2 belongs to P
Problem 1 belongs to P set and 2 belongs to NP Complete set
Both problems belong to P set
Both problems belong to NP complete set

Given the following statements: S1 : Every context-sensitive language L is recursive S2 : There exists a recursive language that is not context-sensitive Which statements are true?

Both S1 and S2 are not correct
Both S1 and S2 are correct

The problems 3-SAT and 2-SAT are

NP-complete and in P, respectively
Undecidable and NP-complete, respectively

For problems X and Y, Y is NP-complete and X reduces to Y in polynomial time. Which of the following is TRUE?

If X can be solved in polynomial time, then so can Y
X is in NP, but not necessarily NP-complete

There are 20 questions to complete.

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