$A$ cylindrical tank of radius $10 \ m$ is being filled with wheat at the rate of $314 \ m^3/h$. The rate at which the depth of the wheat is increasing is: (in $m/h$)

$A$ ladder of length $13 \ m$ has one end resting against a vertical wall and the other on the ground. If the lower end moves away from the wall at a speed of $2 \ m/min$, then the speed (in $m/min$) at which the upper end falls when the bottom is $5 \ m$ away from the wall is

The total cost $C(x)$ in Rupees, associated with the production of $x$ units of an item is given by $C(x) = 0.05x^3 - 0.2x^2 + 3x + 500$. The marginal cost, where $x = 3$ is $\rule{1cm}{0.15mm}$ (in Rupees).

If $f(x) = x^{2}$,find $\frac{f(1.1) - f(1)}{1.1 - 1}$.

The rate of change of the volume of a sphere with respect to its surface area when the radius is $5 \ m$ is:

The area of a square increases at the rate of $0.5 \text{ cm}^2/\text{sec}$. The rate at which its perimeter is increasing when the side of the square is $10 \text{ cm}$ long,is