If $\lim\limits_{x \to 0}\dfrac{45^x - 9^x - 5^x + 1}{(k^x - 1)(3^x - 1)} = 2$, then the value of $k$ is ...

If the truth value of the compound statement $[(p \leftrightarrow q) \wedge (q \to r) \wedge \sim r] \to (p \wedge \sim q)$ is false, then the truth values of the statement patterns $(p \to q) \leftrightarrow (q \to r)$ and $\sim(p \vee r) \to (q \wedge p)$ are, respectively ...

The negation of the contrapositive of the statement $(p \vee \sim q) \to (p \wedge \sim q)$ is

In triangle ABC, with usual notations, if $a = 4, b = 5$ and $c = 6$, then angle C is equal to...