Find the mean of the following data:

If 4 times the 4^th term of an AP is equal to 18 times the 18^th term, then find the 22^nd term.

OR

How many terms of the AP: 24, 21, 18, ….. must be taken so that their sum is 78?

The angle of elevation of the top a building from the foot of a tower is 30°. The angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 60 m high, find the height of the building.

In DEFG is a square in a triangle ABC right angled at A.

Prove that

(i) ΔAGF ∼ Δ DBG (ii) Δ AGF ∼ Δ EFC

OR

In an obtuse Δ ABC (∠B is obtuse), AD is perpendicular to CB produced. Then prove that AC² = AB² + BC² + 2BC × BD.

An open metal bucket is in the shape of a frustum of cone of height 21 cm with radii of its lower and upper ends are 10 cm and 20 cm respectively. Find the cost of milk which can completely fill the bucket at the rate of Rs 40 per litre.

OR

A solid in the shape of a cone surmounted on a hemisphere. The radius of each of them being 3.5 cm and the total height of the solid is 9.5 cm. Find the volume of the solid.