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

Using the Factor Theorem, show that (3x + 2) is a factor of 3x³ + 2x² – 3x – 2. Hence, factorise the expression 3x³ + 2x² – 3x – 2 completely.

Using the Remainder Theorem, factorise each of the following completely. 

3x³ + 2x² – 23x – 30

If x + a is a common factor of expressions f(x) = x² + px + q and g(x) = x² + mx + n; show that : `a = (n - q)/(m - p)` 

Find the value of ‘a’, if (x – a) is a factor of x³ – ax² + x + 2.

What should be subtracted from 3x³ – 8x² + 4x – 3, so that the resulting expression has x + 2 as a factor?

If x – 2 is a factor of x² + ax + b and a + b = 1, find the values of a and b.

(3x + 5) is a factor of the polynomial (a – 1)x³ + (a + 1)x² – (2a + 1)x – 15. Find the value of ‘a’, factorise the given polynomial completely.

Determine the A.P. Whose 3rd term is 16 and the 7th term exceeds the 5th term by 12.

If numbers n – 2, 4n – 1 and 5n + 2 are in A.P., find the value of n and its next two terms.

Find the sum of the first 22 terms of the A.P. : 8, 3, –2, ………

How many terms of the A.P. : 24, 21, 18, ................ must be taken so that their sum is 78?

Find the sum of 28 terms of an A.P. whose n^th term is 8n – 5.

Find the sum of all odd natural numbers less than 50.

Find the sum of first 12 natural numbers each of which is a multiple of 7.

Find the sum of first 51 terms of an A.P. whose 2^nd and 3^rd terms are 14 and 18 respectively.

The first term of an A.P. is 5, the last term is 45 and the sum of its terms is 1000. Find the number of terms and the common difference of the A.P.

Find the sum of all natural numbers between 250 and 1000 which are divisible by 9.

The first and the last terms of an A.P. are 34 and 700 respectively. If the common difference is 18, how many terms are there and what is their sum?

In an A.P. the first term is 25, n^th term is –17 and the sum of n terms is 132. Find n and the common difference.

If the 8^th term of an A.P. is 37 and the 15^th term is 15 more than the 12^th term, find the A.P. Also, find the sum of first 20 terms of A.P.