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

A circular plot of land is divided into two regions by a chord of length $10\sqrt{3}$ meters such that the chord subtends an angle of $120^\circ$ at the center. Then, the area, in square meters, of the smaller region is

Two circles, each of radius $4$ cm, touch externally. Each of these two circles is touched externally by a third circle. If these three circles have a common tangent, then the radius of the third circle, in cm, is