case study questions class 10 maths with solutions pdf

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Case Study Questions Class 10 Maths with Solutions PDF Download

 case study questions class 10 maths pdf, case study questions class 10 maths with solutions, case study questions class 10 maths cbse chapter wise pdf download, how to solve case-based question in maths.

• First of all, a student needs to read the complete passage thoroughly. Then start solving the question
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• Sometimes the question is very tricky and you will find it very difficult to understand. In that case, Read the question and passage again and again.
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• Remember, write only answering your answer book

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Class 10 Maths Case Study Questions PDF Download

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Are you looking for a reliable source to download Class 10 Maths case study questions in PDF format? Look no further! In this article, we will provide you with a comprehensive collection of case study questions specifically designed for Class 10 Maths Case Study Questions . Whether you are a student or a teacher, these case study questions will prove to be a valuable resource in your preparation or teaching process.

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If you want to want to prepare all the tough, tricky & difficult questions for your upcoming exams, this is where you should hang out.  CBSE Case Study Questions for Class 10  will provide you with detailed, latest, comprehensive & confidence-inspiring solutions to the maximum number of Case Study Questions covering all the topics from your  NCERT Text Books !

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CBSE 10th Maths: Case Study Questions With Answers

Students taking the 10th board examinations will see new kinds of case study questions in class. The board initially incorporated case study questions into the board exam. The chapter-by-chapter case study question and answers are available here.

Chapterwise Case Study Questions for Class 10 Mathematics

Case study questions are an essential component of the Class 10 Mathematics curriculum. They provide students with real-world scenarios where they can apply mathematical concepts and problem-solving skills. By analyzing and solving these case study questions, students develop a deeper understanding of the subject and improve their critical thinking abilities.

The above  Case studies for Class 10 Maths  will help you to boost your scores as Case Study questions have been coming in your examinations. These CBSE Class 10 Mathematics Case Studies have been developed by experienced teachers of schools.studyrate.in for the benefit of Class 10 students.

• Class 10th Science Case Study Questions

Benefits of Case Study Questions for Class 10 Mathematics

Case study questions offer several benefits to both students and teachers. Here are some key advantages:

• Practical Application : Case study questions bridge the gap between theory and real-life situations, allowing students to apply mathematical concepts in practical scenarios.
• Analytical Thinking : By solving case study questions, students enhance their analytical thinking and problem-solving skills.
• Conceptual Clarity : Case study questions help reinforce the fundamental concepts of mathematics, leading to improved conceptual clarity.
• Exam Preparation : Practicing case study questions prepares students for their Class 10 Mathematics exams, as they become familiar with the question formats and types.
• Comprehensive Assessment : Teachers can use case study questions to assess students’ understanding of various mathematical concepts in a comprehensive manner.

How to Use Case Study Questions Effectively

To make the most out of the case study questions, follow these effective strategies:

• Read the question carefully : Understand the given scenario and identify the mathematical concepts involved.
• Analyze the problem : Break down the problem into smaller parts and determine the approach to solve it.
• Apply relevant formulas and concepts : Utilize your knowledge of the subject to solve the case study question.
• Show your working : Clearly demonstrate the steps and calculations involved in reaching the solution.
• Check your answer : Always verify if your solution aligns with the given problem and recheck calculations for accuracy.

Tips for Solving Case Study Questions

Here are some useful tips to excel in solving case study questions:

• Practice regularly : Regular practice will enhance your problem-solving skills and familiarity with different question formats.
• Understand the concepts: Ensure you have a strong foundation in the underlying mathematical concepts related to each chapter.
• Work on time management : Practice solving case study questions within a stipulated time to improve your speed and efficiency during exams.
• Seek clarification : If you encounter any doubts or difficulties, don’t hesitate to seek guidance from your teacher or peers.

Case study questions are an invaluable resource for Class 10 Mathematics students. They provide practical application opportunities and strengthen conceptual understanding. By utilizing the chapter-wise case study questions provided in this article, students can enhance their problem-solving skills, prepare effectively for exams, and develop a deeper appreciation for the subject.

FAQs on Class 10 Maths Case Study Questions

Q1: can i download the class 10 maths case study questions in pdf format.

Yes, you can download the Class 10 Maths case study questions in PDF format from our site free of cost.

Q2: Are the case study questions aligned with the latest curriculum?

Yes, the case study questions presented in this article are designed to align with the latest Class 10 Mathematics curriculum.

Q3: How can case study questions improve my exam preparation?

Case study questions help you understand the practical application of mathematical concepts, enabling you to approach exam questions with greater confidence and clarity.

Q5: Where can I find more resources for Class 10 Mathematics preparation?

Download more resources of Class 10th Maths from schools.studyrate.in, we offer additional resources and practice materials for Class 10 Mathematics.

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myCBSEguide

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• Case Study Class 10...

Case Study Class 10 Maths Questions

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Now, CBSE will ask only subjective questions in class 10 Maths case studies. But if you search over the internet or even check many books, you will get only MCQs in the class 10 Maths case study in the session 2022-23. It is not the correct pattern. Just beware of such misleading websites and books.

We advise you to visit CBSE official website ( cbseacademic.nic.in ) and go through class 10 model question papers . You will find that CBSE is asking only subjective questions under case study in class 10 Maths. We at myCBSEguide helping CBSE students for the past 15 years and are committed to providing the most authentic study material to our students.

Here, myCBSEguide is the only application that has the most relevant and updated study material for CBSE students as per the official curriculum document 2022 – 2023. You can download updated sample papers for class 10 maths .

First of all, we would like to clarify that class 10 maths case study questions are subjective and CBSE will not ask multiple-choice questions in case studies. So, you must download the myCBSEguide app to get updated model question papers having new pattern subjective case study questions for class 10 the mathematics year 2022-23.

Class 10 Maths has the following chapters.

• Real Numbers Case Study Question
• Polynomials Case Study Question
• Pair of Linear Equations in Two Variables Case Study Question
• Quadratic Equations Case Study Question
• Arithmetic Progressions Case Study Question
• Triangles Case Study Question
• Coordinate Geometry Case Study Question
• Introduction to Trigonometry Case Study Question
• Some Applications of Trigonometry Case Study Question
• Circles Case Study Question
• Area Related to Circles Case Study Question
• Surface Areas and Volumes Case Study Question
• Statistics Case Study Question
• Probability Case Study Question

Format of Maths Case-Based Questions

CBSE Class 10 Maths Case Study Questions will have one passage and four questions. As you know, CBSE has introduced Case Study Questions in class 10 and class 12 this year, the annual examination will have case-based questions in almost all major subjects. This article will help you to find sample questions based on case studies and model question papers for CBSE class 10 Board Exams.

Maths Case Study Question Paper 2023

Here is the marks distribution of the CBSE class 10 maths board exam question paper. CBSE may ask case study questions from any of the following chapters. However, Mensuration, statistics, probability and Algebra are some important chapters in this regard.

Case Study Question in Mathematics

Here are some examples of case study-based questions for class 10 Mathematics. To get more questions and model question papers for the 2021 examination, download myCBSEguide Mobile App .

Case Study Question – 1

In the month of April to June 2022, the exports of passenger cars from India increased by 26% in the corresponding quarter of 2021–22, as per a report. A car manufacturing company planned to produce 1800 cars in 4th year and 2600 cars in 8th year. Assuming that the production increases uniformly by a fixed number every year.

• Find the production in the 1 st year.
• Find the production in the 12 th year.
• Find the total production in first 10 years. OR In which year the total production will reach to 15000 cars?

Case Study Question – 2

In a GPS, The lines that run east-west are known as lines of latitude, and the lines running north-south are known as lines of longitude. The latitude and the longitude of a place are its coordinates and the distance formula is used to find the distance between two places. The distance between two parallel lines is approximately 150 km. A family from Uttar Pradesh planned a round trip from Lucknow (L) to Puri (P) via Bhuj (B) and Nashik (N) as shown in the given figure below.

• Find the distance between Lucknow (L) to Bhuj(B).
• If Kota (K), internally divide the line segment joining Lucknow (L) to Bhuj (B) into 3 : 2 then find the coordinate of Kota (K).
• Name the type of triangle formed by the places Lucknow (L), Nashik (N) and Puri (P) OR Find a place (point) on the longitude (y-axis) which is equidistant from the points Lucknow (L) and Puri (P).

Case Study Question – 3

• Find the distance PA.
• Find the distance PB
• Find the width AB of the river. OR Find the height BQ if the angle of the elevation from P to Q be 30 o .

Case Study Question – 4

• What is the length of the line segment joining points B and F?
• The centre ‘Z’ of the figure will be the point of intersection of the diagonals of quadrilateral WXOP. Then what are the coordinates of Z?
• What are the coordinates of the point on y axis equidistant from A and G? OR What is the area of area of Trapezium AFGH?

Case Study Question – 5

The school auditorium was to be constructed to accommodate at least 1500 people. The chairs are to be placed in concentric circular arrangement in such a way that each succeeding circular row has 10 seats more than the previous one.

• If the first circular row has 30 seats, how many seats will be there in the 10th row?
• For 1500 seats in the auditorium, how many rows need to be there? OR If 1500 seats are to be arranged in the auditorium, how many seats are still left to be put after 10 th row?
• If there were 17 rows in the auditorium, how many seats will be there in the middle row?

Case Study Question – 6

• Draw a neat labelled figure to show the above situation diagrammatically.

• What is the speed of the plane in km/hr.

More Case Study Questions

We have class 10 maths case study questions in every chapter. You can download them as PDFs from the myCBSEguide App or from our free student dashboard .

As you know CBSE has reduced the syllabus this year, you should be careful while downloading these case study questions from the internet. You may get outdated or irrelevant questions there. It will not only be a waste of time but also lead to confusion.

Here, myCBSEguide is the most authentic learning app for CBSE students that is providing you up to date study material. You can download the myCBSEguide app and get access to 100+ case study questions for class 10 Maths.

How to Solve Case-Based Questions?

Questions based on a given case study are normally taken from real-life situations. These are certainly related to the concepts provided in the textbook but the plot of the question is always based on a day-to-day life problem. There will be all subjective-type questions in the case study. You should answer the case-based questions to the point.

What are Class 10 competency-based questions?

Competency-based questions are questions that are based on real-life situations. Case study questions are a type of competency-based questions. There may be multiple ways to assess the competencies. The case study is assumed to be one of the best methods to evaluate competencies. In class 10 maths, you will find 1-2 case study questions. We advise you to read the passage carefully before answering the questions.

Case Study Questions in Maths Question Paper

CBSE has released new model question papers for annual examinations. myCBSEguide App has also created many model papers based on the new format (reduced syllabus) for the current session and uploaded them to myCBSEguide App. We advise all the students to download the myCBSEguide app and practice case study questions for class 10 maths as much as possible.

Case Studies on CBSE’s Official Website

CBSE has uploaded many case study questions on class 10 maths. You can download them from CBSE Official Website for free. Here you will find around 40-50 case study questions in PDF format for CBSE 10th class.

10 Maths Case Studies in myCBSEguide App

You can also download chapter-wise case study questions for class 10 maths from the myCBSEguide app. These class 10 case-based questions are prepared by our team of expert teachers. We have kept the new reduced syllabus in mind while creating these case-based questions. So, you will get the updated questions only.

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CBSE Case Study Questions for Class 10 Maths Real Numbers Free PDF

Mere Bacchon, you must practice the CBSE Case Study Questions Class 10 Maths Real Numbers  in order to fully complete your preparation . They are very very important from exam point of view. These tricky Case Study Based Questions can act as a villain in your heroic exams!

I have made sure the questions (along with the solutions) prepare you fully for the upcoming exams. To download the latest CBSE Case Study Questions , just click ‘ Download PDF ’.

CBSE Case Study Questions for Class 10 Maths Real Numbers PDF

Mcq set 1 -, mcq set 2 -, checkout our case study questions for other chapters.

• Chapter 2: Polynomials Case Study Questions
• Chapter 3: Pair of Linear Equations in Two Variables Case Study Questions
• Chapter 4: Quadratic Equation Case Study Questions
• Chapter 5: Arithmetic Progressions Case Study Questions

How should I study for my upcoming exams?

First, learn to sit for at least 2 hours at a stretch

Solve every question of NCERT by hand, without looking at the solution.

Solve NCERT Exemplar (if available)

Sit through chapter wise FULLY INVIGILATED TESTS

Practice MCQ Questions (Very Important)

Practice Assertion Reason & Case Study Based Questions

Sit through FULLY INVIGILATED TESTS involving MCQs. Assertion reason & Case Study Based Questions

After Completing everything mentioned above, Sit for atleast 6 full syllabus TESTS.

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CBSE 10th Standard Maths Subject Case Study Questions with Solutions

By QB365 on 20 May, 2021

QB365 Provides the updated CASE Study Questions for Class 10 , and also provide the detail solution for each and every case study questions . Case study questions are latest updated question pattern from NCERT, QB365 will helps to get  more marks in Exams

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Case Study on Real Numbers Class 10 Maths PDF

The passage-based questions are commonly known as case study questions. Students looking for Case Study on Real Numbers Class 10 Maths can use this page to download the PDF file. 

The case study questions on Real Numbers are based on the CBSE Class 10 Maths Syllabus, and therefore, referring to the Real Numbers case study questions enable students to gain the appropriate knowledge and prepare better for the Class 10 Maths board examination. Continue reading to know how should students answer it and why it is essential to solve it, etc.

Case Study on Real Numbers Class 10 Maths with Solutions in PDF

Our experts have also kept in mind the challenges students may face while solving the case study on Real Numbers, therefore, they prepared a set of solutions along with the case study questions on Real Numbers.

The case study on Real Numbers Class 10 Maths with solutions in PDF helps students tackle questions that appear confusing or difficult to answer. The answers to the Real Numbers case study questions are very easy to grasp from the PDF - download links are given on this page.

Why Solve Real Numbers Case Study Questions on Class 10 Maths?

There are three major reasons why one should solve Real Numbers case study questions on Class 10 Maths - all those major reasons are discussed below:

• To Prepare for the Board Examination: For many years CBSE board is asking case-based questions to the Class 10 Maths students, therefore, it is important to solve Real Numbers Case study questions as it will help better prepare for the Class 10 board exam preparation.
• Develop Problem-Solving Skills: Class 10 Maths Real Numbers case study questions require students to analyze a given situation, identify the key issues, and apply relevant concepts to find out a solution. This can help CBSE Class 10 students develop their problem-solving skills, which are essential for success in any profession rather than Class 10 board exam preparation.
• Understand Real-Life Applications: Several Real Numbers Class 10 Maths Case Study questions are linked with real-life applications, therefore, solving them enables students to gain the theoretical knowledge of Real Numbers as well as real-life implications of those learnings too.

How to Answer Case Study Questions on Real Numbers?

Students can choose their own way to answer Case Study on Real Numbers Class 10 Maths, however, we believe following these three steps would help a lot in answering Class 10 Maths Real Numbers Case Study questions.

• Read Question Properly: Many make mistakes in the first step which is not reading the questions properly, therefore, it is important to read the question properly and answer questions accordingly.
• Highlight Important Points Discussed in the Clause: While reading the paragraph, highlight the important points discussed as it will help you save your time and answer Real Numbers questions quickly.
• Go Through Each Question One-By-One: Ideally, going through each question gradually is advised so, that a sync between each question and the answer can be maintained. When you are solving Real Numbers Class 10 Maths case study questions make sure you are approaching each question in a step-wise manner.

What to Know to Solve Case Study Questions on Class 10 Real Numbers?

 A few essential things to know to solve Case Study Questions on Class 10 Real Numbers are -

• Basic Formulas of Real Numbers: One of the most important things to know to solve Case Study Questions on Class 10 Real Numbers is to learn about the basic formulas or revise them before solving the case-based questions on Real Numbers.
• To Think Analytically: Analytical thinkers have the ability to detect patterns and that is why it is an essential skill to learn to solve the CBSE Class 10 Maths Real Numbers case study questions.
• Strong Command of Calculations: Another important thing to do is to build a strong command of calculations especially, mental Maths calculations.

Where to Find Case Study on Real Numbers Class 10 Maths?

Use Selfstudys.com to find Case Study on Real Numbers Class 10 Maths. For ease, here is a step-wise procedure to download the Real Numbers Case Study for Class 10 Maths in PDF for free of cost.

Since you are already on this page, you can scroll to the top section of this page to get access to the Case Study on Real Numbers. To help others reach this page let them know these steps:

• Open Selfstudys.com on your computer/laptop or Smartphone 
• Once the website gets loaded, click on the navigation button

• Find CBSE from the given menu

• Click on Case Study

• Choose Class 10 
• Search Maths and then navigate to the Real Numbers Class 10 Maths Case Study

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CBSE Class 10 Maths Case Study Questions for Maths Chapter 5 - Arithmetic Progression (Published by CBSE)

Case study questions on cbse class 10 maths chapter 5 - arithmetic progression are provided here. these questions are published by cbse to help students prepare for their maths exam..

CBSE Class 10 Case Study Questions for Maths Chapter 5 - Arithmetic Progression are available here with answers. All the questions have been published by the CBSE board. Students must practice all these questions to prepare themselves for attempting the case study based questions with absolute correctness and obtain a high score in their Maths Exam 2021-22.

Case Study Questions for Class 10 Maths Chapter 5 - Arithmetic Progression

CASE STUDY 1:

India is competitive manufacturing location due to the low cost of manpower and strong technical and engineering capabilities contributing to higher quality production runs. The production of TV sets in a factory increases uniformly by a fixed number every year. It produced 16000 sets in 6th year and 22600 in 9th year.

Based on the above information, answer the following questions:

1. Find the production during first year.

2. Find the production during 8th year.

3. Find the production during first 3 years.

4. In which year, the production is Rs 29,200.

5. Find the difference of the production during 7th year and 4th year.

2. Production during 8th year is (a+7d) = 5000 + 2(2200) = 20400

3. Production during first 3 year = 5000 + 7200 + 9400 = 21600

4. N = 12 5.

Difference = 18200 - 11600 = 6600

CASE STUDY 2:

Your friend Veer wants to participate in a 200m race. He can currently run that distance in 51 seconds and with each day of practice it takes him 2 seconds less. He wants to do in 31 seconds.

1. Which of the following terms are in AP for the given situation

a) 51,53,55….

b) 51, 49, 47….

c) -51, -53, -55….

d) 51, 55, 59…

Answer: b) 51, 49, 47….

2. What is the minimum number of days he needs to practice till his goal is achieved

Answer: c) 11

3. Which of the following term is not in the AP of the above given situation

Answer: b) 30

4. If nth term of an AP is given by an = 2n + 3 then common difference of an AP is

Answer: a) 2

5. The value of x, for which 2x, x+ 10, 3x + 2 are three consecutive terms of an AP

Answer: a) 6

CASE STUDY 3:

Your elder brother wants to buy a car and plans to take loan from a bank for his car. He repays his total loan of Rs 1,18,000 by paying every month starting with the first instalment of Rs 1000. If he increases the instalment by Rs 100 every month , answer the following:

1. The amount paid by him in 30th installment is

Answer: a) 3900

2. The amount paid by him in the 30 installments is

Answer: b) 73500

3. What amount does he still have to pay offer 30th installment?

Answer: c) 44500

4. If total installments are 40 then amount paid in the last installment?

Answer: a) 4900

5. The ratio of the 1st installment to the last installment is

Answer: b) 10:49

Also Check:

CBSE Case Study Questions for Class 10 Maths - All Chapters

Tips to Solve Case Study Based Questions Accurately

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• NCERT Solutions
• NCERT Solutions for Class 10
• NCERT Solutions for Class 10 Maths
• Chapter 1: Real Numbers

NCERT Solutions for Class 10 Maths Chapter 1- Real Numbers

NCERT Solutions Class 10 Maths Chapter 1 Real Numbers are provided here. These solutions are prepared by our expert faculty to help students in their board exam preparations. They solve and provide the NCERT Solutions for Maths to aid the students in solving the problems easily. They also focus on preparing the solutions in such a way that it is easy to understand for the students. A detailed and step-wise explanation is given for each question given in the exercises of NCERT books.

Download Exclusively Curated Chapter Notes for Class 10 Maths Chapter – 1 Real Numbers

Download most important questions for class 10 maths chapter – 1 real numbers.

Answers to the questions present in Real Numbers are given in the first chapter of Maths Solutions of NCERT Class 10. Here, students are introduced to several important concepts that will be useful for those who wish to pursue mathematics as a subject in their Class 11. Based on these solutions of Class 10 NCERT , students can prepare for their upcoming board exam. These solutions are helpful as they are in accordance with the CBSE Syllabus for 2023-24.

• Chapter 1 Real Numbers
• Chapter 2 Polynomials
• Chapter 3 Pair of Linear Equations in Two Variables
• Chapter 4 Quadratic Equations
• Chapter 5 Arithmetic Progressions
• Chapter 6 Triangles
• Chapter 7 Coordinate Geometry
• Chapter 8 Introduction to Trigonometry
• Chapter 9 Some Applications of Trigonometry
• Chapter 10 Circles
• Chapter 11 Constructions
• Chapter 12 Areas Related to Circles
• Chapter 13 Surface Areas and Volumes
• Chapter 14 Statistics
• Chapter 15 Probability
• Exercise 1.1 Chapter 1 Real Numbers
• Exercise 1.2 Chapter 1 Real Numbers
• Exercise 1.3 Chapter 1 Real Numbers
• Exercise 1.4 Chapter 1 Real Numbers

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Access Answers to NCERT Class 10 Maths Chapter 1 – Real Numbers

Exercise 1.1 page: 7.

1. Use Euclid’s division algorithm to find the HCF of:

i. 135 and 225

ii. 196 and 38220

iii. 867 and 255

As you can see from the question, 225 is greater than 135. Therefore, by Euclid’s division algorithm, we have,

225 = 135 × 1 + 90

Now, remainder 90 ≠ 0, thus again using division lemma for 90, we get,

135 = 90 × 1 + 45

Again, 45 ≠ 0, repeating the above step for 45, we get,

90 = 45 × 2 + 0

The remainder is now zero, so our method stops here. Since, in the last step, the divisor is 45, therefore, HCF (225,135) = HCF (135, 90) = HCF (90, 45) = 45.

Hence, the HCF of 225 and 135 is 45.

In this given question, 38220>196, therefore the by applying Euclid’s division algorithm and taking 38220 as divisor, we get,

38220 = 196 × 195 + 0

We have already got the remainder as 0 here. Therefore, HCF(196, 38220) = 196.

Hence, the HCF of 196 and 38220 is 196.

As we know, 867 is greater than 255. Let us apply now Euclid’s division algorithm on 867, to get,

867 = 255 × 3 + 102

Remainder 102 ≠ 0, therefore taking 255 as divisor and applying the division lemma method, we get,

255 = 102 × 2 + 51

Again, 51 ≠ 0. Now 102 is the new divisor, so repeating the same step we get,

102 = 51 × 2 + 0

The remainder is now zero, so our procedure stops here. Since, in the last step, the divisor is 51, therefore, HCF (867,255) = HCF(255,102) = HCF(102,51) = 51.

Hence, the HCF of 867 and 255 is 51.

2. Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.

Let a be any positive integer and b = 6. Then, by Euclid’s algorithm, a = 6q + r, for some integer q ≥ 0, and r = 0, 1, 2, 3, 4, 5, because 0≤r<6.

Now substituting the value of r, we get,

If r = 0, then a = 6q

Similarly, for r= 1, 2, 3, 4 and 5, the value of a is 6q+1, 6q+2, 6q+3, 6q+4 and 6q+5, respectively.

If a = 6q, 6q+2, 6q+4, then a is an even number and divisible by 2. A positive integer can be either even or odd Therefore, any positive odd integer is of the form of 6q+1, 6q+3 and 6q+5, where q is some integer.

3. An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

Number of army contingent members = 616

Number of army band members = 32

If the two groups have to march in the same column, we have to find out the highest common factor between the two groups. HCF(616, 32), gives the maximum number of columns in which they can march.

By using Euclid’s algorithm to find their HCF, we get,

Since, 616>32, therefore,

616 = 32 × 19 + 8

Since, 8 ≠ 0, therefore, taking 32 as new divisor, we have,

32 = 8 × 4 + 0

Now we have got remainder as 0, therefore, HCF (616, 32) = 8.

Hence, the maximum number of columns in which they can march is 8.

4. Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m.

Let x be any positive integer and y = 3.

By Euclid’s division algorithm, then,

x = 3q + r for some integer q≥0 and r = 0, 1, 2, as r ≥ 0 and r < 3.

Therefore, x = 3q, 3q+1 and 3q+2

Now as per the question given, by squaring both the sides, we get,

x 2 = (3q) 2 = 9q 2 = 3 × 3q 2

Let 3q 2 = m

Therefore, x 2 = 3m ……………………..(1)

x 2 = (3q + 1) 2 = (3q) 2 +1 2 +2×3q×1 = 9q 2 + 1 +6q = 3(3q 2 +2q) +1

Substitute, 3q 2 +2q = m, to get,

x 2 = 3m + 1 ……………………………. (2)

x 2 = (3q + 2) 2 = (3q) 2 +2 2 +2×3q×2 = 9q 2 + 4 + 12q = 3 (3q 2 + 4q + 1)+1

Again, substitute, 3q 2 +4q+1 = m, to get,

x 2 = 3m + 1…………………………… (3)

Hence, from equation 1, 2 and 3, we can say that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m.

5. Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m, 9m + 1 or 9m + 8.

x = 3q+r, where q≥0 and r = 0, 1, 2, as r ≥ 0 and r < 3.

Therefore, putting the value of r, we get,

Now, by taking the cube of all the three above expressions, we get,

Case (i): When r = 0, then,

x 2 = (3q) 3 = 27q 3 = 9(3q 3 )= 9m; where m = 3q 3

Case (ii): When r = 1, then,

x 3 = (3q+1) 3 = (3q) 3 +1 3 +3×3q×1(3q+1) = 27q 3 +1+27q 2 +9q

Taking 9 as common factor, we get,

x 3 = 9(3q 3 +3q 2 +q)+1

Putting = m, we get,

Putting (3q 3 +3q 2+ q) = m, we get ,

Case (iii): When r = 2, then,

x 3 = (3q+2) 3 = (3q) 3 +2 3 +3×3q×2(3q+2) = 27q 3 +54q 2 +36q+8

x 3 =9(3q 3 +6q 2 +4q)+8

Putting (3q 3 +6q 2 +4q) = m, we get ,

Therefore, from all the three cases explained above, it is proved that the cube of any positive integer is of the form 9m, 9m + 1 or 9m + 8.

Exercise 1.2 Page: 11

1. Express each number as a product of its prime factors:

By taking the LCM of 140, we will get the product of its prime factor.

Therefore, 140 = 2 × 2 × 5 × 7 × 1 = 2 2 ×5×7

By Taking the LCM of 156, we will get the product of its prime factor.

Hence, 156 = 2 × 2 × 13 × 3 × 1 = 2 2 × 13 × 3

By taking the LCM of 3825, we will get the product of its prime factor.

Hence, 3825 = 3 × 3 × 5 × 5 × 17 × 1 = 3 2 ×5 2 ×17

By Taking the LCM of 5005, we will get the product of its prime factor.

Hence, 5005 = 5 × 7 × 11 × 13 × 1 = 5 × 7 × 11 × 13

By taking the LCM of 7429, we will get the product of its prime factor.

Hence, 7429 = 17 × 19 × 23 × 1 = 17 × 19 × 23

2. Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers.

(i) 26 and 91

(ii) 510 and 92

(iii) 336 and 54

Expressing 26 and 91 as product of its prime factors, we get,

26 = 2 × 13 × 1

91 = 7 × 13 × 1

Therefore, LCM (26, 91) = 2 × 7 × 13 × 1 = 182

And HCF (26, 91) = 13

Verification

Now, product of 26 and 91 = 26 × 91 = 2366

And product of LCM and HCF = 182 × 13 = 2366

Hence, LCM × HCF = product of the 26 and 91.

Expressing 510 and 92 as product of its prime factors, we get,

510 = 2 × 3 × 17 × 5 × 1

92 = 2 × 2 × 23 × 1

Therefore, LCM(510, 92) = 2 × 2 × 3 × 5 × 17 × 23 = 23460

And HCF (510, 92) = 2

Now, product of 510 and 92 = 510 × 92 = 46920

And Product of LCM and HCF = 23460 × 2 = 46920

Hence, LCM × HCF = product of the 510 and 92.

Expressing 336 and 54 as product of its prime factors, we get,

336 = 2 × 2 × 2 × 2 × 7 × 3 × 1

54 = 2 × 3 × 3 × 3 × 1

Therefore, LCM(336, 54) = = 3024

And HCF(336, 54) = 2×3 = 6

Now, product of 336 and 54 = 336 × 54 = 18,144

And product of LCM and HCF = 3024 × 6 = 18,144

Hence, LCM × HCF = product of the 336 and 54.

3. Find the LCM and HCF of the following integers by applying the prime factorisation method.

(i) 12, 15 and 21

(ii) 17, 23 and 29

(iii) 8, 9 and 25

Writing the product of prime factors for all the three numbers, we get,

HCF(12,15,21) = 3

LCM(12,15,21) = 2 × 2 × 3 × 5 × 7 = 420

HCF(17,23,29) = 1

LCM(17,23,29) = 17 × 23 × 29 = 11339

HCF(8,9,25)=1

LCM(8,9,25) = 2×2×2×3×3×5×5 = 1800

4. Given that HCF (306, 657) = 9, find LCM (306, 657).

Solution: As we know that,

HCF×LCM=Product of the two given numbers

9 × LCM = 306 × 657

LCM = (306×657)/9 = 22338

Hence, LCM(306,657) = 22338

5. Check whether 6 n can end with the digit 0 for any natural number n.

Solution: If the number 6 n ends with the digit zero (0), then it should be divisible by 5, as we know any number with unit place as 0 or 5 is divisible by 5.

Prime factorization of 6 n = (2×3) n

Therefore, the prime factorization of 6 n doesn’t contain prime number 5.

Hence, it is clear that for any natural number n, 6 n is not divisible by 5, and thus it proves that 6 n cannot end with the digit 0 for any natural number n.

6. Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.

Solution: By the definition of composite number, we know, if a number is composite, then it means it has factors other than 1 and itself. Therefore, for the given expression;

7 × 11 × 13 + 13

Taking 13 as common factor, we get,

=13(7×11×1+1) = 13(77+1) = 13×78 = 13×3×2×13

Hence, 7 × 11 × 13 + 13 is a composite number.

Now let’s take the other number,

7 × 6 × 5 × 4 × 3 × 2 × 1 + 5

Taking 5 as a common factor, we get,

=5(7×6×4×3×2×1+1) = 5(1008+1) = 5×1009

Hence, 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 is a composite number.

7. There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?

Solution: Since, Both Sonia and Ravi move in the same direction and at the same time, the method to find the time when they will be meeting again at the starting point is LCM of 18 and 12.

Therefore, LCM(18,12) = 2×3×3×2×1=36

Hence, Sonia and Ravi will meet again at the starting point after 36 minutes.

Exercise 1.3 Page: 14

1. Prove that √ 5 is irrational.

Solutions: Let us assume, that √ 5 is rational number.

i.e.  √ 5 = x/y (where, x and y are co-primes)

Squaring both the sides, we get,

(y √ 5) 2 = x 2

⇒5y 2 = x 2 ……………………………….. (1)

Thus, x 2 is divisible by 5, so x is also divisible by 5.

Let us say, x = 5k, for some value of k and substituting the value of x in equation (1), we get,

5y 2 = (5k) 2

⇒y 2 = 5k 2

is divisible by 5 it means y is divisible by 5.

Clearly, x and y are not co-primes. Thus, our assumption about  √ 5 is rational is incorrect.

Hence,  √ 5 is an irrational number.

2. Prove that 3 + 2√5 + is irrational.

Solutions: Let us assume 3 + 2 √ 5 is rational.

Then we can find co-prime x and y (y ≠ 0) such that 3 + 2√5 = x/y

Rearranging, we get,

Since, x and y are integers, thus,

Therefore, √ 5 is also a rational number. But this contradicts the fact that √ 5 is irrational.

So, we conclude that 3 + 2 √ 5 is irrational.

3. Prove that the following are irrationals:

(iii) 6 + √ 2

Let us assume 1/√2 is rational.

Then we can find co-prime x and y (y ≠ 0) such that 1/√2 = x/y

Since, x and y are integers, thus, √2 is a rational number, which contradicts the fact that √2 is irrational.

Hence, we can conclude that 1/√2 is irrational.

Let us assume 7√5 is a rational number.

Then we can find co-prime a and b (b ≠ 0) such that 7√5 = x/y

Since, x and y are integers, thus, √5 is a rational number, which contradicts the fact that √5 is irrational.

Hence, we can conclude that 7√5 is irrational.

Let us assume 6 +√2 is a rational number.

Then we can find co-primes x and y (y ≠ 0) such that 6 +√2 = x/y⋅

√2 = (x/y) – 6

Since, x and y are integers, thus (x/y) – 6 is a rational number and therefore, √2 is rational. This contradicts the fact that √2 is an irrational number.

Hence, we can conclude that 6 +√2 is irrational.

Exercise 1.4 Page: 17

1. Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:

(i) 13/3125 (ii) 17/8 (iii) 64/455 (iv) 15/1600 (v) 29/343 (vi) 23/(2 3 5 2 ) (vii) 129/(2 2 5 7 7 5 ) (viii) 6/15 (ix) 35/50 (x) 77/210

Note: If the denominator has only factors of 2 and 5 or in the form of 2 m ×5 n then it has terminating decimal expansion.

If the denominator has factors other than 2 and 5 then it has a non-terminating decimal expansion.

(i) 13/3125

Factorizing the denominator, we get,

3125 = 5 × 5 × 5 × 5 × 5 = 5 5

Since, the denominator has only 5 as its factor, 13/3125 has a terminating decimal expansion.

8 = 2×2×2 = 2 3

Since, the denominator has only 2 as its factor, 17/8 has a terminating decimal expansion.

(iii) 64/455

455 = 5×7×13

Since, the denominator is not in the form of 2 m × 5 n , thus 64/455 has a non-terminating decimal expansion.

(iv) 15/ 1600

1600 = 2 6 ×5 2

Since, the denominator is in the form of 2 m × 5 n , thus 15/1600 has a terminating decimal expansion.

343 = 7×7×7 = 7 3 Since, the denominator is not in the form of 2 m × 5 n thus 29/343 has a non-terminating decimal expansion.

(vi)23/(2 3 5 2 )

Clearly, the denominator is in the form of 2 m × 5 n .

Hence, 23/ (2 3 5 2 ) has a terminating decimal expansion.

(vii) 129/(2 2 5 7 7 5 )

As you can see, the denominator is not in the form of 2 m × 5 n .

Hence, 129/ (2 2 5 7 7 5 ) has a non-terminating decimal expansion.

(viii) 6/15

Since, the denominator has only 5 as its factor, thus, 6/15 has a terminating decimal expansion.

35/50 = 7/10

Factorising the denominator, we get,

Since, the denominator is in the form of 2 m × 5 n thus, 35/50 has a terminating decimal expansion.

77/210 = (7× 11)/ (30 × 7) = 11/30

30 = 2 × 3 × 5

As you can see, the denominator is not in the form of 2 m × 5 n .Hence, 77/210 has a non-terminating decimal expansion.

2. Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.

13/3125 = 0.00416

17/8 = 2.125

(iii) 64/455 has a non terminating decimal expansion

(iv)15/ 1600

15/1600 = 0.009375

(v) 29/ 343 has a non terminating decimal expansion

(vi)23/ (2 3 5 2 ) = 23/(8×25)= 23/200

23/ (2 3 5 2 ) = 0.115

(vii) 129/ (2 2 5 7 7 5 ) has a non terminating decimal expansion

(viii) 6/15 = 2/5

(ix) 35/50 = 7/10

35/50 = 0.7

(x) 77/210 has a non-terminating decimal expansion.

3. The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form, p q what can you say about the prime factors of q?

(i) 43.123456789

(ii) 0.120120012000120000. . .

Since it has a terminating decimal expansion, it is a rational number in the form of p/q and q has factors of 2 and 5 only.

Since, it has non-terminating and non- repeating decimal expansion, it is an irrational number.

Since it has non-terminating but repeating decimal expansion, it is a rational number in the form of p/q and q has factors other than 2 and 5.

NCERT Solutions for Class 10 Maths Chapter 1 – Real Numbers

Real Number is one of the important topics in Maths, and it has a weightage of 6 marks in Class 10 (Unit – Number Systems) Maths board exams. The average number of questions asked in this chapter is usually 3. Three questions were asked from this chapter in the previous year board examination (2018).

• One out of three questions in part A (1 mark).
• One out of three questions in part B (2 marks).
• One out of three questions in part C (3 marks).

This chapter talks about

• Euclid’s Division Algorithm
• The Fundamental Theorem of Arithmetic
• Revisiting Rational & Irrational Numbers
• Decimal Expansions

List of Exercises in Class 10 Maths Chapter 1: Exercise 1.1 Solutions 5 Questions ( 4 long, 1 short) Exercise 1.2 Solutions 7 Questions ( 4 long, 3 short) Exercise 1.3 Solutions 3 Questions ( 3 short) Exercise 1.4 Solutions 3 Questions ( 3 short)

Real Numbers is introduced in Class 9, and this is discussed in further detail in Class 10. NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers provides the answers to the questions present in this chapter. The chapter discusses real numbers and their applications. The divisibility of integers using Euclid’s division algorithm says that any positive integer a can be divided by another positive integer b such that the remainder will be smaller than b. On the other hand, The Fundamental Theorem of Arithmetic works on the multiplication of positive integers.

The chapter starts with the introduction of real numbers in section 1.1, followed by two very important topics in sections 1.2 and 1.3

• Euclid’s Division Algorithm – It includes 5 questions based on Theorem 1.1 – Euclid’s Division Lemma.
• The Fundamental Theorem of Arithmetic – Explore the applications of this topic which talks about the multiplication of positive integers, through solutions of the 7 problems in Exercise 1.2.

Next, it discusses the following topics, which were introduced in Class 9.

• Revisiting Rational & Irrational Numbers – In this, the solutions for 3 problems in Exercise 1.3 are given, which also use the topic in the last Exercise 1.2.
• Decimal Expansions – It explores when the decimal expansion of a rational number is terminating and when it is recurring. It includes a total of 3 problems with sub-parts in Exercise 1.4

Key Features of NCERT Solutions for Class 10 Maths Chapter 1- Real Numbers

• These NCERT Solutions help you solve and revise the updated CBSE syllabus of Class 10 for 2023-24.
• After going through the stepwise solutions given by our subject expert teachers, you will be able to score more marks.
• It follows NCERT guidelines which help in preparing the students competently.
• It contains all the important questions from the examination point of view.

Disclaimer –

Dropped Topics – 

1.2 Euclid’s division lemma 1.5 Revisiting rational numbers and their decimal Expansions

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CBSE Class 10 Maths: Case Study Questions of Chapter 7 Coordinate Geometry PDF Download

Case study Questions in the Class 10 Mathematics Chapter 7  are very important to solve for your exam. Class 10 Maths Chapter 7 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving case study-based   questions for Class 10 Maths Chapter 7  Coordinate Geometry

In CBSE Class 10 Maths Paper, Students will have to answer some questions based on  Assertion and Reason . There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Coordinate Geometry Case Study Questions With answers

Here, we have provided case-based/passage-based questions for Class 10 Maths  Chapter 7 Coordinate Geometry

Case Study/Passage-Based Questions

Question 1:

Answer: (d) none of these

(ii) The distance of the bus stand from the house is

Answer: (b) 10 cm

(iii) If the grocery store and electrician’s shop lie on a line, the ratio of the distance of the house from the grocery store to that from the electrician’s shop, is

Answer: (c) 1.2

(iv) The ratio of distances of the house from the bus stand to food cart is

Answer: (c) 1.1

(v) The coordinates of positions of bus stand, grocery store, food cart, and electrician’s shop form a

Question 2:

The class X student’s school in krishnagar has been allotted a rectangular plot of land for their gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1 m from each other. There is a triangular grassy lawn in the plot as shown in the figure. The students are to sow seeds of flowering plants on the remaining area of the plot.

1. Taking A as origin, find the coordinates of P

Answer: a) (4,6)

2. What will be the coordinates of R, if C is the origin?

Answer: c) (10,3)

3. What will be the coordinates of Q, if C is the origin?

b) b) (-6,13)

Answer: d) (13,6)

4. Calculate the area of the triangles if A is the origin

Answer: a) 4.5

5. Calculate the area of the triangles if C is the origin

Answer: d) 4.5

Hope the information shed above regarding Case Study and Passage Based Questions for Class 10 Maths Chapter 7 Coordinate Geometry with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 10 Maths Coordinate Geometry Case Study and Passage Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team Study Rate

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