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1
GATE CSE 2026 Set 1
MCQ (More than One Correct Answer)
+1
-0

Consider the following grammar where $S$ is the start symbol, and $a$ and $b$ are terminal symbols.

$$ S \rightarrow a S b S|b S| \in $$

Which of the following statements is/are true?

A

The grammar is ambiguous.

B

The string $a b b$ has two distinct derivations in this grammar.

C

The string $a b a b$ has only one rightmost derivation.

D

The language generated by the grammar is undecidable.

2
GATE CSE 2025 Set 2
MCQ (Single Correct Answer)
+1
-0.33

Which ONE of the following languages is accepted by a deterministic pushdown automaton?

A
Any regular language.
B
Any context-free language.
C
Any language accepted by a non-deterministic pushdown automaton.
D
Any decidable language.
3
GATE CSE 2025 Set 2
MCQ (Single Correct Answer)
+1
-0.33

Let $G_1, G_2$ be Context Free Grammars (CFGs) and $R$ be a regular expression. For a grammar $G$, let $L(G)$ denote the language generated by $G$. Which ONE among the following questions is decidable?

A
Is $L\left(G_1\right)=L\left(G_2\right)$ ?
B
Is $L\left(G_1\right) \cap L\left(G_2\right)=\varnothing$ ?
C
Is $L\left(G_1\right)=L(R)$ ?
D
Is $L\left(G_1\right)=\varnothing$ ?
4
GATE CSE 2025 Set 2
MCQ (More than One Correct Answer)
+1
-0

Consider the two lists List-I and List-II given below:

List - I List - II
(i) Context free languages (a) Closed under union
(ii) Recursive languages (b) Not closed under complementation
(iii) Regular languages (c) Closed under intersection

For matching of items in List-I with those in List-II, which of the following option(s) is/ are CORRECT?

A
(i) - (a), (ii) - (b), and (iii) - (c)
B
(i) - (b), (ii) - (a), and (iii) - (c)
C
(i) - (b), (ii) - (c), and (iii) - (a)
D
(i) - (a), (ii) - (c), and (iii) - (b)
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