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?

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.

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.