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CBSE 8th Standard CBSE all question papers, important notes , study materials , Previuous Year questions, Syllabus and exam patterns. Free 8th Standard CBSE all books and syllabus online. Practice Online test for free in QB365 Study Material. Important keywords, Case Study Questions and Solutions. Updates about latest education news and Scholorships in one place.

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• Rational Numbers Class 8 Case Study Questions Maths Chapter 1

Last Updated on April 9, 2024 by XAM CONTENT

Hello students, we are providing case study questions for class 8 maths. Case study questions are the new question format that is introduced in CBSE board. The resources for case study questions are very less. So, to help students we have created chapterwise case study questions for class 8 maths. In this article, you will find case study questions for CBSE Class 8 Maths Chapter 1 Rational Numbers. It is a part of Case Study Questions for CBSE Class 8 Maths Series.

Table of Contents

Case Study Questions on Rational Numbers

Passage 1: Aditya who is working in a multinational company earns ₹150000 per month. Out of his earnings he spend 1/10th on food items, 1/4th on shopping with family, 1/5th of remaining on education of his two kids and rest of his money he puts in his savings.

Difficulty Level: Easy

On basis of this information given in passage answer the following questions.

Q. 1. How much money he spends on food items? (a) 15000 (b) 1500 (c) 1050 (d) 10500

Q. 2. How much money he spend on shopping? (a) 32000 (b) 37500 (c) 25000 (d) 27500

Q. 3. How much money was left with him after spending on food and shopping? (a) 90000 (b) 95000 (c) 98500 (d) 97500

Ans. Option (d) is correct. Explanation: Total earning = ₹ 150000 Money spent on food and shopping = ₹ 15000 + ₹ 37500 = ₹ 52500 Money left after food and shopping = ₹ 150000 – ₹ 52500 = ₹ 97500

Q. 4. Calculate the amount spend by Aditya on education of children?

Sol. Total money earn by Aditya = ₹150000 Total amount spend by him on shopping and food = ₹52500 Money left = ₹150000 – ₹52500= ₹97500 Money spend on education of children $=\frac{1}{5}$ of Money left $\quad=\frac{1}{5}$ of 97500 = ₹19500

Q. 5. How much money he saved?

Sol. Saving = Total earning – total expenditure = 150000 – (15000 + 37500 + 19500) = 150000 – 72000 = ₹78000. Thus money saved by Aditya is ₹78000.

Linear Equations in One Variable Class 8 Case Study Questions Maths Chapter 2

Topics from which case study questions may be asked.

• Rational Number and its identification.
• Whole Number, Natural Number and their Properties.
• Difference between Rational and Irrational Number.

Case study questions from the above given topic may be asked.

Frequently Asked Questions (FAQs) on Rational Numbers Case Study

Q1: what is the significance of rational numbers in mathematics.

A1: Rational numbers play a crucial role in mathematics as they represent quantities that can be expressed as fractions of integers. They include both integers and fractions, making them essential for various mathematical operations and real-life applications.

Q2: How are rational numbers defined, and what are their properties?

A2: Rational numbers are defined as numbers that can be expressed in the form p/q ​, where p and q are integers and q≠0. They possess properties such as closure under addition, subtraction, multiplication, and division, as well as the commutative, associative, and distributive properties.

Q3: Can you provide real-life examples where rational numbers are used?

A3: Real-life examples of rational numbers include measurements such as length, mass, and time, as well as quantities like money, fractions of a whole, and ratios in cooking recipes or construction projects.

Q4: What are the key concepts covered in Chapter 1 of CBSE Class 8 Maths regarding rational numbers?

A4: Chapter 1 of CBSE Class 8 Maths covers concepts such as understanding rational numbers, representation on the number line, operations on rational numbers, and solving problems involving rational numbers. More Precisely, (i) Rational Number and its identification. (ii) Whole Number, Natural Number and their Properties. (iii) Difference between Rational and Irrational Number.

Q5: Can you explain the operations (addition, subtraction, multiplication, division) involving rational numbers with examples?

A5: Addition, subtraction, multiplication, and division of rational numbers follow specific rules. For example, to add or subtract rational numbers, we find a common denominator, while for multiplication and division, we multiply or divide the numerators and denominators.

Q6: What are the common misconceptions students have about rational numbers, and how can they be clarified?

A6: Common misconceptions include confusion between rational and irrational numbers, misunderstanding the concept of fractions, and errors in performing operations. These can be clarified through hands-on practice, visual representations, and providing clear explanations of concepts.

Q7: Are there any online resources or tools available for practicing rational number case study questions?

A7: We provide case study 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.

Q8: What are the important keywords for CBSE Class 8 Maths Rational Numbers?

A8: List of important keywords given below – Natural Numbers: Positive Counting number starting from 1. Whole Number: All natural number together with 0. 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

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Cbse, ncert and icse solution online, class 8 science case study question, case study question class 8 science (cbse / ncert board).

Class 8 Science Case Study Question and Answer: CBSE / NCERT Board Class 8 Science Case Study Question prepared by expert Science Teacher. Students can learn Case Based Question / Paragraph Type Question for NCERT Class 8 Science.

There are total 18 chapter Crop Production and Management, Microorganisms: Friend and Foe

, Synthetic Fibres and Plastics, Materials: Metals and Non-Metals, Coal and Petroleum, Combustion and Flame, Conservation of Plants and Animals, Cell – Structure and Functions, Reproduction in Animals, Reaching the Age of Adolescence, Force and Pressure, Friction, Sound, Chemical Effects of Electric Current, Some Natural Phenomena, Light, Stars and the Solar System, Pollution of Air and Water

For any problem during learning any Case or any doubts please comment us. We are always ready to help You.

CBSE Class 8 Science Case Study Question

• Chapter 1 Crop Production and Management Case Study Question
• Chapter 2 Microorganisms: Friend and Foe Case Study Question
• Chapter 3 Synthetic Fibres and Plastics Case Study Question
• Chapter 4 Materials: Metals and Non-Metals Case Study Question
• Chapter 5 Coal and Petroleum Case Study Question
• Chapter 6 Combustion and Flame Case Study Question
• Chapter 7 Conservation of Plants and Animals Case Study Question
• Chapter 8 Cell – Structure and Functions Case Study Question
• Chapter 9 Reproduction in Animals Case Study Question
• Chapter 10 Reaching the Age of Adolescence Case Study Question
• Chapter 11 Force and Pressure Case Study Question
• Chapter 12 Friction Case Study Question
• Chapter 13 Sound Case Study Question
• Chapter 14 Chemical Effects of Electric Current Case Study Question
• Chapter 15 Some Natural Phenomena Case Study Question
• Chapter 16 Light Case Study Question
• Chapter 17 Stars and the Solar System Case Study Question
• Chapter 18 Pollution of Air and Water Case Study Question

What is Case Study Question?

Ans. At case Study there will one paragraph and on the basis of that concept some question will made. Students have to solve that question.

How many marks will have at case based question?

Most of time 5 questions will made from each case. There will 1 or 2 marks for each question.

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Important Questions for CBSE Class 8 Maths 2023-24

Home » CBSE » 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.

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Class 8 (Old)

Unit 1: rational numbers, unit 2: linear equations in one variable, unit 3: understanding quadrilaterals, unit 4: data handling, unit 5: squares and square roots, unit 6: cubes and cube roots, unit 7: comparing quantities, unit 8: algebraic expressions and identities, unit 9: mensuration, unit 10: exponents and powers, unit 11: factorisation, unit 12: introduction to graphs, unit 13: playing with numbers, unit 14: visualising solid shapes.

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Friday 23 December 2022

Class 8 - chemistry - case study based questions - #class8science #cbseclass8 #eduvictors, class 8 - chemistry - case study-based questions.

Chapter: Chemical Effects of Current

Directions : Read the following and answer the questions given below:

Take out carbon rods carefully from two discarded cells. Clean their metal caps with sandpaper. Wrap copper wires around the metal caps of the carton rods to form electrodes and join them to a battery, Pour a cupful of water into a glass/plastic bowl. Add a teaspoonful of salt or a few drops of lemon juice to water to make it more conducting. Now immerse the electrodes in this solution. Make sure that the metal caps of the carbon rods are outside the water. Wait for 3-4 minutes, Observe the electrodes carefully.

Q(i) Which of the following is not a chemical effect of electric current?

(a) Bubbles of a gas may be formed on the electrodes.

(b) Deposits of metal may be seen on the electrodes.

(c) An electric bulb connected to the circuit may start glowing.

(d) Changes in the colour of solutions may occur.

Q(ii) Gas bubbles of ___________will be evolved near the electrodes in the given experiment.

(a) Oxygen and Hydrogen

(b) Carbon dioxide and Hydrogen

(c) Oxygen and Carbon dioxide

(d) None of these

Q(iii) A tester is used to check the conduction of electricity through two liquids, A and B. It is found that the bulb of the tester glows brightly for liquid A while it glows very dimly for liquid B. You would conclude that;

(a) liquid A is a better conductor than liquid B.

(b) liquid B is a better conductor than liquid A.

(c) both liquids are equally conducting.

(d) conducting properties of liquid cannot be compared in this manner.

Q(iv) Why do we clean the metal caps with sandpaper before using them?

(a) to make the metal caps smooth

(b) to make the metal cops appear bright and shiny

(c) to make the metal caps insulating

(d) to make the metal caps free of any rust

i.  (a) gas bubbles may be formed on the electrodes.

ii. (a) Oxygen and Hydrogen

iii.(a) liquid A is a better conductor than liquid B.

iv. (d) to make the metal caps free of any rust

Ch 14 - Chemical Effects of Electric Current (NCERT Solutions) Ch 14 - Chemical Effects of Electric Current (MCQs) Ch 14 - Chemical Effects of Electric Current (Q & A) Ch 14 - Chemical Effects of Electric Current (Worksheet) Ch 14 - Chemical Effects of Electric Current (Worksheet-2)

CBSE All In One NCERT Based Science Class 8 2022-23 Edition

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Case Study Questions Class 8 Civics The Indian Constitution

Case study questions class 8 civics chapter 1 the indian constitution.

CBSE Class 8 Case Study Questions Civics The Indian Constitution. Important Case Study Questions for Class 8 Board Exam Students. Here we have arranged some Important Case Base Questions for students who are searching for Paragraph Based Questions The Indian Constitution.

At Case Study Questions there will given a Paragraph. In where some Important Questions will made on that respective Case Based Study. There will various types of marks will given 1 marks, 2 marks, 3 marks, 4 marks.

CBSE Case Study Questions Class 8 Civics The Indian Constitution

Case Study 1

While all democratic countries are likely to have a Constitution, it is not necessary that all countries that have a Constitution are democratic. The Constitution serves several purposes. First, it lays out certain ideals that form the basis of the kind of country that we as citizens aspire to live in. Or, put another way, a Constitution tells us what the fundamental nature of our society is. A country is usually made up of different communities of people who share certain beliefs but may not necessarily agree on all issues. A Constitution helps serve as a set of rules and principles that all persons in a country can agree upon as the basis of the way in which they want the country to be governed. This includes not only the type of government but also an agreement on certain ideals that they all believe the country should uphold.

1.) In a democracy, what is the main function of the Constitution?

Answer: In a democracy, a Constitution’s main function is extremely important since it lays forth the fundamental goals and rules that all citizens concur upon. The Constitution offers a thorough set of laws and principles that not only direct the country’s government but also profoundly mould society’s very foundation. reflecting the beliefs and ambitions of its citizens.

2.) What role does a constitution play in managing societies with diverse cultures and complex identities?

Answer: By promoting social cohesiveness and harmony among multiple identities, a constitution plays a crucial role in regulating varied communities. Additionally, it offers a cohesive framework of accepted guidelines and precepts, enabling the defence of personal freedoms. Promote inclusive policies and encourage equal representation at the same time. Thus, a strong sense of national identity and a common goal are created.

3.) Why does having a Constitution not automatically assure a democracy in a country?

Answer: Although establishing a constitution is an important first step towards democracy, it does not ensure it. The efficacy of the constitution depends on the people and the government’s honest commitment and engagement. Both of these organisations must sincerely work to defend democratic principles, the rule of law, protect human rights, and foster political diversity.

4.) How many different ways does a constitution help a country grow and become strong?

Answer: Flexibility is ensured by a constitution’s capacity to modify itself in response to shifting social circumstances.Furthermore, it represents rigidity in its capacity as an unyielding moral compass for equity and inclusivity. These are only a handful of the numerous ways that constitutions support a country’s development and adaptability. As a result, transparency and democratic accountability in government are ensured. Citizens have the chance to actively contribute to the advancement of their nation.

Case Study 2

Until recently, Nepal was a monarchy. The previous Constitution of Nepal, which had been adopted in 1990, reflected the fact that the final authority rested with the King. A people’s movement in Nepal fought for several decades to establish democracy and in 2006 they finally succeeded in putting an end to the powers of the King. The people had to write a new Constitution to establish Nepal as a democracy. The reason that they did not want to continue with the previous Constitution is because it did not reflect the ideals of the country that they want Nepal to be, and that they have fought for. As in the game of football, in which a change in the constitutive rules will change the game altogether, Nepal, by moving from a monarchy to a democratic government, needs to change all its constitutive rules in order to usher in a new society. This is why, the people of Nepal adopted a new Constitution for the country in 2015. The caption alongside elaborates Nepal’s struggle for democracy. The second important purpose of a Constitution is to define the nature of a country’s political system. For example, Nepal’s earlier Constitution stated that the country was to be ruled by the King and his council of ministers. In countries that have adopted a democratic form of government or polity, the Constitution plays a crucial role in laying out certain important guidelines that govern decision-making within these societies. In a democracy, we choose our leaders so that they can exercise power responsibly on our behalf. However, there is always the possibility that these leaders might misuse their authority and the Constitution usually provides safeguards against this.

1.) What significant historical event led to the adoption of a new Constitution in Nepal in 2015?

Answer: The people’s movement in Nepal worked for decades to bring about democracy until ultimately succeeding in 2006 in ending the King’s authority. As a result, a new Constitution was adopted in 2015 to reflect their aspirations for the country and to make Nepal a democratic country.

2.) A change in the Constitution affects a nation’s political system Using Nepal’s transition from a monarchy to a democracy as an example, reflect on the statement.

Answer: Changing Nepal’s Constitution from a monarchy to a democracy brought a very large change in the political structure of the nation. The previous Constitution granted the King and his council of ministers ultimate power rule without criticisms. Whereas the new democratic Constitution established rules for decision-making, gave the people the power to elect their leaders. Furthermore, provided safeguards against potential abuse of power by elected officials.

3.) Describe the Constitution’s second most important function in a democratic society?

Answer: In a democracy, defining the character of the political system is the second essential function of the Constitution. It sets the framework for decision-making. While it also ensures that elected officials utilise their authority in a responsible manner on behalf of the people. Moreover it also includes protections against potential abuses of power.

4.) How will the process of drafting a new Constitution affect Nepal’s society and political structure?

Answer: As we have seen in Nepal’s struggle for democracy, the process of drafting a new Constitution has a profound impact on all aspects of society.. Significant socioeconomic reforms are introduced, and the country’s monarchical political structure is replaced with a democratic one. The new Constitution alters decision-making while strengthening the voice of the people. It gives people the chance to actively take part in governance, laying the path for a society that is more accountable and inclusive.

Case study 3

The Constitution usually contains rules that ensure that minorities are not excluded from anything that is routinely available to the majority. Another reason why we have a Constitution is precisely to prevent this tyranny or domination by the majority of a minority. This can refer to one community dominating another, i.e. inter-community domination, or members of one community dominating others within the same community, i.e. intra-community domination. The third significant reason why we need a Constitution is to save us from ourselves. This may sound strange but what is meant by this is that we might at times feel strongly about an issue that might go against our larger interests and the Constitution helps us guard against this. the Constitution helps to protect us against certain decisions that we might take that could have an adverse effect on the larger principles that the country believes in. For example, it is possible that many people who live in a democracy might come to strongly feel that party politics has become so acrimonious that we need a strong dictator to set this right. Swept by this emotion, they may not realise that in the long run, dictatorial rule goes against all their interests. A good Constitution does not allow these whims to change its basic structure. It does not allow for the easy overthrow of provisions that guarantee rights of citizens and protect their freedom.

1.)  How does the Constitution prevent minorities from being left out of democratic society?

Answer: The Constitution protects minorities’ rights and interests through a thorough collection of laws and tenets. It guarantees that minorities are not denied of opportunities and benefits that are typically available to the majority by enshrining the principles of equality and non-discrimination. It prohibits any sort of dominance between or within communities. This fosters an inclusive society where everyone has access to equal legal protection, regardless of their personal history or religious convictions.

2.) What is the third crucial argument for any nation having a constitution?

Answer: The capacity of the Constitution to protect society against itself is the third important justification for having one. The Constitution ensures that the country’s fundamental values and long-term well-being are upheld by serving as a barrier against rash judgement and short-sighted interests. It serves as a constant reminder to not let fleeting emotions cause us to compromise the core principles that the nation upholds.

3.) How can a Constitution guard against rash choices that might compromise a nation’s core values?

Answer:  A constitution’s inclusion of clauses that resist sudden changes to its fundamental structure has a significant impact on deterring rash decisions. It establishes a strong framework that safeguards citizens’ rights and upholds their liberties, making it difficult to undermine these guiding ideals. The Constitution ensures that any proposed modifications receive careful examination and public consideration by setting significant procedural safeguards. It inhibits hasty decisions that might betray the nation’s cherished ideals and guiding principles.

4.) How does the Constitution help a nation’s fundamental values and interests be upheld over time?

Answer: In maintaining a nation’s fundamental values and interests across time, the Constitution acts as a durable and unchanging foundation. The Constitution serves as a framework for decision-making, guaranteeing that the nation’s treasured principles and fundamental rights be upheld regardless of fleeting political feelings. The Constitution promotes continuity and stability by having the flexibility to adjust to changing conditions while preserving its underlying precepts, protecting the nation’s fundamental values and interests for future generations.

Case Study 4

By the beginning of the twentieth century, the Indian national movement had been active in the struggle for independence from British rule for several decades. During the freedom struggle the nationalists had devoted a great deal of time to imagining and planning what a free India would be like. Under the British, they had been forced to obey rules that they had had very little role in making. The long experience of authoritarian rule under the colonial state convinced Indians that free India should be a democracy in which everyone should be treated equally and be allowed to participate in government. What remained to be done then was to work out the ways in which a democratic government would be set up in India and the rules that would determine its functioning. This was done not by one person but by a group of around 300 people who became members of the Constituent Assembly in 1946 and who met periodically for the next three years to write India’s Constitution. These members of the Constituent Assembly had a huge task before them. The country was made up of several different communities who spoke different languages, belonged to different religions, and had distinct cultures. Also, when the Constitution was being written, India was going through considerable turmoil. The partition of the country into India and Pakistan was imminent, some of the Princely States remained undecided about their future, and the socio-economic condition of the vast mass of people appeared dismal. All of these issues played on the minds of the members of the Constituent Assembly as they drafted the Constitution. They rose to the occasion and gave this country a visionary document that reflects a respect for maintaining diversity while preserving national unity. The final document also reflects their concern for eradicating poverty through socio-economic reforms as well as emphasising the crucial role the people can play in choosing their representatives.

1.) Reflect upon the primary aims of the anti-British national movement in India.

Answers:  The Indian national movement not only desired independence from British rule but also a democratic India where everyone would be treated equally and fairly. Additionally, they favoured giving citizens a chance to engage in politics. Indians, who had previously lived under repressive colonial rule, yearned to establish a free nation that upheld democratic principles and respected the rights of all individuals..

2.) Describe the process used to draught the Indian Constitution.

Answer: The work of writing India’s Constitution was assigned to a group of roughly 300 people. These individuals won seats in the Constituent Assembly in 1946. They worked together to create the Constitution for the ensuing three years as they met frequently. In light of the imminent partition, the unreliable Princely States, and socioeconomic inequality, they thought about the diversity and difficulties facing the nation.

3.) What difficulties did the Constituent Assembly members encounter when they drafted the Indian Constitution?

Answer: During the writing process, the Constituent Assembly members faced numerous difficulties. A Constitution that honoured and safeguarded national unity while recognising diversity was required due to India’s diverse population, which includes people who speak different languages, practise different religions, and have different cultural traditions. The challenge of creating a visionary statement that addressed these complex issues was further exacerbated by the coming division, uncertainty of some Princely States, and socioeconomic hardships.

4.) What concerns and goals of the Constituent Assembly were reflected in the final draught of the Indian Constitution?

Answer: In addition to fostering national unity while respecting variety, the final draught of the Indian Constitution also addressed socio-economic disparities and sought to end poverty through progressive reforms. In order to ensure democratic involvement and representation, the Constitution emphasised the importance of the people’s role in choosing their representatives.

5.) How did the Indian Constitution’s formulation reflect the Constituent Assembly’s commitment to building a progressive and inclusive society?

Answer: By establishing a framework that upheld individual rights, encouraged democratic governance, and aimed to help the socioeconomically disadvantaged, the Constituent Assembly’s crafting of India’s Constitution displayed its steadfast commitment to forging a progressive and inclusive nation. The Constituent Assembly rose to the occasion and gave India a visionary Constitution that provided the groundwork for a democratic and multiethnic country, despite the difficulties faced by partition and societal inequalities.

Case Study 5

Federalism refers to the existence of more than one level of government in the country. In India, we have governments at the state level and at the centre. Panchayati Raj is the third tier of government. The vast number of communities in India meant that a system of government needed to be devised that did not involve only persons sitting in the capital city of New Delhi and making decisions for everyone. Instead, it was important to have another level of government in the states so that decisions could be made for that particular area. While each state in India enjoys autonomy in exercising powers on certain issues, subjects of national concern require that all of these states follow the laws of the central government. The Constitution contains lists that detail the issues that each tier of government can make laws on. In addition, the Constitution also specifies where each tier of government can get the money from for the work that it does. Under federalism, the states are not merely agents of the federal government but draw their authority from the Constitution as well. All persons in India are governed by laws and policies made by each of these levels of government.

1.) What does the term “federalism” mean? how is it organised in India?

Answer: In a country, having numerous levels of governance is referred to as federalism. In India, federalism is organised with a third tier of government known as Panchayati Raj in addition to state and federal administrations. With this structure, decision-making power can be decentralised so that states can have autonomy while still complying to the laws of the federal government on topics of national importance.

2.)  How does the Indian Constitution ensure a distribution of powers and responsibilities between different levels of government?

Answer: The Indian Constitution contains lists that delineate the issues on which each tier of government can make laws, ensuring a clear distribution of powers and responsibilities. While some issues are under the control of the states, the federal government is in charge of problems of national significance. The Constitution also establishes a framework for fiscal autonomy and accountability by outlining the financing sources for each level of government.

3.)  What role does Panchayati Raj play in India’s federal structure?

Answer: Panchayati Raj serves as the third tier of government in India’s federal structure, promoting local governance and community participation in decision-making. It empowers rural areas with the authority to address region-specific issues and manage local resources. Panchayats derive their legitimacy and authority from the Constitution, making them vital components of India’s federal system.

4.)  How does federalism ensure effective governance and representation in India?

Answer: Federalism in India facilitates effective governance and representation by allowing decisions to be made at different levels of government. This ensures that local concerns are addressed by state and local authorities, while issues of national significance are handled by the central government. The distribution of powers under federalism fosters a cooperative approach among different levels of government, catering to the diverse needs of India’s vast population and promoting inclusive governance.

Case Study 6

The Constitution of India guarantees universal adult suffrage for all citizens. When they were making the Constitution, the members of the Constituent Assembly felt that the freedom struggle had prepared the masses for universal adult suffrage and that this would help encourage a democratic mindset and break the clutches of traditional caste, class and gender hierarchies. This means that the people of India have a direct role in electing their representatives. Also, every citizen of the country, irrespective of his/her social background, can also contest in elections. These representatives are accountable to the people. According to the Constitution, there are three organs of government. These are the legislature, the executive and the judiciary. The legislature refers to our elected representatives. The executive is a smaller group of people who are responsible for implementing laws and running the government. In order to prevent the misuse of power by any one branch of government, the Constitution says that each of these organs should exercise different powers. Through this, each organ acts as a check on the other organs of government and this ensures the balance of power between all three.

1.) What is universal adult suffrage? Why is it so necessary?

Answer: The visionary architects of our Constitution foresaw that embracing universal adult suffrage would act as a potent disruptor, shattering the age-old barriers of caste, class, and gender norms, steering us toward a more egalitarian and inclusive societal structure.It would allow the people to directly choose the nation’s leaders.

1.) Name the three organs of the government? How are they different from one another?

Answer: The legislative, executive, and judicial branches of Indian government each have a distinct function. The judiciary guarantees that laws passed by the Legislature are interpreted correctly. The executive branch is in charge of leading the nation and upholding the law. The Constitution’s guiding principles guide how the Legislature creates laws.

2.) The Constitution allows every citizen to run for elections. why?

Answer: To encourage inclusiveness and diversity, every citizen—regardless of their socioeconomic status—must have the opportunity to cast a ballot. Representative democracy is promoted by this practise. By providing equitable chances for political participation, the Constitution encourages variety among possible candidates. As a result, the country’s government can incorporate a vast variety of perspectives, reflecting the needs and ambitions of its multiethnic populace.

3.) How does India’s democratic process benefit from the Constitution’s emphasis on elected officials’ accountability?

Answer:The public’s right to hold elected authorities accountable is emphasised strongly in the Constitution. By making sure that representatives answer for their deeds and decisions, it maintains democratic values like accountability, responsiveness, and public service. As a result, a strong and accountable democratic system is fostered, with elected officials prioritising the welfare of their constituents.

Case Study 7

The section on Fundamental Rights has often been referred to as the ‘conscience’ of the Indian Constitution. Colonial rule had created a certain suspicion of the State in the minds of the nationalists and they wanted to ensure that a set of written rights would guard against the misuse of State power in independent India. Fundamental Rights, therefore, protect citizens against the arbitrary and absolute exercise of power by the State. The Constitution, thus, guarantees the rights of individuals against the State as well as against other individuals. Moreover, the various minority communities also expressed the need for the Constitution to include rights that would protect their groups. The Constitution, therefore, also guarantees the rights of minorities against the majority. As Dr Ambedkar has said about these Fundamental Rights, their object is two-fold. The first objective is that every citizen must be in a position to claim those rights. And secondly, these rights must be binding upon every authority that has got the power to make laws. In addition to Fundamental Rights, the Constitution also has a section called Directive Principles of State Policy. This section was designed by the members of the Constituent Assembly to ensure greater social and economic reforms, and to serve as a guide to the independent Indian State to institute laws and policies that help reduce the poverty of the masses.

1.) Why is the Indian Constitution’s Fundamental Rights clause frequently referred to as its “conscience”?

Answer: Due to its significant significance in defending people’ rights against the arbitrary exercise of power by the State, the section on Fundamental Rights is frequently referred to as the “conscience” of the Indian Constitution. By guaranteeing individual rights not only against the State but also against other individuals, and providing protections for minority communities against the majority, the Fundamental Rights uphold democratic principles and promote a just and inclusive society, making it a cornerstone of the nation’s conscience.

2.)  What was the objective behind including Fundamental Rights in the Indian Constitution, as stated by Dr Ambedkar?

Answer: Dr Ambedkar’s vision behind including Fundamental Rights in the Indian Constitution was multifaceted. Firstly, he envisioned that every citizen must possess the ability to claim these rights, empowering them against any infringement on their liberties. By offering a shield against arbitrary actions, the Fundamental Rights ensure that individuals can freely exercise their rights without fear of undue interference. Secondly, Dr Ambedkar stressed that these rights should be binding upon every authority with the power to make laws, thus establishing an unequivocal commitment to uphold and protect these fundamental guarantees, securing justice and equality for all.

3.)  What is the purpose of including Directive Principles of State Policy in the Constitution?

Answer: The inclusion of Directive Principles of State Policy in the Constitution serves as a visionary guidepost for the independent Indian State to actively pursue social and economic reforms.This could help to uplift the marginalized and reduce poverty. Though not enforceable in courts, these principles provide a moral imperative for the government to work towards creating a just and egalitarian society. By setting forth guidelines for policymaking, the Directive Principles imbue the governance process with a sense of welfare and social responsibility, ensuring the equitable distribution of resources and opportunities for the welfare of the masses.

4.)  How did the Constitution address the concerns of minority communities regarding their rights and protections?

Answer: The Constitution effectively addressed the concerns of minority communities by incorporating provisions that guarantee their rights against any potential majority domination. The Constitution prioritises inclusivity and equal protection, and it works to safeguard the interests and cultural identities of minority groups in order to promote a cohesive and peaceful society. The Constitution shows a commitment to fostering diversity and guaranteeing that all people are entitled to equal rights and opportunities, regardless of their origin or views, by enshrining these protections.

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Exponents and Powers Class 8 Questions

Exponents and powers class 8 questions are provided here with solutions and explanations, to help students understand the basic concepts of exponents and powers. These questions are designed as per the latest CBSE/ICSE curriculum guidelines for class 8. Practising these worksheets will clear their doubts and help them to solve higher-order thinking level questions asked in the examinations.

Also, Check

• Important 2 Marks Questions for CBSE 8th Maths
• Important 3 Marks Questions for CBSE 8th Maths
• Important 4 Marks Questions for CBSE 8th Maths

If x is added n times repeatedly, it simply implies n × x = nx, but if we multiply x, n times repeatedly it means x n . Thus, x n is an exponential form, any number written like this is called exponents. In x n , x is called the base of the exponent and n is called the power

Learn more about exponents and powers .

Exponents and Powers Class 8 Questions with Solutions

Below are the practice questions on exponents and powers for class 8 with detailed solutions.

Question 1: Simplify (27) 2/3 – (81) 1/2 .

(27) 2/3 – (81) 1/2 = (3 3 ) 2/3 – (9 2 ) 1/2

= 3 3 × ⅔ – 9 2 × ½

= 9 – 9 = 0

∴ (27) 2/3 – (81) 1/2 = 0.

Question 2: If 3 x – y = 27 and 3 x + y = 243, then what is the value of x and y?

Given, 3 x – y = 27 = 3 3 and 3 x + y = 243 = 3 5

Comparing the powers on both sides of the exponents, we get

⇒ x – y = 3 ….(i)

x + y = 5 ….(ii)

Adding equations (i) and (ii),

then y = 1.

Question 3: Simplify the following:

\(\begin{array}{l}\frac{3^{-5}\times 5^{-7}\times (-2)^{3}}{3^{4}\times 5^{-2}\times (-2)^{-3}}\end{array} \)

Using the laws of exponents,

\(\begin{array}{l}\frac{3^{-5}\times 5^{-7}\times (-2)^{3}}{3^{4}\times 5^{-2}\times (-2)^{-3}}=3^{(-5-4)}\times 5^{(-7+2)}\times (-2)^{(3+3)}\end{array} \)

= -2 6 /(3 9 × 5 5 ).

Question 4: Determine (8x) x if 9 x + 2 = 240 + 9 x .

9 x + 2 = 240 + 9 x

⇒ 9 x . 9 2 – 9 x = 240

⇒ 9 x (9 2 – 1) = 240

⇒ 9 x × (81 – 1) = 240

⇒ 9 x = 240/80 = 3

⇒ (3 2 ) x = 3

Comparing powers on both the sides,

2x = 1 ⇒ x = ½

∴ (8x) x = (8 × ½) ½ = 4 1/2 = 2.

• Ratio and Proportion
• Scientific Notation
• Algebraic Expressions
• Factorisation

Question 5: Simplify:

(i) 8x 5 y 7 / 12x 9 y 4

(ii) ( –5x 3 /2y –4 ) –3

(i)8x 5 y 7 / 12x 9 y 4 = ⅔ (x 5 – 9 y 7 – 4 ) = 2y 3 /3x 4 .

(ii) ( –5x 3 /2y –4 ) -3 = [( –5) – 3 × (x 3 ) – 3 ] / [2 –3 . (y –4 ) – 3 ]

= { –8 × x –9 }/{125 y 12 }

= –8/125x 9 y 12 .

Question 6: Given, 10 0.48 = x and 10 0.70 = y and x z = y 2 , then find the approximate value of z.

Given, x z = y 2 ⇒ (10 0.48 ) z = (10 0.70 ) 2

⇒ 10 0.48z = 10 1.40 ⇒ 0.48z = 1.40

⇒ z = 140/48 = 2.9 (approx.)

Question 7: If 5 3x + 2 = 25 × 5 (4x – 1) , then find the value of x.

We have, 5 3x + 2 = 25 × 5 (4x – 1)

⇒ 5 3x + 2 = 5 2 × 5 (4x – 1)

⇒ 5 3x + 2 = 5 (2 + 4x – 1)

⇒ 5 3x + 2 = 5 4x + 1

As the bases are equal, comparing powers on both side we get,

3x + 2 = 4x + 1

⇒ 4x – 3x = 2 – 1

Question 8: If 5 x = 3 y = 45 z , then prove that 1/z = 1/x + 2/y.

Given, 5 x = 3 y = 45 z

Then, 5 x = 45 z = (5 × 9) z

⇒ 5 x = 5 z × (3 2 ) z

⇒ 5 x = 5 z × 3 2z …(i)

Similarly, 3 y = 5 z × 3 2z …(ii)

Multiplying equation (i) and (ii), we get,

5 x .3 y = (5 z × 3 2z ) 2

⇒ 5 x .3 y = 5 2z . 3 4z

Comparing powers on both sides.

x = 2z and y = 4z

⇒ 2/x = 1/z and 4/y = z

Adding both the equations,

2/z = 2/x + 4/y

⇒ 1/z = 1/x + 2/y.

Question 9: Simplify:

\(\begin{array}{l}\frac{5(81)^{n+1}-3^{4n+5}}{3\times 3^{4n}+(81)^{n}}\end{array} \)

\(\begin{array}{l}\frac{5(81)^{n+1}-3^{4n+5}}{3\times 3^{4n}+(81)^{n}}=\frac{5\times (3^{4})^{n+1}-3^{4n+5}}{3^{1+4n}+(3^{4})^{n}}\end{array} \)

\(\begin{array}{l}=\frac{5.3^{4}-3^{5}}{3+1}=\frac{5\times 81 – 243}{(3+1)} \end{array} \) \(\begin{array}{l} =\frac{405-243}{4}\end{array} \)

Question 10: Evaluate: (21 2 – 15 2 ) 4/3

(21 2 – 15 2 ) 4/3 . = (441 – 225) 4/3 = (216) 4/3

= (∛216) 4 = 6 4 = 1296

Question 11: If (1331) – x = (225) y , where x and y are integers, then find the value of 3xy.

(1331) – x = (225) y

⇒ (11 3 ) –x = (15 2 ) y

⇒ 11 –3x = 15 2y

The above equation is true only for x = y = 0

∴ 3xy = 3 × 0 × 0 = 0.

Question 12: If (243) – x = (729) y = 3 3 , then find the value of 5x + 6y.

Now, (243) –x = 3 3

⇒ (3 5. ) –x = 3 3

Comparing the powers,

–5x = 3 ⇒ x = –⅗

Again, (729) y = 3 3.

⇒ (9 3 ) y = 3 3

⇒ (3 2 ) 3y = 3 3

⇒ 3 6y = 3 3

6y = 3 ⇒ y = ½

∴ 5x + 6y = 5 × ( –3/5) + 6 × ½

= –3 + 3 = 0

Question 13: If 2 = 10 m and 3 = 10 n , then find the value of 0.15.

0.15 = 1.5/10 = 3/(2 × 10) [as 1.5 = 3/2]

= 10 n /(10 m × 10)

= 10 n – m – 1

Question 14: Given, a = 2 x , b = 4 y , c = 8 z and ac = b 2 . Find the relation between x, y and z.

Given, ac = b 2

⇒ 2 x . 8 z = (4 y ) 2

⇒ 2 x . 2 3z = 2 4y

⇒ 2 x + 3z = 2 4y

Comparing the powers on both sides,

x + 3z = 4y.

Question 15: Find the value of [169 –3 / 196 – 8 ] 1/48 .

[169 –3 / 196 – 8 ] 1/48 = [(13 2 ) –3 / (14 2 ) – 8 ] 1/48

= [13 –3 × 2 / 14 – 8 × 2 ] 1/48

= [13 –6 / 14 – 16 ] 1/48

= [14 16 / 13 6 ] 1/48

= (14) 16 × 1/48 / 13 6 × 1/48

= 14 1/3 / 13 ⅛ .

Practice Worksheet

1. Simplify:

(i) [3 6 ÷ 3 4 ] 3

(ii) [(–2) 5 × (3) 5 ] 2 ÷ [12 × 3 7 ]

(iii) [(2 3 × 3 4 ) 3 × (–5) 3 ] ÷ [60 × (–2) 5 ]

2. If (1331) – x = (225) y , where x and y are integers, then find the value of 3 + xy.

3. If (243) – x = (729) y = 27, then find the value of 5x – 6y.

4. (4) ½ × (0.5) 4 is equal to _______.

5. If 2 x = 4 y = 8 z and xyz = 288, then prove that 1/2x + 1/4y + 1/8z = 11/96.

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