1. Which of the following obey the closure properties of Regular language?
a. Homomorphism
b. Inverse Homomorphism
c. Reversal
d. All of the mentioned
Ans- d. All of the mentioned
2. Which among the following is the closure property of a regular language?
a. Emptiness
b. Universality
c. Membership
d. None of the mentioned
Ans- d. None of the mentioned
3. Which among the following are the boolean operations that under which regular languages are closed?
a. Union
b. Intersection
c. Complement
d. All of the mentioned
Ans- d. All of the mentioned
4. Suppose a regular language L is closed under the operation halving, then the result would be:
a. 1/4 L will be regular
b. 1/2 L will be regular
c. 1/8 L will be regular
d. All of the mentioned
Ans- d. All of the mentioned
5. If L1, L2 are regular and op(L1, L2) is also regular, then L1 and L2 are said to be ____ under an operation op.
a. open
b. closed
c. decidable
d. none of the mentioned
Ans- b. closed
6. Which of the following is not an example of counting argument?
a. Pigeonhole principle
b. Dirichlet's drawer principle
c. Dirichlet's box principle
d. None of the mentioned
Ans- d. None of the mentioned
7. Which of the following can refer a language to be non regular?
a. Pumping Lemma
b. Myphill Nerode
c. Both (a) and (b)
d. None of the mentioned
Ans- c. Both (a) and (b)
8. Which of the following fields may have pigeonhole principle violated?
a. Discrete mathematics
b. Computer Science
c. Quantum Mechanics
d. None of the mentioned
Ans- c. Quantum Mechanics
9. If n objects are distributed over m places, and n < m, then some of the places receive:
a. at least 2 objects
b. at most 2 objects
c. no object
d. none of the mentioned
Ans- c. no object
10. Pigeonhole principle can be applied in the following computer science algorithms:
a. hashing algorithm
b. lossless compression algorithm
c. both (a) and (b)
d. None of the mentioned
Ans- c. both (a) and (b)