1
GATE CSE 2024 Set 2
MCQ (More than One Correct Answer)
+2
-0.66

Consider a context-free grammar $G$ with the following 3 rules.

$S \rightarrow aS, \ S \rightarrow aSbS, S \rightarrow c$

Let $w \in L(G)$.

Let $n_a(w)$, $n_b(w)$, $n_c(w)$ denote the number of times $a$, $b$, $c$ occur in $w$, respectively. Which of the following statements is/are TRUE?

A

$n_a(w) > n_b(w)$

B

$n_a(w) > n_c(w) - 2$

C

$n_c(w) = n_b(w) + 1$

D

$n_c(w) = n_b(w) * 2$

2
GATE CSE 2024 Set 2
Numerical
+2
-0.66

Let L1 be the language represented by the regular expression b*ab*(ab*ab*)* and L2 = { w ∈ (a + b)* | |w| ≤ 4 }, where |w| denotes the length of string w. The number of strings in L2 which are also in L1 is __________.

Your input ____
3
GATE CSE 2024 Set 2
MCQ (Single Correct Answer)
+1
-0.33

If ‘→’ denotes increasing order of intensity, then the meaning of the words [walk → jog → sprint] is analogous to [bothered → _______ → daunted].

Which one of the given options is appropriate to fill the blank?

A

phased

B

phrased

C

fazed

D

fused

4
GATE CSE 2024 Set 2
MCQ (Single Correct Answer)
+1
-0.33

Two wizards try to create a spell using all the four elements, water, air, fire, and earth. For this, they decide to mix all these elements in all possible orders. They also decide to work independently. After trying all possible combinations of elements, they conclude that the spell does not work.

How many attempts does each wizard make before coming to this conclusion, independently?

A

24

B

48

C

16

D

12

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