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

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?

If a matrix has 8 elements, what are the possible order it can have?

Construct a 2 x 2 matrix whose elements a_ij are given by a_ij = 2i – j

Construct a 2 x 2 matrix whose elements a_ij are given by a_ij = i.j

Let `"M" xx [(1, 1),(0, 2)]` = [1 2] where M is a matrix.

1. State the order of matrix M
2. Find the matrix M

Given `[(2, 1),(-3, 4)], "X" = [(7),(6)]` the order of the matrix X