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

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

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

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

If a, b, c, d are in continued proportion, prove that: (a² – b²) (c² – d²) = (b² – c²)² 

If a, b, c, d are in continued proportion, prove that: (a + d)(b + c) – (a + c)(b + d) = (b – c)² 

If a, b, c, d are in continued proportion, prove that: a : d = triplicate ratio of (a – b) : (b – c)

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

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If x, 12, 8 and 32 are in proportion, then the value of x is

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The fourth proportional to 3, 4, 5 is

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The third proportional to `6(1)/(4)` and 5 is

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The mean proportional between `(1)/(2)` and 128 is

What number must be added to each of the numbers 15, 17, 34 and 38 to make them proportional?

If (a + 2 b + c), (a – c) and (a – 2 b + c) are in continued proportion, prove that b is the mean proportional between a and c.