Question 1 |

Which of the following statements is/are CORRECT?

The intersection of two regular languages is regular. | |

The intersection of two context-free languages is context-free. | |

The intersection of two recursive languages is recursive. | |

The intersection of two recursively enumerable languages is recursively enumerable. |

Question 1 Explanation:

Question 2 |

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 2 Explanation:

Question 3 |

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 3 Explanation:

Question 4 |

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 4 Explanation:

Question 5 |

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 5 Explanation:

There are 5 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.