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

Prove the following trigonometric identities.

`1/(sec A - 1) + 1/(sec A + 1) = 2 cosec A cot A`

if `x/a cos theta + y/b sin theta = 1` and `x/a sin theta - y/b cos theta = 1` prove that `x^2/a^2 + y^2/b^2  = 2`

Find the remainder when x⁴ – 3x² + 2x + 1 is divided by x – 1.

Find the remainder when x³ + 3x² – 12x + 4 is divided by x – 2.

Find the remainder when x⁴ + 1 is divided by x + 1.

Use the Remainder Theorem to find which of the following is a factor of 2x³ + 3x² – 5x – 6. 

x + 1

Use the Remainder Theorem to find which of the following is a factor of 2x³ + 3x² – 5x – 6. 

2x – 1 

Use the Remainder Theorem to find which of the following is a factor of 2x³ + 3x² – 5x – 6. 

x + 2

Find the value of a, if the division of ax³ + 9x² + 4x – 10 by x + 3 leaves a remainder 5.

When x³ + 2x² – kx + 4 is divided by x – 2, the remainder is k. Find the value of constant k.

If x³ + ax² + bx + 6 has x – 2 as a factor and leaves a remainder 3 when divided by x – 3, find the values of a and b.

The expression 2x³ + ax² + bx – 2 leaves remainder 7 and 0 when divided by 2x – 3 and x + 2 respectively. Calculate the values of a and b.

What number should be added to 3x³ – 5x² + 6x so that when resulting polynomial is divided by x – 3, the remainder is 8?

What number should be subtracted from x³ + 3x² – 8x + 14 so that on dividing it by x – 2, the remainder is 10? 

The polynomials 2x³ – 7x² + ax – 6 and x³ – 8x² + (2a + 1)x – 16 leaves the same remainder when divided by x – 2. Find the value of ‘a’. 

If (x – 2) is a factor of the expression 2x³ + ax² + bx – 14 and when the expression is divided by (x – 3), it leaves a remainder 52, find the values of a and b.

Find ‘a‘ if the two polynomials ax³ + 3x² – 9 and 2x³ + 4x + a, leave the same remainder when divided by x + 3. 

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

3x³ + 2x² − 19x + 6 

Using the Remainder Theorem, factorise the following completely:

2x³ + x² – 13x + 6 

Using the Remainder Theorem, factorise the following completely:

3x³ + 2x² – 23x – 30