The value of $\dfrac{\tan^{-1}(1) + \cos^{-1}\left(\dfrac{1}{2}\right) + \sin^{-1}\left(\dfrac{1}{2}\right)}{\tan^{-1}(\sqrt{3}) - \sec^{-1}(-2)}$ is equal to

If $g(x)$ is the inverse function of $f(x)$, where $f(x) = \dfrac{5x+3}{4x-1}$, then $g(1) =$

If $f(x)$ is continuous at $x = 0$, where $f(x) = \dfrac{8^x - 2^x}{k^x - 1}$, for $x \neq 0$ and $f(0) = 2$, then the value of $k$ is ...

$\dfrac{d}{dx}\left[\sin^2\left\{\cot^{-1}\sqrt{\dfrac{1-x}{1+x}}\right\}\right] =$ ...