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

Two integers differ by 2 and sum of their squares is 52. The integers are ______.

The sum of the squares of two consecutive integers is 41. The integers are ______.

In a school, a class has 40 students out of which x are girls. If the product of the number of girls and number of boys in the class is 375; the number of boys in the class is ______.

The product of two whole numbers, each greater than 4, is 35; the numbers are ______.

The difference between the digits of a two-digit number is 2 and the product of digits is 24. If tens digit is bigger, the number is ______.

If 18 is added to a two-digit number, its digits are reversed. If the product of the digits of the number is 24, the number is ______.

The sum of a number and its reciprocal is 4.25; the number is ______.

The sum of two whole numbers is 18 and their product is 45, the numbers are ______.

Using quadratic formula find the value of x.

p²x² + (p² – q²)x – q² = 0

If secθ + tanθ = p, show that `(p^{2}-1)/(p^{2}+1)=\sin \theta`

Prove the following identities, where the angles involved are acute angles for which the expressions are defined:

`(sin theta-2sin^3theta)/(2cos^3theta -costheta) = tan theta`

What must be subtracted from 16x³ – 8x² + 4x + 7 so that the resulting expression has 2x + 1 as a factor?

How much should a man invest in Rs. 50 shares selling at Rs. 60 to obtain an income of Rs. 450, if the rate of dividend declared is 10%. Also find his yield percent, to the nearest whole number.

The angles of depression of two ships A and B as observed from the top of a light house 60 m high are 60° and 45° respectively. If the two ships are on the opposite sides of the light house, find the distance between the two ships. Give your answer correct to the nearest whole number.

Using remainder theorem, find the value of k if on dividing 2x³ + 3x² – kx + 5 by x – 2, leaves a remainder 7.

If `x/a=y/b = z/c` show that `x^3/a^3 + y^3/b^3 + z^3/c^3 = (3xyz)/(abc)`.

The histogram below represents the scores obtained by 25 students in a mathematics mental test. Use the data to:

1. Frame a frequency distribution table.
2. To calculate mean.
3. To determine the Modal class.

Prove that `cosA/(1+sinA) + tan A =  secA`

Prove that `sqrt(sec^2 theta + cosec^2 theta) = tan theta + cot theta`

A man invests Rs. 22,500 in Rs. 50 shares available at 10% discount. If the dividend paid by the company is 12%, calculate:

1. The number of shares purchased.
2. The annual dividend received.
3. The rate of return he gets on his investment. Give your answer correct to the nearest whole number.