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

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`

Use ruler and compass to answer this question. Construct ∠ABC = 90°, where AB = 6 cm, BC = 8 cm.

1. Construct the locus of points equidistant from B and C.
2. Construct the locus of points equidistant from A and B.
3. Mark the point which satisfies both the conditions (a) and (b) as 0. Construct the locus of points keeping a fixed distance OA from the fixed point 0.
4. Construct the locus of points which are equidistant from BA and BC.

A polynomial in ‘x’ is divided by (x – a) and for (x – a) to be a factor of this polynomial, the remainder should be ______.

Prove the following trigonometry identity:

(sin θ + cos θ)(cosec θ – sec θ) = cosec θ ⋅ sec θ – 2 tan θ

The table given below shows the runs scored by a cricket team during the overs of a match.

Use graph sheet for this question.

Take 2 cm = 10 overs along one axis and 2 cm = 10 runs along the other axis.

1. Draw a histogram representing the above distribution.
2. Estimate the modal runs scored.

If x²⁵ + x²⁴ is divided by (x + 1), the result is ______.