$\sum\limits_{k=1}^{2026} \sin^{-1}\left(\cos\dfrac{k\pi}{4}\right) =$

If $\sin^{-1}\left(\tan\dfrac{\pi}{4}\right) - \sin^{-1}\left(\sqrt{\dfrac{3}{x}}\right) = \dfrac{\pi}{6}$ then $x$ is a root of the equation

If $f(x) = x^2$ and $g(x) = [x^2]$ where $[\cdot]$ represents the greatest integer function then, $(f \circ g)\left(\dfrac{3}{2}\right) + (g \circ f)\left(\dfrac{3}{2}\right)$ is equal to ...

If $y = \sin(2\sin^{-1} x)$ then $\dfrac{dy}{dx} =$..