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

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.

Given f(x) = ax² + bx + 2 and g(x) = bx² + ax + 1. If x – 2 is a factor of f(x) but leaves the remainder – 15 when it divides g(x), find the values of a and b. With these values of a and b, factorise the expression. f(x) + g(x) + 4x² + 7x.

When x³ – 3x² + 5x – 7 is divided by x – 2,then the remainder is

When 2x³ – x² – 3x + 5 is divided by 2x + 1, then the remainder is

If on dividing 4x² – 3kx + 5 by x + 2, the remainder is – 3 then the value of k is

If on dividing 2x³ + 6x² – (2k – 7)x + 5 by x + 3, the remainder is k – 1 then the value of k is

If x + 1 is a factor of 3x³ + kx² + 7x + 4, then the value of k is

Find the remainder when 2x³ – 3x² + 4x + 7 is divided by x – 2

Find the remainder when 2x³ – 3x² + 4x + 7 is divided by x + 3

Find the remainder when 2x³ – 3x² + 4x + 7 is divided by 2x + 1

When 2x³ – 9x² + 10x – p is divided by (x + 1), the remainder is – 24.Find the value of p.

When a polynomial f(x) is divided by (x – 1), the remainder is 5 and when it is,, divided by (x – 2), the remainder is 7. Find – the remainder when it is divided by (x – 1) (x – 2).

tan θ × `sqrt(1 - sin^2 θ)` is equal to:

Use graph paper for this question. Estimate the mode of the given distribution by plotting a histogram. [Take 2 cm = 10 marks along one axis and 2 cm = 5 students along the other axis]

(1 + sin A)(1 – sin A) is equal to ______.

Prove the following identity:

(sin²θ – 1)(tan²θ + 1) + 1 = 0

What must be subtracted from the polynomial x³ + x² – 2x + 1, so that the result is exactly divisible by (x – 3)?

Statement 1: sin²θ + cos²θ = 1

Statement 2: cosec²θ + cot²θ = 1

Which of the following is valid?

The given graph with a histogram represents the number of plants of different heights grown in a school campus. Study the graph carefully and answer the following questions:

1. Make a frequency table with respect to the class boundaries and their corresponding frequencies.
2. State the modal class.
3. Identify and note down the mode of the distribution.
4. Find the number of plants whose height range is between 80 cm to 90 cm.

Factorize: sin³θ + cos³θ

Hence, prove the following identity:

`(sin^3θ + cos^3θ)/(sin θ + cos θ) + sin θ cos θ = 1`