If $y = \cos^{-1}\left(\dfrac{1 - 4^x}{1 + 4^x}\right)$, then $\dfrac{dy}{dx}$ at $x = 1$ is

A cylindrical tank without a top lid is being manufactured to hold a fixed volume of $125\pi$ cubic cm. The minimum surface area required to construct this tank is ............square cm

A spherical snow ball is melting so that its volume is decreasing at the rate of 8 c.c./sec then the rate of change of radius when the radius is 2 cm, is :

The equation of tangent to the curves $x = 1 - 3t^2$ and $y = t - 3t^3$ at the point $(-2, 2)$ is...