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

By dropping a stone in a quiet lake, a wave in the form of circle is generated. The radius of the circular wave increases at the rate of $2.1 \mathrm{~cm} / \mathrm{sec}$. Then the rate of increase of the enclosed circular region, when the radius of the circular wave is 10 cm , is (Given $\pi=\frac{22}{7}$)

The angle between the curves $x y=6$ and $x^2 y=12$ is