English Medium कक्षा ९ - CBSE Question Bank Solutions for Mathematics

Expand the following:

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

Expand the following:

`(4 - 1/(3x))^3`

Find the following product:

`(x/2 + 2y)(x^2/4 - xy + 4y^2)`

Find the following product:

(x² – 1)(x⁴ + x² + 1)

Without actually calculating the cubes, find the value of:

`(1/2)^3 + (1/3)^3 - (5/6)^3`

Without actually calculating the cubes, find the value of:

(0.2)³ – (0.3)³ + (0.1)³

Find the value of x³ + y³ – 12xy + 64, when x + y = – 4

Find the value of x³ – 8y³ – 36xy – 216, when x = 2y + 6

Give possible expressions for the length and breadth of the rectangle whose area is given by 4a² + 4a – 3.

Simplify (2x – 5y)³ – (2x + 5y)³.

Multiply x² + 4y² + z² + 2xy + xz – 2yz by (–z + x – 2y).

If a + b + c = 5 and ab + bc + ca = 10, then prove that a³ + b³ + c³ – 3abc = – 25.

Prove that (a + b + c)³ – a³ – b³ – c³ = 3(a + b)(b + c)(c + a).

In the following figure, if AB || CD || EF, PQ || RS, ∠RQD = 25° and ∠CQP = 60°, then ∠QRS is equal to ______.

In the following figure, POQ is a line. The value of x is ______.

For what value of x + y in figure will ABC be a line? Justify your answer.

In the following figure, which of the two lines are parallel and why? 

In the following figure, OD is the bisector of ∠AOC, OE is the bisector of ∠BOC and OD ⊥ OE. Show that the points A, O and B are collinear.

In the following figure, ∠1 = 60° and ∠6 = 120°. Show that the lines m and n are parallel.

Q is a point on the side SR of a ∆PSR such that PQ = PR. Prove that PS > PQ.