English Medium Class 10 - CBSE Question Bank Solutions for Mathematics

The houses in a row numbered consecutively from 1 to 49. Show that there exists a value of x such that sum of numbers of houses preceding the house numbered x is equal to sum of the numbers of houses following x.

Find the 9^th term from the end (towards the first term) of the A.P. 5, 9, 13, ...., 185

If `x=2/3` and x =−3 are roots of the quadratic equation ax² + 7x + b = 0, find the values of a and b.

How many terms of the A.P. 18, 16, 14, .... be taken so that their sum is zero?

If the sum of first 7 terms of an A.P. is 49 and that of its first 17 terms is 289, find the sum of first n terms of the A.P.

How many terms of the A.P. 27, 24, 21, .... should be taken so that their sum is zero?

How many terms of the A.P. 65, 60, 55, .... be taken so that their sum is zero?

If x=−`1/2`, is a solution of the quadratic equation 3x²+2kx−3=0, find the value of k

Find that non-zero value of k, for which the quadratic equation kx² + 1 − 2(k − 1)x + x² = 0 has equal roots. Hence find the roots of the equation.

If S_n¹ denotes the sum of first n terms of an A.P., prove that S₁₂ = 3(S₈ − S₄).

Solve the quadratic equation 2x² + ax − a² = 0 for x.

Ramkali required Rs 2,500 after 12 weeks to send her daughter to school. She saved Rs 100 in the first week and increased her weekly saving by Rs 20 every week. Find whether she will be able to send her daughter to school after 12 weeks.

What value is generated in the above situation?

Find the values of k for which the quadratic equation (k + 4) x² + (k + 1) x + 1 = 0 has equal roots. Also find these roots.

If the sum of the first n terms of an A.P. is `1/2`(3n² +7n), then find its n^th term. Hence write its 20^th term.

Find that value of p for which the quadratic equation (p + 1)x² − 6(p + 1)x + 3(p + 9) = 0, p ≠ − 1 has equal roots. Hence find the roots of the equation.

The first and the last terms of an AP are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.

Solve the following quadratic equation for x :

9x² − 6b²x − (a⁴ − b⁴) = 0

Find the values of k for which the quadratic equation (3k + 1) x² + 2(k + 1) x + 1 = 0 has equal roots. Also, find the roots.

If S_n denotes the sum of first n terms of an A.P., prove that S₃₀ = 3[S₂₀ − S₁₀]

The first and the last terms of an AP are 8 and 65 respectively. If the sum of all its terms is 730, find its common difference.