English Medium Class 10 - CBSE Question Bank Solutions for Mathematics

An arithmetic progression 5, 12, 19, …. has 50 terms. Find its last term. Hence find the sum of its last 15 terms.

Construct a triangle ABC in which AB = 5 cm, BC = 6 cm and ∠ABC = 60˚. Now construct another triangle whose sides are 5/7 times the corresponding sides of ΔABC.

The probability of selecting a red ball at random from a jar that contains only red, blue and  orange balls is 1/4. The probability of selecting a blue ball at random from the same jar 1/3. If the jar contains 10 orange balls, find the total number of balls in the jar.

The 16^th term of an A.P. is five times its third term. If its 10^th term is 41, then find the sum of its first fifteen terms.

Find the 60^th term of the A.P. 8, 10, 12, ……., if it has a total of 60 terms and hence find the sum of its last 10 terms.

A bus travels at a certain average speed for a distance of 75 km and then travels a distance of 90 km at an average speed of 10 km/h more than the first speed. If it takes 3 hours to complete the total journey, find its first speed?

The 14^th term of an A.P. is twice its 8^th term. If its 6^th term is -8, then find the sum of its first 20 terms.

Construct a Δ ABC in which AB = 6 cm, ∠A = 30° and ∠B = 60°, Construct another ΔAB’C’ similar to ΔABC with base AB’ = 8 cm.

The probability that a number selected at random from the numbers 1, 2, 3, ..., 15 is a multiple of 4, is

`(A)4/15`

`(B)2/15`

`(C)1/5`

`(D)1/3`

The angle of depression of a car parked on the road from the top of a 150 m high tower is 30°. The distance of the car from the tower (in metres) is

`(A) 50sqrt3`

`(B) 150sqrt 3`

`(C) 150sqrt2`

`(D) 75`

Two circles touch each other externally at P. AB is a common tangent to the circles touching them at A and B. The value of ∠ L APB is

(A) 30°

(B) 45°

(C) 60°

(D) 90°

If k, 2k- 1 and 2k + 1 are three consecutive terms of an A.P., the value of k is

(A) 2

(B) 3

(C) -3

(D) 5

A chord of a circle of radius 10 em subtends a right angle at its centre. The length of the chord (in em) is

`(A) 5sqrt 2`

`(B) 10 sqrt2`

`(C)5/sqrt2`

`(D) 10sqrt 3`

In a family of 3 children, the probability of having at least one boy is

`(A)7/8`

`(B)1/8`

`(C)5/8`

`(D)3/4`

In Figure 1, common tangents AB and CD to the two circles with centres 0₁and 0₂ intersect at E. Prove that AB = CD.

Two different dice are tossed together. Find the probability
(i) that the number on each die is even.
(ii) that the sum of numbers appearing on the two dice is 5.

If the total surface area of a solid hemisphere is 462 cm2 , find its volume.[Take π=22/7]

The angle of elevation of an aeroplane from a point on the ground is 60°. After a flight of 30 seconds the angle of elevation becomes 300 If the aeroplane is flying at a constant height of 3000 3 m, find the speed of the aeroplane.

The largest possible sphere is carved out of a wooden solid cube of side 7 em. Find the volume of the wood left. (Use\[\pi = \frac{22}{7}\]).

Water in a canal, 6 m wide and 1.5 m deep, is flowing at a speed of 4 km/h. How much area will it irrigate in 10 minutes, if 8 cm of standing water is needed for irrigation?