English Medium Class 9 - CBSE Question Bank Solutions

Factorise:

x³ + x² – 4x – 4

Factorise:

3x³ – x² – 3x + 1

The equation 2x + 5y = 7 has a unique solution, if x, y are ______.

Any point on the x-axis is of the form ______.

The point of the form (a, a) always lies ______.

Let y varies directly as x. If y = 12 when x = 4, then write a linear equation. What is the value of y when x = 5?

In the following figure, BA ⊥ AC, DE ⊥ DF such that BA = DE and BF = EC. Show that ∆ABC ≅ ∆DEF.

ABC and DBC are two triangles on the same base BC such that A and D lie on the opposite sides of BC, AB = AC and DB = DC. Show that AD is the perpendicular bisector of BC.

ABC is an isosceles triangle in which AC = BC. AD and BE are respectively two altitudes to sides BC and AC. Prove that AE = BD.

Prove that sum of any two sides of a triangle is greater than twice the median with respect to the third side.

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.