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

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:

The table given below shows the ages of patients being treated in a hospital. Construct a cumulative frequency distribution table for the same:

The electricity bills of 45 houses in a particular locality are given below. Tabulate the given data and present it as a cumulative frequency table with one of the classes being 300 - 450:
784, 567, 890, 231, 150, 458, 356, 762, 386, 824, 525, 663, 724, 841, 315, 641, 156, 715, 156, 317, 814, 547, 879, 456, 463, 664, 175, 584, 515, 487, 871, 511, 522, 454, 247, 819, 412, 326, 445, 311, 321, 545, 344, 266, 351.

From the cumulative frequency distribution given below, construct a frequency distribution table:

Construct a frequency distribution table from the given cumulative frequency distribution showing the weights of 750 students in a school:

a. Find the number of students whose weight lie in the interval 40-45
b. Find the interval which has the most number of students.

Prove that the area of a rhombus is equal to half the rectangle contained by its diagonals.

Simplify:

`(sqrt(x^2 + y^2) - y)/(x - sqrt(x^2 - y^2)) ÷ (sqrt(x^2 - y^2) + x)/(sqrt(x^2 + y^2) + y)`

Evaluate, correct to one place of decimal, the expression `5/(sqrt20 - sqrt10)`, if `sqrt5` = 2.2 and `sqrt10` = 3.2.