English Medium कक्षा 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?

How will you describe the position of a table lamp on your study table to another person?

(Street Plan): A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction.

All the other streets of the city run parallel to these roads and are 200 m apart. There are 5 streets in each direction. Using 1cm = 200 m, draw a model of the city on your notebook. Represent the roads/streets by single lines.

There are many cross- streets in your model. A particular cross-street is made by two streets, one running in the North - South direction and another in the East - West direction. Each cross street is referred to in the following manner : If the 2^nd street running in the North - South direction and 5^th in the East - West direction meet at some crossing, then we will call this cross-street (2, 5). Using this convention, find:

1. how many cross - streets can be referred to as (4, 3).
2. how many cross - streets can be referred to as (3, 4).

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.