Suppose that L₁ is a regular and L₂ 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)?

In a pushdown automaton P = (Q, ∑, Γ, δ, q₀, F), a transition of the form,

where p, q ∈ Q, a ∈ Σ ∪ {ϵ}, and X, Y ∈ Γ ∪ {ϵ}, represents

(q, Y) ∈ δ(p, a, X).

Consider the following pushdown automaton over the input alphabet ∑ = {a, b} and stack alphabet Γ = {#, A}.

The number of strings of length 100 accepted by the above pushdown automaton is ______

Let $$\left\langle M \right\rangle $$ denote an encoding of an automation M. Suppose that ∑ = {0, 1}. Which of the following languages is/are NOT recursive?