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 *G = (V, Σ, S, P)* be a context-free grammar in Chomsky Normal Form with *Σ = { a, b, c }* and *V* containing 10 variable symbols including the start symbol *S*. The string *w = a ^{30}b^{30}c^{30}* is derivable from

*S*. The number of steps (application of rules) in the derivation

*S ⟹ w*is _______

_{1}is a regular and L

_{2}is a context-free language, Which one of the following languages is NOT necessarily context-free?

Consider the following context-free grammar where the set of terminals is {a, b, c, d, f}.

S → d a T | R f

T → a S | b a T | ϵ

R → c a T R | ϵ

The following is a partially-filled LL(1) parsing table.

Which one of the following choices represents the correct combination for the numbered cells in the parsing table ("blank" denotes that the corresponding cell is empty)?