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

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

$$\begin{aligned} & S \rightarrow a a B \mid A b b \\ & A \rightarrow a \mid a A \\ & B \rightarrow b \mid b B \end{aligned}$$

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

A
$L(G)=\left\{a^2 b^n \mid n \geq 1\right\} \cup\left\{a^n b^2 \mid n \geq 1\right\}$
B
$L(G)=\left\{a^n b^{2 n} \mid n \geq 1\right\} \cup\left\{a^{2 n} b^n \mid n \geq 1\right\}$
C
$L(G)=\left\{a^n b^n \mid n \geq 1\right\}$
D
$L(G)=\left\{a^{2 n} b^{2 n} \mid n \geq 1\right\}$
3
GATE CSE 2021 Set 2
MCQ (More than One Correct Answer)
+1
-0
Let L1 be a regular language and L2 be a context-free language. Which of the following languages is/are context-free?
A
L1 ∩ L̅2
B
L1 ∪ (L2 ∪ L̅2)
C
$$\overline {{{\bar L}_1} \cup {{\bar L}_2}} $$
D
(L∩ L2) ∪ (L̅1 ∩ L2)
4
GATE CSE 2021 Set 1
MCQ (Single Correct Answer)
+1
-0.33
Suppose that L1 is a regular and L2 is a context-free language, Which one of the following languages is NOT necessarily context-free?
A
L1 ⋅ L2
B
L1 ∪ L2
C
L1 ∩ L2
D
L1 - L2
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