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

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 ______.

The remainder, when x³ – x² + x – 1 is divided by x + 1, is ______.

4x² – kx + 5 leaves a remainder 2 when divided by x – 1. The value of k is ______.

If the sum of first 7 terms of an A.P. is 49 and that of its first 17 terms is 289, find the sum of first n terms of the A.P.

Check whether -150 is a term of the A.P. 11, 8, 5, 2, ....

An A.P. consists of 50 terms of which 3^rd term is 12 and the last term is 106. Find the 29^th term of the A.P.

If the 3rd and the 9th terms of an AP are 4 and –8 respectively, which term of this AP is zero?

How many multiples of 4 lie between 10 and 250?

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

Find the 20^th term from the last term of the A.P. 3, 8, 13, …, 253.

Ramkali saved Rs 5 in the first week of a year and then increased her weekly saving by Rs 1.75. If in the n^th week, her week, her weekly savings become Rs 20.75, find n.

Find the sum of the following APs:

2, 7, 12, ..., to 10 terms.

Find the sum of the following APs:

–37, –33, –29, ... to 12 terms.

Find the sum of the following APs:

0.6, 1.7, 2.8, ... to 100 terms. 

Find the sum of the following APs:

`1/15, 1/12, 1/10`, ... to 11 terms.

Find the sum given below:

34 + 32 + 30 + ... + 10