If the total surface area of a solid hemisphere is 462 cm², find its volume. [Take π = 22/7]

The incircle of an isosceles triangle ABC, in which AB = AC, touches the sides BC, CA and AB at D, E and F respectively. Prove that BD = DC.

Two different dice are tossed together. Find the probability

(i) That the number on each die is even.

(ii) That the sum of numbers appearing on the two dice is 5.

Solve for x:

; x ≠ 0, -1

The sum of the 5^th and the 9^th terms of an AP is 30. If its 25^th term is three times its 8^th term, find the AP.