English Medium Class 10 - CBSE Question Bank Solutions for Mathematics

Find the value of 𝑚 so that the quadratic equation 𝑚𝑥(5𝑥 − 6) = 0 has two equal roots.

Solve for x: 9x² – 6px + (p² – q²) = 0

Find the zeroes of the quadratic polynomial 6x² – 3 – 7x and verify the relationship between the zeroes and the coefficients.

In the month of April to June 2022, the exports of passenger cars from India increased by 26% in the corresponding quarter of 2021-22, as per a report. A car manufacturing company planned to produce 1800 cars in 4th year and 2600 cars in 8th year. Assuming that the production increases uniformly by a fixed number every year.

Based on the above information answer the following questions.

1. Find the production in the 1^st year
2. Find the production in the 12^th year.
3. Find the total production in first 10 years.
   [OR]
   In how many years will the total production reach 31200 cars?

Let p be a prime number. The quadratic equation having its roots as factors of p is ______.

If α and β are the zeros of a polynomial f(x) = px² – 2x + 3p and α + β = αβ, then p is ______.

If the zeroes of the polynomial x² + px + q are double in value to the zeroes of the polynomial 2x² – 5x – 3, then find the values of p and q.

Solve the quadratic equation: `x^2 + 2sqrt(2)x - 6` = 0 for x.

Find the sum of first 20 terms of an A.P. whose n^th term is given as a_n = 5 – 2n.

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.