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

Solve:

`1/(x + 1) - 2/(x + 2) = 3/(x + 3) - 4/(x + 4)`

For the equation given below, find the value of ‘m’ so that the equation has equal roots. Also, find the solution of the equation:

(m – 3)x² – 4x + 1 = 0

For the equation given below, find the value of ‘m’ so that the equation has equal roots. Also find the solution of the equation:

3x² + 12x + (m + 7) = 0

For the equation given below, find the value of ‘m’ so that the equation has equal roots. Also, find the solution of the equation:

x² – (m + 2)x + (m + 5) = 0

Without solving the following quadratic equation Find the value of p for which the roots are equal

`px^2 - 4x + 3 = 0`

The product of two consecutive integers is 56. Find the integers.

The sum of the squares of two consecutive natural numbers is 41. Find the numbers.

Find the two natural numbers which differ by 5 and the sum of whose squares is 97.

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

Two natural numbers differ by 3. Find the numbers, if the sum of their reciprocals is `7/10`.

Divide 15 into two parts such that the sum of their reciprocals is `3/10`.

The sum of the squares of two consecutive positive even numbers is 52. Find the numbers.

Find two consecutive positive odd numbers, the sum of whose squares is 74.

The denominator of a positive fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is 2.9; find the fraction.

Three positive numbers are in the ratio `1/2 : 1/3 : 1/4`. Find the numbers if the sum of their squares is 244.

Divide 20 into two parts such that three times the square of one part exceeds the other part by 10.

Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by 60. Assume the middle number to be x and form a quadratic equation satisfying the above statement. Hence; find the three numbers.

Out of three consecutive positive integers, the middle number is p. If three times the square of the largest is greater than the sum of the squares of the other two numbers by 67; calculate the value of p.

The product of the digits of a two digit number is 24. If its unit’s digit exceeds twice its ten’s digit by 2; find the number.

The sum S of first n even natural numbers is given by the relation S = n(n + 1). Find n, if the sum is 420.