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# GATE CS 2021 : Theory of computation Quiz 6 (App update required to attempt this test)

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Question 1

Consider the following statements regarding to the pumping lemma-

I. If NFA accept a string of length having atleast equal to the number of states I.e |w|<=n then language is infinite.

II. If n state FA is accepting infinite language it surely accept the string between length n & 2n-1.

Then which of the following is true regarding it?

I. If NFA accept a string of length having atleast equal to the number of states I.e |w|<=n then language is infinite.

II. If n state FA is accepting infinite language it surely accept the string between length n & 2n-1.

Then which of the following is true regarding it?

Question 2

Consider the following statements:

S_{1} : {(a^{n})^{m} |n __<__ m __>__ 0}

S_{2} :{(a^{n}b^{n})|n __>__1} {a^{n}b^{m} |n__>__1, m __>__ 1}

Which of the following is regular?

Question 3

The language of primes in unary is:

Question 4

Whether the language given by L = {a

^{n}b^{2n}c^{3n}| n>=1} is CFL or not? Write 1 for true or 0 for false.Question 5

Which one of the following languages over Σ = {a, b}is NOT context-free?

Question 6

Consider the following sentences.

I. If L_{1} ⋃ L_{2} is regular, then both L_{1} and L_{2} must be regular.

II. The class of regular languages is closed under infinite union.

Which of the above statements is/are TRUE?

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