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

If a, b, c, d are in continued proportion, prove that: `(a^3 + b^3 + c^3)/(b^3 + c^3 + d^3) = a/d`

If a, b, c, d are in continued proportion, prove that: (a² – b²) (c² – d²) = (b² – c²)² 

If a, b, c, d are in continued proportion, prove that: (a + d)(b + c) – (a + c)(b + d) = (b – c)² 

If a, b, c, d are in continued proportion, prove that: a : d = triplicate ratio of (a – b) : (b – c)

If a, b, c, d are in continued proportion, prove that: `((a - b)/c + (a - c)/b)^2 - ((d - b)/c + (d - c)/b)^2 = (a - d)^2 (1/c^2 - 1/b^2)`.

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If x, 12, 8 and 32 are in proportion, then the value of x is

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The fourth proportional to 3, 4, 5 is

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The third proportional to `6(1)/(4)` and 5 is

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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`