NCERT Solutions for Exercise 2.1 Class 9 Maths Chapter 2 - Polynomials

# NCERT Solutions for Exercise 2.1 Class 9 Maths Chapter 2 - Polynomials

Edited By Safeer PP | Updated on Jul 22, 2022 05:25 PM IST

NCERT Solutions for exercise 2.1 Class 9 Maths chapter 2 polynomials, which would be quite handy when performing assignments. We know that "Polynomial" derives from the words "Poly" (Meaning Many) and "nominal" (in this case meaning Term)—so it means "many terms" as we learned in previous sessions. Exercise 2.1 Class 9 Maths is a chapter-opening exercise that incorporates a number of questions. Here We'll look at polynomials in NCERT book exercise 2.2. The notion of the relationship between polynomials and non-polynomials is explored in chapter 2 of NCERT Mathematics for Class 9.

The Class 9 Maths chapter 2 exercise 2.1 lists a few practice problems on polynomials that involve the identification of the degree of Polynomials. The Class 9 Maths chapter 2 exercise 2.1 covers the topics like tracing the coefficients of given polynomials. The concept of classification of polynomials with linear, quadratic, and cubic degrees will also discuss in NCERT syllabus Class 9 Maths chapter 2 exercise 2.1. Along with Class 9 Maths chapter 1 exercise 2.1 the following exercises are also present.

## Polynomials Class 9 Chapter 2 Exercise: 2.1

YES
Given polynomial $4x^2 - 3x + 7$ has only one variable which is x

YES
Given polynomial has only one variable which is y

NO
Because we can observe that the exponent of variable t in term $3\sqrt t$ is $\frac{1}{2}$ which is not a whole number.
Therefore this expression is not a polynomial.

NO
Because we can observe that the exponent of variable y in term $\dpi{100} \frac{2}{y}$ is $-1$ which is not a whole number. Therefore this expression is not a polynomial.

NO
Because in the given polynomial $x^{10} + y^3 + t^{50}$ there are 3 variables which are x, y, t. That's why this is polynomial in three variable not in one variable.

Coefficient of $x^2$ in polynomial $2 + x^2 +x$ is 1.

Coefficient of $x^2$ in polynomial $2 - x^2 + x^3$ is -1.

Coefficient of $x^2$ in polynomial $\frac{\pi}{2}x^2 + x$ is $\frac{\pi}{2}$

Coefficient of $x^2$ in polynomial $\sqrt2 x - 1$ is 0

Degree of a polynomial is the highest power of the variable in the polynomial.
In binomial, there are two terms
Therefore, binomial of degree 35 is
Eg:- $x^{35}+1$
In monomial, there is only one term in it.
Therefore, monomial of degree 100 can be written as $y^{100}$

Degree of a polynomial is the highest power of the variable in the polynomial.
Therefore, the degree of polynomial $5x^3 + 4x^2 + 7x$ is 3 .

Degree of a polynomial is the highest power of the variable in the polynomial.

Therefore, the degree of polynomial $4 - y^2$ is 2.

Degree of a polynomial is the highest power of the variable in the polynomial.

Therefore, the degree of polynomial $5t - \sqrt7$ is 1

Degree of a polynomial is the highest power of the variable in the polynomial.

In this case, only a constant value 3 is there and the degree of a constant polynomial is always 0.

Linear polynomial, quadratic polynomial, and cubic polynomial has its degrees as 1, 2, and 3 respectively

Given polynomial is $x^2+x$ with degree 2

Therefore, it is a quadratic polynomial.

Linear polynomial, quadratic polynomial, and cubic polynomial has its degrees as 1, 2, and 3 respectively

Given polynomial is $x - x^3$ with degree 3

Therefore, it is a cubic polynomial

Linear polynomial, quadratic polynomial, and cubic polynomial has its degrees as 1, 2, and 3 respectively

Given polynomial is $y + y^2 + 4$ with degree 2

Linear polynomial, quadratic polynomial, and cubic polynomial has its degrees as 1, 2, and 3 respectively

Given polynomial is $1 +x$ with degree 1

Therefore, it is linear polynomial

Linear polynomial, quadratic polynomial, and cubic polynomial has its degrees as 1, 2, and 3 respectively

Given polynomial is $3t$ with degree 1

Therefore, it is linear polynomial

Linear polynomial, quadratic polynomial, and cubic polynomial has its degrees as 1, 2, and 3 respectively

Given polynomial is $r^2$ with degree 2

Linear polynomial, quadratic polynomial, and cubic polynomial has its degrees as 1, 2, and 3 respectively

Given polynomial is $7x^3$ with degree 3

Therefore, it is a cubic polynomial

## More About NCERT Solutions for Class 9 Maths Chapter 2 Exercise 2.1

The problems from the concepts of attaining the expression of Polynomials are covered in exercise 2.1 Class 9 Maths. The Initial questions of NCERT solutions for Class 9 Maths chapter 2 exercise 2.1 is to identify if the given polynomial expression is in one variable or not. And later on questions of Class 9 Maths chapter 2 exercise, 2.1 is to solve and find the degrees of polynomial expression, the concept of linear, quadratic, and cubic polynomials will also be discussed as in Class 9 Maths chapter 2 exercise 2.1 is to simplify mathematical scenario from the perspective of students to get the broader way of thought process.

Also Read| Polynomials Class 9 Notes

Benefits of NCERT Solutions for Class 9 Maths Chapter 2 Exercise 2.1

• Benefits of the exercise 2.1 Class 9 Maths and starts with a keen understanding of Polynomials analysis

• If students can solve each question of this exercise 2.1 Class 9 Maths they will be able to grasp the actual concept offered on the Polynomials as given in Class 9 Maths chapter 2 exercise 2.1

• Last but not the least benefit of studying Class 9 Maths chapter 1 exercise 2.1 is Students can easily crack other questions appeared in many competitive exams

Also see-

## Subject Wise NCERT Exemplar Solutions

1. Can we say y + 3/y is a Polynomial?

No, we can't say the given term a Polynomial, because it does not follow the fundamental definition of Polynomial

2. Is Introductory exercise exercise 2.1 in chapter 2 important?

There are a total of 5 exercises in chapter 2 i.e. Ex 2.1, 2.2, 2.3, 2.4, 2.5, hence knowledge of preceding exercise make it more effective for students to understand more.

3. What are the attached topics related to chapter 2?

Well there are many more topics like a polynomial in one variable, remainder theorem, factorization, and algebraic identities

4. Can you give an example of a monomial?

Monomial is a type of polynomial that contains only one term example =  ax²

5. Can you give an example of binomial?

Binomial is a type of polynomial that contains only 2 terms example =  ax² + b

6. What is the degree of polynomial x² +x?

The highest power of  x² +x is 2

Therefore degree = 2 hence it is a quadratic polynomial

7. What does polynomial with degree = 4 called?

A polynomial with degree  = 4 is called bi quadratic  polynomial, which is not in the course of chapter 2 Class 9

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A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

 Option 1) Option 2) Option 3) Option 4)

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

 Option 1) 2.45×10−3 kg Option 2)  6.45×10−3 kg Option 3)  9.89×10−3 kg Option 4) 12.89×10−3 kg

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

 Option 1) Option 2) Option 3) Option 4)

A particle is projected at 600   to the horizontal with a kinetic energy . The kinetic energy at the highest point

 Option 1) Option 2) Option 3) Option 4)

In the reaction,

 Option 1)   at STP  is produced for every mole   consumed Option 2)   is consumed for ever      produced Option 3) is produced regardless of temperature and pressure for every mole Al that reacts Option 4) at STP is produced for every mole Al that reacts .

How many moles of magnesium phosphate, will contain 0.25 mole of oxygen atoms?

 Option 1) 0.02 Option 2) 3.125 × 10-2 Option 3) 1.25 × 10-2 Option 4) 2.5 × 10-2

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

 Option 1) decrease twice Option 2) increase two fold Option 3) remain unchanged Option 4) be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

 Option 1) Molality Option 2) Weight fraction of solute Option 3) Fraction of solute present in water Option 4) Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

 Option 1) twice that in 60 g carbon Option 2) 6.023 × 1022 Option 3) half that in 8 g He Option 4) 558.5 × 6.023 × 1023

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

 Option 1) less than 3 Option 2) more than 3 but less than 6 Option 3) more than 6 but less than 9 Option 4) more than 9