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?

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?

Only S1 is true | |

Only S2 is true | |

Both S1 and S2 are true | |

Neither S1 nor S2 is true |

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?

L - \{01\} | |

L \cup \{01\} | |

\{0,1\}^* -L | |

L \cdot L |

Question 2 Explanation:

Question 3 |

Which of the following is true?

Every subset of a regular set is regular | |

Every finite subset of non-regular set is regular | |

The union of two non regular set is not regular | |

Infinite union of finite set is regular |

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?

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?

I only | |

II only | |

Both I and II | |

Neither I nor II |

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?

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?

3 | |

5 | |

9 | |

24 |

Question 5 Explanation:

Question 6 |

If L is a regular language over \Sigma =\{a,b\}, which one of the following languages is NOT regular ?

L\cdot L^R=\{xy|x \in L,y^R \in L\} | |

\{ww^R|w \in L\} | |

Prifix(L)={x \in \Sigma ^*|\exists y \in \Sigma ^* such that xy \in L} | |

Suffix(L)={y \in \Sigma ^*|\exists x \in \Sigma ^* such that xy \in L} |

Question 6 Explanation:

Question 7 |

Choose the correct statement -

A=\left\{a^{n} b^{n} \mid n=1,2,3, \ldots\right\} is a regular language | |

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 | |

L\left(A^{*} B\right) \cap B gives the set A | |

None of the above |

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?

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?

Both P and Q are true | |

P is true and Q is false | |

P is false and Q is true | |

Both P and Q are false |

Question 8 Explanation:

Question 9 |

Let R_{1} and R_{2} be regular sets defined over the alphabet, then

R_{1} \cap R_{2} is not regular | |

R_{1} \cup R_{2} is not regular | |

\Sigma^{*}-R_{1} is regular | |

R_{1}^{*} is not regular |

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\}

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\}

L1 and L3 only | |

L2 only | |

L2 and L3 only | |

L3 only |

Question 10 Explanation:

There are 10 questions to complete.

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.

Edit on question number 17.

It is “Which of the following statement is Correct.” ?

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

For Question 2, please add a comma in Option c -> {0,1}* – L