1
GATE CSE 2022
MCQ (More than One Correct Answer)
+1
-0.33

Consider the following languages:

L1 = {an wan | w $$\in$$ {a, b}*}

L2 = {wxwR | w, x $$\in$$ {a, b}*, | w | , | x | > 0}

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

A
L1 and L2 are regular.
B
L1 and L2 are context-free
C
L1 is regular and L2 is context-free.
D
L1 and L2 are context-free but not regular.
2
GATE CSE 2022
MCQ (More than One Correct Answer)
+1
-0.33

Consider the following languages:

$$\eqalign{ & {L_1} = \{ ww|w \in \{ a,b\} *\} \cr & {L_2} = \{ {a^n}{b^n}{c^m}|m,\,n \ge 0\} \cr & {L_3} = \{ {a^m}{b^n}{c^n}|m,\,n \ge 0\} \cr} $$

Which of the following statements is/are FALSE?

A
L1 is not context-free but L2 and L2 are deterministic context-free.
B
Neither L1 nor L2 is context-free.
C
L2, L3 and L2 $$\cap$$ L3 all are context-free.
D
Neither L1 nor its complement is context-free.
3
GATE CSE 2020
MCQ (Single Correct Answer)
+1
-0.33
Consider the language
L = { $${a^n}|n \ge 0$$ } $$ \cup $$ { $${a^n}{b^n}|n \ge 0$$ }
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?
A
I only
B
II only
C
I and III only
D
III only
4
GATE CSE 2016 Set 1
MCQ (Single Correct Answer)
+1
-0.3
Which of the following languages is generated by the given grammar? $$$S \to aS|bS|\varepsilon $$$
A
$$\left\{ {{a^n}{b^m}|n,m \ge 0} \right\}$$
B
$$\left\{ {w \in \left\{ {a,b} \right\}{}^ * |w} \right.$$ has equal number of $$a’s$$ and $$\left. {b's} \right\}$$
C
$$\left\{ {{a^n}|n \ge 0} \right\} \cup \left\{ {{b^n}|n \ge 0} \right\} \cup \left\{ {{a^n}{b^n}|n \ge 0} \right\}$$
D
$${\left\{ {a,b} \right\}^ * }$$
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