From a point on the ground, the angles of elevation of the bottom and top of a transmission tower fixed on the top of a 20 m high building are 45° and 60° respectively. Find the height of the tower.

If the line segment joining the points A(2, 1) and B(5, –8) is trisected at the points P and Q, find the coordinates of P.

For what value of n are the n^th terms of two A.P.’s 63, 65, 67, ... and 3, 10, 17, ... equal?

From a solid cylinder whose height is 8 cm and radius 6 cm, a conical cavity of same height and same base radius is hollowed out. Find the total surface area of the remaining solid. (Take π = 3.14)

A wire when bent in the form of an equilateral triangle encloses an area of 121√3 cm². If the wire is bent in the form of a circle, find the area enclosed by the circle (use ).