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

Find the compound ratio of:
(a + b)² : (a – b )² ,
(a² – b²) : (a² + b²),
(a⁴ – b⁴) : (a + b)⁴

If (7p + 3q) : (3p – 2q) = 43 : 2 find p : q.

If a : b = 3 : 5, find (3a + 5b): (7a – 2b).

The ratio of the shorter sides of a right angled triangle is 5 : 12. If the perimeter of the triangle is 360 cm, find the length of the longest side.

The ratio of the pocket money saved by Lokesh and his sister is 5 : 6. If the sister saves Rs 30 more, how much more the brother should save in order to keep the ratio of their savings unchanged?

In an examination, the number of those who passed and the number of those who failed were in the ratio of 3 : 1. Had 8 more appeared, and 6 less passed, the ratio of passed to failures would have been 2 : 1. Find the number of candidates who appeared.

If `a/b = c/d = c/f`, prove that each ratio is `sqrt((3a^2 - 5c^2 + 7e^2)/(3b^2 - 5d^2 + 7f^2)`

If `a/b = c/d = e/f`, prove that each ratio is `[(2a^3 + 5c^3 + 7e^3)/(2b^3 + 5d^3 + 7f^3)]^(1/3)`

If `x/a = y/b = z/c`, prove that `(3x^3 - 5y^3 + 4z^3)/(3a^3 - 5b^3 + 4c^3) = ((3x - 5y + 4z)/(3a - 5b + 4c))^3`.

If x : a = y : b, prove that `(x^4 + a^4)/(x^3 + a^3) + (y^4 + b^4)/(y^3 + b^3) = ((x + y)^4 + (a + b)^4)/((x+ y)^3 + (a + b)^3`

If `x/(b + c - a) = y/(c + a - b) = z/(a + b - c)`  prove that each ratio’s equal to `(x + y + z)/(a + b + c)`.

If a : b = 9 : 10, find the value of `(5a + 3b)/(5a - 3b)`

If a : b = 9 : 10, find the value of `(2a^2 - 3b^2)/(2a^2 + 3b^2)`

`[(2, -1),(5, 1)]`

[2 3 – 7]

`[(3),(0),(-1)]`

`[(2 ,- 4),(0 ,0),(1 , 7)]`

`[(2 , 7, 8),(-1 , sqrt(2), 0)]`

`[(0, 0, 0),(0, 0, 0)]`

If a matrix has 4 elements, what are the possible order it can have?