English Medium Class 9 - CBSE Question Bank Solutions for Mathematics

Find the zero of the polynomial in the following case:

p(x) = 2x + 5

Find the zero of the polynomial in the following case:

p(x) = 3x – 2

Find the zero of the polynomial in the following case:

p(x) = 3x

Find the zero of the polynomial in the following case:

p(x) = ax, a ≠ 0

Find the zero of the polynomial in the following case:

p(x) = cx + d, c ≠ 0, c, d are real numbers.

What is the name of horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane?

See the given figure and write the following:

The coordinates of the point M.

The following statement is true or false? Give reason for your answer.

Only one line can pass through a single point.

Give a definition of the following term. Are there other terms that need to be defined first? What are they, and how might you define them?

parallel lines

Give a definition of the following term. Are there other terms that need to be defined first? What are they, and how might you define them?

perpendicular lines

Give a definition of the following term. Are there other terms that need to be defined first? What are they, and how might you define them?

line segment

Give a definition of the following term. Are there other terms that need to be defined first? What are they, and how might you define them?

radius of a circle

Give a definition of the following term. Are there other terms that need to be defined first? What are they, and how might you define them?

square

Consider two ‘postulates’ given below:-

1. Given any two distinct points A and B, there exists a third point C which is in between A and B.
2. There exist at least three points that are not on the same line.

Do these postulates contain any undefined terms? Are these postulates consistent? Do they follow from Euclid’s postulates? Explain.

If a point C lies between two points A and B such that AC = BC, then prove that AC = `1/2` AB. Explain by drawing the figure.

If a point C lies between two points A and B such that AC = BC, point C is called a mid-point of line segment AB. Prove that every line segment has one and only one mid-point.

In the following figure, if AC = BD, then prove that AB = CD.

Why is Axiom 5, in the list of Euclid’s axioms, considered a ‘universal truth’? (Note that the question is not about the fifth postulate.)

Which of the following figures lie on the same base and between the same parallels. In such a case, write the common base and the two parallels.

A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’. Find the area of the signal board, using Heron’s formula. If its perimeter is 180 cm, what will be the area of the signal board?