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

If a, b and c are in continued proportion, prove that `(a^2 + ab + b^2)/(b^2 + bc + c^2) = a/c`

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

Using properties of proportion, solve for x: 

`(sqrt(x + 5) + sqrt(x - 16))/(sqrt(x + 5) - sqrt(x - 16)) = 7/3`

Using properties of proportion, solve for x:

`(sqrt(x + 1) + sqrt(x - 1))/(sqrt(x + 1) - sqrt(x - 1)) = (4x - 1)/2`

Using properties of proportion, solve for x:

`(3x + sqrt(9x^2 - 5))/(3x - sqrt(9x^2 - 5)) = 5`

If `x = (sqrt(a + 3b) + sqrt(a - 3b))/(sqrt(a + 3b) - sqrt(a - 3b))`, prove that: 3bx² – 2ax + 3b = 0.

Find the fourth proportional to 2xy, x² and y².

Find the third proportional to a² – b² and a + b.

Find the mean proportional to (x – y) and (x³ – x²y).

Find two numbers such that the mean proportional between them is 14 and third proportional to them is 112.

If x and y be unequal and x : y is the duplicate ratio of x + z and y + z, prove that z is mean proportional between x and y.

If q is the mean proportional between p and r prove that `(p^3 + q^3 + r^3)/(p^2q^2r^2) = 1/p^3 + 1/q^3 = 1/r^3`

If a, b and c are in continued proportion, prove that: a: c = (a² + b²) : (b² + c²)

If `(4m + 3n)/(4m - 3n) = 7/4`, use properties of proportion to find m : n

If `(4m + 3n)/(4m - 3n) = 7/4`, use properties of proportion to find `(2m^2 - 11n^2)/(2m^2  + 11n^2)`

If x, y, z are in continued proportion prove that `(x + y)^2/(y + z)^2 = x/z`

Find the mean proportional of the following:

17.5, 0.007

What least number must be added to each of the numbers 16, 7, 79 and 43 so that the resulting
numbers are in proportion?

What number must be added to each of the number 16, 26 and 40 so that the resulting numbers may be in continued proportion?

Given, `x/(b - c ) = y/(c - a ) = z/(a - b)` , Prove that

ax+ by + cz = 0