A hemispherical depression is cut out from one face of a cuboidal block of side 7cm such that the diameter of the hemisphere is equal to the edge of the cube. Find the surface area of the remaining solid.

If the angle of elevation of a cloud from a point 10 metres above a lake is 30° and the angle of depression of its reflection in the lake is 60°, find the height of the cloud from the surface of lake.

OR

A vertical tower of height 20 m stands on a horizontal plane and is surmounted by a vertical flag - staff of height h. At a point on the plane, the angle of elevation of the bottom and top of the flag staff are 45° and 60° respectively. Find the value of h.

Show that (12)ⁿ cannot end with digit 0 or 5 for any natural number n.

OR

Prove that (√2 + √5) is irrational.

For the following frequency distribution, draw a cumulative frequency curve of 'more than' type and hence obtain the median value.

If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes 1/2 if we only add 1 to the denominator. What is the fraction?