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

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`.

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.