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?

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 __________.

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?

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?