If $\lim\limits_{x \to 0} \dfrac{(4^x - 1)^3}{\tan\left(\dfrac{x}{4}\right)\log\left(1 + \dfrac{x^2}{3}\right)} = 96(\log a)^b$, then $(a + b) = $

The dual of the converse of the inverse of the logical statement $p \to (q \to r)$ is equivalent to...

The statements p, q and r have truth values True, False and False respectively. The truth values of a logical statement $[\sim(p \wedge \sim q) \vee (q \vee \sim r)]$ and its dual are, respectively.....

In $\triangle ABC$ with usual notations, if $1 + \tan\left(\dfrac{A}{2}\right)\tan\left(\dfrac{B}{2}\right) = \dfrac{k}{s}$ (where $s$ is the semi-perimeter), then the value of $k$ is...