A person standing on the bank of a river observes that the angles elevation of the top of a tree standing on opposite bank is 60°. When he moves 30 m away from the bank, he finds the angle of elevation to be 30°. Find the height of the tree and width of the river. [Take = 1732]

A horse is tethered to one corner of a rectangular field of dimensions 70 m × 52 m, by rope of length 21 m. How much area of the field can it graze?

Find the quadratic polynomial, the sum and product of whose zeroes are –3 and 2 respectively. Hence find the zeroes.

From a solid cylinder whose height is 15 cm and the diameter 15 16 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of remaining solid. (give your answer in terms of π)

OR

The height of a cone is 10 cm. The cone is divided into two parts using a plane parallel to its base at the middle of its height. Find the ratio of the volumes of the two parts.

Prove that the ratio of the areas of two similar triangle is equal to the ratio of the squares of their corresponding sides.

OR

Prove the length of tangents drawn from an external point to a circle are equal.