NCERT Solutions for Exercise 2.1 Class 9 Maths Chapter 2

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.

Aakash iACST Scholarship Test. Up to 90% Scholarship. Register Now

New: JEE Main 2027: Narayana Scholarship Test Preparation Kit for Class 9

This Story also Contains

Polynomials Class 9 Chapter 2 Exercise: 2.1
More About NCERT Solutions for Class 9 Maths Chapter 2 Exercise 2.1
NCERT Solutions of Class 10 Subject Wise
Subject Wise NCERT Exemplar Solutions

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

Q1 (i) Is the following expression polynomial in one variable? State reasons for your answer. $4x^2 - 3x + 7$

Answer:

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

Q1 (ii) Is the following expression polynomial in one variable? State reasons for your answer. $y^2 + \sqrt2$

Answer:

YES
Given polynomial has only one variable which is y

Q1 (iii) Is the following expression polynomial in one variable? State reasons for your answer. $3\sqrt t + t\sqrt2$

Answer:

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.

Q1 (iv) Is the following expression polynomial in one variable? State reasons for your answer. $y + \frac{2}{y}$

Answer:

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

Q1 (v) Is the following expression polynomial in one variable? State reasons for your answer. $x^{10} + y^3 + t^{50}$

Answer:

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.

Q2 (i) Write the coefficients of $x^2$ in the following: $2 + x^2 +x$

Answer:

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

Q2 (ii) Write the coefficients of $x^2$ in the following: $2 - x^2 + x^3$

Answer:

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

Q2 (iii) Write the coefficients of $x^2$ in the following: $\frac{\pi}{2}x^2 + x$

Answer:

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

Q2 (iv) Write the coefficients of $x^2$ in the following: $\sqrt2 x - 1$

Answer:

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

Q3 Give one example each of a binomial of degree 35, and of a monomial of degree 100.

Answer:

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 $y^{100}$

Q4 (i) Write the degree the following polynomial: $5x^3 + 4x^2 + 7x$

Answer:

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 .

Q4 (ii) Write the degree the following polynomial: $4 - y^2$

Answer:

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

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

Q4 (iii) Write the degree the following polynomial: $5t - \sqrt7$

Answer:

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

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

Q4 (iv) Write the degree the following polynomial: 3

Answer:

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.

Q5 (i) Classify the following as linear, quadratic and cubic polynomial: $x^2+x$

Answer:

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.

Q5 (ii) Classify the following as linear, quadratic and cubic polynomial: $x - x^3$

Answer:

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

Q5 (iii) Classify the following as linear, quadratic and cubic polynomial: $y + y^2 + 4$

Answer:

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

Therefore, it is quadratic polynomial.

Q5 (iv) Classify the following as linear, quadratic and cubic polynomial: $1 +x$

Answer:

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

Q5 (v) Classify the following as linear, quadratic and cubic polynomial: $3t$

Answer:

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

Q5 (vi) Classify the following as linear, quadratic and cubic polynomial: $r^2$

Answer:

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

Given polynomial is $r^2$ with degree 2

Therefore, it is quadratic polynomial

Q5 (vii) Classify the following as linear, quadratic and cubic polynomial: $7x^3$

Answer:

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

NCERT Solutions of Class 10 Subject Wise

Subject Wise NCERT Exemplar Solutions

Frequently Asked Question (FAQs)

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

Also Read

NCERT Solutions for Class 9 - Subject-wise PDFs Updated for 2024-25

NCERT Solutions for Class 9 Science

NCERT Solutions for Class 9 Maths

NCERT Syllabus for Class 9 Maths 2023 - Download Syllabus Pdf

NCERT Solutions For Class 9 Science Chapter 1 Matter in Our Surroundings

NCERT Solutions for Exercise 2.5 Class 9 Maths Chapter 2 Polynomials

NCERT Class 9 Maths Notes - Download Chapter Wise PDFs

NCERT Class 9 Maths Chapter 8 Notes Quadrilaterals - Download PDF

NCERT Class 9 Maths Chapter 2 Notes Polynomials - Download PDF

NCERT Class 9 Maths Chapter 1 Notes Number System - Download Free PDF

NCERT Class 9 Maths Chapter 5 Notes Introduction To Euclid’s Geometry - Download PDF

NCERT Class 9 Maths Chapter 6 Notes Lines and Angles - Download PDF

NCERT Exemplar Class 9 Maths Solutions - Chapter Wise Problems with Solutions

NCERT Exemplar Class 9 Solutions - Subject Wise Problems with Solutions

NCERT Exemplar Class 9 Science Solutions Chapter 15 Improvement in Food Resources

NCERT Exemplar Class 9 Science Solutions Chapter 14 Natural Resources

NCERT Exemplar Class 9 Science Solutions Chapter 13 Why do we fall ill?

NCERT Exemplar Class 9 Science Solutions Chapter 12 Sound

Articles

High Salary Courses After Class 12 Science

Jul 26, 2024

Ophthalmology Courses After 12th - Eligibility, Duration, Institutes

Jul 26, 2024

BiPC Courses After 12th - Fees, Duration & Top Institutes

Jul 25, 2024

ICSO Sample Papers 2024-25 with Answers For Classes 1 to 10

Jul 25, 2024

NMMS Chhattisgarh Result 2024-25: Check Merit List, Cut Off Marks

Jul 25, 2024

UPTAC Counselling 2024 (Started): Document Verification, Date, Registration, Seat Allotment, Rules, Guidelines

Jul 25, 2024

Essay on Diwali for Students: Short Paragraph, 10 Lines on Deepavali

Jul 24, 2024

How to Study at Home? - Check 10 Tips to Study at Home

Jul 23, 2024

IIM Courses After 12th - Eligibility, Exams, Top Colleges

Jul 19, 2024

Upcoming School Exams

National Means Cum-Merit Scholarship

Application Date:15 July,2024 - 14 August,2024

Eligibility Criteria

Application Process

Exam Pattern

National Institute of Open Schooling 12th Examination

Late Fee Application Date:22 July,2024 - 31 July,2024

Application Process

Exam Pattern

Admit Card

National Institute of Open Schooling 10th examination

Late Fee Application Date:22 July,2024 - 31 July,2024

Application Process

Exam Pattern

Mock Test

Chhattisgarh Board of Secondary Education 12th Examination

Exam Date:23 July,2024 - 12 August,2024

Exam Pattern

Admit Card

Result

Chhattisgarh Board of Secondary Education 10th Examination

Exam Date:24 July,2024 - 08 August,2024

Exam Pattern

Admit Card

Result

View All School Exams

Get answers from students and experts

Popular Questions

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) $0.34\; J$	Option 2) $0.16\; J$
Option 3) $1.00\; J$	Option 4) $0.67\; J$

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 3.8×10⁷J 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) $2,000 \; J - 5,000\; J$	Option 2) $200 \, \, J - 500 \, \, J$
Option 3) $2\times 10^{5}J-3\times 10^{5}J$	Option 4) $20,000 \, \, J - 50,000 \, \, J$

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

Option 1) $K/2\,$	Option 2) $\; K\;$
Option 3) $zero\;$	Option 4) $K/4$

In the reaction,

$2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}$

Option 1) $11.2\, L\, H_{2(g)}$ at STP is produced for every mole $HCL_{(aq)}$ consumed	Option 2) $6L\, HCl_{(aq)}$ is consumed for ever $3L\, H_{2(g)}$ produced
Option 3) $33.6 L\, H_{2(g)}$ is produced regardless of temperature and pressure for every mole Al that reacts	Option 4) $67.2\, L\, H_{2(g)}$ at STP is produced for every mole Al that reacts .

How many moles of magnesium phosphate, $Mg_{3}(PO_{4})_{2}$ 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