Question 1 |
The problem 3-SAT and 2-SAT are
both in P | |
both NP complete | |
NP -complete and in P respectively | |
undecidable and NP complete respectively |
Question 1 Explanation:
Question 2 |
Language L_{1} is polynomial time reducible to language L_{2}. Language L_{3} is polynomial time reducible to L_{2}, which in turn is polynomial time reducible to language L_{4}. Which of the following is/are true?
I. if L_{4} \in P, then L_{2} \in P
II. if L_{1} \in P or L_{3} \in P, then L_{2} \in P
III. L_{1} \in P, if and only if L_{3} \in P
IV. if L_{4} \in P, then L_{1} \in P and L_{3} \in P
I. if L_{4} \in P, then L_{2} \in P
II. if L_{1} \in P or L_{3} \in P, then L_{2} \in P
III. L_{1} \in P, if and only if L_{3} \in P
IV. if L_{4} \in P, then L_{1} \in P and L_{3} \in P
II only | |
III only | |
I and IV only | |
I only |
Question 2 Explanation:
Question 3 |
Consider two decision problems Q1,Q2 such that Q1 reduces in polynomial time to 3-SAT and 3-SAT reduces in polynomial time to Q2. Then which one of the following is consistent with the above statement?
Q1 is in NP, Q2 is NP hard. | |
Q2 is in NP, Q1 is NP hard | |
Both Q1 and Q2 are in NP . | |
Both Q1 and Q2 are NP hard |
Question 3 Explanation:
Question 4 |
Consider the decision problem 2CNFSAT defined as follows:
{ \phi | \phi is a satisfiable propositional formula in CNF with at most two literal per clause}
For example, \phi =(x_{1} \vee x_{2}) \wedge (x_{1} \vee \bar{x_{3}}) \wedge (x_{2} \vee x_{4}) is a Boolean formula and it is in 2CNFSAT.
The decision problem 2CNFSAT is
{ \phi | \phi is a satisfiable propositional formula in CNF with at most two literal per clause}
For example, \phi =(x_{1} \vee x_{2}) \wedge (x_{1} \vee \bar{x_{3}}) \wedge (x_{2} \vee x_{4}) is a Boolean formula and it is in 2CNFSAT.
The decision problem 2CNFSAT is
NP-Complete | |
solvable in polynomial time by reduction to directed graph reachability. | |
solvable in constant time since any input instance is satisfiable | |
NP-hard, but not NP-complete |
Question 4 Explanation:
Question 5 |
Suppose a polynomial time algorithm is discovered that correctly computes the largest clique
in a given graph. In this scenario, which one of the following represents the correct Venn
diagram of the complexity classes P, NP and NP Complete (NPC)?


A | |
B | |
C | |
D |
Question 5 Explanation:
Question 6 |
Which of the following statements are TRUE?
1. The problem of determining whether there exists a cycle in an undirected graph is in P.
2. The problem of determining whether there exists a cycle in an undirected graph is in NP.
3. If a problem A is NP-Complete, there exists a non-deterministic polynomial time algorithm to solve A.
1. The problem of determining whether there exists a cycle in an undirected graph is in P.
2. The problem of determining whether there exists a cycle in an undirected graph is in NP.
3. If a problem A is NP-Complete, there exists a non-deterministic polynomial time algorithm to solve A.
1, 2 and 3 | |
1 and 2 only | |
2 and 3 only | |
1 and 3 only |
Question 6 Explanation:
Question 7 |
Assuming P \neq NP, which of the following is TRUE?
NP-complete = NP | |
NP-complete \cap P = \phi | |
NP-hard = NP | |
P = NP-complete |
Question 7 Explanation:
Question 8 |
Let \pi _{A} be a problem that belongs to the class NP. Then which one of the following is TRUE?
There is no polynomial time algorithm for \pi _{A}. | |
If \pi _{A} can be solved deterministically in polynomial time, then P = NP. | |
If \pi _{A} is NP-hard, then it is NP-complete. | |
\pi _{A} may be undecidable |
Question 8 Explanation:
Question 9 |
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 9 Explanation:
Question 10 |
The subset-sum problem is defined as follows: Given a set S of n positive
integers and a positive integer W, determine whether there is a subset of S
Whose elements sum to W.
An algorithm Q solves this problem in O(nW) time. Which of the following statements is false?
An algorithm Q solves this problem in O(nW) time. Which of the following statements is false?
Q solves the subset-sum problem in polynomial time when the input is
encoded in unary | |
Q solves the subset-sum problem in polynomial time when the input is
encoded in binary | |
The subset sum problem belongs to the class NP | |
The subset sum problem is NP-hard |
Question 10 Explanation:
There are 10 questions to complete.