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

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)`

If a, b, c and d are in proportion, prove that: `(a + c)^3/(b + d)^3 = (a(a - c)^2)/(b(b - d)^2)`

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

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