English Medium Class 10 - CBSE Question Bank Solutions

If the quadratic equation px² − 2√5px + 15 = 0 has two equal roots then find the value of p.

In an A.P., if S5 + S7 = 167 and S₁₀₌235, then find the A.P., where Sn denotes the sum of its first n terms.

Solve for x: `sqrt(3x^2)-2sqrt(2)x-2sqrt3=0`

Solve for x : ` 2x^2+6sqrt3x-60=0`

Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.

Find the values of k for which the quadratic equation 9x² - 3kx + k = 0 has equal roots.

If -5 is a root of the quadratic equation 2x² + px – 15 = 0 and the quadratic equation p(x² + x)k = 0 has equal roots, find the value of k.

If the ratio of the sum of first n terms of two A.P’s is (7n +1): (4n + 27), find the ratio of their mth terms.

Solve for x: `1/(x+1)+2/(x+2)=4/(x+4), `x ≠ -1, -2, -3

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.