English Medium कक्षा १० - CBSE Question Bank Solutions for Mathematics

Find the nature of the roots of the quadratic equation:

4x² – 5x – 1 = 0

Find the value of 'p' for which the quadratic equation p(x – 4)(x – 2) + (x –1)² = 0 has real and equal roots.

If the last term of an A.P. of 30 terms is 119 and the 8^th term from the end (towards the first term) is 91, then find the common difference of the A.P. Hence, find the sum of all the terms of the A.P.

If the first term of an A.P. is 5, the last term is 15 and the sum of first n terms is 30, then find the value of n.

In an A.P., the sum of first n terms is `n/2 (3n + 5)`. Find the 25^th term of the A.P.

Find the value of ‘k’ for which the quadratic equation 2kx² – 40x + 25 = 0 has real and equal roots.

Solve for x: `5/2 x^2 + 2/5 = 1 - 2x`.

Find the sum of all 11 terms of an A.P. whose 6^th term is 30.

‘The sum of the ages of a boy and his sister (in years) is 25 and product of their ages is 150. Find their present ages.

Solve the equation: 3x² – 8x – 1 = 0 for x.

Find the value of 'k' so that the quadratic equation 3x² – 5x – 2k = 0 has real and equal roots.

Find the sum of first 16 terms of the A.P. whose n^th term is given by an = 5n – 3.

Find the value(s) of 'a' for which the quadratic equation x² – ax + 1 = 0 has real and equal roots.

If the quadratic equation ax² + bx + c = 0 has two real and equal roots, then 'c' is equal to ______.

Statement A (Assertion): If 5 + `sqrt(7)` is a root of a quadratic equation with rational co-efficients, then its other root is 5 – `sqrt(7)`.

Statement R (Reason): Surd roots of a quadratic equation with rational co-efficients occur in conjugate pairs.

If one root of the quadratic equation x² + 12x – k = 0 is thrice the other root, then find the value of k.

Assertion (A): a, b, c are in A.P. if and only if 2b = a + c.

Reason (R): The sum of first n odd natural numbers is n².

If one zero of the polynomial p(x) = 6x² + 37x – (k – 2) is reciprocal of the other, then find the value of k.

Find the sum and product of the roots of the quadratic equation 2x² – 9x + 4 = 0.

If α, β are the zeroes of the polynomial p(x) = 4x² – 3x – 7, then `(1/α + 1/β)` is equal to ______.