English Medium Class 9 - CBSE Question Bank Solutions

Simplify (2x + p - c)² - (2x - p + c)²

If a + b + c = 0 and a² + b² + c² = 16, find the value of ab + bc + ca.

If a² + b² + c² = 16 and ab + bc + ca = 10, find the value of a + b + c.

If a + b + c = 9 and ab + bc + ca = 23, find the value of a² + b² + c².

Find the value of 4x² + y² + 25z² + 4xy − 10yz − 20zx when x = 4, y = 3 and z = 2.

Simplify the expression: 

`(x + y + z)^2 + (x + y/2 + 2/3)^2 - (x/2 + y/3 + z/4)^2`

Simplify the following expressions:

`(x + y - 2z)^2 - x^2 - y^2 - 3z^2 +4xy`

Simplify the following expressions:

`(x^2 - x + 1)^2 - (x^2 + x + 1)^2`

In Fig., below, ABCD is a parallelogram in which ∠A = 60°. If the bisectors of ∠A and ∠B meet at P, prove that AD = DP, PC = BC and DC = 2AD.

In a parallelogram ABCD, determine the sum of angles ∠C and ∠D .

In a parallelogram ABCD, if `∠`B = 135°, determine the measures of its other angles .

ABCD is a square. AC and BD intersect at O. State the measure of ∠AOB.

The sides AB and CD of a parallelogram ABCD are bisected at E and F. Prove that EBFD is a parallelogram.

P and Q are the points of trisection of the diagonal BD of a parallelogram AB Prove that CQ is parallel to AP. Prove also that AC bisects PQ.

In a ΔABC median AD is produced to X such that AD = DX. Prove that ABXC is a
parallelogram.

Fill in the blank:

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

Fill in the blank:

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

In Fig. below, AB = AC and CP || BA and AP is the bisector of exterior ∠CAD of ΔABC.
Prove that (i) ∠PAC = ∠BCA (ii) ABCP is a parallelogram

Prove that the line joining the mid-point of a chord to the centre of the circle passes through the mid-point of the corresponding minor arc.

Prove that a diameter of a circle which bisects a chord of the circle also bisects the angle subtended by the chord at the centre of the circle.