Pre Boards

Practice to excel and get familiar with the paper pattern and the type of questions. Check you answers with answer keys provided.

Sample Papers

Download the PDF Sample Papers Free for off line practice and view the Solutions online.

CBSE Class 10 Mathematics Solved Question Paper 2017

Long Answer Type

21.

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

22.
Two different dice are thrown together. Find the probability that the numbers obtained have

(i) even sum, and

(ii) even product

Elementary events associated to the random experiment of throwing two dice are:

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6),

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6),

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6),

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6),

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6),

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6),

$∴$ Total number of elementary events = 6 x 6 = 36.

(i) Let A be the event of getting an even number as the sum.

i.e. 2, 4, 6, 8, 10, 12.

Elementary events favourable to event A are:

(1,1), (1,3), (1,5), (2,2), (2,4), (2,6),

(3,1), (3,3), (3,5), (4,2), (4,4), (4,6),

(5,1), (5,3), (5,5), (6,2), (6,4), (6,6).

$∴$ Total number of favourable events = 18.

Hence, required probability = $\frac{18}{36} = \frac{1}{2}$

(ii) Let B be the event of getting an even number as the product.

i.e. 2, 4, 6, 8, 10, 12, 16, 18, 20, 24, 30, 36.

Elementary events favourable to event B are:

(1,2), (1,4), (1,6), (2,1), (2,2), (2,3),

(2,4), (2,5), (2,6), (3,2), (3,4), (3,6),

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6),

(5,2), (5,4), (5,6), (6,1), (6,2), (6,3),

(6,4), (6,5), (6,6).

$∴$ Total number of favourable events = 27.

Hence, required probability = $\frac{27}{36} = \frac{3}{4}$ .

23.

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

24.

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 3.5m. If the tank is full, find the rainfall in cm. Write your views on water conservation

25.

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

26.

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.

27.

Solve for x:

$\frac{x - 1}{2 x + 1} + \frac{2 x + 1}{x - 1} = 2, Where x \neq - \frac{1}{2}, 1$

28.

A takes 6 days less than B to do a work. If both A and B working together can do it in 4 days, how many days will B take to finish it?

29.

From the top of a tower, 100 m high, a man observe two cars on the opposite sides of the tower and in same straight line with its base, with its base, with angles of depression 30° and 45°. Find the distance between the cars.
[Take $\sqrt{3}$ = 1.732]