The value of $\lim_{x \to 3} \dfrac{[x] - 3}{x - 3}$, where $[\cdot]$ denotes the greatest integer function, is.....

If the truth value of the compound statement $[(p \vee q) \wedge (q \rightarrow r) \wedge (\sim r)] \rightarrow (p \wedge q)$ is False then the truth values of $p \rightarrow q$ and $q \rightarrow p$ are respectively......

The statement pattern $(p \vee q) \rightarrow \sim r$ is logically equivalent to

In $\triangle ABC$, with usual notations, if $\cos A = \dfrac{1}{2}, a = 3, \angle B = \dfrac{\pi^c}{6}$, then the values of $b$ and $c$ are.....