(English Medium) ICSE Class 10 - CISCE Question Bank Solutions for Mathematics

If (x + 2) and (x – 3) are factors of x³ + ax + b, find the values of a and b. With these values of a and b, factorise the given expression.

If ax³ + 3x² + bx – 3 has a factor (2x + 3) and leaves remainder – 3 when divided by (x + 2), find the values of a and b. With these values of a and b, factorise the given expression.

If (2x – 3) is a factor of 6x² + x + a, find the value of a. With this value of a, factorise the given expression.

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

How many terms of the A.P. 27, 24, 21, ..., should be taken so that their sum is zero?

In an A.P. (with usual notations) : given d = 5, S₉ = 75, find a and a₉ 

In an A.P. (with usual notations) : given a = 8, a_n = 62, S_n = 210, find n and d

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

Solve for x: 1 + 4 + 7 + 10 + ... + x = 287.

How many terms of the A.P. 25, 22, 19, … are needed to give the sum 116 ? Also find the last term.

How many terms of the A.P. 24, 21, 18, … must be taken so that the sum is 78? Explain the double answer.

If the third term of an A.P. is 1 and 6th term is – 11, find the sum of its first 32 terms.

Show that a₁, a₂, a₃, … form an A.P. where a_n is defined as a_n = 3 + 4n. Also find the sum of first 15 terms.

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

 Find the common difference of an A.P. whose first term is 5 and the sum of first four terms is half the sum of next four terms.

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.

The sum of first six terms of an arithmetic progression is 42. The ratio of the 10th term to the 30th term is `(1)/(3)`. Calculate the first and the thirteenth term.

In an A.P., the sum of its first n terms is 6n – n². Find is 25th term.

If x – 2 is a factor of x³ – kx – 12, then the value of k is ______.

Find the value of 'a' if x – a is a factor of the polynomial 3x³ + x² – ax – 81.