The rate of change of area of a circle with respect to its circumference when radius in 6 cm, is

A solid sphere of gold of radius 5 cm, is being melted in a furnace such that the radius is decreasing uniformly. When the radius is 1cm, the rate at which surface area (A) is decreasing w.r.t. time ($t$) is equal to

($\frac{dv}{dt}$ = rate at which volume is decreasing w.r.t. $t$)

The rate of change in area of a triangle having sides 10 cm and 12 cm when the variable angle between them is $\theta = 60°$, is :

Consider a closed cylinder of radius $r$ with a fixed surface area. The volume of the cylinder is maximum when its height is

The interval on which the function $f(x) = x^4 - \frac{x^3}{3}$ is strictly decreasing, is:

The function $f(x) = \frac{x}{2} + \frac{2}{x}, x \neq 0$ is increasing on

(A) $(-\infty, -2)$

(B) $(-2, 2)$

(C) $(2, \infty)$

(D) $(-1, 1)$

Choose the correct answer from the options given below:

Match List-I with List-II

Choose the correct answer from the options given below: