#### On a straight line passing through the foot of a tower, two points C and D are at distances of 4 m and 16 m from the foot respectively. If the angles of elevation from C and D of the top of the tower are complementary, then find the height of the tower.

#### A bag contains 15 white and some black balls. If the probability of drawing a black ball from the bag is thrice that of drawing a white ball, find the number of black balls in the bag.

#### Three semicircles each of diameter 3 cm, a circle of diameter 4.5 cm and a semicircle of radius 4.5 cm are drawn in the given figure. Find the area of the shaded region.

#### In what ratio does the point \{({\frac{24}{11}, 1})}) divide the line segment joining the points P(2, -2) and Q(3, 7)? Also find the value of y.

#### Water in a canal, 5.4 m wide and 1.8 m deep, is flowing with a speed of 25 km/hour. How much area can it irrigate in 40 minutes, if 10 cm of standing water is required for irrigation?

#### In the given figure, two concentric circles with centre O have radii 21 cm and 42 cm. If ∠AOB = 60^{o}, find the area of the shaded region. Use π = \\frac{22}{7})

#### The dimensions of a solid iron cuboid are 4.4 m × 2.6 m × 1.0 m. It is melted and recast into a hollow cylindrical pipe of 30 cm inner radius and thickness 5 cm. Find the length of the pipe.

#### A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius on its circular face. The total height of the toy is 15.5 cm. Find the total surface area of the toy.

#### How many terms of an A.P. 9, 17, 25, .... must be taken to give a sum of 636?

#### If the roots of the equation (a^{2} + b^{2}) x^{2} – 2(ac + bd) x + (c^{2} + d^{2}) = 0 are equal, prove that \\frac{a}{c} = \frac{b}{d})