English Medium Class 9 - CBSE Question Bank Solutions

The circumcentre of the triangle ABC is O. Prove that ∠OBC + ∠BAC = 90º.

In the following figure, ∠ADC = 130° and chord BC = chord BE. Find ∠CBE.

A quadrilateral ABCD is inscribed in a circle such that AB is a diameter and ∠ADC = 130º. Find ∠BAC.

In the following figure, ∠OAB = 30º and ∠OCB = 57º. Find ∠BOC and ∠AOC.

Prove that angle bisector of any angle of a triangle and perpendicular bisector of the opposite side if intersect, they will intersect on the circumcircle of the triangle.

If two chords AB and CD of a circle AYDZBWCX intersect at right angles (see figure), prove that arc CXA + arc DZB = arc AYD + arc BWC = semi-circle.

If ABC is an equilateral triangle inscribed in a circle and P be any point on the minor arc BC which does not coincide with B or C, prove that PA is angle bisector of ∠BPC.

In the following figure, O is the centre of the circle, ∠BCO = 30°. Find x and y.

In the following figure, O is the centre of the circle, BD = OD and CD ⊥ AB. Find ∠CAB.

The total surface area of a cube is 96 cm². The volume of the cube is ______.

Following expression is polynomial in one variable or not? State reason for your answer.

`y^2+sqrt2`

Following expression is polynomial in one variable or not? State reason for your answer.

`3sqrtt + tsqrt2`

Following expression is polynomial in one variable or not? State reason for your answer.

`y+2/y`

Following expression is polynomial in one variable or not? State reason for your answer.

x¹⁰ + y³ + t⁵⁰

The lateral surface area of a cube is 256 m². The volume of the cube is ______.

Classify the following as linear, quadratic, and cubic polynomial:

x - x³

Classify the following as linear, quadratic and cubic polynomial:

y + y² + 4

Classify the following as linear, quadratic and cubic polynomial:

1 + x

Classify the following as linear, quadratic and cubic polynomial:

3t

Classify the following as linear, quadratic and cubic polynomial:

r²