# Regular Language

 Question 1
Consider the following two statements about regular languages:

S1: Every infinite regular language contains an undecidable language as a subset.
S2: Every finite language is regular.

Which one of the following choices is correct?
 A Only S1 is true B Only S2 is true C Both S1 and S2 are true D Neither S1 nor S2 is true
GATE CSE 2021 SET-2   Theory of Computation
Question 1 Explanation:
 Question 2
Let $L \subseteq \{0,1\}^*$ be an arbitrary regular language accepted by a minimal DFA with k states. Which one of the following languages must necessarily be accepted by a minimal DFA with k states?
 A $L - \{01\}$ B $L \cup \{01\}$ C $\{0,1\}^* -L$ D $L \cdot L$
GATE CSE 2021 SET-2   Theory of Computation
Question 2 Explanation:

 Question 3
Which of the following is true?
 A Every subset of a regular set is regular B Every finite subset of non-regular set is regular C The union of two non regular set is not regular D Infinite union of finite set is regular
ISRO CSE 2020   Theory of Computation
Question 3 Explanation:
 Question 4
Consider the following statements.

I. If $L_1\cup L_2$ 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?
 A I only B II only C Both I and II D Neither I nor II
GATE CSE 2020   Theory of Computation
Question 4 Explanation:
 Question 5
For $\Sigma =\{a,b\}$, let us consider the regular language
$L=\{x|x=a^{2+3k} \; or \; x=b^{10+12k}, k\geq 0\}$.
Which one of the following can be a pumping length (the constant guaranteed by the pumping lemma) for L?
 A 3 B 5 C 9 D 24
GATE CSE 2019   Theory of Computation
Question 5 Explanation:

There are 5 questions to complete.

### 7 thoughts on “Regular Language”

1. Remove the words “is prime” from the question number 8, option a, I think it’s get written by mistake.

• Thank you for your suggestions. We have updated the correction suggested by You.

2. Edit on question number 17.
It is “Which of the following statement is Correct.” ?