If $\lim\limits_{x \to k} \dfrac{x^3 - k^3}{x^2 - k^2} = \lim\limits_{x \to 0} \dfrac{1 - \cos(2x)}{x \sin x}$, then the value of $k$ is $\ldots$

In a switching circuit, if the combination $(S_1 \wedge S_2)$ is connected in parallel to the combination $(S_1' \wedge S_2')$, then the room is lit only when $\ldots$

If the truth value of the statement pattern $(\sim p \wedge q) \vee (\sim p \wedge \sim q) \vee (p \wedge \sim q)$ is $F$, then the truth values of $(p \vee \sim q)$ and $(p \to q)$ are $\ldots$ respectively.

The minimum number of switches in the simplified form of the following switching circuit is