BM Sharma Solutions for Chapter: Basic Mathematics, Exercise 6: DPP

A ladder is resting with the wall at an angle of $30°.$ A man is ascending the ladder at the rate of $3 \mathrm{ft} {\mathrm{s}}^{-1}$. His rate of approaching the wall is

If the edge of a cube increases at the rate of $60 \mathrm{cm} {\mathrm{s}}^{-1}$, at what rate the volume is increasing when the edge is $90 \mathrm{cm}$?

If the rate of increase of the area of a circle is not constant but the rate of increase of perimeter is constant, then the rate of increase of area varies

The sides of an equilateral triangle are increasing at a rate of $2 \mathrm{cm} {\sec }^{-1}$. The rate at which the area increases, when the side is$10 \mathrm{cm}$ is

A spherical iron ball $10 \mathrm{cm}$ in radius is coated with a layer of ice of uniform thickness that melts at a rate of $50 {\mathrm{cm}}^3 {\min }^{-1}$. When the thickness of ice is$5 \mathrm{cm}$, then the rate at which the thickness of ice decreases, is

A spherical balloon is being inflated at a rate of $35 \mathrm{cc} {\min }^{-1}$. The rate of increase of the surface area of the balloon when its diameter is $14 \mathrm{cm}$ is

A population $p\left(t\right)$ of $1000$ bacteria introduced into nutrient medium grows according to the relation $p\left(t\right)=1000+\frac{1000t}{100+t^2}$. The maximum size of this bacterial population is

A ladder $10 \mathrm{m}$ long rests against a vertical wall with the lower end on the horizontal ground. The lower end of the ladder is pulled along the ground away from the wall at a rate of $3 \mathrm{cm} {\sec }^{-1}$. The height of the upper end while it is descending at the rate of $4 \mathrm{cm} {\sec }^{-1}$ is