(English Medium) ICSE Class 10 - CISCE Question Bank Solutions for Mathematics

If A, B, C are the interior angles of a triangle ABC, prove that `\tan \frac{B+C}{2}=\cot \frac{A}{2}`

If (k – 3), (2k + l) and (4k + 3) are three consecutive terms of an A.P., find the value of k.

Find the value of k for which the following equation has equal roots.

x² + 4kx + (k² – k + 2) = 0

The 4th term of an A.P. is 22, and the 15th term is 66. Find the first term and the common difference. Hence, find the sum of the series to 8 terms.

Without using trigonometric tables evaluate:

`(sin 65^@)/(cos 25^@) + (cos 32^@)/(sin 58^@) - sin 28^2. sec 62^@ + cosec^2 30^@`

In the figure, m∠DBC = 58°. BD is the diameter of the circle. Calculate:

1) m∠BDC

2) m∠BEC

3) m∠BAC

Solve for x using the quadratic formula. Write your answer corrected to two significant figures. (x - 1)² - 3x + 4 = 0

A two digit positive number is such that the product of its digits is 6. If 9 is added to the number, the digits interchange their places. Find the number.

In the given figure, ∠BAD = 65°, ∠ABD = 70°, ∠BDC = 45°

1) Prove that AC is a diameter of the circle.

2) Find ∠ACB

A car covers a distance of 400 km at a certain speed. Had the speed been 12 km/h more, the time taken for the journey would have been 1 hour 40 minutes less. Find the original speed of the car.

Solve the following equation:

`x - 18/x = 6` Give your answer correct to two significant figures.

Calculate the area of the shaded region, if the diameter of the semicircle is equal to 14 cm. Take `pi = 22/7`

When divided by x – 3 the polynomials x3 – px2 + x + 6 and 2x3 – x2 – (p + 3) x – 6 leave the same remainder. Find the value of ‘p’.

Without solving the following quadratic equation, find the value of ‘p’ for which the roots are equal.

px² – 4x + 3 = 0

The speed of an ordinary train is x km per hr and that of an express train is (x + 25) km per hr.

1. Find the time taken by each train to cover 300 km.
2. If the ordinary train takes 2 hrs more than the express train; calculate speed of the express train.

If the speed of a car is increased by 10 km per hr, it takes 18 minutes less to cover a distance of 36 km. Find the speed of the car.

If the speed of an aeroplane is reduced by 40 km/hr, it takes 20 minutes more to cover 1200 km. Find the speed of the aeroplane.

A girl goes to her friend’s house, which is at a distance of 12 km. She covers half of the distance at a speed of x km/hr and the remaining distance at a speed of (x + 2) km/hr. If she takes 2 hrs 30 minutes to cover the whole distance, find ‘x’.

A goods train leaves a station at 6 p.m., followed by an express train which leaved at 8 p.m. and travels 20 km/hour faster than the goods train. The express train arrives at a station, 1040 km away, 36 minutes before the goods train. Assuming that the speeds of both the train remain constant between the two stations; calculate their speeds.

The distance by road between two towns A and B is 216 km and by rail it is 208 km. A car travels at a speed of x km/hr and the train travels at a speed which is 16 km/hr faster than the car. Calculate:

1. the time taken by the car to reach town B from A, in terms of x;
2. the time taken by the train to reach town B from A, in terms of x.
3. If the train takes 2 hours less than the car, to reach town B, obtain an equation in x and solve it.
4. Hence, find the speed of the train.