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

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`.

Given four quantities a, b, c and d are in proportion. Show that: (a – c)b² : (b – d)cd = (a² – b² – ab) : (c² – d² – cd)

Find two numbers such that the mean proportional between them is 12 and the third proportional to them is 96.

Find the third proportional to `x/y + y/x` and `sqrt(x^2 + y^2)`

If p : q = r : s; then show that: mp + nq : q = mr + ns : s.

If p + r = mq and `1/q + 1/s = m/r`; then prove that p : q = r : s.

If `a/b = c/d` prove that each of the given ratios is equal to

`(5a + 4c)/(5b + 4d)`

If a/b = c/d prove that each of the given ratio is equal to `(13a - 8c)/(13b - 8d)`

If a/b = c/d prove that each of the given ratio is equal to `sqrt((3a^2 - 10c^2)/(3b^2 - 10d^2))`

if `a/b = c/d` prove that each of the given ratio is equal to: `((8a^3 + 15c^3)/(8b^3 + 15d^3))^(1/3)`

If a, b, c and d are in proportion prove that `(13a + 17b)/(13c + 17d) = sqrt((2ma^2 - 3nb^2)/(2mc^2 - 3nd^2)`

If a, b, c and d are in proportion prove that `sqrt((4a^2 + 9b^2)/(4c^2 + 9d^2)) = ((xa^3 - 4yb^3)/(xc^3 - 5yd^3))^(1/3)`

If `x/a = y/b = z/c` prove that `(2x^3 - 3y^3 + 4z^3)/(2a^3 - 3b^3 + 4c^3) = ((2x - 3y + 4z)/(2a - 3b + 4c))^3`

If (a² + b²)(x² + y²) = (ax + by)²; prove that: `a/x = b/y`.