The slope of normal to the curve $y = 3x^2 + 3 \sin 3x$, at $x = 0$ is:

The slope of normal to the curve $y = kx^2 - 3x + 2$ at $x = \frac{1}{2}$ is 5. The value of 'k' 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 of volume of a sphere with respect to its surface area when radius of the sphere is 4 cm, is

The interval, on which the function $f(x) = x^2e^{-x}$ is increasing, is equal to

If $x$ is real, then the minimum value of $x^2 - 8x + 25$ is

Water is running into a conical vessel, 18cm deep and 6cm in radius, at the rate of 0.1 $cm^3$/sec. If the water is 4cm deep, then the water level rising at the rate