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

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"`

If a, b, c and d are in proportion, prove that: `abcd [(1/a^2 + 1/b^2 + 1/c^2 + 1/d^2]` = a² + b² + c² + d² 

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

If a, b, c are in continued proportion, prove that: `(pa^2+ qab+ rb^2)/(pb^2+qbc+rc^2) = a/c`

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

If a, b, c are in continued proportion, prove that: `(1)/a^3 + (1)/b^3 + (1)/c^3 = a/(b^2c^2) + b/(c^2a^2) + c/(a^2b^2)`

If a, b, c are in continued proportion, prove that: a : c = (a² + b²) : (b² + c²)

If a, b, c are in continued proportion, prove that: a² b² c² (a^-4 + b^-4 + c^-4) = b^-2(a⁴ + b⁴ + c⁴)

If a, b, c are in continued proportion, prove that: abc(a + b + c)³ = (ab + bc + ca)³