English Medium कक्षा १० - CBSE Question Bank Solutions

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.

The zeroes of the polynomial 3x² + 11x – 4 are ______.

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.

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 ______.

Read the following passage:

1. In which year, the production is 29,200 sets?
2. Find the production in the 8^th year.
   OR
   Find the production in first 3 years.
3. Find the difference of the production in 7^th year and 4^th year.

Assertion (A): If one root of the quadratic equation 4x² – 10x + (k – 4) = 0 is reciprocal of the other, then value of k is 8.

Reason (R): Roots of the quadratic equation x² – x + 1 = 0 are real.

Find the discriminant of the quadratic equation `3x^2 - 2x + 1/3` = 0 and hence find the nature of its roots.

Find the sum of first 25 terms of the A.P. whose nth term is given by a_n = 5 + 6n. Also, find the ratio of 20^th term to 45^th term.

The number of polynomials having zeroes – 3 and 4 is ______.

The graph of y = f(x) is shown in the figure for some polynomial f(x).

The number of zeroes of f(x) is ______.

The zeroes of the quadratic polynomial 16x² – 9 are ______.

Find the value of k for which the roots of the quadratic equation 5x² – 10x + k = 0 are real and equal.

If one root of the quadratic equation 3x² – 8x – (2k + 1) = 0 is seven times the other, then find the value of k.

The graph of y = f(x) is shown in the figure for some polynomial f(x). The number of zeroes of f(x) are ______.

The sum of the 4^th and 8^th term of an A.P. is 24 and the sum of the 6^th and 10^th term of the A.P. is 44. Find the A.P. Also, find the sum of first 25 terms of the A.P.

The given linear polynomial y = f(x) has

The nature of roots of the quadratic equation 9x² – 6x – 2 = 0 is ______.