English Medium कक्षा १० - CBSE Question Bank Solutions for Mathematics

Find the value of k for which the roots of the equation 3x² -10x +k = 0 are reciprocal of each other.

Which term of the  AP  3, 15, 27, 39, ...... will be 120 more than its 21st term?

If the sum of the first four terms of an AP is 40 and that of the first 14 terms is 280. Find the sum of its first n terms.

For what value of k, the roots of the equation x² + 4x + k = 0 are real?

Find the value of k for which the roots of the equation 3x² - 10x + k = 0 are reciprocal of each other.

Find the value(s) of k for which the pair of equations
kx +  2y = 3
3x + 6y = 10 has a unique solution.

Find the value of x, when in the A.P. given below 2 + 6 + 10 + ... + x = 1800.

Write the discriminant of the quadratic equation (x + 5)² = 2 (5x − 3).

Find the sum of the first 10 multiples of 6.

In the quadratic equation kx² − 6x − 1 = 0, determine the values of k for which the equation does not have any real root.

Check whether g(x) is a factor of p(x) by dividing polynomial p(x) by polynomial g(x),
where p(x) = x⁵ − 4x³ + x² + 3x +1, g(x) = x³ − 3x + 1

The sum of the first three numbers in an Arithmetic Progression is 18. If the product of the first and the third term is 5 times the common difference, find the three numbers.

Which of the following equations has 2 as a root?

If `(1)/(2)` is a root of the equation `x^2 + kx - (5)/(4) = 0`, then the value of k is ______.

The quadratic equation `2x^2 - sqrt(5)x + 1 = 0` has ______.

Which of the following equations has no real roots?

Find whether 55 is a term of the A.P. 7, 10, 13,... or not. If yes, find which term is it.

The sum of first 15 terms of an A.P. is 750 and its first term is 15. Find its 20^th term.

If a_n = 3 – 4n, show that a₁, a₂, a₃,... form an AP. Also find S₂₀.

The sum of first n terms of an A.P. whose first term is 8 and the common difference is 20 equal to the sum of first 2n terms of another A.P. whose first term is – 30 and the common difference is 8. Find n.