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

Choose the correct answer from the given options :

The mean proportional between `(1)/(2)` and 128 is

What number must be added to each of the numbers 15, 17, 34 and 38 to make them proportional?

If (a + 2 b + c), (a – c) and (a – 2 b + c) are in continued proportion, prove that b is the mean proportional between a and c.

If 2, 6, p, 54 and q are in continued proportion, find the values of p and q.

If a, b, c, d, e are in continued proportion, prove that: a : e = a⁴ : b⁴.

Find two numbers whose mean proportional is 16 and the third proportional is 128.

If q is the mean proportional between p and r, prove that: p³ – 3q² + r² = `q^4(1/p^2 - 3/q^2 + 1/r^2)`

The mean proportional between 4 and 9 is ______.

In the given figure, AC || DE || BF. If AC = 24 cm, EG = 8 cm, GB = 16 cm, BF = 30 cm.

1. Prove ΔGED ∼ ΔGBF
2. Find DE
3. DB : AB

What number must be added to each of the numbers 4, 6, 8, 11 in order to get the four numbers in proportion?

If `(a + b)^3/(a - b)^3 = 64/27`

1. Find `(a + b)/(a - b)`
2. Hence using properties of proportion, find a : b.

If x, y and z are in continued proportion, Prove that:

`x/(y^2.z^2) + y/(z^2.x^2) + z/(x^2.y^2) = 1/x^3 + 1/y^3 + 1/z^3`

If x, 2, 10 and y are in continued proportion, the values of x and y are respectively:

If x : y = y : z, then x² : y² is ______.

The mean proportion between `3 + 2sqrt(2)` and `3 - 2sqrt(2)` is ______.

If 2x, 9 and 18 are in continued proportion, the value of x is ______.

If x + y + z = 0, the value of `x/(y + z)` is ______.

If a, b, c and d are in proportion, the value of `(8a^2 - 5b^2)/(8c^2 - 5d^2)` is equal to ______.

The mean proportional to `sqrt(3) + sqrt(2)` and `sqrt(3) - sqrt(2)` is ______.

The table, given below, shows the values of x and y, where x is proportional (directly proportional) to y.

The values of A and B are: