Let $L_1$ and $L_2$ be two languages over a finite alphabet, such that $L_1 \cap L_2$ and $L_2$ are regular languages.

Which of the following statements is/are always true?

Consider the following context-free grammar $G$ :

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

In the above grammar, $S$ is the start symbol, $a$ and $b$ are terminal symbols, and $A$ and $B$ are non-terminal symbols.

Let $L(G)$ be the language generated by the grammar $G$. For a string $s \in L(G)$, let $n_1(s)$ be the number of a's in $s$ and $n_2(s)$ be the number of b's in $s$.

Which of the following statements is/are true?

The antonym of the word protagonist is $\_\_\_\_$ .

The figure shows two 4-tile patterns.

Either one or both of the patterns can be used any number of times and in any orientation to construct a new pattern. Which one of the options below cannot be constructed by using only these two 4-tile patterns assuming there are no overlaps among them?