CAT (QA) PYQs

$AB$ is a diameter of a circle of radius $5 \mathrm{~cm}$. Let $P$ and $Q$ be two points on the circle so that the length of $PB$ is $6 \mathrm{~cm}$, and the length of $AP$ is twice that of $AQ$ . Then the length, in cm , of $QB$ is nearest to

Three circles of equal radii touch (but not cross) each other externally. Two other circles, X and Y, are drawn such that both touch (but not cross) each of the three previous circles. If the radius of X is more than that of Y, the ratio of the radii of X and Y is

From a rectangle $ABCD$ of area $768 \text{ sq cm}$, a semicircular part with diameter $AB$ and area $72\pi \text{ sq cm}$ is removed. The perimeter of the leftover portion, in cm, is