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

The 5^th term and the 9^th term of an Arithmetic Progression are 4 and – 12 respectively.

Find:

1. the first term
2. common difference
3. sum of 16 terms of the AP.

Which term of the Arithmetic Progression (A.P.) 15, 30, 45, 60...... is 300?

Hence find the sum of all the terms of the Arithmetic Progression (A.P.)

The n^th term of an Arithmetic Progression (A.P.) is given by the relation T_n = 6(7 – n)..

Find:

1. its first term and common difference
2. sum of its first 25 terms

A solid sphere is cut into two identical hemispheres.

Statement 1: The total volume of two hemispheres is equal to the volume of the original sphere.

Statement 2: The total surface area of two hemispheres together is equal to the surface area of the original sphere.

Which of the following is valid?

An Arithmetic Progression (A.P.) has 3 as its first term. The sum of the first 8 terms is twice the sum of the first 5 terms. Find the common difference of the A.P.

A manufacturing company prepares spherical ball bearings, each of radius 7 mm and mass 4 gm. These ball bearings are packed into boxes. Each box can have a maximum of 2156 cm³ of ball bearings. Find the:

1. maximum number of ball bearings that each box can have.
2. mass of each box of ball bearings in kg.
   (Use π = `22/7`)

Use ruler and compasses for the following question taking a scale of 10 m = 1 cm. A park in a city is bounded by straight fences AB, BC, CD and DA. Given that AB = 50 m, BC = 63 m, ∠ABC = 75°. D is a point equidistant from the fences AB and BC. If ∠BAD = 90°, construct the outline of the park ABCD. Also locate a point P on the line BD for the flag post which is equidistant from the corners of the park A and B.

x – 1 is a factor of 8x² – 7x + m; the value of m is ______.

Which of the following is a factor of (x – 2)² – (x² – 4)?

Factors of 3x³ – 2x² – 8x are ______.

Factors of 4 + 4x – x² – x³ are ______.

If x – 3 is a factor of x² + kx + 15; the value of k is ______.

Is (x – 2) a factor of x³ – 4x² – 11x + 30?

If mx² – nx + 8 has x – 2 as a factor, then ______.

The sum of 41 terms of an A.P. with middle term 40 is ______.

The sum of all two digit numbers is ______.

The sum of A.P. 4, 7, 10, 13, ........ upto 20 terms is ______.

The sum of 40 terms of the A.P. 7 + 10 + 13 + 16 + .......... is ______.

The nth term of an A.P. is 6n + 4. The sum of its first 2 terms is ______.

k + 2, 2k + 7 and 4k + 12 are the first three terms of an A.P. The first term of this A.P. is ______.