The surface area of a spherical ball is increasing at the rate of $4\pi\ \text{cm}^2$/second. The rate at which the radius is increasing when the surface area is $16\pi\ \text{cm}^2$ is

The maximum value of $\left(\dfrac{1}{x}\right)^x$, $x > 0$ is

The point on the curve $9y^2 = x^3$ where the normal to the curve makes equal intercepts with the co-ordinate axes is

A spherical mothball has initial radius 3 cm. Due to evaporation, the radius of the ball reduces to 1 cm in 4 months. In how many months would the mothball evaporate completely if the volume is lost at a rate proportional to the surface area ?