Question 1 |

Consider the following languages:

\begin{aligned} L_1&= \{ ww|w \in \{a,b \}^* \} \\ L_2&= \{a^nb^nc^m | m,n \geq 0 \} \\ L_3 &= \{a^mb^nc^n|m,n \geq 0 \} \end{aligned}

Which of the following statements is/are FALSE?

\begin{aligned} L_1&= \{ ww|w \in \{a,b \}^* \} \\ L_2&= \{a^nb^nc^m | m,n \geq 0 \} \\ L_3 &= \{a^mb^nc^n|m,n \geq 0 \} \end{aligned}

Which of the following statements is/are FALSE?

**MSQ**L_1 is not context-free but L_2 and L_3 are deterministic context-free. | |

Neither L_1 nor L_2 is context-free. | |

L_2,L_3 and L_2 \cap L_3 all are context-free. | |

Neither L_1 nor its complement is context-free. |

Question 1 Explanation:

Question 2 |

Consider the following languages:

\begin{aligned} L_1&= \{a^n wa^n|w \in \{a,b \}^* \} \\ L_2&= \{wxw^R | w,x \in \{a,b \}^*, |w|,|x| \gt 0 \} \end{aligned}

Note that w^R is the reversal of the string w. Which of the following is/are TRUE?

\begin{aligned} L_1&= \{a^n wa^n|w \in \{a,b \}^* \} \\ L_2&= \{wxw^R | w,x \in \{a,b \}^*, |w|,|x| \gt 0 \} \end{aligned}

Note that w^R is the reversal of the string w. Which of the following is/are TRUE?

**MSQ**L_1 and L_2 are regular. | |

L_1 and L_2 are context-free. | |

L_1 is regular and L_2 is context-free. | |

L_1 and L_2 are context-free but not regular. |

Question 2 Explanation:

Question 3 |

For a string w, we define w^R to be the reverse of w. For example, if w=01101 then w^R=10110.

Which of the following languages is/are context-free?

Which of the following languages is/are context-free?

**[MSQ]**\{ wxw^Rx^R \mid w,x \in \{0,1\} ^* \} | |

\{ ww^Rxx^R \mid w,x \in \{0,1\} ^* \} | |

\{ wxw^R \mid w,x \in \{0,1\} ^* \} | |

\{ wxx^Rw^R \mid w,x \in \{0,1\} ^* \} |

Question 3 Explanation:

Question 4 |

Let L_1 be a regular language and L_2 be a context-free language. Which of the following languages is/are context-free?

**[MSQ]**L_1 \cap \overline{L_2} | |

\overline{\overline{L_1} \cup \overline{L_2}} | |

L_1 \cup (L_2 \cup \overline{L_2}) | |

(L_1 \cap L_2) \cup (\overline{L_1} \cap L_2) |

Question 4 Explanation:

Question 5 |

Suppose that L_1 is a regular language and L_2 is a context-free language. Which one of the following languages is NOT necessarily context-free?

L_1\cap L_2 | |

L_1\cdot L_2 | |

L_1 - L_2 | |

L_1\cup L_2 |

Question 5 Explanation:

Question 6 |

Consider the following languages.

L_1=\{wxyx|w,x,y \in (0+1)^+\}

L_2=\{xy|x,y \in (a+b)^*,|x|=|y|,x\neq y\}

Which one of the following is TRUE?

L_1=\{wxyx|w,x,y \in (0+1)^+\}

L_2=\{xy|x,y \in (a+b)^*,|x|=|y|,x\neq y\}

Which one of the following is TRUE?

L_1 is regular and L_2 is context- free. | |

L_1 context- free but not regular and L_2 is context-free. | |

Neither L_1 nor L_2 is context- free. | |

L_1 context- free but L_2 is not context-free. |

Question 6 Explanation:

Question 7 |

Consider the language L=\{a^n|n\geq 0\}\cup \{a^nb^n|n\geq 0\} and the following statements.

I. L is deterministic context-free.

II. L is context-free but not deterministic context-free.

III. L is not LL(k) for any k.

Which of the above statements is/are TRUE?

I. L is deterministic context-free.

II. L is context-free but not deterministic context-free.

III. L is not LL(k) for any k.

Which of the above statements is/are TRUE?

I only | |

II only | |

I and III only | |

III only |

Question 7 Explanation:

Question 8 |

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

\{ww^R|w \in \{a,b\}^*\} | |

\{wa^nb^nw^R|w \in \{a,b\}^*,n\geq 0\} | |

\{wa^nw^Rb^n|w \in \{a,b\}^*,n\geq 0\} | |

\{a^nb^i|i \in \{n,3n,5n\},n\geq 0\} |

Question 8 Explanation:

Question 9 |

Consider the following languages:

I. \{a^{m}b^{n}c^{p}d^{q}|m+p=n+q, \; where \; m,n,p,q \geq 0 \}

II. \{a^{m}b^{n}c^{p}d^{q}|m=n \; and \; p=q, \; where \; m,n,p,q\geq 0 \}

III. \{a^{m}b^{n}c^{p}d^{q}|m=n=p \; and \; p\neq q, \; where \; m,n,p,q\geq 0 \}

IV. \{a^{m}b^{n}c^{p}d^{q}|mn=p+q, \; where\; m,n,p,q\geq 0\}

Which of the languages above are context-free?

I. \{a^{m}b^{n}c^{p}d^{q}|m+p=n+q, \; where \; m,n,p,q \geq 0 \}

II. \{a^{m}b^{n}c^{p}d^{q}|m=n \; and \; p=q, \; where \; m,n,p,q\geq 0 \}

III. \{a^{m}b^{n}c^{p}d^{q}|m=n=p \; and \; p\neq q, \; where \; m,n,p,q\geq 0 \}

IV. \{a^{m}b^{n}c^{p}d^{q}|mn=p+q, \; where\; m,n,p,q\geq 0\}

Which of the languages above are context-free?

I and IV only | |

I and II only | |

II and III only | |

II and IV only |

Question 9 Explanation:

Question 10 |

Consider the following languages

L_{1}=\{a^{p}|p is a prime number}

L_{2}=\{a^{n}b^{m}c^{2m}|n\geq 0,m\geq 0\}

L_{3}=\{a^{n}b^{n}c^{2n}|n\geq 0\}

L_{4}=\{a^{n}b^{n}|n\geq 1\}

Which of the following are CORRECT ?

I.L_{1} is context-free but not regular.

II. L_{2} is not context-free.

III. L_{3} is not context-free but recursive.

IV. L_{4} is deterministic context-free.

L_{1}=\{a^{p}|p is a prime number}

L_{2}=\{a^{n}b^{m}c^{2m}|n\geq 0,m\geq 0\}

L_{3}=\{a^{n}b^{n}c^{2n}|n\geq 0\}

L_{4}=\{a^{n}b^{n}|n\geq 1\}

Which of the following are CORRECT ?

I.L_{1} is context-free but not regular.

II. L_{2} is not context-free.

III. L_{3} is not context-free but recursive.

IV. L_{4} is deterministic context-free.

I ,II and IV only | |

II and III only | |

I and IV only | |

III and IV only |

Question 10 Explanation:

There are 10 questions to complete.

Question 14 4th point L2 is complement PLZZ correct it. 🙏

In question no 21 check the power of B in L1. 🙏

17th Question and option , both are wrong .

please correct it .

Thank You shivam,

We have updated the answer.

In Question 13, Both B and C options are the same.

Thank You Rashmi,

We have updated the option.

question no. 13 option b and c both are same , please update

Thank You dp kushwaha,

We have updated the option.

question no. 26 wrong please update with L intersection M

Thank You dp,

We have updated the question.