The father's age is 15 times his son's age. After 10 years, the age of the father will be 5 times his son's age. The present ages of the son and the father are, respectively

In the given figure, ^@ PA ^@ is a tangent from an external point ^@ P ^@ to a circle with centre ^@ O ^@. If ^@ \angle BOP = 127^\circ ^@, find ^@ \angle APO ^@.

To warn ships for underwater rocks, a lighthouse throws a red colored light over a sector of angle ^@ 75^\circ ^@ to a distance of ^@ 2.8 \space km^@. Find the area of the sea over which the ships are warned. ^@ \bigg( ^@ Use ^@ \pi = \dfrac { 22 } { 7 } \bigg)^@

A hemisphere depression is cut out from one face of a cubical wooden block such that the diameter of the hemisphere is equal to the edge of the cube. Choose the correct surface area of the remaining solid.

In this diagram, the triangle represents men, the square represents engineers and the circle represents employed. Find the number of men who are employed but not engineers.