GATE CSE 2025 Session 1 Q19: Language generated by S → aaB | Abb

Theory of Computation
1 mark
MCQ
−1/3 if wrong

Consider the following context-free grammar $G$ , where $S$ , $A$ , and $B$ are the variables (non-terminals), $a$ and $b$ are the terminal symbols, $S$ is the start variable, and the rules of $G$ are described as:

$\begin{aligned} S &\to aaB \mid Abb \\ A &\to a \mid aA \\ B &\to b \mid bB \end{aligned}$

Which ONE of the languages $L(G)$ is accepted by $G$ ?

Try it: multiple choice: exactly one correct option

Wrong answer costs 1/3 mark in GATE.

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Answer: A (official GATE 2025 final answer key)

Concept used: Reading off the language of a simple CFG rule by rule.

First step: $A$ generates $a^n$ ( $n \ge 1$ ) and $B$ generates $b^n$ ( $n \ge 1$ ); substitute them into $aaB$ and $Abb$ .

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Source: official GATE 2025 Session 1 CS question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key

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GATE CSE 2025 Session 1 Q19: Language generated by S → aaB | Abb

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