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• NCERT Solutions for Class 9 Maths Chapter 2: Polynomials - Exercise 2.2
• NCERT Solutions

Important Topics under NCERT Solutions for Class 9 Maths Chapter 2 Polynomials (Ex 2.2)

Chapter 2 of the class 9 maths syllabus is on Polynomials. It is a very important chapter that is covered in class 9 and is divided into 8 major topics. Students are advised to learn from ad practice the solved questions time and again to be able to master the concept of polynomials.

The following list has been provided to give the students a glimpse at the important topics that are covered under the chapter on Polynomials.

Classification of polynomials

Degree of a polynomial

Types of polynomial based on the degree

Constant polynomial

Linear polynomial

Quadratic polynomial

Cubic polynomial

Types of polynomial based on terms

Value of a polynomial

Zero of a polynomial

Operations on polynomials

Importance of Polynomials in Class 9

Polynomials are expressions having more than two algebraic terms. They can also be defined as the sum of several terms where the same variable/variables has/have different powers. 

Polynomials are practically a language used in most mathematical expressions and are used to represent appropriate relations between different variables or numbers. Students are encouraged to gather as much information from this chapter to be able to solve tricky problems based on polynomials easily in exams.

NCERT Solutions for Class 9 Maths Chapter 2 teach you about polynomials. Vedantu’s NCERT Solutions for Class 9 Maths Chapter 2 PDF makes you aware of every aspect of Polynomials - be it finding value, using algebraic identities or factorization of polynomials. Our Exercise 2.2 Class 9 Maths solution explains everything about polynomials in an easy to understand way. Vedantu provides students with a Free PDF download option for all the NCERT Book Solutions of updated CBSE textbooks . Subjects like Science, Maths, English will become easy to study if you have access to NCERT Solution for Class 9 Science , Maths solutions, and solutions of other subjects that are available on Vedantu only.

Access NCERT Solutions for Class 9 Maths Chapter 2 – Polynomials

Exercise 2.2

1. Find the value of the polynomial $\text{5x - 4}{{\text{x}}^{\text{2}}}\text{ + 3}$  at 

i) $\text{x = 0}$

Ans: Let $\text{p}\left( \text{x} \right)\text{ = 5x - 4}{{\text{x}}^{\text{2}}}\text{ + 3}$

We will simply put the value of $\text{x}$ in the given polynomial.

$\Rightarrow \text{p}\left( \text{0} \right)\text{ = 5}\left( \text{0} \right)\text{ - 4}\left( {{\text{0}}^{\text{2}}} \right)\text{ + 3}$

$\Rightarrow \text{p}\left( \text{0} \right)\text{ = 3}$

Hence, the value of the polynomial at $\text{x = 0}$ is $\text{3}$.

ii) $\text{x = -1}$ 

$\Rightarrow \text{p}\left( \text{-1} \right)\text{ = 5}\left( \text{-1} \right)\text{ - 4}\left[ {{\left( \text{-1} \right)}^{\text{2}}} \right]\text{ + 3}$

$\Rightarrow \text{p}\left( \text{-1} \right)\text{ = - 5 - 4 + 3}$

$\Rightarrow \text{p}\left( \text{-1} \right)\text{ = - 6}$

Hence, the value of the polynomial at $\text{x = -1}$ is $\text{-6}$.

iii) $\text{x = 2}$ 

$\Rightarrow \text{p}\left( \text{2} \right)\text{ = 5}\left( \text{2} \right)\text{ - 4}\left( {{\text{2}}^{\text{2}}} \right)\text{ + 3}$

$\Rightarrow \text{p}\left( \text{2} \right)\text{ = 10 - 16 + 3}$

$\Rightarrow \text{p}\left( \text{2} \right)\text{ = - 3}$

Hence, the value of the polynomial at $\text{x = 2}$ is $\text{-3}$.

2. Find $\text{p}\left( \text{0} \right)$, $\text{p}\left( \text{1} \right)$  and $\text{p}\left( \text{2} \right)$  for each of the following polynomials:

i) $\text{p}\left( \text{y} \right)\text{ = }{{\text{y}}^{\text{2}}}\text{ - y + 1}$ 

$\text{p}\left( \text{0} \right)\text{ = }{{\text{0}}^{\text{2}}}\text{ - 0 + 1}$.

So, we get the value of $\text{p}\left( \text{0} \right)\text{ = 1}$.

$\text{p}\left( \text{1} \right)\text{ = }{{\text{1}}^{\text{2}}}\text{ - 1 + 1 = 1}$

So, we get the value of $\text{p}\left( \text{1} \right)\text{ = 1}$.

$\text{p}\left( \text{2} \right)\text{ = }{{\text{2}}^{\text{2}}}\text{ - 2 + 1}$

$\Rightarrow \text{p}\left( \text{2} \right)\text{ = 4 - 2 + 1}$

$\Rightarrow \text{p}\left( \text{2} \right)\text{ = 3}$

So, we get the value of $\text{p}\left( \text{2} \right)\text{ = 3}$.

ii) $\text{p}\left( \text{t} \right)\text{ = 2 + t + 2}{{\text{t}}^{\text{2}}}\text{ - }{{\text{t}}^{\text{3}}}$

$\text{p}\left( \text{0} \right)\text{ = 2 + 0 + 2}\left( {{\text{0}}^{\text{2}}} \right)\text{ - }\left( {{\text{0}}^{\text{3}}} \right)\text{ = 2}$

So, we get the value of $\text{p}\left( \text{0} \right)\text{ = 2}$.

$\text{p}\left( \text{1} \right)\text{ = 2 + 1 + 2}\left( {{\text{1}}^{\text{2}}} \right)\text{ - }\left( {{\text{1}}^{\text{3}}} \right)\text{ = 4}$

So, we get the value of $\text{p}\left( \text{1} \right)\text{ = 4}$.

$\text{p}\left( \text{2} \right)\text{ = 2 + 2 + 2}\left( {{\text{2}}^{\text{2}}} \right)\text{ - }\left( {{\text{2}}^{\text{3}}} \right)$

$\Rightarrow \text{p}\left( \text{2} \right)\text{ = 4 + 8 - 8}$

$\Rightarrow \text{p}\left( \text{2} \right)\text{ = 4}$

So, we get the value of $\text{p}\left( \text{2} \right)\text{ = 4}$.

iii) $\text{p}\left( \text{x} \right)\text{ = }{{\text{x}}^{\text{3}}}$

$\text{p}\left( \text{0} \right)\text{ = }{{\text{0}}^{\text{3}}}\text{ = 0}$

So, we get the value of $\text{p}\left( \text{0} \right)\text{ = 0}$.

$\text{p}\left( \text{1} \right)\text{ = }{{\text{1}}^{\text{3}}}\text{ = 1}$

$\text{p}\left( \text{2} \right)\text{ = }{{\text{2}}^{\text{3}}}\text{ = 8}$

So, we get the value of $\text{p}\left( \text{2} \right)\text{ = 8}$.

iv) $\text{p}\left( \text{x} \right)\text{ =}\left( \text{x - 1} \right)\left( \text{x + 1} \right)$

$\text{p}\left( \text{0} \right)\text{ =}\left( \text{0 - 1} \right)\left( \text{0 + 1} \right)\text{ = -1}$

So, we get the value of $\text{p}\left( \text{0} \right)\text{ = -1}$.

$\text{p}\left( \text{1} \right)\text{ =}\left( \text{1 - 1} \right)\left( \text{1 + 1} \right)\text{ = 0}$

So, we get the value of $\text{p}\left( \text{1} \right)\text{ = 0}$.

$\text{p}\left( \text{2} \right)\text{ =}\left( \text{2 - 1} \right)\left( \text{2 + 1} \right)$

$\Rightarrow \text{p}\left( \text{2} \right)\text{ = }\left( \text{1} \right)\left( \text{3} \right)\text{ = 3}$

3. Verify whether the following are zeroes of the polynomial, indicated against them.

i) $\text{p}\left( \text{x} \right)\text{ = 3x + 1}$,$\text{x = -}\frac{\text{1}}{\text{3}}$

Ans: We are given: $\text{x = -}\frac{\text{1}}{\text{3}}$. If it is the zero of the polynomial $\text{p}\left( \text{x} \right)\text{ = 3x + 1}$, then $\text{p}\left( \text{-}\frac{\text{1}}{\text{3}} \right)$ should be  $\text{0}$.

$\text{p}\left(\text{-}\frac{\text{1}}{\text{3}}\right)\text{=3}\left(\text{-}\frac{\text{1}}{\text{3}} \right)\text{ + 1 = -1 + 1 = 0}$

Hence, we can say that $\text{x = -}\frac{\text{1}}{\text{3}}$ is a zero of the given polynomial.

ii) $\text{p}\left( \text{x} \right)\text{= 5x - }\!\!\pi\!\!\text{ }$ ,$\text{x = }\frac{\text{4}}{\text{5}}$

Ans: We are given: $\text{x = }\frac{\text{4}}{\text{5}}$. If it is the zero of the polynomial $\text{p}\left( \text{x} \right)\text{ = 5x -  }\text{ }\!\!\pi\!\!\text{ }$, then $\text{p}\left( \frac{\text{4}}{\text{5}} \right)$ should be  $\text{0}$.

$\text{p}\left( \frac{\text{4}}{\text{5}} \right)\text{ = 5}\left( \frac{\text{4}}{\text{5}} \right)\text{ - 3}\text{.14 = 4 - 3}\text{.14 }\ne \text{ 0}$

Hence, we can say that $\text{x = }\frac{\text{4}}{\text{5}}$ is not a zero of the given polynomial.

iii) $\text{p(x) = }{{\text{x}}^{\text{2}}}\text{-1, x = 1, -1}$

Ans: We are given: $\text{x = 1}$  and  $\text{x = -1}$ . 

If they are zeros of polynomial  $\text{p(x) = }{{\text{x}}^{\text{2}}}\text{-1}$ , then $\text{p}\left( \text{1} \right)$ and $\text{p}\left( \text{-1} \right)$ should both be $\text{0}$.

$\text{p}\left( \text{1} \right)\text{ = }{{\left( \text{1} \right)}^{\text{2}}}\text{-1 = 0}$

$\text{p}\left( \text{-1} \right)\text{ = }{{\left( \text{-1} \right)}^{\text{2}}}\text{-1 = 0}$

Hence, we can say that $\text{x = 1}$ and $\text{x = -1}$  are zeroes of the given polynomial.

iv) $\text{p(x) = (x+1)(x-2), x = -1, 2}$

Ans: We are given: $\text{x = -1}$ and $\text{x = 2}$. 

If they are zeroes of the polynomial $\text{p}\left( \text{x} \right)\text{ = }\left( \text{x+1} \right)\left( \text{x-2} \right)$ , then $\text{p}\left( \text{-1} \right)$ and $\text{p}\left( \text{2} \right)$ should be $\text{0}$.

$\text{p}\left( \text{-1} \right)\text{ = }\left( \text{-1+1} \right)\left( \text{-1-2} \right)\text{ = }\left( \text{0} \right)\left( \text{-3} \right)\text{ = 0}$

$\text{p}\left( \text{2} \right)\text{ = }\left( \text{2+1} \right)\left( \text{2-2} \right)\text{ = }\left( \text{3} \right)\left( \text{0} \right)\text{ = 0}$

Hence, we can say that $\text{x = -1}$ and $\text{x = 2}$  are zeroes of the given polynomial.

v) $\text{p(x) = }{{\text{x}}^{\text{2}}}\text{, x = 0}$

Ans: We are given $\text{x = 0}$. 

If it is a zero of the polynomial $\text{p}\left( \text{x} \right)\text{ = }{{\text{x}}^{\text{2}}}$  , then $\text{p}\left( \text{0} \right)$ should be $\text{0}$.

$\text{ p}\left( \text{0} \right)\text{ = }{{\left( \text{0} \right)}^{\text{2}}}\text{ = 0}$

Hence, we can say that $\text{x = 0}$ is a zero of the given polynomial.

vi) $\text{p(x) = lx + m, x = -}\frac{\text{m}}{\text{l}}$

Ans: We are given: $\text{x = -}\frac{\text{m}}{\text{l}}$. 

If it is a zero of the polynomial  $\text{p}\left( \text{x} \right)\text{ = lx + m}$ , then $\text{p}\left( \text{-}\frac{\text{m}}{\text{l}} \right)$ should be  $\text{0}$ .

Here, $\text{p}\left( \text{-}\frac{\text{m}}{\text{l}} \right)\text{ = l}\left( \text{-}\frac{\text{m}}{\text{l}} \right)\text{ + m = -m + m = 0}$

Hence, we can say that $\text{x = -}\frac{\text{m}}{\text{l}}$  is a zero of the given polynomial.

vii)$\text{p(x)=3}{{\text{x}}^{\text{2}}}\text{-1,x=-}\frac{\text{1}}{\sqrt{\text{3}}}\text{,}\frac{\text{2}}{\sqrt{\text{3}}}$

Ans: We are given:$\text{x = }\frac{\text{-1}}{\sqrt{\text{3}}}$  and  $\text{x = }\frac{\text{2}}{\sqrt{\text{3}}}$. 

If they are zeroes of the polynomial $\text{p}\left( \text{x} \right)\text{ = 3}{{\text{x}}^{\text{2}}}\text{-1}$, then $\text{p}\left( \frac{\text{-1}}{\sqrt{\text{3}}} \right)$and $\text{p}\left( \frac{\text{2}}{\sqrt{\text{3}}} \right)$   should be $\text{0}$ .

$\text{p}\left( \frac{\text{-1}}{\sqrt{\text{3}}} \right)\text{ = 3}{{\left( \frac{\text{-1}}{\sqrt{\text{3}}} \right)}^{\text{2}}}\text{-1 = 3}\left( \frac{\text{1}}{\text{3}} \right)\text{-1 = 1-1 = 0}$

$\text{p}\left( \frac{\text{2}}{\sqrt{\text{3}}} \right)\text{ = 3}{{\left( \frac{\text{2}}{\sqrt{\text{3}}} \right)}^{\text{2}}}\text{-1 = 3}\left( \frac{\text{4}}{\text{3}} \right)\text{-1 = 4-1 = 3}$

Hence, we can say that $\text{x = }\frac{\text{-1}}{\sqrt{\text{3}}}$ is a zero of the given polynomial.

However, the value of $\text{x = }\frac{\text{2}}{\sqrt{\text{3}}}$ is not a zero of the given polynomial.

viii) $\text{p(x) = 2x+1, x = }\frac{\text{1}}{\text{2}}$

Ans: We are given: $\text{x = }\frac{\text{1}}{\text{2}}$. 

If it is a zero of polynomial $\text{p}\left( \text{x} \right)\text{ = 2x+1}$ , then $\text{p}\left( \frac{\text{1}}{\text{2}} \right)$ should be $\text{0}$

Here, $\text{p}\left( \frac{\text{1}}{\text{2}} \right)\text{ = 2}\left( \frac{\text{1}}{\text{2}} \right)\text{+1 = 1+1 = 2}$.

So, we get the value $\text{p}\left( \frac{\text{1}}{\text{2}} \right)\ne \text{0}$  .

Hence, we can say that $\text{x = }\frac{\text{1}}{\text{2}}$ is not a zero of the given polynomial.

4. Find the zero of the polynomial in each of the following cases:

i) $\text{p}\left( \text{x} \right)\text{ = x+5}$

Ans:  If $\text{x}$ is zero of the polynomial, then we can say that $\text{p}\left( \text{x} \right)\text{ = 0}$.

Let $\text{p}\left( \text{x} \right)\text{ = 0}$

$\Rightarrow \text{x+5 = 0}$

$\Rightarrow \text{x = -5}$

Therefore, $\text{x = -5}$ is a zero of the given polynomial.

ii) $\text{p}\left( \text{x} \right)\text{ = x-5}$ 

$\Rightarrow \text{x-5 = 0}$

$\Rightarrow \text{x = 5}$

Therefore, $\text{x = 5}$ is a zero of the given polynomial.

iii) $\text{p}\left( \text{x} \right)\text{ = 2x+5}$

$\Rightarrow \text{2x+5 = 0}$

$\Rightarrow \text{x = -}\frac{\text{5}}{\text{2}}$

Therefore, $\text{x = -}\frac{\text{5}}{\text{2}}$ is a zero of the given polynomial.

iv) $\text{p}\left( \text{x} \right)\text{ = 3x-2}$

$\Rightarrow \text{3x-2 = 0}$

$\Rightarrow \text{x = }\frac{\text{2}}{\text{3}}$

Therefore, $\text{x = }\frac{\text{2}}{\text{3}}$  is a zero of the given polynomial.

v) $\text{p}\left( \text{x} \right)\text{ = 3x}$

$\Rightarrow \text{3x = 0}$

$\Rightarrow \text{x = 0}$

Therefore, $\text{x = 0}$ is a zero of the given polynomial.

vi) $\text{p}\left( \text{x} \right)\text{ = ax, a}\ne \text{0}$

$\Rightarrow \text{ax = 0}$

It is also given that $\text{a}$ is non-zero. 

vii) $\text{p}\left( \text{x} \right)\text{ = cx+d, c}\ne \text{0, c, d}$ are real numbers.

$\Rightarrow \text{cx+d = 0}$

It is also given that $\text{c}$ is non-zero.

$\Rightarrow \text{x = -}\frac{\text{d}}{\text{c}}$

Therefore, $\text{x = -}\frac{\text{d}}{\text{c}}$  is a zero of the given polynomial.

Class 9 Maths Chapter 2 - Exercise 2.2

Vedantu’s Class 9 Maths Chapter 2 Exercise 2.2 includes the following problems from polynomial-

Finding the value of polynomial when the value of the variable is randomly fixed by the teacher,For example, if I ask you to find the value of 2x + 3x when I have randomly set the value of X as 5, you will put the value - 5 in place of X and then multiply 2 and 3 with 5.

Finding whether a particular value of the variable will result in the polynomial to be equated as  For example, if X equals to 5 in the equation 2X - 10, then the X = 5 is a zero of the given polynomial.

Finding which value of the variable will result in the polynomial to be equated as 0. For example, if I want to make the value of 3X+1-7 then I have to assign the value of X as 2.

What are Polynomials? Constants and Variables

Before discussing polynomials, it is necessary that you have a clear idea about variables and exponents. Consider the following equation -

2x + 3x = 10

Here we don't know at first what X is. When we solve the equation, we come to the conclusion that here X is 2. So, what X does here is it answers the ‘what’ of a question. In this equation, the question that is implied is - what should we multiply 2 and 3 with so that the addition of the product results in 10?

Again when we are confronted with the following equation - 

2x + 3x = 20

the result of X changes. So, the value of X varies the situation.

This is what we call variable. This variable is generally denoted by x,y,z etc.

Again, if you look at the above two examples, the values of 2 and 3 never change. In both situations, the values of 2 and 3 remain fixed. These are called constants.

Now, look at this,

Here the value of 2 increases exponentially ( 2*2*2). The power 3 is known as an exponent.

If you look at the algebraic expression - 2x + 3x - written above, you will see there are two parts in it - 2x and 3x. These parts are called terms.

Polynomial is a mathematical expression that has multiple terms and consists of constants, variables and non-negative or non-fractionated exponents. The polynomial will only involve addition, subtraction or multiplication.

So 2x + 3x is a polynomial in the variable X.

Again, 2³ + X³ + 3² is a polynomial.

But X + 1∕X is not a polynomial since 1/x can be written as . As said earlier, a polynomial does not allow negative exponents.

Expressions that have √X are not polynomials too since √X can be written as and we know that this is not accepted by polynomials.

If you look at the expression 2x + 3x, the numbers before the variables are called coefficients. 

Class 9 Maths Chapter 2 – Other Exercises (2.1 and 2.3)

Here are a few other exercises that you will find in the NCERT Solutions for Class 9 Maths Chapter 2 PDF – 

Exercise 2.1  

In this exercise of Class 9 Maths Chapter 2, students will be introduced to the concept of polynomials. They will obtain an indent knowledge regarding polynomials in one variable and how to solve the associated sums through shortcut techniques. Here are some important questions for exams that are provided in the exercise.

Question 1 : Finding the polynomials among the expressions in one variable and stating reasons for the answers.

Question 2 : Finding the coefficients of x2 in the provided expressions.

Question 3 : Examples of a binomial of degree 35 and monomial of degree 100.

Question 4: Determining the degree of polynomials.

Question 5 : Classifying linear, quadratic and cubic polynomial expressions.

Exercise 2.3

This chapter is a continuation of Exercise 2.2 Class 9 of NCERT maths book. Students will get in-depth knowledge about the Factor Theorem by solving all questions provided in this exercise step by step. 

Question 1 : Finding the remainder when divided by expressions provided.

Question 2: Determining remainders. 

Question 3: Checking if provided expressions are factors.

How Can Vedantu Help You?

Vedantu's Polynomials Class 9 solutions will help you understand all the topics included in the Polynomials chapter. NCERT guidelines specifically advise teachers to build the fundamental knowledge of the subjects in the students. Vedantu follows this NCERT advice thoroughly. That is why you will find not only solutions to the questions on polynomials but also the explanations on the logic behind our solutions. For example - in question number 2 of Ex 2.1 of our Polynomials Class 9 NCERT Solutions when we are asked to find the coefficients of given polynomials we showed how has an invisible 1 before it. So the coefficient of X² is 1.

Our answers in Class 9th Maths NCERT Solutions Chapter 2 include every step. No step has been skipped. You will not struggle to understand how we reached the result from a given equation. So in question 1(i) of Ex 2.2, we showed how we arrived at the answer 3 by solving the equation step by step. This will not only help the students to understand the granularities in the chapter but will also help them to get good marks.

Every Polynomial formula Class 9 has been used in our solution. The students will get to learn all the aspects of the chapter. Reading our PDF, a student can answer any question from this chapter with confidence.

The Polynomials Class 9 PDF is written in a lucid language. Apart from the Maths expressions, we have used simple, easy to understand words so that students can understand the solutions. Even the math expressions are adequately explained wherever deemed fit.

The Class 9 Maths Chapter 2 PDF has accurate solutions to every polynomials problem. The answers are written by expert teachers who know how to solve a Maths problem so that students understand the process and even the examiners get impressed by the detailed process. These teachers are well aware of NCERT guidelines and follow them to write their answers. There is no unnecessary information in our solutions.

Vedantu’s Polynomial Class 9 PDF is neatly organised. The solutions are written in an uncluttered, easy to understand way. That is why in question 1 of Ex2.3, you will find that we have used red ink to indicate the cutting off of -2x² and +2x². This visually pleasurable way of reading the solutions will help the students to maintain their focus on the solutions.

You can use our NCERT Solutions for Class 9 Maths Chapter 2 Exercise 2.2 to learn all the intricacies of polynomials. These solutions can provide you with everything that you need to excel in the chapter. The answers in our PDF are not written by part-time bloggers, but they are written by professional teachers who took care to make the solutions as helpful as possible.

The Class 9 Maths Chapter 2 Exercise 2.2 Solutions are absolutely free of cost. You don’t need to pay a single penny to download our PDF. You can simply enter your email id and we will send the download link to your email. Vedantu is not motivated by profit; we are genuinely interested in making the learning process of students better. We believe every Indian student has the right to get a quality education. 

Learn Online with Vedantu’s Online Class

Our PDF on polynomials is exhaustive and can help you in finding solutions to all the questions asked in the textbook. Maths needs explanation - countless of times. You might want to ask questions about a particular solution in our PDF. So to help you, Vedantu holds online classes where you can ask questions directly to the teachers. This interaction is particularly necessary for understanding Maths chapters. The schedule of the classes is announced beforehand. We have helpful videos too which will help you understand the solutions in a much more easy and efficient way.

Our online teachers are experts in their subjects and come from respectable institutions like IITs. These teachers know how to teach Maths to students in such a way that students do not get bored. The teachers are aided by simultaneous images, videos and slides. This visual way of teaching ensures easy retention in students.

With our Master Class, you can experience a whole new learning experience. We are offering free seats in our master class for a limited period of time. These masterclasses can enhance your knowledge in ways you cannot fathom. We do not employ cheap tricks and tips. Our main focus is on building the basic knowledge of the students. Our Master Class is not just for advanced students, intermediate students can get benefit from the Master Classes as they will shed fear for Maths and grow a love for the subject.

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Vedantu is here to help the students move forward with confidence. With Vedantu, you have a golden opportunity to make the pillars of your knowledge strong.

NCERT Solutions for Class 9 Maths

Chapter 1 - Number System

Chapter 3 - Coordinate Geometry

Chapter 4 - Linear Equations in Two Variables

Chapter 5 - Introductions to Euclid's Geometry

Chapter 6 - Lines and Angles

Chapter 7 - Triangles

Chapter 8 - Quadrilaterals

Chapter 9 - Areas of Parallelogram and Triangles

Chapter 10 - Circles

Chapter 11 - Constructions

Chapter 12 - Heron's formula

Chapter 13 - Surface area and Volumes

Chapter 14 - Statistics

Chapter 15 - Probability

FAQs on NCERT Solutions for Class 9 Maths Chapter 2: Polynomials - Exercise 2.2

1.  Give a brief description of the topic.

Polynomial is acquired from the word “poly” which means “many” and the word “nominal” refers to “term”. In Math subject, a polynomial expression consists of variables which are also known as coefficients and indeterminates. The coefficients require the operations of addition, subtraction, non-negative integer exponents of variables and multiplication. 

Polynomials are utterances with one or more phrases with a non-zero coefficient. A polynomial can also have one or more than one number of terms. In the form of a polynomial, each utterance in it is known as a term.  Suppose x 2 + 4x+ 2 is polynomial, then the expressions x 2 , 4x, and 2 are the terms of the polynomial.  Each term of the polynomial has a coefficient. For example, if 4x+1 is the polynomial, then the coefficient of x is 4.

2. What are the important terms of a polynomial?

A term might either be a variable or a single digit or it also could be a sequence of the variable with digits.

The degree of the polynomial is the most distinguished power of the variable in a polynomial.

A polynomial of degree 1 will be termed as a linear polynomial.

A polynomial of degree 2 will be described as a quadratic polynomial.

A polynomial of degree 3 is termed as a cubic polynomial.

A polynomial of 1 term is termed as a monomial.

A polynomial of 2 terms is termed as binomial.

A polynomial of 3 terms is termed as a trinomial.

A real number ‘a’ is a zero of a polynomial p(x) if p(a) = 0, where a is also termed as root of the equation p(x) = 0.

A linear polynomial in one variable holds an individual zero, a polynomial of a non-zero constant has no zero, and every real character is a zero of the zero polynomial.

3. What are the topics that are covered in this chapter?

Polynomial is an algebraic expression which includes constants, variables and exponents. It is the expression where the variables have just certain elemental powers. The topics that are covered in this chapter are:

Introduction

Polynomials in One Variable

Zeros of Polynomials

Remainder Theorem

Factorisation of Polynomials

Algebraic Identities

Polynomial expressions are algebraic equations which will have two or more terms with the equal variables of different exponents. This is one of the notable topics for class 9 Mathematics, which students require to learn in order to gain profound knowledge about complex algebraic expressions. Mathematics is one of those subjects that serve as a foundation of numbers, analysis, figures and logic.

4. Are the answers provided by Vedantu, sufficient to attain accurate marks?

Our answers are made to the point and they are drafted to aid you from the exam portion of the view. Answers to the exercising questions are certainly given with examples and they are 100% curate. Our answers will make your learning easy for the exam as they are fitted to be compatible with the tips given with the assistance of using CBSE maths Syllabus and NCERT Book.

Our answers will assist you in advancing a conceptual basis with all the principal ideas in a comprehensible language. The exercising covers all of the vital topics and subtopics of the chapter which might occur for your Class 9 maths exams. You also can clear all of your doubts from here and in this manner, you can definitely perform well in your Class 9 maths exam.

5. Do I need to practice all the questions given in the NCERT Solutions for Class 9 Maths Chapter 2?

The NCERT textbook is the best textbook to prepare for the final exams as it is where most of the questions are asked in the final exam. The exercises and the examples are explained in a simpler manner for all students to understand. Important concepts are also explained in the PDFs. It is important that you practice all the questions and concepts while preparing for the exam. You should not leave any questions. Being thorough with all the questions will help you score good marks in the final exam. You can visit the Vedantu website or download the Vedantu app to access these resources at free of cost.

6. How many exercises are there in this chapter?

Chapter 2 of Maths from the NCERT textbook has three exercises- 2.1, 2.2 and 2.3. Each exercise and its solution is explained step by step in the NCERT Solutions for Class 9 Maths Chapter 2. Not a single question or step has been skipped where they are explained. The examples from within the chapter are also explained. The solutions have been written by professionals with the aim of making it easier for all the students depending on their calibre to understand. 

7. How many questions are there in each exercise?

There are a total of three exercises in the Chapter 2 of Class 10 NCERT Maths textbook. Exercise 2.1 has five questions that cover introduction to polynomials and linear and quadratic linear expressions. Exercise 2.2 has four questions that mainly concentrate on finding the value of the polynomials. The last exercise is 2.3 which focuses on the factor theorem. The questions ask to find the remainders and their division. 

8. What are constants and variables?

Constants are the numeric values attached to a variable (x,y) in any equation. They stay the same and do not change. They help you determine the value of the variable. Variables are the X or Y attached to a constant whose value needs to be determined. It may vary in different situations.  It is a result of the constants and the answer on the other side that helps determine the value of the variables.

9. Is Class 9 Maths NCERT Solutions enough to revise for the final exam?

The NCERT Solutions for each subject and chapter provides summaries and revision notes for the students to refer to and prepare from. These are sufficient as they cover every aspect of the chapter and do not exclude any topic. The students can take the help of the Class 9 Maths NCERT Solutions to prepare for the exam and revise by going through the revision notes provided. The formulas and concepts are explained in an easy and systematic manner. 

NCERT Solutions for Class 9

Cbse study materials for class 9, cbse study materials.

NCERT Solutions for Class 9 Maths Chapter 2 – Polynomials

Ncert solutions for class 9 maths chapter 2 – polynomials pdf.

Free PDF of NCERT Solutions for Class 9 Maths Chapter 2 – Polynomials includes all the questions provided in NCERT Books prepared by Mathematics expert teachers as per CBSE NCERT guidelines from Mathongo.com. To download our free pdf of Chapter 2 Polynomials Maths NCERT Solutions for Class 9 to help you to score more marks in your board exams and as well as competitive exams.

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NCERT Solutions for Class 9 Maths Chapter 2 Polynomials

Here We have given NCERT Solutions for Class 9 Maths Chapter 2 Polynomials. These solutions are posted very carefully without any errors.

You may already be familiar with the concepts of variables and constants, and solving equations with them. For instance, finding the value of the variable in an equation or applying the algebraic identities to them.

Table of Contents

Ncert solutions for class 9 maths chapter 2 polynomials exercise 2.1.

NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Exercise 2.2

NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Exercise 2.3

NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Exercise 2.4

Class 9 Maths NCERT Solutions Chapter 2

Check:- NCERT Solutions for Class 9 Maths

Class 9 NCERT chapter 2 solutions will require you to recall these concepts to build up on them and understand the new concepts associated with polynomials. As a refresher polynomials are expressions made of constants, variables and exponents which are related via arithmetic operators.  2x + 1, is a polynomial but more specifically it is a linear polynomial in one variable with 2 being the coefficient of the variable x. The above polynomial has two terms i.e. 2x and 1.

Additional requirements include:   The terms in the polynomial must have whole number exponent values so x + x1/2  is not a polynomial and there are only a finite number of terms in them.

Key terms in Chapter 2 – polynomials

• Constant polynomial: A polynomial having only the constant and no variable for instance p(x) = 2 is a polynomial as well.
• Degree of the polynomials: The highest exponent in the polynomial. It is always zero for a non-zero constant polynomial. One having degree 2 is called quadratic, and one with degree 3 is a cubic polynomial.
• Polynomials in multiple variables: Some polynomials may have more than one variable for instance p(x) = 4x + 3y or 7z +21x + 35y.
• Zeros of a polynomial: The value of the variable in the polynomial that is obtained by equating the polynomial to 0. In the equation f(x) = 2x +1, f(-1/2) gives 0 so we can say that -½  is a 0 of the polynomial 2x + 1.

Remainder theorem

In simple terms the remainder theorem states that a polynomial that is p(x) (a polynomial of degree >= 1) is divided by x-a (where a is any real number) then the remainder will be p(a). This definition may need a lot of work and a thorough understanding of some fundamental ideas to understand properly. In NCERT Class 9 maths solutions, this may arguably be one of the trickiest concepts to grasp purely because of the length of the explanations given in the text. Just remember the following :

• The number being divided is the dividend and the number dividing is the divisor. The quotient is the answer given from the division and the remainder if any remaining value that occurs when the dividend is not exactly divisible by the divisor.
• In 12 ፥  5, 12 is the dividend, 5 is the divisor, 2 is the quotient and 2 is the remainder.
• Dividend = (Divisor * Quotient) + Remainder
• Additionally if Remainder  = 0, then the Quotient is a factor of the divisor.
• These concepts can also be extended to two polynomial equations.
• The equation 2×2 + x  = x(2x+1)so x and 2x +1 are the factors of the equation

When going through NCERT solutions for chapter 2 polynomials we suggest keeping the points in mind when doing the examples because it will make understanding the examples much easier.

Factor Theorem of Class 9

The remainder theorem acts as the proof for the factor theorem, which is signified by the definition: If a polynomial p(x) of degree n>=1 and a is any real number then x-a is a factor of p(x) if p(a) = 0. Additionally, for quadratic polynomials in particular you can obtain the factors by splitting the middle terms . There are several questions in the exercises that use the factor theorem in various ways and doing all the problems therein will be highly beneficial for fully understanding the concept.

FAQs (Frequently Asked Questions)

How many exercises are in ncert solutions for class 9 maths chapter 2.

There are 5 rather sizable exercises in the NCERT Maths class 9 chapter 2 and each one will allow you to become more proficient at different concepts introduced throughout the chapter. Some questions will include finding missing values given a polynomial and its factor, some will ask you to identify the type of polynomial, and some will enquire about the remainder of a polynomial if its divisor is given. 

Why are Class 9 Maths NCERT Solutions Chapter 2 Important?

This chapter represents a particular increase in difficulty for most students entering class 9 because it introduces a large number of concepts at once because they are all interrelated. So students may frequently encounter problems in understanding the concept or attempting the questions. Because of these challenges, we provide you the step-by-step detailed solutions for NCERT Class 9 Maths exercises so that you may become better at learning how to solve the questions and become more familiar with the type of questions you can expect in the exams.

What is a Polynomial?

Polynomials are expressions in algebra characterized by the presence of variables and coefficients. These variables, indeterminates, can be manipulated using various arithmetic operations like addition, subtraction, and multiplication. Polynomial expressions also allow for the use of positive integer exponents. 

Are NCERT Solutions for Class 9 Maths Chapter 2 difficult to learn?

Seeing the sheer amount of information laid out in this article you may be intimidated by the prospect of having to learn everything. However, once you get over your own misgiving the chapter is rather intuitive. It builds up on things that have already been taught and the absolute best way to practise it is via doing each example yourself and giving multiple tries to problems you struggle with; with each trial, you will become much better at answering the questions.

So fret not whenever you do get stuck we have the solutions for Class 9 Chapter 2 polynomials ready to go. We hope you will gain greatly from the resources we provide.

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NCERT Solutions for Class 9 Maths Chapter 2 Polynomials

Ncert solutions for class 9 maths chapter 2 polynomials| pdf download.

• Exercise 2.1 Chapter 2 Class 9 Maths NCERT Solutions
• Exercise 2.2 Chapter 2 Class 9 Maths NCERT Solutions
• Exercise 2.3 Chapter 2 Class 9 Maths NCERT Solutions
• Exercise 2.4 Chapter 2 Class 9 Maths NCERT Solutions
• Exercise 2.5 Chapter 2 Class 9 Maths NCERT Solutions

NCERT Solutions for Class 9 Maths Chapters:

How can i download chapter 2 polynomials class 9 ncert solutions pdf , what do you mean by algebraic expressions, what is the coefficient of a zero polynomial, what is biquadratic polynomial, contact form.

NCERT Solutions for Class 9 Maths Chapter 2 Exercise 2.2

NCERT Solutions for class 9 Maths chapter 2 exercise 2.2 Polynomials in Hindi and English Medium modified for session 2024-25. The question-answers of ex. 2.2 class 9 Maths are revised and updated according to rationlaise syllabus for academic year 2024-25.

Class 9 Maths Exercise 2.2 Solutions

• Class 9 Maths Exercise 2.2 in English
• Class 9 Maths Exercise 2.2 in Hindi
• 9th Maths Chapter 2 in PDF
• Class 9 Maths Chapter 2 Solutions
• Class 9 Maths NCERT Solutions
• Class 9 all Subjects Solutions

Download (Exercise 2.2) here as a PDF file type. Practice is key to success in Maths, so do practice as much as possible understanding the concepts. All the solutions and NCERT Apps are based on latest NCERT (https://ncert.nic.in/) Books for academic session 2024-25.

Do not try to learn the solutions as there are only for help to understand the difficult questions not for cramming. Class 9 Maths chapter 2 exercise 2.2 Polynomial in English Medium online to use for academic session 2024-25. It provides a general way of solving each questions of exercise 2.2 in the simplest way. There may be other methods also for the same. So, students must try to find various methods so solve a question. Go back to Class 9 Maths Chapter 2 Solutions to see other exercises.

Assignments, notes, sample papers related to this chapter will be uploaded in July 2024-25 for the preparation of class test, half-yearly exams as well as pre-board and final exams in year 2024-25. For any suggestion regarding Maths, Science, Social Science, Hindi or English, you are welcome, we will try to implement the contents as per you suggestions.

Ask your doubts and share your knowledge with your friends and other users through Discussion Forum. You can ask questions related to NCERT Books, General educational questions, related to NIOS board or any other question following CBSE Syllabus.

• If (x – 2) is one of the factor of 3x – 2a, then find the value of a.
• If p(x) = x³ – 3x² + 2x – 3, find the value of p(1) + p(– 1).
• Yadi x²³ + 32 ko x + 1 se bhaag diya jaye to sheshfal kya hoga?
• Bahupad ke maan gyaat keejie, jab p(x) = 3x³ – x² + 2x – 9 ho tatha x = 2 ho.
• Vaastavik vibhaajan dvaara bhaagaphal aur sheshaphal gyaat keejie jab pahale bahupad ko doosare bahupad se bhaag diya jaata hai: x⁴ + 1, x – 1.
• Yadi x + 1 bahupad ax³ + x² – 2x + 4a – 9 ka ek gunankhand ho to a ka maan gyat kijie.

What are the main objectives of exercise 2.2 of class 9th Maths?

The main objectives of exercise 2.2 of class 9th Maths are to teach students:

• The meaning of zeroes of a polynomial.
• How to find zeroes of the polynomial.
• How to check whether the given number is a zero of polynomial or not.
• How to find the value of polynomial p(x) when the value of variable x is given.

Is exercise 2.2 of class 9th Maths easy among second term exams topics?

Yes, exercise 2.2 of class 9th Maths is very easy. There are only four questions and four examples (examples 2, 3, 4, 5) in exercise 2.2 and these questions and examples are nice and easy. Students enjoy doing this exercise. One mark and two marks questions can come from this exercise.

Which examples of 9th Maths exercise 2.2 are of the same kind?

Exercise 2.2 of class 9 Maths contains four questions and four examples (examples 2, 3, 4, 5). Example 2 and questions 1, 2 are of the same type. Examples 3, 5 and question 3 are of the same kind. Example 4 and question 4 are of the same kind.

Which questions of exercise 2.2 of class 9th Maths are compulsory to do for second term exam?

Examples 3, 4, 5 and questions 3, 4 of exercise 2.2 of class 9th Maths are compulsory to do because these examples and questions are very important from the exam point of view. These questions and examples have been asked in the exam several times.

« Class 9 Maths Chapter 2 Exercise 2.1

Class 9 maths chapter 2 exercise 2.3 ».

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NCERT Solutions Class 9 Maths Chapter 2 Exercise 2.2 Polynomials

NCERT solutions for class 9 maths Chapter 2 exercise 2.2 Polynomials cover the questions regarding the concept of zero of the polynomial, which means that the polynomial should be equated to zero, and the value obtained thereafter solving the equation is said to be the ‘zero’ of that particular polynomial, or also known as the root of the polynomial. The NCERT solutions class 9 maths Chapter 2 exercise 2.2 consists of overall 22 questions, out of which 16 questions are short and follow the simple logic, while the rest 6 are of medium complexity.

A pointer to keep in mind before solving the exercises should be that every real number is supposed to be the zero of the polynomial, which is zero . Class 9 maths NCERT solutions Chapter 2 exercise 2.2 Polynomials can be found in the form of a pdf file below:

☛ Download NCERT Solutions Class 9 Maths Chapter 2 Exercise 2.2

Exercise 2.2 Class 9 Chapter 2   Download PDF

More Exercises in Class 9 Maths Chapter 2

• NCERT Solutions Class 9 Maths Chapter 2 Ex 2.1
• NCERT Solutions Class 9 Maths Chapter 2 Ex 2.3
• NCERT Solutions Class 9 Maths Chapter 2 Ex 2.4
• NCERT Solutions Class 9 Maths Chapter 2 Ex 2.5

NCERT Solutions Class 9 Maths Chapter 2 Exercise 2.2 Tips

NCERT solutions class 9 maths Chapter 2 exercise 2.2 Polynomials are a good way to understand the basics of the polynomials as the exercises deal with simple concepts and basic questions, which can be done easily if the students have followed the chapter closely. The students should understand that all the linear polynomials in one variable consist of a unique zero. Also, a constant polynomial which is non-zero does not contain zero.

NCERT solutions for class 9 maths Chapter 2 exercise 2.2 consists of basic exercises including questions to find the degrees and zeros of the polynomials. The detailed examples given in the chapter will help the students to understand the flow of the problems asked in the exercises.

Download Cuemath NCERT Solutions PDFs for free and start learning!

Class 9 Maths NCERT Solutions Video Chapter 2 Exercise 2.2

RS Aggarwal Solutions Class 9 Chapter 2 Polynomials

RS Aggarwal Solutions for Class 9 Maths Book Chapter 2 Polynomials are available here. Study path has prepared solutions of all the exercises of the chapter by our expert math teachers to help you to get good marks in exams. This lesson has a ton of questions that are very important from the examination point of view.

We at Study Path solved each questions step by step with detailed explanations. Students must practice from practice these problems to score high marks in Maths. Below we have listed the Class 9 RS Aggarwal Solutions Chapter 2 Polynomials Exercise 2A, Ex 2B, Ex 2C, Ex 2D and Multiple Choice Questions (MCQs).

Class 9 RS Aggarwal Solutions Chapter 2 Polynomials

Class 9 rs aggarwal solutions chapter 2 ex 2a.

Class 9 RS Aggarwal Solutions Chapter 2 Ex 2B

Class 9 RS Aggarwal Solutions Chapter 2 Ex 2C

Class 9 RS Aggarwal Solutions Chapter 2 Ex 2D

Class 9 RS Aggarwal Solutions Chapter 2 MCQs

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Chapter 2 – Real and Complex Numbers

Exercise 2.1, exercise 2.2, exercise 2.3, exercise 2.4, exercise 2.5, exercise 2.6, review exercise, multiple choice questions, this post has 24 comments.

Assalam-o-Alaikum please check ex 2.4 Q1 it’s wrong according to question given on book please reply me

Thanks for correction. we have make it correct.

is there any way, i can download these notes

Yes, you can. By click top right corner arrow button. And download it.

Exercise 2.1 question 2 part 1 is wrong please check

Too 👍👍👍👍👍 good ots really help me in any problem but ex 2.4 q 1 Is wrong I hope u will ✔️✔️check it

yeah. we have make corrections in it.

Thanks for correction.

there is some mistakes in values like in excersice 2.4,question 1,part 1

You’ve given review ex in place of ex 2.1… Kindly provide ex 2.1 plz……☺

Ok, I will make it.

well described

Rashid Aziz MSC Mathematics

Nice notes😇

Thanks So much

There is something wrong in question no 6 part 6 of ex 2.6 check it ok

Kindly mention the mistake.

The question is 1/2i not 1/2

I’ve corrected the mistake. Thanks for the correction.

Kindly recheck the McQs answer

Thank u so much for giving notes. Is there any teacher who taught theorems

It is very good link But this link can’t show the Example …They show only exercises

I solved a question with the method used in question seven part one of exercise 2.6 and my maths teacher did not accepted it 😔 in a test

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NCERT Book for Class 9th Maths PDF (2024-25)

Ncert book for class 9 maths: download the latest class 9th maths ncert book in a chapter-wise pdf for the current academic session 2024-25. .

NCERT Book for Class 9 Maths: Get the latest NCERT Book for Class 9 Maths for the 2024-25 session for English and Hindi medium. The NCERT Book for Class 9 Maths is revised by the National Council of Educational Research and Training (NCERT) where they have rationalised the contents of the old textbook. Students must check here the names of chapters and topics that have been deleted from the old book and are not relevant for the current academic session. Download the latest and revised book to study Mathematics effectively and perform well in your class tests and the annual CBSE Class 9 Maths Exam 2024-25. 

NCERT Book for Class 9 Maths (2024-25) - in English

List of rationalised content in class 9 maths ncert book.

CBSE Class 9 Maths Deleted Syllabus

NCERT Book for Class 9 Maths  (2023-24) -  in Hindi

Check detailed ncert solutions for class 9 maths (by subject experts).

Why you should read NCERT Book for Class 9 Maths?

NCERT books are best known for presenting the concepts most simply so that students can grasp them effortlessly. Therefore, students are always recommended to use NCERT books to excel in their studies.

• Designed to offer in-depth knowledge in easy and simple language.
• Strictly adheres to the CBSE curriculum which is considered to be sufficient enough to form the base for the annual examinations. 
• Ideal for a comprehensive study to develop a clear concept. 
• Includes several questions of different formats which are perfect to test students' understanding of concepts.

You can also get the latest NCERT Books and exclusive NCERT Solutions for all other subjects of Class 9 by clicking on the following links:

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• Where can I get PDF of Class 9 Maths NCERT Book? + Get free PDF download for the latest and revised edition of Class 9 Maths NCERT Book from this article of Jagran Josh. You will get NCERT Book in English and Hindi languages here.
• Is Maths easy in class 9? + Class 9 Mathematics has some complex topics which can be challenging for some students. However, regular practice and perseverance can contribute to making mathematics more manageable for all. A positive approach towards the subjects helps make it less daunting.
• Which book is best for class 9 Maths exam? + NCERT book is considered the best book for clearing all concepts of Class 9 Maths. The book offers several advantages, including a comprehensive coverage of the syllabus, clear explanations, and a variety of practice problems to enhance understanding and problem-solving skills.
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Class 9 Mathematics Assignments

We have provided below free printable Class 9 Mathematics Assignments for Download in PDF. The Assignments have been designed based on the latest NCERT Book for Class 9 Mathematics . These Assignments for Grade 9 Mathematics cover all important topics which can come in your standard 9 tests and examinations. Free printable Assignments for CBSE Class 9 Mathematics , school and class assignments, and practice test papers have been designed by our highly experienced class 9 faculty. You can free download CBSE NCERT printable Assignments for Mathematics Class 9 with solutions and answers. All Assignments and test sheets have been prepared by expert teachers as per the latest Syllabus in Mathematics Class 9. Students can click on the links below and download all Pdf Assignments for Mathematics class 9 for free. All latest Kendriya Vidyalaya Class 9 Mathematics Assignments with Answers and test papers are given below.

Mathematics Class 9 Assignments Pdf Download

We have provided below the biggest collection of free CBSE NCERT KVS Assignments for Class 9 Mathematics . Students and teachers can download and save all free Mathematics assignments in Pdf for grade 9th. Our expert faculty have covered Class 9 important questions and answers for Mathematics as per the latest syllabus for the current academic year. All test papers and question banks for Class 9 Mathematics and CBSE Assignments for Mathematics Class 9 will be really helpful for standard 9th students to prepare for the class tests and school examinations. Class 9th students can easily free download in Pdf all printable practice worksheets given below.

Topicwise Assignments for Class 9 Mathematics Download in Pdf

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Advantages of Class 9 Mathematics Assignments

• As we have the best and largest collection of Mathematics assignments for Grade 9, you will be able to easily get full list of solved important questions which can come in your examinations.
• Students will be able to go through all important and critical topics given in your CBSE Mathematics textbooks for Class 9 .
• All Mathematics assignments for Class 9 have been designed with answers. Students should solve them yourself and then compare with the solutions provided by us.
• Class 9 Students studying in per CBSE, NCERT and KVS schools will be able to free download all Mathematics chapter wise worksheets and assignments for free in Pdf
• Class 9 Mathematics question bank will help to improve subject understanding which will help to get better rank in exams

Frequently Asked Questions by Class 9 Mathematics students

At https://www.cbsencertsolutions.com, we have provided the biggest database of free assignments for Mathematics Class 9 which you can download in Pdf

We provide here Standard 9 Mathematics chapter-wise assignments which can be easily downloaded in Pdf format for free.

You can click on the links above and get assignments for Mathematics in Grade 9, all topic-wise question banks with solutions have been provided here. You can click on the links to download in Pdf.

We have provided here topic-wise Mathematics Grade 9 question banks, revision notes and questions for all difficult topics, and other study material.

We have provided the best collection of question bank and practice tests for Class 9 for all subjects. You can download them all and use them offline without the internet.

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