Punjab Board-2018

Using differentials find approximate value of $0.{37}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$.

A window is in the form of rectangle surmounted by a semi-circular opening. The perimeter of window is $30\mathrm{m}$. Find the dimensions of window so that it can admit maximum light through the whole opening.

Prove that volume of largest cone, which can be inscribed in a sphere, is $\frac{8}{27}$ part of sphere.

If the height of right circular cylinder of maximum volume that can be inscribed in a sphere of radius $\sqrt{3}$ is $k\mathrm{\pi }$ cubic units, then the value of $k$ is

An open box is to be made of a square sheet of tin with side $20 \mathrm{cm}$ by cutting off small squares from each corner and folding the flaps Find the side of small square which is to be cut off so that volume of box is maximum.