GATE CSE 2025 Set 2 | GATE CSE Year Wise Previous Years Questions

GATE CSE 2025 Set 2

MCQ (Single Correct Answer)

-0.33

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

Any regular language.

Any context-free language.

Any language accepted by a non-deterministic pushdown automaton.

Any decidable language.

GATE CSE 2025 Set 2

MCQ (Single Correct Answer)

-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?

Is $L\left(G_1\right)=L\left(G_2\right)$ ?

Is $L\left(G_1\right) \cap L\left(G_2\right)=\varnothing$ ?

Is $L\left(G_1\right)=L(R)$ ?

Is $L\left(G_1\right)=\varnothing$ ?

GATE CSE 2025 Set 2

MCQ (More than One Correct Answer)

-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?

(i) - (a), (ii) - (b), and (iii) - (c)

(i) - (b), (ii) - (a), and (iii) - (c)

(i) - (b), (ii) - (c), and (iii) - (a)

(i) - (a), (ii) - (c), and (iii) - (b)

GATE CSE 2025 Set 2

MCQ (More than One Correct Answer)

-0

Let $\Sigma=\{a, b, c\}$. For $x \in \Sigma^{\star}$, and $\alpha \in \Sigma$, let $\#_\alpha(x)$ denote the number of occurrences of a in $x$. Which one or more of the following option(s) define(s) regular language(s)?

$\left\{a^m b^n \mid m, n \geq 0\right\}$

$\{a, b\}^* \cap\left\{a^m b^n c^{m-n} \mid m \geq n \geq 0\right\}$

$\left\{w \mid w \in\{a, b\}^*, \#_a(w) \equiv 2(\bmod 7)\right.$, and $\left.\#_b(w) \equiv 3(\bmod 9)\right\}$

$\left\{w \mid w \in\{a, b\}^*, \#_a(w) \equiv 2(\bmod 7)\right.$, and $\left.\#_a(w)=\#_b(w)\right\}$

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