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

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 ______.

The sum of n terms of an A.P. is 3n². The second term of this A.P. is ______.

If the quadratic equation px² − 2√5px + 15 = 0 has two equal roots then find the value of p.

Find the values of k for which the quadratic equation 9x² - 3kx + k = 0 has equal roots.

If -5 is a root of the quadratic equation 2x² + px – 15 = 0 and the quadratic equation p(x² + x)k = 0 has equal roots, find the value of k.

If A, B, C are the interior angles of a triangle ABC, prove that `\tan \frac{B+C}{2}=\cot \frac{A}{2}`