(English Medium) ICSE Class 9 - CISCE Question Bank Solutions

If x = `(7 + 4sqrt(3))`, find the value of

`sqrt(x) + (1)/(sqrt(x)`

If x = `(7 + 4sqrt(3))`, find the value of

`x^2 + (1)/x^2`

If x = `(7 + 4sqrt(3))`, find the value of `x^3 + (1)/x^3`.

If x = `(7 + 4sqrt(3))`, find the values of :

`(x + (1)/x)^2`

If x = `(4 - sqrt(15))`, find the values of 

`(1)/x`

If x = `(4 - sqrt(15))`, find the values of

`x + (1)/x`

If x = `(4 - sqrt(15))`, find the values of 

`x^2 + (1)/x^2`

If x = `(4 - sqrt(15))`, find the values of

`x^3 + (1)/x^3`

If x = `(4 - sqrt(15))`, find the values of:

`(x + (1)/x)^2` 

If x = `((2 + sqrt(5)))/((2 - sqrt(5))` and y = `((2 - sqrt(5)))/((2 + sqrt(5))`, show that (x² - y²) = `144sqrt(5)`.

If x = `((sqrt(3) + 1))/((sqrt(3) - 1)` and y = `((sqrt(3) - 1))/((sqrt(3) + 1)`, find the values of 

x² + y²

If x = `((sqrt(3) + 1))/((sqrt(3) - 1)` and y = `((sqrt(3) - 1))/((sqrt(3) + 1)`, find the values of 

x³ + y³

If x = `((sqrt(3) + 1))/((sqrt(3) - 1)` and y = `((sqrt(3) - 1))/((sqrt(3) - 1)`, find the values of 

x² - y² + xy

If x = `(1)/((3 - 2sqrt(2))` and y = `(1)/((3 + 2sqrt(2))`, find the values of

x² + y²

If x = `(1)/((3 - 2sqrt(2))` and y = `(1)/((3 + 2sqrt(2))`, find the values of 

x³ + y³

State, true of false:
log (x + y) = log xy

Prove that the quadrilateral formed by joining the mid-points of consecutive sides of a rectangle is a rhombus.

Prove that the quadrilateral formed by joining the mid-points of consecutive sides of a rhombus is a rectangle.

Prove that if the diagonals of a quadrilateral bisect each other at right angles then it is a rhombus.

Prepare a cumulative frequency distribution table of the marks scored by 60 students in a test are given below: