Mathematics All India Set 2 2016-2017 English Medium Class 10 Question Paper Solution

If a tower 30 m high, casts a shadow `10sqrt3` m long on the ground, then what is the angle of elevation of the sun?

The probability of selecting a rotten apple randomly from a heap of 900 apples is 0.18. What is the number of rotten apples in the heap?

What is the common difference of an A.P. in which a₂₁ – a₇ = 84?

If the angle between two tangents drawn from an external point P to a circle of radius a and centre O, is 60°, then find the length of OP

A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, –5) is the mid-point of PQ, then find the coordinates of P and Q.

If the distances of P(x, y) from A(5, 1) and B(–1, 5) are equal, then prove that 3x = 2y

Find the value of p, for which one root of the quadratic equation px² – 14x + 8 = 0 is 6 times the other.

Prove that the tangents drawn at the end points of a chord of a circle make equal angles with the chord.

A circle touches all the four sides of a quadrilateral ABCD. Prove that AB + CD = BC + DA.

Which term of the A.P. 8, 14, 20, 26, ... will be 72 more than its 41^st term?

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

In Figure , two concentric circles with centre O, have radii 21cm and 42 cm. If ∠ AOB = 60°, find the area of the shaded region. [use π=22/7]

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 what ratio does the point `(24/11, y)` divide the line segment joining the points P(2, –2) and Q(3, 7)? Also find the value of y.

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

From a solid right circular cylinder of height 2.4 cm and radius 0.7 cm, a right circular cone of same height and same radius is cut out. Find the total surface area of the remaining solid.

If the 10^th term of an A.P. is 52 and the 17^th term is 20 more than the 13^th term, find the A.P.

If the roots of the equation (c² – ab) x² – 2 (a² – bc) x + b² – ac = 0 in x are equal, then show that either a = 0 or a³ + b³ + c³ = 3abc

If the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k − 1, 5k) are collinear, then find the value of k

Two different dice are thrown together. Find the probability that the numbers obtained have

1) even sum, and

2) even product.

Construct a triangle ABC with sides BC = 7 cm, ∠B = 45° and ∠A = 105°. Then construct a triangle whose sides are `3/4` times the corresponding sides of ∆ABC.

In a rain-water harvesting system, the rain-water from a roof of 22 m × 20 m drains into a cylindrical tank having diameter of base 2 m and height 3·5 m. If the tank is full, find the rainfall in cm. Write your views on water conservation.

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

In the given figure, XY and X’Y’ are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X’Y’ at B. Prove that ∠AOB = 90°

If the ratio of the sum of the first n terms of two A.Ps is (7n + 1) : (4n + 27), then find the ratio of their 9^th terms.

Solve for x :

`1/(2x - 3) + 1/(x - 5) = 1 1/9 , X != 3/2, 5`

A train covers a distance of 300 km at a uniform speed. If the speed of the train is increased by 5 km/hour, it takes 2 hours less in the journey. Find the original speed of the train

A man observes a car from the top of a tower, which is moving towards the tower with a uniform speed. If the angle of depression of the car changes from 30^° to 45^° in 12 minutes, find the time taken by the car now to reach the tower.

In the given figure, ∆ ABC is a right-angled triangle in which ∠ A is 90°. Semicircles are drawn on AB, AC and BC as diameters. Find the area of the shaded region