English Medium कक्षा १० - CBSE Question Bank Solutions

The first three terms of an A.P. respectively are 3y − 1, 3y + 5 and 5y + 1. Then, y equals

Let the four terms of the AP be a − 3d, a − d, a + d and a + 3d. find A.P.

Suppose three parts of 207 are (a − d), a , (a + d) such that , (a + d)  >a >  (a − d). 

Suppose the angles of a triangle are (a − d), a , (a + d) such that , (a + d)  >a >  (a − d).

The term  A.P is 8, 10, 12, 14,...., 126 . find A.P.

x is nth term of the given A.P. a_n = x find x .

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?

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.