The total revenue in Rupees received from the sale of $x$ units of a product is given by $R(x) = x^2 + 6x + 5$. The marginal revenue,when $x = 20$,is . . . . . . .

Find the rate of change of the area of a circle with respect to its radius $r$ when $r = 3 \text{ cm}$. (in $\pi \text{ cm}$)

The volume $V$ and depth $x$ of water in a vessel are connected by the relation $V = 5x - \frac{x^2}{6}$. If the volume of water is increasing at the rate of $5 \, cm^3/sec$,find the rate at which the depth of water is increasing when $x = 2 \, cm$.

Two ships $A$ and $B$ are sailing straight away from a fixed point $O$ along routes such that $\angle AOB$ is always $120^o$. At a certain instance,$OA = 8 \ km$,$OB = 6 \ km$ and the ship $A$ is sailing at the rate of $20 \ km/hr$ while the ship $B$ is sailing at the rate of $30 \ km/hr$. Then the distance between $A$ and $B$ is changing at the rate (in $km/hr$):

$A$ ladder of length $17 \,m$ rests with one end against a vertical wall and the other on the level ground. If the lower end slips away at the rate of $1 \,m/sec$, then when it is $8 \,m$ away from the wall, its upper end is coming down at the rate of

The volume of a cube is increasing at a rate of $9 \text{ cm}^3/\text{s}$. How fast is the surface area increasing when the length of an edge is $10 \text{ cm}$ (in $\text{ cm}^2/\text{s}$)?