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

Find the values of constants a and b when x – 2 and x + 3 both are the factors of expression x³ + ax² + bx – 12.

Find the value of a, if x – 2 is a factor of 2x⁵ – 6x⁴ – 2ax³ + 6ax² + 4ax + 8. 

Find the values of m and n so that x – 1 and x + 2 both are factors of x³ + (3m + 1)x² + nx – 18.

Using the Factor Theorem, show that (x – 2) is a factor of x³ – 2x² – 9x + 18. Hence, factorise the expression x³ – 2x² – 9x + 18 completely.

Using the Factor Theorem, show that (x + 5) is a factor of 2x³ + 5x² – 28x – 15. Hence, factorise the expression 2x³ + 5x² – 28x – 15 completely.  

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.