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

What least number must be added to each of the numbers 6, 15, 20 and 43 to make them proportional?

Using the properties of proportion, solve for x, given `(x^4 + 1)/(2x^2) = 17/8`.

6 is the mean proportion between two numbers x and y and 48 is the third proportional of x and y. Find the numbers.

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

Find the fourth proportional to 1.5, 4.5 and 3.5

Find the fourth proportional to 3a, 6a² and 2ab²

Find the third proportional to `2 2/3` and 4

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

Find the mean proportional between `6 + 3sqrt(3)` and `8 - 4sqrt(3)`

Find the mean proportional between a – b and a³ – a²b

If x + 5 is the mean proportional between x + 2 and x + 9; find the value of x.

If x², 4 and 9 are in continued proportion, find x.

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

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

If `a/b = c/d`, show that: `(a^3c + ac^3)/(b^3d + bd^3) = (a + c)^4/(b + d)^4`.

What least number must be subtracted from each of the numbers 7, 17 and 47 so that the remainders are in continued proportion?

If y is the mean proportional between x and z; show that xy + yz is the mean proportional between x² + y² and y² + z².

If q is the mean proportional between p and r, show that: pqr(p + q + r)³ = (pq + qr + rp)³.

If three quantities are in continued proportion; show that the ratio of the first to the third is the duplicate ratio of the first to the second.

If y is the mean proportional between x and z, prove that: `(x^2 - y^2 + z^2)/(x^(-2) - y^(-2) + z^(-2)) = y^4`.