English Medium कक्षा १० - CBSE Question Bank Solutions

The given terms are 2k + 1, 3k + 3 and 5k − 1. find AP.

For what values 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.

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

Find the value of k such that the polynomial  x²-(k +6)x+ 2(2k - 1) has some of its zeros equal to half of their product.

A fraction becomes `1/3` when 2 is subtracted from the numerator and it becomes `1/2` when 1 is subtracted from the denominator. Find the fraction.

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 of k such that the polynomial x2 − (k + 6)x + 2(2k −1) has sum of its zeros equal to half of their product.

A fraction becomes `(1)/(3)` when 2 is subtracted from the numerator and it becomes `(1)/(2)` when 1 is subtracted from the denominator. Find the fraction.

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.

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 ______.