CAT (QA) PYQs

A rectangle with the largest possible area is drawn inside a semicircle of radius $2$ cm. Then, the ratio of the lengths of the largest to the smallest side of this rectangle is

A circle is inscribed in a rhombus with diagonals $12 \mathrm{~cm}$ and $16 \mathrm{~cm}$. The ratio of the area of circle to the area of rhombus is

All the vertices of a rectangle lie on a circle of radius $R$. If the perimeter of the rectangle is $P$, then the area of the rectangle is