Spheres of unit diameter are centered at ( $l, m, n$ ) where $l, m$ and $n$ take every possible integer values.

The distance between two spheres is computed from the center of one sphere to the center of the other sphere. For a given sphere, $x$ is the distance to its nearest sphere and $y$ is the distance to its next nearest sphere. The value of $\frac{y}{x}$ is :

In the triangle PQR , the lengths of PT and TR are in the ratio of $3: 2$.

ST is parallel to QR. Two semi-circles are drawn with PS and PQ as diameters, as shown in the figure.

Which one of the following statements is true about the shaded area PQS?

Note: The figure shown is representative.