#### O is the centre of a circle such that diameter AB = 13 cm and AC = 12 cm. BC is joined. Find the area of the shaded region. (Take π = 3.14)

#### A tent is in the shape of a cylinder surmounted by a conical top of same diameter. If the height and diameter of cylindrical part are 2.1 m and 3 m respectively and the slant height of conical part is 2.8 m, find the cost of canvas needed to make the tent if the canvas is available at the rate of ` 500/sq.metre. (Use π \\frac{22}{7}))

#### If the point P(x, y) is equidistant from the points A(a + b, b – a) and P(a – b, a + b). Prove that bx = ay.

#### Find the area of the shaded region, enclosed between two concentric circles of radii 7 cm and 14 cm where ∠AOC = 40°. (Use π = \\frac{22}{7})

#### If the ratio of the sum of first n terms of two A.P's is (7n + 1) : (4n + 27), find the ratio of their m^{th} terms.

#### Solve for x : \\frac{1}{(x-1)(x-2)}) + \\frac{1}{(x-2)(x-3)}) = x ≠ 1, 2, 3.

#### A conical vessel, with base radius 5 cm and height 24 cm, is full of water. This water is emptied into a cylindrical vessel of base radius 10 cm. Find the height to which the water will rise in the cylindrical vessel, (Use π = \\frac{22}{7}))

#### A sphere of diameter 12 cm, is dropped in a right circular cylindrical vessel, partly filled with water. If the sphere is completely submerged in water, the water level in the cylindrical vessel rises by 3\\frac{5}{9}) cm. Find the diameter of the cylindrical vessel.

#### A man standing on the deck of a ship, which is 10 m above water level, observes the angle of elevation of the top of a hill as 60° and the angle of depression of the base of hill as 30°. Find the distance of the hill from the ship and the height of the hill.

#### Three different coins are tossed together. Find the probability of getting

(i) exactly two heads

(ii) at least two heads

(iii) at least two tails.