# 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:
 Question 6
If L is a regular language over $\Sigma =\{a,b\}$, which one of the following languages is NOT regular ?
 A $L\cdot L^R=\{xy|x \in L,y^R \in L\}$ B $\{ww^R|w \in L\}$ C Prifix(L)={$x \in \Sigma ^*|\exists y \in \Sigma ^*$ such that $xy \in L$} D Suffix(L)={$y \in \Sigma ^*|\exists x \in \Sigma ^*$ such that $xy \in L$}
GATE CSE 2019   Theory of Computation
Question 6 Explanation:
 Question 7
Choose the correct statement -
 A $A=\left\{a^{n} b^{n} \mid n=1,2,3, \ldots\right\}$ is a regular language B The set B, consisting of all strings made up of only $a^{\prime} s$ and $b^{\prime} s$ having equal number of $a^{\prime} s$ and bs defines a regular language C $L\left(A^{*} B\right) \cap B$ gives the set A D None of the above
ISRO CSE 2018   Theory of Computation
Question 7 Explanation:
 Question 8
Language L1 is defined by the grammar: $S_{1}\rightarrow aS_{1}b|\varepsilon$
Language L2 is defined by the grammar: $S_{2}\rightarrow abS_{2}|\varepsilon$
Consider the following statements:
P: L1 is regular
Q: L2 is regular
Which one of the following is TRUE?
 A Both P and Q are true B P is true and Q is false C P is false and Q is true D Both P and Q are false
GATE CSE 2016 SET-2   Theory of Computation
Question 8 Explanation:
 Question 9
Let $R_{1}$ and $R_{2}$ be regular sets defined over the alphabet, then
 A $R_{1} \cap R_{2}$ is not regular B $R_{1} \cup R_{2}$ is not regular C $\Sigma^{*}-R_{1}$ is regular D $R_{1}^{*}$ is not regular
ISRO CSE 2015   Theory of Computation
Question 9 Explanation:
 Question 10
Which of the following languages is/are regular?
$L_{1}:\{wxw^{R}|w,x \in \{a,b\}^{*} \; and \; |w|,|x| \gt 0 \}, w^{R}$ is the reverse of string w
$L_{2}:\{a^{n}b^{m}|m\neq n \; and \; m,n\geq 0\}$
$L_{3}:\{a^{p}b^{q}c^{r}|p,q,r\geq 0\}$
 A L1 and L3 only B L2 only C L2 and L3 only D L3 only
GATE CSE 2015 SET-2   Theory of Computation
Question 10 Explanation:
There are 10 questions to complete.

### 5 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.