UGC-NET | UGC NET CS 2017 Jan – III | Question 19

Which of the following are not regular?
(A) Strings of even number of a’s.
(B) Strings of a’s, whose length is a prime number.
(C) Set of all palindromes made up of a’s and b’s.
(D) Strings of a’s whose length is a perfect square.
(A) (A) and (B) only
(B) (A), (B) and (C) only
(C) (B), (C) and (D) only
(D) (B) and (D) only


Answer: (C)

Explanation:

  1. Strings of even number of a’s is Regular because we can draw Finite acceptor(FA) for this.
  2. Strings of a’s, whose length is a prime number – There are infinite No. which are prime and we can’t design FA for infinite language.This is not Regular
  3. Set of all palindromes made up of a’s and b’s.This is not Regular because we can’t design FA for infinite language.
  4. Strings of a’s whose length is a perfect square.This is not Regular because we can’t design FA for infinite language.

So, option (C) is correct.

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