Top MCQs on NP Complete Complexity with Answers

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Question 1

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

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Question 2

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

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Question 3

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

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Question 4

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

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Question 5

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
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Question 6

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

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Question 7

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
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Question 8

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

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Question 9

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

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Question 10

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

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There are 20 questions to complete.

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