case study questions class 8 maths chapter 2

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Chapter 2 Class 8 Linear Equations in One Variable

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Updated for new NCERT - 2023-24 Book.

Get NCERT Solutions of all Exercise Questions and Examples of Chapter 2 Class 8 Linear Equations in One Variable free at Teachoo. Answers to each and every question with detailed explanation for your understanding. Best answers guaranteed!

We studied Equations and Expressions in Algebra ( Chapter 9 Class 8 ). Equation has an = sign, expression does not have it

In this chapter, we will learn

• What is an Equation 
• What is a Linear Equation
• What is a Linear Equation in one variable
• Solving Linear Equations - by taking variables on one side, numbers on the side
• Making Equations from Statements , and then Solving.
• Perimeter and Area Questions
• Fraction questions - where we need to find Numerator or Denominator
• Cost, Sale, Profit Questions
• Questions where we have Consecutive Numbers
• Questions involving Consecutive Multiples
• Coins and Currency Notes Questions
• Questions where numbers are added or subtracted
• Questions where a Two Digit number is given, and we reverse its digits
• Questions involving Age

Click on an exercise or topic link below to start doing the chapter.

Note: Important Questions of this chapter have been marked. When you click on a link, at the bottom of the page there is a list with arrows. In that list, you can find all the questions of that exercise and find Important Questions marked as blue.

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Important Questions for CBSE Class 8 Maths 2023-24

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Maths Important Questions for Class 8

Maths is a vast subject. The concept students learn in the lower classes helps in developing skills for higher classes. Thus, solving important questions for class 8 Maths helps students to score good marks.

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Class 8 Maths gives the student a chapter-wise plan to prepare the student for the CBSE class 8 examination. Important questions for class 8 Maths will help the students with practice for exam preparation. The questions are prepared by expert teachers of the subject so that all the topics and concepts are covered.

The important questions for class 8 Mathes will help students to gauge their understanding of the major concepts that are taught in class 8 Maths. By practising them, students will get an idea of what type of questions will be asked in the exam. Solving the important questions of Maths for class 8 CBSE will help students understand the concept well.

To access the important questions for class 8 Maths, students may register at Extramarks.

Class 8 Maths Important Questions – Chapters Covered

There are 16 Chapters and sub-topics that have important questions for class 8 Maths. The list here is created as per the NCERT books and the latest CBSE syllabus and is mentioned below.

 Chapter 1: Rational Numbers

Rational numbers are the numbers that can be represented in the form of p/q, where p and q are integers, and q is not equal to 0.

• Ex 1.1 Introduction to Rational Numbers
• Ex 1.2 Properties of Rational Numbers
• Ex 1.3 Representation of Rational Numbers on the Number Line
• Ex 1.4 Rational Numbers between Two Rational Numbers

Chapter 2: Linear Equations in One Variable

Linear equations in one variable are algebraic expressions that have only one variable.

• Ex 2.1 Introduction to Linear Equations in One Variable
• Ex 2.2 Solving Equations which have Linear Expressions on one Side and Numbers on the Other Side
• Ex 2.3 Some Applications
• Ex 2.4 Solving Equations having the Variable on Both Sides
• Ex 2.5 Some More Applications
• Ex 2.6 Reducing Equations to Simpler Form
• Ex 2.7 Equations Reducible to the Linear Form

Chapter 3: Understanding Quadrilaterals

Understanding quadrilaterals teaches different types of quadrilaterals and their properties.

• Ex 3.1 Introduction to Quadrilaterals
• Ex 3.2 Polygons
• Ex 3.3 Sum of the Measures of the Exterior Angles of a Polygon
• Ex 3.4 Kinds of Quadrilaterals
• Ex 3.5 Some Special Parallelograms

Chapter 4: Practical Geometry

In this chapter, students will learn to construct the quadrilaterals based on certain given conditions, such as when the dimensions are given for its sides and diagonals or for angles.

• Ex 4.1 Introduction to Practical Geometry
• Ex 4.2 Constructing a Quadrilateral
• Ex 4.3 Some Special Cases

Chapter 5: Data Handling

Students will understand the significance of data and its management in small and large industries.

• Ex 5.1 Looking for Information – Data Handling
• Ex 5.2 Organising Data
• Ex 5.3 Grouping Data
• Ex 5.4 Circle Graph or Pie Chart
• Ex 5.5 Chance and Probability

Chapter 6: Squares and Square Roots.

Students will learn how to find squares and square roots for different numbers.

• Ex 6.1 Introduction to Square and Square Roots
• Ex 6.2 Properties of Square Numbers
• Ex 6.3 Some More Interesting Patterns
• Ex 6.4 Finding the Square of a Number
• Ex 6.5 Square Roots
• Ex 6.6 Square Roots of Decimals
• Ex 6.7 Estimating Square Root

Chapter 7: Cubes and Cube Roots

In this chapter, students will learn to find cube and cube roots for different numbers.

• Ex 7.1 Introduction to Cubes and Cube Roots
• Ex 7.2 Cubes
• Ex 7.3 Cube Roots

Chapter 8: Comparing Quantities

This chapter is based on finding percentage, cost price, selling price, profit, loss, and compound interest.

• Ex 8.1 Recalling Ratios and Percentages
• Ex 8.2 Finding the Increase or Decrease in percent
• Ex 8.3 Finding Discounts
• Ex 8.4 Prices Related to Buying and Selling (Profit and Loss)
• Ex 8.5 Sales Tax/Value Added Tax/Goods and Services Tax
• Ex 8.6 Compound Interest
• Ex 8.7 Deducing a Formula for Compound Interest
• Ex 8.8 Rate Compounded Annually or Half Yearly (Semi-Annually)
• Ex 8.9 Applications of Compound Interest Formula

Chapter 9: Algebraic Expressions and Identities

The chapter teaches students to find the degree of the polynomial, dividing a monomial by monomial, dividing a polynomial by a monomial, and dividing polynomial by polynomial. It also teaches the students to divide the algebraic expression employing factorisation.

• Ex 9.1 What are Expressions?
• Ex 9.2 Terms, Factors and Coefficients
• Ex 9.3 Monomials , Binomials and Polynomials
• Ex 9.4 Like and Unlike Terms
• Ex 9.5 Addition and Subtraction of Algebraic Expressions
• Ex 9.6 Multiplication of Algebraic Expressions: Introduction
• Ex 9.7 Multiplying a Monomial by a Monomial
• Ex 9.8 Multiplying a Monomial by a Polynomial
• Ex 9.9 Multiplying a Polynomial by a Polynomial
• Ex 9.10 What is an Identity?
• Ex 9.11 Standard Identities
• Ex 9.12 Applying Identities

Chapter 10: Visualising Solid Shapes

The chapter introduces some very interesting concepts, such as visualising solid shapes, and views of 3d-shapes like cubes, cylinders, cones, spheres, etc.

• Ex 10.1 Introduction to Visualising Solid Shapes
• Ex 10.2 Views of 3D-Shapes
• Ex 10.3 Mapping Space Around Us
• Ex 10.4 Faces, Edges and Vertices

Chapter 11: Mensuration

This chapter deals with the measurement of area, perimeter, surface area and volume of different types of shapes.

• Ex 11.2 Introduction to Mensuration
• Ex 11.2 Let us Recall
• Ex 11.3 Area of Trapezium
• Ex 11.4 Area of a General Quadrilateral
• Ex 11.5 Area of a Polygon
• Ex 11.6 Solid Shapes
• Ex 11.7 Surface Area of Cube, Cuboid and Cylinder
• Ex 11.8 Volume of Cube, Cuboid and Cylinder
• Ex 11.9 Volume and Capacity

Chapter 12: Exponents and Powers

Here students will learn how to write large numbers easily using exponents and powers.

• Ex 12.1 Introduction to Exponents and Powers
• Ex 12.2 Powers with Negative Exponents
• Ex 12.3 Laws of Exponents
• EX 12.4 Use of Exponents to Express Small Numbers in Standard Form

Chapter 13: Direct and Inverse Proportions.

A direct and inverse proportion are applied to determine how the quantities and amounts are correlated with each other.

• Ex 13.1 Introduction to Direct and Inverse Proportions
• Ex 13.2 Direct Proportion
• Ex 13.3 Inverse Proportion

Chapter 14: Factorisation

This chapter deals with writing a given expression as the product of two or more factors is called factorisation.

• Ex 14.1 Introduction to Factorisation
• Ex 14.2 What is Factorisation?
• Ex 14.3 Division of Algebraic Expressions
• Ex 14.4 Division of Algebraic Expressions Continued (Polynomial ÷ Polynomial)
• Ex 14.5 Can you Find the Error?

Chapter 15: Introduction to Graphs 

This chapter deals primarily with the representation of data using different graph diagrams.

• Ex 15.1 Introduction
• Ex 15.2 Linear Graphs
• Ex 15.3 Some Applications

Chapter 16: Playing with Numbers

Playing with Numbers, introducing Numbers in General Form, Games with Numbers and Divisibility test by some numbers.

• Ex 16.1 Introduction
• Ex 16.2 Numbers in General Form
• Ex 16.3 Games with Numbers
• Ex 16.4 Letters for Digits
• Ex 16.5 Tests of Divisibility

Important Questions For Class 8 Maths Weightage

Practicing important questions for class 8 Maths will build the student’s confidence which will help them to score better during examinations. It will help in building a strong foundation for students. While class 8 Maths’ important questions are crucial, it is also vital to revise all topics under the chapter before trying to solve the important questions. 

All important questions for class 8 Maths are prepared according to the latest syllabus and follow the guidelines set by CBSE, India. Solving these Maths questions for class 8 will assist the students in judging their understanding of the chapter.

Important Questions for Class 8 Maths Chapter Wise

Extramarks important questions for class 8 Maths are equipped with chapter-wise plans for the students to prepare well for the CBSE class 8 examination. The solutions provided for the Maths important questions for class 8 are prepared by subject experts who have got very good teaching experience. These questions are compiled with reference to NCERT Books, several years of examination papers and based on how crucial the topic is for higher studies.

Students can click on the link for chapter-wise important questions for class 8 Maths with solutions.

• Chapter 1. Rational Numbers
• Chapter 2. Linear Equation in One Variable
• Chapter 3. Understanding Quadrilaterals
• Chapter 4. Practical Geometry
• Chapter 5. Data Handling
• Chapter 6. Squares and Square Roots
• Chapter 7. Cubes and Cube Roots 
• Chapter 8. Comparing Quantities
• Chapter 9. Algebraic Expressions and Identities
• Chapter 10. Visualising Solid Shapes
• Chapter 11. Mensuration
• Chapter 12. Exponents and Powers
• Chapter 13. Direct and Inverse Proportions
• Chapter 14. Factorisation
• Chapter 15. Introduction to Graphs
• Chapter 16. Playing with Numbers

Maths Questions for Class 8 with Answers – Types of Questions

The important questions for class 8 Maths include MCQs, short answer type questions, long answer type questions, and case study-based questions. These questions are a vital part of the study schedule. The chapter-wise important questions are good for students for self-study, which will help them in preparing for examinations. In addition to it, solving sample papers will be a great help for students.

Along with important questions for class 8 Maths, students can use various study materials during revision by clicking the link below.

Important Questions For Class 8 Maths With Solutions

• CBSE revision notes
• CBSE Sample papers
• CBSE previous year question papers
• CBSE extra questions

Benefits Of Solving Maths Questions for Class 8

Some of the benefits of Extramarks important questions for class 8 Maths include the following.

• Solving these questions increases the confidence in the student, which in turn helps them to score good marks.
• Practicing important questions for class 8 Maths helps students to improve in their weak topics.
•  Solving them helps students to learn the formulae and understand the concepts well.
• It covers all the important topics that will be asked in the exam.
• Solving important questions for class 8 Maths increases students’ problem-solving skills and critical thinking abilities.
• Students will understand the pattern of the question paper and the marking scheme of the exam.
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CBSE Class 8 Maths Important Questions

Chapter 1 - rational numbers.

Chapter 2 - Linear Equations in One Variable

Chapter 3 - understanding quadrilaterals, chapter 4 - practical geometry, chapter 5 - data handling, chapter 6 - squares and square roots, chapter 7 - cubes and cube roots, chapter 8 - comparing quantities, chapter 9 - algebraic expressions and identities, chapter 10 - visualising solid shapes, chapter 11 - mensuration, chapter 12 - exponents and powers, chapter 13 - direct and inverse proportions, chapter 14 - factorisation, chapter 15 - introduction to graphs, chapter 16 - playing with numbers, faqs (frequently asked questions), 1. how are chapter-wise important questions for class 8 maths helpful for students.

The chapter-wise important questions for class 8 Maths can help the students to clear their doubts, improve in their weak topics and prepare themselves for the exam in a better way. They also help with board exam preparation.

2. Which chapter is interesting in class 8 Maths?

Playing with numbers is an interesting chapter in class 8 Mathcs. Students will enjoy puzzles of missing numbers.

3. How to score the highest marks in class 8 Maths?

One can score 90% and above in class 8 Maths by practising important questions for class 8 Maths, solving past  years’ question papers, revision notes, and sample papers.

CBSE Related Links

NCERT Solutions for Class 8 Maths Chapter 2 Linear Equations in one Variable

Class 8 Maths Exercise 2.1 Solutions Class 8 Maths Exercise 2.2 Solutions

Revised NCERT Solutions for Class 8 Maths Chapter 2 Linear Equations in one Variable in English and Hindi Medium modified and updated for new session 2024-25. According to new syllabus 2024-25 for 8th Maths, there are only two exercises in chapter 2 Linear Equations.

8th Maths Chapter 2 Solutions for CBSE Board

• Class 8 Maths Exercise 2.1 in English
• Class 8 Maths Exercise 2.2 in English

8th Maths Chapter 2 Solutions for State Boards

• Class 8 Maths Chapter 2 Exercise 2.1
• Class 8 Maths Chapter 2 Exercise 2.2
• Class 8 Maths Chapter 2 Exercise 2.3
• Class 8 Maths Chapter 2 Exercise 2.4
• Class 8 Maths Chapter 2 Exercise 2.5

8th Maths Chapter 2 Solutions in Hindi Medium

• Class 8 Maths Exercise 2.1 in Hindi
• Class 8 Maths Exercise 2.2 in Hindi
• Class 8 Maths Chapter 2 NCERT Book
• Class 8th Maths Solutions Page
• Class 8 all Subjects Solutions

Class VIII Maths based on latest NCERT Books for new session. Download Prashnavali 2.1 and Prashnavali 2.2 in Hindi Medium or Exercise 2.1 and Exercise 2.2 in English Medium free to use online or download in PDF to use offline. NCERT Solutions 2024-25 for other subjects are also given as downloadable format. All the solutions are in updated format based on latest NCERT Books .

NCERT Solutions App for Class 8

NCERT Solutions of Class 8 Mathematics Chapter 2 Linear Equations in One Variable all Exercises are in English as well as in Hindi Medium to use online. NCERT Solutions Offline Apps 2024-25 are also given to free download based on latest NCERT Books.

In Chapter 2, we are concerned about algebraic equations in an equality involving variables. It means the value of expression on the both sides are equal. The solution of the equation may be any Rational Number. During the solutions, the variables can be transported from one side to other side of the equation. In order to solve the equation, first make it simplified and convert it into simple linear equation and then shift all the variables one side and constants on the other side. Download Class 8 Maths App for offline use or Kaksha 8 Ganit App in Hindi Medium.

Class 8 Maths Chapter 2 Practice questions with Solution

A positive number is 5 times another number. if 21 is added to both the numbers, then one of the new numbers becomes twice the other new number. what are the numbers.

Let another number be x. Then positive number = 5x According to the question, 5x + 21 = 2 (x + 21) ⇒ 5x + 21 = 2x + 42 ⇒ 5x + 21 = 2x + 42 – 21 ⇒5x = 21 ⇒ x = 21/3 = 7 Hence another number = 7 and positive number = 5 x 7 =35

Shobo’s mother’s present age is six times Shobo’s present age. Shobo’s age five years from now will be one third of his mother’s present age. What are their present age?

Let Shobo’s present age be x years. And Shobo’s mother’s present age = 6x years According to the question, x + 5 = (1/3) × 6x ⇒ x + 5 = 2x ⇒ 2x = x + 5 ⇒ 2x – x = 5 ⇒ x = 5 years. Hence, Shobo’s present age = 5 years and Shobo’s mother’s present age = 6 x 5 = 30 years

Convert multiple situations of linear equations into simple equations first and then solve them. In this lesson, questions based on numbers, questions on age and distances, questions based on perimeters and currency have to be converted first into simple equations and then solved.

Download NCERT Books and Offline apps based on new CBSE Syllabus . Ask your doubts and share your knowledge with your friends and other users.

« Chapter 1: Rational Numbers

Chapter 3: understanding quadrilaterals ».

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NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12

NCERT Solutions for Class 8 Maths Chapter 2 Linear Equations in One Variable

February 24, 2021 by Sastry CBSE

NCERT Solutions for Class 8 Maths Chapter 2 Linear Equations in One Variable Ex 2.1

• Class 8 Maths Linear Equations in One Variable Exercise 2.1
• Class 8 Maths Linear Equations in One Variable Exercise 2.2
• Class 8 Maths Linear Equations in One Variable Exercise 2.3
• Class 8 Maths Linear Equations in One Variable Exercise 2.4
• Class 8 Maths Linear Equations in One Variable Exercise 2.5
• Class 8 Maths Linear Equations in One Variable Exercise 2.6
• Linear Equations in One Variable Class 8 Extra Questions

NCERT Solutions for Class 8 Maths Chapter 2 Linear Equations in One Variable Exercise 2.1

Ex 2.1 Class 8 Maths Question 1. Solve the equation: x – 2 = 7. Solution: Given: x – 2 = 7 ⇒ x – 2 + 2 = 7 + 2 (adding 2 on both sides) ⇒ x = 9 (Required solution)

Ex 2.1 Class 8 Maths Question 2. Solve the equation: y + 3 = 10. Given: y + 3 = 10 ⇒ y + 3 – 3 = 10 – 3 (subtracting 3 from each side) ⇒ y = 7 (Required solution)

Ex 2.1 Class 8 Maths Question 3. Solve the equation: 6 = z + 2 Solution: We have 6 = z + 2 ⇒ 6 – 2 = z + 2 – 2 (subtracting 2 from each side) ⇒ 4 = z Thus, z = 4 is the required solution.

Ex 2.1 Class 8 Maths Question 5. Solve the equation 6x = 12. Solution: We have 6x = 12 ⇒ 6x ÷ 6 = 12 ÷ 6 (dividing each side by 6) ⇒ x = 2 Thus, x = 2 is the required solution.

Ex 2.1 Class 8 Maths Question 6. Solve the equation \(\frac { t }{ 5 }\) = 10. Solution: Given \(\frac { t }{ 5 }\) = 10 ⇒ \(\frac { t }{ 5 }\) × 5 = 10 × 5 (multiplying both sides by 5) ⇒ t = 50 Thus, t = 50 is the required solution.

Ex 2.1 Class 8 Maths Question 7. Solve the equation \(\frac { 2x }{ 3 }\) = 18. Solution: We have \(\frac { 2x }{ 3 }\) = 18 ⇒ \(\frac { 2x }{ 3 }\) × 3 = 18 × 3 (multiplying both sides by 3) ⇒ 2x = 54 ⇒ 2x ÷ 2 = 54 ÷ 2 (dividing both sides by 2) ⇒ x = 27 Thus, x = 27 is the required solution.

Ex 2.1 Class 8 Maths Question 8. Solve the equation 1.6 = \(\frac { y }{ 1.5 }\) Solution: Given: 1.6 = \(\frac { y }{ 1.5 }\) ⇒ 1.6 × 1.5 = \(\frac { y }{ 1.5 }\) × 1.5 (multiplying both sides by 1.5) ⇒ 2.40 = y Thus, y = 2.40 is the required solution.

Ex 2.1 Class 8 Maths Question 9. Solve the equation 7x – 9 = 16. Solution: We have 7x – 9 = 16 ⇒ 7x – 9 + 9 = 16 + 9 (adding 9 to both sides) ⇒ 7x = 25 ⇒ 7x ÷ 7 = 25 ÷ 7 (dividing both sides by 7) ⇒ x = \(\frac { 25 }{ 7 }\) Thus, x = \(\frac { 25 }{ 7 }\) is the required solution.

Ex 2.1 Class 8 Maths Question 10. Solve the equation 14y – 8 = 13. Solution: We have 14y – 8 = 13 ⇒ 14y – 8 + 8 = 13 + 8 (adding 8 to both sides) ⇒ 14y = 21 ⇒ 14y ÷ 14 = 21 ÷ 14 (dividing both sides by 14) ⇒ y = \(\frac { 21 }{ 14 }\) ⇒ y = \(\frac { 3 }{ 2 }\) Thus, y = \(\frac { 3 }{ 2 }\) is the required solution.

Ex 2.1 Class 8 Maths Question 11. Solve the equation 17 + 6p = 9. Solution: We have, 17 + 6p = 9 ⇒ 17 – 17 + 6p = 9 – 17 (subtracting 17 from both sides) ⇒ 6p = -8 ⇒ 6p ÷ 6 = -8 ÷ 6 (dividing both sides by 6) ⇒ p = \(\frac { -8 }{ 6 }\) ⇒ p = \(\frac { -4 }{ 3 }\) Thus, p = \(\frac { -4 }{ 3 }\) is the required solution.

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NCERT Solutions Class 8 Maths Chapter 2 Linear Equations in One Variable

NCERT solutions for class 8 maths chapter 2 linear equations in one variable tell us that a Mathematical equation can come in many different forms with several variables, differing degrees, number of coefficients , etc. However, a linear equation in one variable is defined as a mathematical expression in which the highest power of the polynomial is 1 and it consists of a single variable. These solutions greatly emphasize on the meaning of a linear equation in one variable and how to effectively solve problems based on the same. As mentioned before there can be many types of linear equations and each has its own method of solving. Thus, students need to go through the NCERT solutions class 8 maths chapter 2 in order to get a good understanding of the procedures. This is a very important chapter because as kids proceed to higher grades they will have to build on the concepts taught in this lesson to solve problems on sister chapters such as linear equations in two variables .

Class 8 maths NCERT solutions chapter 2 comprises a well-structured and detailed explanation of all the NCERT textbook questions. They have been presented using vernacular language so that these solutions can be comprehended by kids of all intelligence levels. NCERT solutions Chapter 2 linear equations in one variable also give real-life applications of the topic helping students to get a holistic view of it. In this article, we will take a deeper look into the subtopics associated with this lesson and also you can find some of these in the exercises given below.

• NCERT Solutions Class 8 Maths Chapter 2 Ex 2.1
• NCERT Solutions Class 8 Maths Chapter 2 Ex 2.2
• NCERT Solutions Class 8 Maths Chapter 2 Ex 2.3
• NCERT Solutions Class 8 Maths Chapter 2 Ex 2.4
• NCERT Solutions Class 8 Maths Chapter 2 Ex 2.5
• NCERT Solutions Class 8 Maths Chapter 2 Ex 2.6

NCERT Solutions for Class 8 Maths Chapter 2 PDF

An important topic covered in this chapter is how to interpret a word problem into a linear mathematical equation and what techniques have to be applied in order to solve them. The NCERT solutions class 8 maths chapter 2 acts as a guide for kids when they solve NCERT problems. As these are well-crafted solutions students can refer to them for clarity of concepts. Given below are the exercise-wise links to all the NCERT solutions .

☛ Download Class 8 Maths NCERT Solutions Chapter 2

NCERT Class 8 Maths Chapter 2   Download PDF

NCERT Solutions for Class 8 Maths Chapter 2

As this chapter is long and has various methods and formulas required to solve a linear equation students need to regularly visit the above links and practice the solutions. This will help them gain confidence thus, helping kids to get the best possible score in an examination. A detailed breakdown of all the components in the NCERT Solutions Class 8 Maths Chapter 2 linear equations in one variable is given below.

• Class 8 Maths Chapter 2 Ex 2.1 - 12 Questions
• Class 8 Maths Chapter 2 Ex 2.2 - 16 Questions
• Class 8 Maths Chapter 2 Ex 2.3 - 10 Questions
• Class 8 Maths Chapter 2 Ex 2.4 - 10 Questions
• Class 8 Maths Chapter 2 Ex 2.5 - 10 Questions
• Class 8 Maths Chapter 2 Ex 2.6 - 7 Questions

☛ Download Class 8 Maths Chapter 2 NCERT Book

Topics Covered: The important topics covered under class 8 maths NCERT solutions chapter 2 are solving equations with only numbers on one side, applications of linear equations, determining the value of an equation with variables on both sides, and simplifying linear equations . 

Total Questions: Class 8 maths chapter 2 Linear Equations in One Variable has a total of 65 well-researched questions out of which 20 are straightforward, 38 are of a medium level, and 7 complex problems.

List of Formulas in NCERT Solutions Class 8 Maths Chapter 2

NCERT solutions class 8 maths chapter 2 does not have formulas that need to be memorized as kids have to rely on their calculation and analytical skills in order to solve the problem sums. However, there are some pointers and steps that need to be kept in mind while attempting any question in this particular lesson. Given below are the necessary steps that kids need to follow for going through the NCERT solutions for class 8 maths chapter 2.

• In case of a problem sum read the question with care so as to translate it into the correct mathematical linear equation.
• In an equation take all the terms with variables on one side and the constant on the other side of the equal sign to solve it.
• Always simplify an equation into the standard form of a linear equation, i.e., ax + b = 0 before solving it.

Important Questions for Class 8 Maths NCERT Solutions Chapter 2

NCERT Solutions for Class 8 Maths Video Chapter 2

FAQs on NCERT Solutions Class 8 Maths Chapter 2

Why are ncert solutions class 8 maths chapter 2 important.

While solving sums kids are bound to hit some form of a roadblock due to doubt or an incorrect result. In order to combat this confusion, the NCERT solutions class 8 maths chapter 2 is important. They give a step-by-step solution to all NCERT textbook questions helping kids to identify and work on their pain points.

Do I Need to Practice all Questions Provided in NCERT Solutions Class 8 Maths Linear Equations in One Variable?

The questions in the NCERT coursebook are handpicked by experts. They cover a wide variety of topics to give students an all-around experience. Thus, it is imperative to practice all problems in the NCERT Solutions Class 8 Maths Linear Equations in One Variable to build a robust mathematical foundation for this lesson.

What are the Important Topics Covered in NCERT Solutions Class 8 Maths Chapter 2?

All topics in the NCERT Solutions Class 8 Maths Chapter 2 are essential as they cover different aspects of linear equations. However, kids need to reserve an ample amount of time to practice converting a word problem to a linear equation and the methods that can be used to solve the same.

How Many Questions are there in NCERT Solutions Class 8 Maths Chapter 2 Linear Equations in One Variable?

There are a total of 65 sums in the NCERT Solutions Class 8 Maths Chapter 2 Linear Equations in One Variable that have been split into 6 exercises. Each exercise covers a different topic. The questions are a mix of easy and difficult to give children the opportunity of exploring the different ways in which a problem can be framed.

How CBSE Students can utilize NCERT Solutions Class 8 Maths Chapter 2 effectively?

To effectively utilize the NCERT Solutions Class 8 Maths Chapter 2 kids must go through the solved examples, highlights, and theory that the exercises are based on. Once they get an understanding of the underlying concepts students can proceed to practicing the NCERT questions and using the solutions as a reference.

Why Should I Practice NCERT Solutions Class 8 Maths Linear Equations in One Variable Chapter 2?

Practice is the road to perfection. Students must revise the NCERT Solutions Class 8 Maths Linear Equations in One Variable Chapter 2 so that they can clear their concepts and solve problems with ease. If kids practice these solutions with dexterity and sincerity they are sure to ace any exam be it home or competitive.

NCERT Solutions for Class 8 Maths Chapter 2 Linear Equations in One Variable

NCERT Solutions for Class 8 Maths Chapter 2 Linear Equations In One Variable are provided below. Our solutions covered each questions of the chapter and explains every concept with a clarified explanation. To score good marks in Class 8 Mathematics examination, it is advised to solve questions provided at the end of each chapter in the NCERT book.

NCERT Solutions for Class 8 Maths Chapter 2 Linear Equations In One Variable are prepared based on Class 8 NCERT syllabus, taking the types of questions asked in the NCERT textbook into consideration. Further, all the CBSE Class 8 Solutions Maths Chapter 2 are in accordance with the latest CBSE guidelines and marking schemes.

Class 8 Maths Chapter 2 Exercise 2.1 Solutions

Class 8 Maths Chapter 2 Exercise 2.2 Solutions

Class 8 Maths Chapter 2 Exercise 2.3 Solutions

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Class 8 Maths Chapter 2 Exercise 2.5 Solutions

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• NCERT Solutions for Class 8 Maths Chapter 2 Free PDF Download

NCERT Solutions for Class 8 Maths Chapter 2 – Linear Equations in One Variable

First of all, NCERT solutions for class 8 Maths Chapter 2 is an excellent helping tool. Experts of high-quality prepare these solutions. Most noteworthy, these experts have superior skills and rich experience in Maths. The experts make these solutions student-friendly. Difficult concepts are explained in an easy manner. There is the breaking of difficult parts into smaller parts.

One efficient way to learn NCERT solutions is by Toppr. It’s certainly rare to find such a well-equipped learning platform. Toppr helps students gain maximum advantage from NCERT solutions.

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CBSE Class 8 Maths Chapter 2 Linear Equations in One Variable NCERT Solutions

NCERT solutions for class 8 maths chapter 2 deal with linear expression in one variable. A Linear Equation is an equation of a straight line and written in one variable. Furthermore, Linear Equations in one variable may assume the form ax + b = 0. Their solution is with the help of basic algebraic expressions. The most noteworthy, Linear equation is of three types.

Sub-topics covered under NCERT Solutions for Class 8 Maths Chapter 2

• Ex. 2.1 Introduction
• Ex. 2.2 Solving Equations which have Linear Expressions on one Side and Numbers on the other side.
• Ex. 2.3 Some Applications
• Ex. 2.4 Solving Equations having the Variable on both sides
• Ex. 2.5 Some more applications
• Ex. 2.6 Reducing Equation to Simpler to a simpler form
• Ex. 2.7 Equations reducible to the Linear form.

NCERT Solutions for Class 8 Maths Chapter 2

Students probably know that an algebraic equation is an equality involving variables. It certainly has an equality sign. The expression on the left of this equality sign is the Left-hand side. Similarly, the expression on the right of equality sign is the Right-hand side. In an equation the values of expressions on Right and Left-hand side are equal. However, this is true only for certain values. The solution of the equation are these values. Linear equations form a large of Algebra. Hence, this chapter will help students with a lot of other Algebra topics. Let us see what will we learn from each chapter.

Ex. 2.1 Introduction– First of all, a general idea of Linear equations. The students get basic information of Linear Equations in One Variable.

Ex. 2.2 Solving Equations which have Linear Expressions on one Side and Numbers on the other side– This is an important part.

Following is an example from this topic –

Solve 2x−3=52x−3=5

Transporting 3 to the other side 2x=5+32x=5+3 2x=82x=8 Dividing both the sides by 2 X=4 Hence, there is a linear expression on one side and numbers on the other side.

Ex. 2.3. Some Applications– Here some Applications of the above are there.

Ex. 2.4. Solving Equations having the Variable on both sides – Here students must transpose both the variable and number to the side. This is so that one side has the number and the other side has the variable. Hence, an equation comes into existence.

Ex. 2.5. Some more applications– Once again some more applications of the above.

Ex. 2.6. Reducing Equation to Simpler form– Sometimes Linear Equation may have a number in Denominator. Therefore, a student should take LCM of the denominator of both the left and right-hand side. Furthermore, a student must multiply on both sides. This will solve the problem. Hence, Equation is reduced to a simpler form.

Ex. 2.7. Equations reducible to the Linear form– Finally, this is the last sub-unit. Here an equation which is not Linear can be reduced to Linear Equation.

You can download NCERT Solutions for Class 8 Maths Chapter 2 by clicking on the button below

Solved Questions for You

Question 1: Solve the equation:

Answer: Transporting 2 to RHS, we obtain x =7+2 x =9

Question 2: Sum of two numbers is 95. If one exceeds the other number 15, find the numbers

Answer: Let one number = x ,

∴ The other will be:  x +15 As per the question:

x + x +15=95,2 x =80 x =4

One number ⇒40

Other number will be:  x +15⇒40+15 =55

Question 3: Fifteen years from now Ravi’s age will be four times his present age. What is Ravi’s present age?

Answer : Let Ravi’s present age :  x Fifteen years later, Ravi’s age =4× x x +15=4 x 15=4 x − x 3 x =15 ∴ x =5 Ravi’s present age 5 years

Question 4: Solve the equation:

Answer: Transporting 3 to RHS, we obtain y =10−3=7 ∴ y =7

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NCERT Solutions for Class 8 Maths

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CBSE Class 8th Maths Value Based Questions PDF Download

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CBSE Class 8th Maths Value Based Questions are the easiest questions which you see in your question paper and the scoring one all student who attempt it surely get they are just little bit difficult and examine your basic knowledge regarding the particular chapter. Maths Value Based Questions for Class 8th are available here at Free of cost. These questions are expected to be asked in the Class 8th board examination. These Maths Value Based Questions are from complete CBSE Syllabus.

CBSE Class 8th Maths Value Based Questions

Most of these Maths Value Based Questions are quite easy and students need only a basic knowledge of the chapter to answer these questions. Download CBSE Maths Value Based Questions for board examinations. These Maths Value Based Questions are prepared by Directorate of Education, Delhi.

CBSE Maths Value Based Questions Class 8th PDF

The purpose of the Maths Value Based Questions is to make students aware of how basic values are needed in the analysis of different situations and how students require to recognize those values in their daily lives. Some questions are subject related. But even if they are not, that one-minute awareness of what we write about value without any specific preparation is a good step indeed.

CBSE Maths Value Based Questions for Class 8th download here in PDF format. The most CBSE Maths Value Based Questions for annual examination are given here for free of cost. The additional questions for practice the Class 8th exam are collected from various sources. It covers questions asked in previous year examinations.

CBSE Maths Value Based Questions for Class 8th Free PDF

Class 8th books have many questions. These questions are regularly asked in exams in one or other way. Practising such most CBSE Maths Value Based Questions certainly help students to obtain good marks in the examinations. 

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NCERT Solutions for Class 8 Maths Exercise 2.2 Chapter 2 - Linear Equations in One Variable

NCERT Solutions for Class 8 Maths Exercise 2.2 of Chapter 2 Linear Equations in One Variable are a set of all the answers to the questions listed under the exercise. NCERT Solutions cover each concept thoroughly using simple language. Class 8 students are encouraged to practise the concepts learned as much as possible. Without practising the CBSE Class 8 NCERT solutions, students may not be exam ready, which is essential. Therefore, NCERT Solutions act as a great resource for scoring well on the exam.

NCERT Solutions for Class 8 Maths Chapter 2 – Linear Equations in One Variable Exercise 2.2

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Exercise 2.1 Solutions 12 Questions (12 Short Answer Questions) Exercise 2.3 Solutions 10 Questions (3 Long Answer Questions, 7 Short Answer Questions) Exercise 2.4 Solutions 10 Questions (4 Long Answer Questions, 6 Short Answer Questions) Exercise 2.5 Solutions 10 Questions (1 Long Answer Question, 9 Short Answer Questions) Exercise 2.6 Solutions 7 Questions (1 Long Answer Question, 6 Short Answer Questions)

Access answers of Maths NCERT Class 8 Chapter 2 – Linear Equations in One Variable 2.2 Page Number 28

1. If you subtract ½ from a number and multiply the result by ½, you get 1/8, what is the number?

Let the number be x.

According to the question,

(x – 1/2) × ½ = 1/8

x/2 – ¼ = 1/8

x/2 = 1/8 + ¼

x/2 = 1/8 + 2/8

x/2 = (1+ 2)/8

x = (3/8) × 2

2. The perimeter of a rectangular swimming pool is 154 m. Its length is 2 m, more than twice its breadth. What are the length and breadth of the pool?

Given that,

The perimeter of the rectangular swimming pool = 154 m. Let the breadth of the rectangle be = x

Length of the rectangle = 2x + 2 We know that,

Perimeter = 2(length + breadth)

⇒ 2(2x + 2 + x) = 154 m

⇒ 2(3x + 2) = 154

⇒ 3x +2 = 154/2

⇒ 3x = 77 – 2

Therefore, Breadth = x = 25 cm

Length = 2x + 2

= (2 × 25) + 2

Base of isosceles triangle = 4/3 cm

Let the length of the equal sides of the triangle be x.

4/3 + x + x = 62/15 cm

⇒ 2x = (62/15 – 4/3) cm

⇒ 2x = (62 – 20)/15 cm

⇒ 2x = 42/15 cm

⇒ x = (42/30) × (½)

⇒ x = 42/30 cm

⇒ x = 7/5 cm

The length of either of the remaining equal sides is 7/5 cm.

4. Sum of two numbers is 95. If one exceeds the other by 15, find the numbers.

Let one of the numbers be= x.

Then, the other number becomes x + 15. According to the question,

x + x + 15 = 95

⇒ 2x + 15 = 95

⇒ 2x = 95 – 15

First number = x = 40

And, other number = x + 15 = 40 + 15 = 55

5. Two numbers are in the ratio 5:3. If they differ by 18, what are the numbers?

Let the two numbers be 5x and 3x. According to the question,

5x – 3x = 18

The numbers are 5x = 5 × 9 = 45

And 3x = 3 × 9 = 27

6. Three consecutive integers add up to 51. What are these integers?

Let the three consecutive integers be x, x+1 and x+2. According to the question,

x + (x+1) + (x+2) = 51

⇒ 3x + 3 = 51

⇒ 3x = 51 – 3

Thus, the integers are

7. The sum of three consecutive multiples of 8 is 888. Find the multiples.

Let the three consecutive multiples of 8 by 8x, 8(x+1) and 8(x+2). According to the question,

8x + 8(x+1) + 8(x+2) = 888

⇒ 8 (x + x+1 + x+2) = 888 (Taking 8 as common)

⇒ 8 (3x + 3) = 888

⇒ 3x + 3 = 888/8

⇒ 3x + 3 = 111

⇒ 3x = 111 – 3

⇒ x = 108/3

Thus, the three consecutive multiples of 8 are

8x = 8 × 36 = 288

8(x + 1) = 8 × (36 + 1) = 8 × 37 = 296

8(x + 2) = 8 × (36 + 2) = 8 × 38 = 304

8. Three consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3 and 4, respectively, they add up to 74. Find these numbers.

2x + 3(x+1) + 4(x+2) = 74

⇒ 2x + 3x +3 + 4x + 8 = 74

⇒ 9x + 11 = 74

⇒ 9x = 74 – 11

Thus, the numbers are

9. The ages of Rahul and Haroon are in the ratio 5:7. Four years later the sum of their ages will be 56 years. What are their present ages?

Let the ages of Rahul and Haroon be 5x and 7x. Four years later,

The ages of Rahul and Haroon will be (5x + 4) and (7x + 4), respectively. According to the question,

(5x + 4) + (7x + 4) = 56

⇒ 5x + 4 + 7x + 4 = 56

⇒ 12x + 8 = 56

⇒ 12x = 56 – 8

⇒ x = 48/12

Therefore, the present age of Rahul = 5x = 5×4 = 20

And, the present age of Haroon = 7x = 7×4 = 28

10. The number of boys and girls in a class is in the ratio of 7:5. The number of boys is 8 more than the number of girls. What is the total class strength?

Let the number of boys be 7x and girls be 5x.

7x = 5x + 8

⇒ 7x – 5x = 8

Therefore, the number of boys = 7×4 = 28

And, the number of girls = 5×4 = 20

Total number of students = 20+28 = 48

11. Baichung’s father is 26 years younger than Baichung’s grandfather and 29 years older than Baichung. The sum of the ages of all three is 135 years. What is the age of each one of them?

Let the age of Baichung’s father be x.

Then, the age of Baichung’s grandfather = (x+26)

and, age of Baichung = (x-29). According to the question,

x + (x+26) + (x-29) = 135

⇒ 3x + 26 – 29 = 135

⇒ 3x – 3 = 135

⇒ 3x = 135 + 3

⇒ x = 138/3

Age of Baichung’s father = x = 46

Age of Baichung’s grandfather = (x+26) = 46 + 26 = 72

Age of Baichung = (x-29) = 46 – 29 = 17

12. Fifteen years from now, Ravi’s age will be four times his present age. What is Ravi’s present age?

Let the present age of Ravi be x.

Fifteen years later, Ravi’s age will be x+15 years. According to the question,

x + 15 = 4x

⇒ 4x – x = 15

Therefore, present age of Ravi = 5 years.

13. A rational number is such that when you multiply it by 5/2 and add 2/3 to the product, you get -7/12. What is the number?

Let the rational be x.

x × (5/2) + 2/3 = -7/12

⇒ 5x/2 + 2/3 = -7/12

⇒ 5x/2 = -7/12 – 2/3

⇒ 5x/2 = (-7- 8)/12

⇒ 5x/2 = -15/12

⇒ 5x/2 = -5/4

⇒ x = (-5/4) × (2/5)

⇒ x = – 10/20

Therefore, the rational number is -½.

14. Lakshmi is a cashier in a bank. She has currency notes of denominations ₹100, ₹50 and ₹10, respectively. The ratio of the number of these notes is 2:3:5. The total cash with Lakshmi is ₹4,00,000. How many notes of each denomination does she have?

Let the numbers of notes of ₹100, ₹50 and ₹10 be 2x, 3x and 5x, respectively.

Value of ₹100 = 2x × 100 = 200x

Value of ₹50 = 3x × 50 = 150x

Value of ₹10 = 5x × 10 = 50x

200x + 150x + 50x = 4,00,000

⇒ 400x = 4,00,000

⇒ x = 400000/400

Numbers of ₹100 notes = 2x = 2000

Numbers of ₹50 notes = 3x = 3000

Numbers of ₹10 notes = 5x = 5000

15. I have a total of ₹300 in coins of denomination ₹1, ₹2 and ₹5. The number of ₹2 coins is 3 times the number of ₹5 coins. The total number of coins is 160. How many coins of each denomination are with me?

Let the number of ₹5 coins be x.

Number ₹2 coins = 3x

and, number of ₹1 coins = (160 – 4x)

Value of ₹5 coins = x × 5 = 5x

Value of ₹2 coins = 3x × 2 = 6x

Value of ₹1 coins = (160 – 4x) × 1 = (160 – 4x)

5x + 6x + (160 – 4x) = 300

⇒ 11x + 160 – 4x = 300

⇒ x = 140/7

Number of ₹5 coins = x = 20

Number of ₹2 coins = 3x = 60

Number of ₹1 coins = (160 – 4x) = 160 – 80 = 80

16. The organisers of an essay competition decide that a winner in the competition gets a prize of ₹100 and a participant who does not win gets a prize of ₹25. The total prize money distributed is ₹3,000. Find the number of winners, if the total number of participants is 63.

Let the number of winners be x.

Then, the number of participants who didn’t win = 63 – x

Total money given to the winner = x × 100 = 100x

Total money given to the participant who didn’t win = 25×(63-x)

100x + 25×(63-x) = 3,000

⇒ 100x + 1575 – 25x = 3,000

⇒ 75x = 3,000 – 1575

⇒ 75x = 1425

⇒ x = 1425/75

Therefore, the numbers of winners are 19.

Exercise 2.2 of NCERT Solutions for Class 8 Maths Chapter 2 – Linear Equations in One Variable is based on some Applications of Linear Equations in One Variable. This will help the students understand the context and situations in which the concepts they learned in the chapter, Linear Equations in One Variable, can be applied.

Also, explore – 

NCERT Solutions for Class 8 Maths

NCERT Solutions for Class 8 

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• CBSE Class 10

CBSE Class 10 Maths Competency-Based Questions With Answers 2024-25: Chapter 1 Real Numbers Download Free PDF

Cbse class 10 maths chapter 1 practice questions 2025: cbse has made available the competency-based practice questions for students of class 10. check and download the questions for cbse class 10 maths chapter 1 real numbers. .

CBSE 2024-25 Competency Based Questions With Answers: To ensure that students are learning with understanding, the Central Board of Secondary Education (CBSE) has created and released the competency-based practice questions for various subjects covered in class 10. These have been released for the academic session 2024-25. These assessment questions are critical to the learning of students. In this article we have covered the CBSE Class 10 Maths Chapter 1 Real Numbers competency-based questions. 

Assessments prove to be of great help in providing feedback about what students have actually understood. The competency-based assessments were introduced as a means to reform curriculum and pedagogical methodologies. They emphasize on the development of higher order skills such as analysis, critical thinking and problem solving. 

CBSE Class 10 Maths Chapter 1 Competency Based-Questions 

Tips to Prepare for CBSE Class 10 Mathematics Examination

1. Students must first familiarize themselves with the syllabus so as to understand which topics carry more weightage. 

2.Mathematics is a subject that demands regular practice. It is important that students practice as much as they can. 

3.Students should prepare an effective study plan and give time to all topics on the basis of their strengths and weaknesses. The schedule should also have time for revision. 

4.Students should solve the problems from CBSE Class 10 subject textbook to clear the concepts and strengthen understanding. While solving problems, students should make it a habit to show rough work clearly which will help them in the examination as well. 

CBSE Video Courses for Class 10 Students 

Class 10 students can study effectively for the exams with the help of video courses prepared by the subject matter experts. These video courses will explain the concepts in a simple and interactive manner which will help learners to understand clearly. Refer to the link below:

CBSE Class 10 Video Courses 

Also, check

CBSE Class 10 Syllabus 2024-25: Download Latest and Revised FREE PDFs

NCERT Books for Class 10 All Subjects PDF (2024-25)

NCERT Solutions for Class 10 (2024-2025) All Subjects & Chapters: Download in PDF

NCERT Rationalised Syllabus Class 10: List of Chapters & Topics Deleted from Books

CBSE Class 10 Maths MCQs: Important for 2024-2025 Exams, Download Chapter-Wise PDF

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NCERT Solutions for Class 8 Hindi (Bharat ki Khoj) Chapter 3: Sindhu Ghati Sabhyata

NCERT Solutions for Class 8 Chapter 3 Hindi (Bharat ki Khoj) - FREE PDF Download

Class 8 Hindi (Bharat ki Khoj) NCERT Solutions for Chapter 3, Sindhu Ghati Sabhyata, or the Indus Valley Civilization. This ancient civilisation, one of the earliest in the world, thrived around the Indus River and its surrounding areas. Students will learn about their daily lives, cultural practices, and technological achievements, offering a glimpse into how this early society shaped the history and development of the Indian subcontinent. Check out the revised CBSE Class 8 Hindi Syllabus and start practising Hindi (Bharat ki Khoj) Class 8 Chapter 3.

Glance on Class 8 Hindi (Bharat ki Khoj)  Chapter 3 - Sindhu Ghati Sabhyata

This chapter explores the Indus Valley Civilization, an ancient society that flourished around the Indus River, known for its advanced urban planning and rich cultural heritage.

Chapter 3 Sindhu Ghati Sabhyata looks at how the people of this civilisation lived, including their impressive city planning, advanced drainage systems, and extensive trade networks. 

Examines the well-organised cities with grid layouts and impressive infrastructure.

Covers their extensive trade networks, economic practices, and interactions with other regions.

Benefits of NCERT Solutions for Class 8 Hindi (Bharat ki Khoj) Chapter 3 Sindhu Ghati Sabhyata

NCERT solutions give students thorough explanations of each chapter, which facilitates their understanding of the important ideas and subjects covered in "Sindhu Ghati Sabhyata."

All of the chapter's problems have precise, well-organised answers provided by these solutions, which aid students in producing well-written exam responses.

The solutions simplify difficult concepts and historical events so that students may comprehend and recall important information.

These solutions are a great revision aid because they cover every topic in detail, making sure that students are ready for their tests.

Students can efficiently manage their study time by adhering to the NCERT solutions, concentrating on important topics, and practising under appropriate guidance.

Important Study Material Links for Hindi (Bharat ki Khoj) Chapter 3 Class 8 - Sindhu Ghati Sabhyata

Chapter 3 of Bharat ki Khoj for Class 8, titled Sindhu Ghati Sabhyata, provides a detailed insight into one of the world's oldest civilizations. The Indus Valley Civilization, with its advanced urban planning, technological innovations, and rich cultural heritage, played an important role in shaping the history of the Indian subcontinent. By studying this chapter, students gain a deeper understanding of how early societies developed and how their achievements laid the foundation for future generations. This knowledge not only enhances our appreciation for ancient civilizations but also highlights the importance of preserving and learning from our historical heritage.

Chapter-wise NCERT Solutions Class 8 Hindi (Bharat ki Khoj)

After familiarising yourself with the Class 8 Hindi (Bharat ki Khoj) Chapter 3 Question Answers, you can access comprehensive NCERT Solutions for all Chapters in Class 8 Hindi (Bharat ki Khoj).

Related Important Links for Hindi (Bharat ki Khoj) Class 8

Along with this, students can also download additional study materials provided by Vedantu for Hindi (Bharat ki Khoj) Class 8.

FAQs on NCERT Solutions for Class 8 Hindi (Bharat ki Khoj) Chapter 3: Sindhu Ghati Sabhyata

1. What is the significance of the Sindhu Ghati Sabhyata in Indian history?

The Sindhu Ghati Sabhyata, or Indus Valley Civilization, is one of the earliest known urban cultures, influencing the development of subsequent Indian civilizations through its advanced urban planning, architecture, and societal structure.

2. What are some key features of the Indus Valley Civilization?

Key features include well-planned cities with grid layouts, advanced drainage systems, public baths, and a strong trade network with other regions.

3. How did the people of the Indus Valley Civilization manage their cities?

The people of this civilization managed their cities with impressive urban planning, including well-organised street grids, efficient drainage systems, and large public buildings.

4. What was the role of trade in the Indus Valley Civilization?

Trade played an important role in the economy of the Indus Valley Civilization, with evidence of extensive trade networks connecting them with distant regions, including Mesopotamia.

5. How did the social structure of the Indus Valley Civilization influence its development?

The social structure was likely well-organised, with clear distinctions in the roles and responsibilities of different groups, which contributed to the civilisation's stability and growth.

6. What evidence do we have of the daily life of the people in the Indus Valley Civilization?

Archaeological findings, such as household items, tools, pottery, and inscriptions, provide insights into the daily life, occupations, and cultural practices of the people.

7. What technological advancements were made by the Indus Valley Civilization?

The civilization was advanced in technology, particularly in urban planning, water management, and the construction of large public baths, which highlighted their engineering skills.

8. How did the geographical location of the Indus Valley Civilization contribute to its success?

The civilization thrived along the fertile plains of the Indus River, which provided ample resources for agriculture, trade, and settlement, contributing to its prosperity.

9. What can students learn from studying the Sindhu Ghati Sabhyata?

Students can learn about the complexities of early human societies, the importance of urban planning, and the significant contributions of ancient civilizations to modern culture and history.

10. Why is the Indus Valley Civilization considered a major achievement in human history?

It is considered a major achievement due to its sophisticated urban infrastructure, social organisation, and lasting influence on future civilizations in the region, marking it as a key period in human development.

• Number Systems Class 9 Assertion Reason Questions Maths Chapter 1

Last Updated on August 26, 2024 by XAM CONTENT

Hello students, we are providing case study questions for class 9 maths. Assertion Reason questions are the new question format that is introduced in CBSE board. The resources for assertion reason questions are very less. So, to help students we have created chapterwise assertion reason questions for class 9 maths. In this article, you will find assertion reason questions for CBSE Class 9 Maths Chapter 1 Number Systems. It is a part of Assertion Reason Questions for CBSE Class 9 Maths Series.

Table of Contents

Assertion Reason Questions on Number Systems

Questions :

Q. 1. Assertion (A): The rationalising factor of $8-\sqrt{7}$ is $8+\sqrt{7}$. Reason (R): If the product of two irrational numbers is rational, then each one is said to be the rationalising factor of the other.

Q. 2. Assertion (A): The sum of two irrational numbers $3-\sqrt{5}$ and $5+\sqrt{5}$ is rational number. Reason (R): The sum of two irrational numbers is always an irrational number.

Q. 3. Assertion (A): The simplified form of $7^4 \times 7^5$ is $7^{20}$. Reason (R): If $a>0$ be a real number and $p$ and $q$ be rational numbers. Then $a^p \times a^q=a^{p+q}$.

1. (a) Assertion (A): It is true that the rationalising factor of $8-\sqrt{7}$ is $8+\sqrt{7}$. Reason (R): It is true to say that each one is rationalising factor in the product of two irrational numbers. Hence, both Assertion (A) and Reason (R) are true and Reason $(R)$ is the correct explanation of Assertion (A).

2. (c) Assertion (A): Here, $3-\sqrt{5}+5+\sqrt{5}=8$, which is a rational number. So, Assertion (A) is true. Reason (R): It is not always true to say that sum of two irrational number is always an irrational number. Hence, Assertion (A) is true but Reason (R) is false.

3. (d) Assertion (A) is false but Reason (R) is true.

Polynomials Class 9 Assertion Reason Questions Maths Chapter 2

Topics from which assertion reason questions may be asked.

• Representation on number line
• Concept of rationalizing the denominator
• Rationalizing the denominator of expressions with square roots
• Applying the laws of exponents to simplify expressions
• Rationalizing surds

The sum or difference of a rational number and an irrational number is irrational. The product or quotient of a non-zero rational number with an irrational number is irrational.

Assertion reason questions from the above given topic may be asked.

Download Customised White Label Study Materials in MS Word Format

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Frequently Asked Questions (FAQs) on Number Systems Assertion Reason Questions Class 9

Q1: what are assertion reason questions.

A1: Assertion-reason questions consist of two statements: an assertion (A) and a reason (R). The task is to determine the correctness of both statements and the relationship between them. The options usually include: (i) Both A and R are true, and R is the correct explanation of A. (ii) Both A and R are true, but R is not the correct explanation of A. (iii) A is true, but R is false. (iv) A is false, but R is true. or A is false, and R is also false.

Q2: Why are assertion reason questions important in Maths?

A2: Students need to evaluate the logical relationship between the assertion and the reason. This practice strengthens their logical reasoning skills, which are essential in mathematics and other areas of study.

Q3: How can practicing assertion reason questions help students?

A3: Practicing assertion-reason questions can help students in several ways: Improved Conceptual Understanding:  It helps students to better understand the concepts by linking assertions with their reasons. Enhanced Analytical Skills:  It enhances analytical skills as students need to critically analyze the statements and their relationships. Better Exam Preparation:  These questions are asked in exams and practicing them can improve your performance.

Q4: What strategies should students use to answer assertion reason questions effectively?

A4: Students can use the following strategies: Understand Each Statement Separately:  Determine if each statement is true or false independently. Analyze the Relationship:  If both statements are true, check if the reason correctly explains the assertion.

Q5: What are common mistakes to avoid when answering Assertion Reason questions?

A5: Common mistakes include: Not reading the statements carefully and missing key details. Assuming the Reason explains the Assertion without checking the logical connection. Confusing the order or relationship between the statements. Overthinking and adding information not provided in the question.

Q6: Are all integers also rational numbers?

A6: Yes, all integers are rational numbers because they can be expressed as a fraction where the denominator is 1. For example, 5 can be written as 5/1​, making it a rational number.

Q7: What are the key concepts covered in Chapter 1 of CBSE Class 9 Maths regarding number systems?

A7: Chapter 1 of CBSE Class 9 Maths covers concepts such as understanding rational numbers, irrational numbers and Laws of exponents. (i) Review of representation of natural numbers and Integers on number line (ii) Rational numbers on the number line. (iii) Rational numbers as recurring/ terminating decimals (iv) Operations on real numbers. (v) Definition of nth root of a real number (vi) Law of exponents with integral powers

Q8: Can a number be both rational and irrational?

A8: No, a number cannot be both rational and irrational. A rational number can be expressed as a fraction of two integers, while an irrational number cannot. They are mutually exclusive categories.

Q9: What are the important keywords for CBSE Class 9 Maths Number Systems?

A9: List of important keywords given below – Natural Numbers:  Positive Counting number starting from 1. Whole Number:  All natural numbers together with 0. Integers (Z):  Set of all whole numbers and negative of natural numbers Rational Number:  Numbers which can be expressed in p/q form, where q  ≠  0 and p and q are integers. Fraction:  Numbers which can be expressed in form of p/q but are only positive Equivalent Rational Numbers:  Two rational numbers are said to be equivalent, if numerator and denominators of both rational numbers are in proportion or they are reducible to be equal.

Q10: Are there any online resources or tools available for practicing linear equations in one variable assertion reason questions?

A10: A9: We provide assertion reason questions for CBSE Class 8 Maths on our  website . Students can visit the website and practice sufficient case study questions and prepare for their exams. If you need more case study questions, then you can visit  Physics Gurukul  website. they are having a large collection of case study questions for all classes.

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