Top MCQs on NP Complete Complexity with Answers

Question 11

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 

• II only
• III only
• I and IV only
• I only

Question 12

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 NP-complete
• X is NP-hard
• X is in NP, but not necessarily NP-complete

Question 13

The problems 3-SAT and 2-SAT are

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

Question 14

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?

• Only S1 is correct
• Only S2 is correct
• Both S1 and S2 are not correct
• Both S1 and S2 are correct

Question 15

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

Question 16

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

Question 17

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

Question 18

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
• All of the above
• None of the above

Question 19

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

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

(C) NP-hard = NP

(D) P = NP-complete

• A

• B

• C

• D

Question 20

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

• Set cover problem

• Traveling salesman problem

• Knapsack problem

• Minimum spanning tree problem