English Medium इयत्ता ९ - CBSE Question Bank Solutions for Mathematics

Factorise the following:

`27p^3-1/216-9/2p^2+1/4p`

Verify:

x³ + y³ = (x + y) (x² – xy + y²)

Verify:

x³ – y³ = (x – y) (x² + xy + y²)

Factorise the following:

27y³ + 125z³

Factorise the following:

64m³ – 343n³ 

Factorise:

27x³ + y³ + z³ – 9xyz

Verify that `x^3+y^3+z^3-3xyz=1/2(x+y+z)[(x-y)^2+(y-z)^2+(z-x)^2]`

If x + y + z = 0, show that x³ + y³ + z³ = 3xyz.

Without actually calculating the cubes, find the value of the following:

(–12)³ + (7)³ + (5)³

Without actually calculating the cubes, find the value of the following:

(28)³ + (–15)³ + (–13)³

Give possible expression for the length and breadth of the following rectangle, in which their area are given:

Give possible expression for the length and breadth of the following rectangle, in which their area is given:

What are the possible expressions for the dimensions of the cuboids whose volume is given below?

What are the possible expressions for the dimensions of the cuboids whose volume is given below?

Fill in the blanks:

The centre of a circle lies in ____________ of the circle. 

Fill in the blanks:

A point, whose distance from the centre of a circle is greater than its radius lies in __________ of the circle. (exterior/ interior)

Fill in the blanks:

The longest chord of a circle is a __________ of the circle.

Fill in the blanks:

An arc is a __________ when its ends are the ends of a diameter.

Fill in the blanks:

Segment of a circle is the region between an arc and __________ of the circle.

Fill in the blanks:

A circle divides the plane, on which it lies, in __________ parts.