GATE CSE 2026 Set 2 | Finite Automata and Regular Language Question 1 | Theory of Computation

GATE CSE 2026 Set 2

MCQ (More than One Correct Answer)

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Consider the following two finite automata $D_1$ and $D_2$. GATE CSE 2026 Set 2 Theory of Computation - Finite Automata and Regular Language Question 1 English

Which of the following statements is/are true?

$\angle\left(D_1\right)=\angle\left(D_2\right)$

$\angle\left(D_1\right)$ is a proper subset of $\angle\left(D_2\right)$

$\angle\left(D_1\right) \cap L\left(D_2\right)=\{\in\}$

$\left(L\left(D_1\right) \cup L\left(D_2\right)\right)^*$ consists of all strings in $\{0,1\}^*$ whose length is divisible by 3 .

GATE CSE 2026 Set 2

Numerical

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The determinant of a $4 \times 4$ matrix $A$ is 3 . The value of the determinant of $2 A$ is

$\_\_\_\_$ . (answer in integer)

Your input ____

GATE CSE 2026 Set 1

MCQ (Single Correct Answer)

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Let $L_1$ and $L_2$ be two languages over a finite alphabet, such that $L_1 \cap L_2$ and $L_2$ are regular languages.

Which of the following statements is/are always true?

$L_1$ is regular

$L_1 \cup L_2$ is regular

$\overline{L_2}$ is context free

$L_1$ is context free

GATE CSE 2025 Set 2

MCQ (More than One Correct Answer)

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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 $\left.\#_a(w)=\#_b(w)\right\}$