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

If x + 5 is the mean proportion between x + 2 and x + 9, find the value of x.

If 2x – 1, 5x – 6, 6x + 2 and 15x – 9 are in proportion, find the value of x.

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

Find two numbers such that the mean proportional between them is 28 and the third proportional to them is 224.

If b is the mean proportional between a and c, prove that a, c, a² + b², and b² + c² are proportional.

If b is the mean proportional between a and c, prove that (ab + bc) is the mean proportional between (a² + b²) and (b² + c²).

If y is mean proportional between x and z, prove that xyz (x + y + z)³ = (xy + yz + zx)³.

If a + c = mb and `1/b + 1/d = m/c`, prove that a, b, c and d are in proportion.

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

If `x/a = y/b = z/c`, prove that `[(a^2x^2 + b^2y^2 + c^2z^2)/(a^2x + b^3y +c^3z)]^3 = "xyz"/"abc"`

If `x/a = y/b = z/c`, prove that `"ax - by"/((a + b)(x- y)) + "by - cz"/((b + c)(y - z)) + "cz - ax"/((c + a)(z - x)` = 3

If `a/c = c/d = c/f` prove that : (b² + d² + f²) (a² + c² + e²) = (ab + cd + ef)²

If `a/c = c/d = e/f` prove that: `(a^3 + c^3)^2/(b^3 + d^3)^2 = e^6/f^6`

If `a/c = c/d = c/f` prove that : `(a^2)/(b^2) + (c^2)/(d^2) + (e^2)/(f^2) = "ac"/"bd" + "ce"/"df" + "ae"/"df"`

If `a/c = c/d = c/f` prove that : `bd f[(a + b)/b + (c + d)/d + (c + f)/f]^3` = 27(a + b)(c + d)(e + f)

If ax = by = cz; prove that `x^2/"yz" + y^2/"zx" + z^2/"xy" = "bc"/a^2 + "ca"/b^2 + "ab"/c^2`

If a, b, c and d are in proportion, prove that: (5a + 7b) (2c – 3d) = (5c + 7d) (2a – 3b).

If a, b, c and d are in proportion, prove that: (ma + nb) : b = (mc + nd) : d

If a, b, c and d are in proportion, prove that: (a⁴ + c⁴) : (b⁴ + d⁴) = a² c² : b² d².

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