The length and breadth of a rectangular piece of land are in the ratio $5:3$. The owner spent ₹ $6000$ for fencing it from all sides at the rate of ₹ $7.50$ per metre. The difference between its length and breadth is (in metres):

In $\triangle ABC$,$\angle A = 90^{\circ}$ and $AD \perp BC$,where $D$ lies on $BC$. If $BC = 8 \ cm$ and $AC = 6 \ cm$,then the ratio of the area of $\triangle ABC$ to the area of $\triangle ACD$ is:

The area of the square inscribed in a circle of radius $8\, cm$ is......$cm^2$

The smallest side of a right-angled triangle is $8\, cm$ less than the side of a square of perimeter $56\, cm$. The second largest side of the right-angled triangle is $4\, cm$ less than the length of the rectangle of area $96\, cm^2$ and breadth $8\, cm$. What is the largest side of the right-angled triangle? (in $cm$)

If $D, E$ and $F$ are the mid-points of the sides of an equilateral triangle $ABC,$ then the ratio of the area of triangle $DEF$ and $DCF$ is

$A$ rectangular tin sheet is $22 \ m$ long and $8 \ m$ broad. It is rolled along its length to form a cylinder by making the opposite edges just to touch each other. The volume of the cylinder (in $m^3$) is