English Medium Class 9 - CBSE Question Bank Solutions for Mathematics

In a right triangle, prove that the line-segment joining the mid-point of the hypotenuse to the opposite vertex is half the hypotenuse.

Two lines l and m intersect at the point O and P is a point on a line n passing through the point O such that P is equidistant from l and m. Prove that n is the bisector of the angle formed by l and m.

Line segment joining the mid-points M and N of parallel sides AB and DC, respectively of a trapezium ABCD is perpendicular to both the sides AB and DC. Prove that AD = BC.

ABCD is a quadrilateral such that diagonal AC bisects the angles A and C. Prove that AB = AD and CB = CD.

ABC is a right triangle such that AB = AC and bisector of angle C intersects the side AB at D. Prove that AC + AD = BC.

ABCD is quadrilateral such that AB = AD and CB = CD. Prove that AC is the perpendicular bisector of BD.

In the following figure, it is given that BDEF and FDCE are parallelograms. Can you say that BD = CD? Why or why not?

In the following figure, ABCD and AEFG are two parallelograms. If ∠C = 55º, determine ∠F.

The length of the longest pole that can be put in a room of dimensions (10 m × 10 m × 5 m) is ______.

A storage tank is in the form of a cube. When it is full of water, the volume of water is 15.625 m³. If the present depth of water is 1.3 m, find the volume of water already used from the tank.

Find:-

`64^(1/2)`

Find:-

`9^(3/2)`

Simplify:-

`2^(2/3). 2^(1/5)`

Use suitable identity to find the following product:

(x + 4) (x + 10) 

Use suitable identity to find the following product:

(x + 8) (x – 10)

Use suitable identity to find the following product:

(3x + 4) (3x – 5)

Use suitable identity to find the following product:

`(y^2+3/2)(y^2-3/2)`

Use suitable identity to find the following product:

(3 – 2x) (3 + 2x)

Evaluate the following product without multiplying directly:

103 × 107

Evaluate the following product without multiplying directly:

95 × 96