English Medium कक्षा ९ - CBSE Question Bank Solutions

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.

S is any point on side QR of a ∆PQR. Show that: PQ + QR + RP > 2PS.

D is any point on side AC of a ∆ABC with AB = AC. Show that CD < BD.

In the following figure, l || m and M is the mid-point of a line segment AB. Show that M is also the mid-point of any line segment CD, having its end points on l and m, respectively.

Bisectors of the angles B and C of an isosceles triangle with AB = AC intersect each other at O. BO is produced to a point M. Prove that ∠MOC = ∠ABC.

In the following figure, AD is the bisector of ∠BAC. Prove that AB > BD.

The image of an object placed at a point A before a plane mirror LM is seen at the point B by an observer at D as shown in the following figure. Prove that the image is as far behind the mirror as the object is in front of the mirror.

[Hint: CN is normal to the mirror. Also, angle of incidence = angle of reflection].

P is a point on the bisector of ∠ABC. If the line through P, parallel to BA meet BC at Q, prove that BPQ is an isosceles triangle.

O is a point in the interior of a square ABCD such that OAB is an equilateral triangle. Show that ∆OCD is an isosceles triangle.