English Medium इयत्ता १० - CBSE Question Bank Solutions

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 ______.

Find the value of ‘p’ for which the quadratic equation px(x – 2) + 6 = 0 has two equal real roots.

Rohan repays his total loan of ₹ 1,18,000 by paying every month starting with the first installment of ₹ 1,000. If he increases the installment by ₹ 100 every month, what amount will be paid by him in the 30^th installment? What amount of loan has he paid after 30^th installment?

If x = 3 is one of the roots of the quadratic equation x² – 2kx – 6 = 0, then the value of k is ______.