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?

Consider a knock-out women's badminton singles tournament where there are no ties. The loser in each game is eliminated from the tournament. Every player plays until she is defeated or remains the last undefeated player. The last undefeated player is declared the winner of the tournament. If there are 64 players in the beginning of the tournament, how many games should be played in total to declare the winner of the tournament?