case study questions class 9 maths cbse

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CBSE Class 9th Maths 2023 : 30 Most Important Case Study Questions with Answers; Download PDF

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CBSE Class 9 Maths exam 2022-23 will have a set of questions based on case studies in the form of MCQs. CBSE Class 9 Maths Question Bank on Case Studies given in this article can be very helpful in understanding the new format of questions.

Each question has five sub-questions, each followed by four options and one correct answer. Students can easily download these questions in PDF format and refer to them for exam preparation.

CBSE Class 9 All Students can also Download here Class 9 Other Study Materials in PDF Format.

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CBSE Case Study Questions for Class 9 Maths - Pdf PDF Download

CBSE Case Study Questions for Class  9 Maths

CBSE Case Study Questions for Class 9 Maths are a type of assessment where students are given a real-world scenario or situation and they need to apply mathematical concepts to solve the problem. These types of questions help students to develop their problem-solving skills and apply their knowledge of mathematics to real-life situations.

Chapter Wise Case Based Questions for Class 9 Maths

The CBSE Class 9 Case Based Questions can be accessed from Chapetrwise Links provided below:

Chapter-wise case-based questions for Class 9 Maths are a set of questions based on specific chapters or topics covered in the maths textbook. These questions are designed to help students apply their understanding of mathematical concepts to real-world situations and events.

Chapter 1: Number System

• Case Based Questions: Number System

Chapter 2: Polynomial

• Case Based Questions: Polynomial

Chapter 3: Coordinate Geometry

• Case Based Questions: Coordinate Geometry

Chapter 4: Linear Equations

• Case Based Questions: Linear Equations - 1
• Case Based Questions: Linear Equations -2

Chapter 5: Introduction to Euclid’s Geometry

• Case Based Questions: Lines and Angles

Chapter 7: Triangles

• Case Based Questions: Triangles

Chapter 8: Quadrilaterals

• Case Based Questions: Quadrilaterals - 1
• Case Based Questions: Quadrilaterals - 2

Chapter 9: Areas of Parallelograms

• Case Based Questions: Circles

Chapter 11: Constructions

• Case Based Questions: Constructions

Chapter 12: Heron’s Formula

• Case Based Questions: Heron’s Formula

Chapter 13: Surface Areas and Volumes

• Case Based Questions: Surface Areas and Volumes

Chapter 14: Statistics

• Case Based Questions: Statistics

Chapter 15: Probability

• Case Based Questions: Probability

Weightage of Case Based Questions in Class 9 Maths

Why are Case Study Questions important in Maths Class  9?

• Enhance critical thinking:  Case study questions require students to analyze a real-life scenario and think critically to identify the problem and come up with possible solutions. This enhances their critical thinking and problem-solving skills.
• Apply theoretical concepts:  Case study questions allow students to apply theoretical concepts that they have learned in the classroom to real-life situations. This helps them to understand the practical application of the concepts and reinforces their learning.
• Develop decision-making skills:  Case study questions challenge students to make decisions based on the information provided in the scenario. This helps them to develop their decision-making skills and learn how to make informed decisions.
• Improve communication skills:  Case study questions often require students to present their findings and recommendations in written or oral form. This helps them to improve their communication skills and learn how to present their ideas effectively.
• Enhance teamwork skills:  Case study questions can also be done in groups, which helps students to develop teamwork skills and learn how to work collaboratively to solve problems.

In summary, case study questions are important in Class 9 because they enhance critical thinking, apply theoretical concepts, develop decision-making skills, improve communication skills, and enhance teamwork skills. They provide a practical and engaging way for students to learn and apply their knowledge and skills to real-life situations.

Class 9 Maths Curriculum at Glance

The Class 9 Maths curriculum in India covers a wide range of topics and concepts. Here is a brief overview of the Maths curriculum at a glance:

• Number Systems:  Students learn about the real number system, irrational numbers, rational numbers, decimal representation of rational numbers, and their properties.
• Algebra:  The Algebra section includes topics such as polynomials, linear equations in two variables, quadratic equations, and their solutions.
• Coordinate Geometry:  Students learn about the coordinate plane, distance formula, section formula, and slope of a line.
• Geometry:  This section includes topics such as Euclid’s geometry, lines and angles, triangles, and circles.
• Trigonometry: Students learn about trigonometric ratios, trigonometric identities, and their applications.
• Mensuration: This section includes topics such as area, volume, surface area, and their applications.
• Statistics and Probability:  Students learn about measures of central tendency, graphical representation of data, and probability.

The Class 9 Maths curriculum is designed to provide a strong foundation in mathematics and prepare students for higher education in the field. The curriculum is structured to develop critical thinking, problem-solving, and analytical skills, and to promote the application of mathematical concepts in real-life situations. The curriculum is also designed to help students prepare for competitive exams and develop a strong mathematical base for future academic and professional pursuits.

Students can also access Case Based Questions of all subjects of CBSE Class 9

• Case Based Questions for Class 9 Science
• Case Based Questions for Class 9 Social Science
• Case Based Questions for Class 9 English
• Case Based Questions for Class 9 Hindi
• Case Based Questions for Class 9 Sanskrit

Frequently Asked Questions (FAQs) on Case Based Questions for Class 9 Maths

What is case-based questions.

Case-Based Questions (CBQs) are open-ended problem solving tasks that require students to draw upon their knowledge of Maths concepts and processes to solve a novel problem. CBQs are often used as formative or summative assessments, as they can provide insights into how students reason through and apply mathematical principles in real-world problems.

What are case-based questions in Maths?

Case-based questions in Maths are problem-solving tasks that require students to apply their mathematical knowledge and skills to real-world situations or scenarios.

What are some common types of case-based questions in class 9 Maths?

Common types of case-based questions in class 9 Maths include word problems, real-world scenarios, and mathematical modeling tasks.

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FAQs on CBSE Case Study Questions for Class 9 Maths - Pdf

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CBSE Class 9 Maths Most Important Case Study Based Questions With Solution

Cbse class 9 mathematics case study questions.

In this post I have provided CBSE Class 9 Maths Case Study Based Questions With Solution. These questions are very important for those students who are preparing for their final class 9 maths exam.

All these questions provided in this article are with solution which will help students for solving the problems. Dear students need to practice all these questions carefully with the help of given solutions.

As you know CBSE Class 9 Maths exam will have a set of cased study based questions in the form of MCQs. CBSE Class 9 Maths Question Bank given in this article can be very helpful in understanding the new format of questions for new session.

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Case studies in class 9 mathematics.

The Central Board of Secondary Education (CBSE) has included case study based questions in the Class 9 Mathematics paper in current session. According to new pattern CBSE Class 9 Mathematics students will have to solve case based questions. This is a departure from the usual theoretical conceptual questions that are asked in Class 9 Maths exam in this year.

Each question provided in this post has five sub-questions, each followed by four options and one correct answer. All CBSE Class 9th Maths Students can easily download these questions in PDF form with the help of given download Links and refer for exam preparation.

There is many more free study materials are available at Maths And Physics With Pandey Sir website. For many more books and free study material all of you can visit at this website.

Given Below Are CBSE Class 9th Maths Case Based Questions With Their Respective Download Links.

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Class 9th Maths - Coordinate Geometry Case Study Questions and Answers 2022 - 2023

By QB365 on 08 Sep, 2022

QB365 provides a detailed and simple solution for every Possible Case Study Questions in Class 9th Maths Subject - Coordinate Geometry, CBSE. It will help Students to get more practice questions, Students can Practice these question papers in addition to score best marks.

QB365 - Question Bank Software

Coordinate geometry case study questions with answer key.

9th Standard CBSE

Final Semester - June 2015

Mathematics

(b) What are the coordinates of C and D respectively?

(c) What is the distance between B and D?

(d) What is the distance between A and C?

(e) What are the coordinates of the point of intersection of AC and BD?

(ii) What are the coordinates of Police Station?

(iii) Distance between school and police station:

(iv) What are the coordinates of Library?

(v) In which quadrant the point (-1, 4) lies?  

(b) What are the coordinates of A and B respectively?

(c) The coordinates of point O in the sketch -2 is

(d) The point on the y-axis ( in sketch 2) which is equidistant from the points B and C is 

(e) The point on the x-axis ( in sketch 2) which is equidistant from the points C and D is

(b) What are the coordinates of R, taking A as origin?

(c) Side of lawn is :

(d) Shape of lawn is :

(e) Area of lawn is :

(ii) What are the coordinates of position 'D'?

(iii) What are the coordinates of position 'H'?

(iv) In which quadrant, the point 'C' lie?

(v) Find the perpendicular distance of the point E from the y-axis.

*****************************************

Coordinate geometry case study questions with answer key answer keys.

(a) (iii) A(3, 5); B(7, 9) (b) (i) C(11, 5); D(7, 1) (c) (iii) 8 units (d) (iii) 8 units (e) (i) (7, 5)

(i) (b) (2, 3) (ii) (a) (2, -1) (iii) (a) 4 (iv) (d) (6, 2) (v) (b) II

(a) (ii) A(13, 10); B(19, 10) (b) (iv) A(19, 6); B(13, 6) (c) (ii) (16, 8) (d) (i) (0, 8) (e)  (ii) (16, 0)

(a) (iv) C(10, 6) (b) (iii) R(5, 6) (c) (ii)   \(\sqrt{34}\)  units PS 2 = AS 2 + AP 2 = 5 2 + 3 2 = 25 + 9 = 34 ⇒ PS =  \(\sqrt{34}\) (d) (iv) Rhombus (e) (i) 30 sq. units Area of rhombus =  \(1 / 2\)  x product of diagonals =  \(1 / 2\)  x 6 x 10  = 30 sq. units

(i) (d) (-4, 3)  (ii) (b) (-3, -2) (iii) (b) (8, 4.5) (iv) (d) IV (v) (b) 10 units

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Class 9 Maths Sample Papers, NCERT Solutions, Online Tests

Get CBSE class 9 Maths Sample Papers, NCERT Solutions, Notes and Important Questions as PDFs to download and access quality content for your exam preparation. 

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Cbse last year papers, user submitted papers, case study questions,   mock tests, number systems, polynomials, coordinate geometry, linear equations in two variables, introduction to euclids geometry, lines and angles, quadrilaterals, herons formula, surface areas and volumes.

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The subject of Maths holds a key position in any given curriculum. The idea behind the inclusion of Mathematics is to develop the learner's ability to think, analyze and articulate logically. The curriculum at the Secondary stage primarily aims at enhancing the capacity of students to employ Mathematics in solving day-to-day life problems and studying the subject as a separate discipline. It is expected that students should acquire the ability to solve problems using algebraic methods and apply the knowledge of simple trigonometry to solve problems of height and distance. CBSE Class 9 Mathematics module available on myCBSEguide provides sample question papers, chapter-wise test papers, quick revision notes, previous year question papers, HOTS, case study questions, videos, and online tests. 

CBSE Class 09 Mathematics Complete Course

The number of downloads of the  myCBSEguide app bears testimony to its authenticity. Our resources contain material for every step of preparation right from the latest syllabus to sample papers. You can access class 9 Maths chapter-wise textbook solutions, revision notes, test papers, and online tests from  myCBSEguide . You can also find  NCERT Exemplar Solutions for CBSE Class 09 Maths. With the release of official sample papers, students would be provided with class 9 sample papers for maths on our  Students' Dashboard . The Class 9 Maths curriculum gives the students a chance of carrying out experiments with numbers and forms of geometry, framing hypothesis, and verifying these with further observations from inherent parts of Mathematics learning at this stage. 

Class 09 Mathematics Syllabus 2023-24

The syllabus in the subject of Mathematics has undergone changes from time to time in accordance with the growth of the subject and the emerging needs of society. The CBSE has released the latest syllabus for the current session of 2023-24. A comparative study shows that not many changes have been done to the Class 9 Maths syllabus. The proposed curriculum includes the study of number system, algebra, geometry, trigonometry, mensuration, statistics, graphs and coordinate geometry, etc. The table below gives the name of the chapters along with the allocated weightage. Every student must know the latest syllabus before beginning their preparation so that they do not prepare something that has been struck down. This will be a waste of time and effort.

Maths Sample Papers for CBSE Class 09

As we are aware that CBSE has already released the sample papers for the forthcoming 2022-23 boards. Students now already have a blueprint of what the question paper will be like. Based on the format of the Class 09CBSE Maths Sample Question Paper, we have modeled 10 more sample papers which can be easily accessed on our student's dashboard . 

The Class 9 Sample Question Paper 2022-23  provided by myCBSEguide strictly abide by the CBSE class 9 Maths syllabus. It also follows the original format of the class 09 maths sample paper provided by the CBSE.

CBSE Class 09 Maths Revision Notes

Chapter-based revision notes with proper explanations are available on our dashboard. These notes can be very handy for students who are doing self-study or are studying independently. They provide a guiding light to clear chapter-related doubts of the students. As we know 

Our Revision Notes for Class 9 Mathematics are available in PDF which is for free download in the  myCBSEguide mobile app . This section has chapter-wise notes which are very helpful for quick preparation of the boards or even annual examinations of the school. Class 9 Mathematics Revision notes are also available for download on the  CBSEguide website .

CBSE Class 09 Maths Test Papers

Mathematics is all about practicing and it is always advisable to practice more to ace the subject. The secondary level is crucial for a student's life because it lays the foundation of their future career. Hence, the students must begin to prep right from stand 9. Those who aim to take up science/mathematics as their future subject must begin practicing seriously and with complete clarity. This is the time they must utilize to their fullest and practice as much as they can. Solving as many CBSE class 9 Maths test papers available on myCBSEguide will really help to achieve better results.

Our practice test papers for class 9 Maths are carefully curated by our able subject matter experts. Students can check their progress with the help of these test papers which cover the final syllabus. After taking each test, students can self-assess with the help of the solutions of the paper.

Class 09 Maths NCERT Solutions

We all know that CBSE prescribes NCERT textbooks only and most of the questions are asked from NCERT books. Especially in class 9 Maths, questions given in NCERT books are very important. You will have hundreds of questions for practice in NCERT books.  We recommend you practice all the questions given in NCERT books including the example questions. Once you are done, you should practice the previous year questions and at the end attempt full syllabus model question papers. You can get class NCERT Solutions for Class 9 Maths on myCBSEguide app and website for free. 

• Exercise 2.1
• Exercise 2.2
• Exercise 2.3
• Exercise 3.1
• Exercise 3.2
• Exercise 3.3
• Exercise 5.1
• Exercise 5.2
• Exercise 8.1
• Exercise 8.2

Constructions

• Exercise 11.1
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• Exercise 12.1
• Exercise 12.2

CBSE Class 09 Mathematics Case Study Questions

The CBSE curriculum is now focusing on promoting competency-based education after the introduction of the NEP 2020. Case study questions are considered to be competency-based questions. The case study is assumed to be one of the best methods to evaluate competencies. The competency-based case study questions available on myCBSEguide have been prepared by expert CBSE teachers you can check the sample questions  CBSE Class 9 Mathematics Case Study Questions  on this link,

We guarantee the quality of our questions which you will find much better than those available over the internet or any publisher books. Most of these books and sites have MCQs-based case-based questions for class 9 Maths that do not have a matching question type as given in the maths sample paper. Download the myCBSEguide App  to get class 9 Maths case study questions for 2023-24 based on the CBSE Maths sample papers.  

CBSE Class 9 Mathematics Case Study Questions

If you’re looking for a comprehensive and reliable study resource and case study questions for class 9 CBSE, myCBSEguide is the perfect door to enter. With over 10,000 study notes, solved sample papers and practice questions, it’s got everything you need to ace your exams. Plus, it’s updated regularly to …

NCERT Solutions for Class 9

NCERT textbook solutions for class 9 are now available in the myCBSEguide App for free. Students can download and access the latest NCERT book chapter-end questions and answers from the myCBSEguide App and student dashboard. We offer NCERT questions and solutions for class 9 Social Science, Science, Mathematics, English Language …

CBSE Class 9 Maths Syllabus 2022-23

CBSE Class 9 Mathematics Syllabus 2022-23 includes Number Systems, Algebra, Coordinate Geometry, Geometry, Mensuration, Statistics & Probability etc for the session 2022 – 2023. Here is the detailed CBSE class 9 Maths syllabus 2022-23. The myCBSEguide app not only provides you with the CBSE class 9 Mathematics model question papers …

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CBSE to Conduct Two Term Exams in 2021-22

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CBSE Class 9 Maths 30 Most Important Case Study Questions with Answers

Cbse class 9 maths 30 most important case study questions with answers download here free in pdf format..

CBSE Class 9 Maths exam 2023 will have a set of questions based on case studies in the form of MCQs. CBSE Class 9 Maths Question Bank on Case Studies given in this webpage can be very helpful in understanding the new format of questions.

Each question has five sub-questions, each followed by four options and one correct answer. Candidates can easily download these questions in PDF format and refer to them for exam preparation 2023.

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• ICSE Class 10 Time Table : ICSE 10 Date Sheet Released Check Now December 2, 2022

CBSE Case Study Questions for Class 9 Maths Surface Areas and Volumes Free PDF

Mere Bacchon, you must practice the CBSE Case Study Questions Class 9 Maths Surface Areas and Volumes  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 9 Maths Surface Areas and Volumes PDF

Checkout our case study questions for other chapters.

• Chapter 11 Constructions Case Study Questions
• Chapter 12 Heron’s Formula Case Study Questions
• Chapter 14 Statistics Case Study Questions
• Chapter 15 Probability 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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Case Study Questions for Class 9 Maths Chapter 12 Herons Formula

Case study questions for class 9 maths chapter 9 areas of parallelograms and triangles, case study questions for class 9 maths chapter 6 lines and angles, case study questions for class 9 maths chapter 7 triangles, case study questions for class 9 maths chapter 5 introduction to euclid’s geometry, case study and passage based questions for class 9 maths chapter 14 statistics, case study questions for class 9 maths chapter 1 real numbers, case study questions for class 9 maths chapter 4 linear equations in two variables, case study questions for class 9 maths chapter 3 coordinate geometry, case study questions for class 9 maths chapter 15 probability, case study questions for class 9 maths chapter 13 surface area and volume, case study questions for class 9 maths chapter 10 circles, case study questions for class 9 maths chapter 9 quadrilaterals, case study questions for class 9 maths chapter 2 polynomials.

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• Data Handling Class 7 Case Study Questions Maths Chapter 3

Last Updated on August 17, 2024 by XAM CONTENT

Hello students, we are providing case study questions for class 7 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 7 maths. In this article, you will find case study questions for CBSE Class 7 Maths Chapter 3 Data Handling. It is a part of Case Study Questions for CBSE Class 7 Maths Series.

Table of Contents

Case Study Questions on Data Handling

Q.1. In which games the number of existing active users is more than 1.5 million? (a) KC (b) RJ (c) CM (d) CR

Sol. Option (a) is correct.

Q. 2. It has been observed that $50 \%$ of the new RJ game users play online with friends? (a) 1.39 million (b) 4.975 million (c) 8.195 million (d) 9.95 million

Sol. Option (c) is correct. Explanation: ($50 \%$ of 1.99 million $=0.995$ million and $36 \%$ of 20 million $=7.2$ million $0.995+7.2=$ 8.195 million)

Q. 3. Mary played 10 HC matches. She scored 45, 36, 50, $27,36,52,50,43,50$ and 47 points in them. What is the most frequent score point? (a) 27 (b) 36 (c) 47 (d) 50

Sol. Option (d) is correct.

Q. 4. Are the mean and median of Mary’s scores equal? Justify your answer.

Sol. Mean score is 43.6 $$ \begin{aligned} 43.6= & (45+36+50+27+36 \\ & +52+50+43+50+47) \\ & \div 10 \text { median score is } 46 . \end{aligned} $$

Ascending order of scores

$$ \begin{aligned} & =(27,36,36,43,45,47,50,50,50,52) \\ (45+47) \div 2 & =46 \\ 46 & \neq 43.6 \end{aligned} $$

Fractions and Decimals Class 7 Case Study Questions Maths Chapter 2

Integers class 7 case study questions maths chapter 1, topics from which case study questions may be asked.

• Representative Values
• Arithmetic Mean

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

• Collection of information in numerical figures is called Data. The data obtained initially is called Raw-data. Arranging numerical figures of the data in ascending or descending order is called an array.
• The difference between highest and lowest value of observation in a set of data is called the Range.
• The number of times a particular observation occurs is called its frequency.
• Mean is the sum of all the values, divided by the total number of values.
• Median is the ‘middle value’ of a list when the data in the list is sorted in increasing or decreasing order.
• Mode is a value which occurs most frequently in a collection of data.
• A bargraph is a form of graphical representation of data. It shows quantity of data according to length of bars which are of inform width with equal spacing.

Different forms of data need different forms of representative or central value to describe them. The most common of them are arithmetic mean, mode and median.

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Frequently Asked Questions (FAQs) on Data Handling Case Study

Q1: what is data handling.

A1: Data handling refers to the process of collecting, organizing, representing, and interpreting data to make it meaningful and useful. It involves various methods and tools to analyze data and draw conclusions.

Q2: What is a bar graph, and how is it used in data handling?

A2: A bar graph is a visual representation of data using rectangular bars of equal width. The length of each bar corresponds to the value or frequency of the data. Bar graphs are used to compare different categories of data, making it easier to understand and interpret information.

Q3: How do you construct a bar graph?

A3: To construct a bar graph, follow these steps:Draw two perpendicular lines (axes), one horizontal (x-axis) and one vertical (y-axis). Label the x-axis with the categories of data and the y-axis with the frequency or value. Choose an appropriate scale for the y-axis. Draw bars for each category, with heights corresponding to their respective values. Ensure the bars are of equal width and are spaced evenly.

Q4: What is a histogram, and how is it different from a bar graph?

A4: A histogram is a type of bar graph that represents the frequency distribution of continuous data. Unlike a bar graph, which represents categorical data, a histogram’s bars are adjacent (without gaps) and represent intervals of data. The height of each bar indicates the frequency of data within each interval.

Q5: What is mean, and how is it calculated?

A5: The mean, or average, is a measure of central tendency that represents the sum of all data values divided by the number of data values.

Q6: What is median, and how is it determined?

A6: The median is the middle value of a data set when the values are arranged in ascending or descending order. If there is an odd number of data values, the median is the middle value. If there is an even number of data values, the median is the average of the two middle values.

Q7: What is mode, and how is it identified?

A7: The mode is the value that appears most frequently in a data set. A data set can have more than one mode if multiple values appear with the same highest frequency, and it can also have no mode if all values appear with the same frequency. For example, in the data set 2, 4, 4, 5, 7, the mode is 4.

Q8: What is the importance of data handling in everyday life?

A8: Data handling is important because it helps us make informed decisions based on collected data. Whether it’s understanding trends, comparing different options, or analyzing information, data handling provides a structured way to organize and interpret data in various fields like education, business, healthcare, and more.

Q9: Are there any online resources or tools available for practicing comparing quantities case study questions?

A9: 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.

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CBSE Case Study Questions Class 9 Maths Chapter 12 Heron’s Formula PDF Download

CBSE Case Study Questions Class 9 Maths Chapter 12  are very important to solve for your exam. Class 9 Maths Chapter 12 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving  case study-based   questions for Class 9 Maths Chapter 12  Heron’s Formula

Case Study Questions Class 9 Maths Chapter 12

Case Study 1: A group of students is learning about Heron’s Formula for finding the area of a triangle. They encountered the following scenario:

Rohan and Kavya came across a triangular field in their village. They made the following observations:

• The lengths of the three sides of the triangular field are 8 meters, 12 meters, and 15 meters.
• The perimeter of the triangular field is 35 meters.

Based on this information, the students were asked to apply Heron’s Formula to find the area of the triangular field. Let’s see if you can answer the questions correctly:

MCQ Questions:

Q1. The semiperimeter of the triangular field is: (a) 8 meters (b) 12 meters (c) 15 meters (d) 17.5 meters

Answer: (d) 17.5 meters

Q2. Using Heron’s Formula, the area of the triangular field is: (a) 24 square meters (b) 30 square meters (c) 36 square meters (d) 40 square meters

Answer: (b) 30 square meters

Q3. The type of triangle formed by the sides of the field is: (a) Equilateral (b) Isosceles (c) Scalene (d) Right-angled

Answer: (c) Scalene

Q4. The length of the altitude corresponding to the side of 15 meters is: (a) 2 meters (b) 4 meters (c) 6 meters (d) 8 meters

Answer: (c) 6 meters

Q5. The lengths of the altitudes corresponding to the sides of 8 meters and 12 meters are: (a) 4 meters and 6 meters (b) 6 meters and 8 meters (c) 8 meters and 10 meters (d) 10 meters and 12 meters

Answer: (a) 4 meters and 6 meters

Case Study 2: A group of students is studying Heron’s Formula for finding the area of a triangle. They encountered the following scenario:

Neha and Mohan went on a field trip to a riverbank. They noticed a triangular piece of land that they wanted to measure and calculate its area. They made the following observations:

• Neha measured the lengths of the three sides of the triangular piece of land as 7 meters, 9 meters, and 11 meters.
• Mohan measured the lengths of the three sides of the same triangular piece of land as 10 meters, 12 meters, and 15 meters.

Based on this information, the students were asked to apply Heron’s Formula to find the area of the triangular piece of land. Let’s see if you can answer the questions correctly:

Q1. Using Neha’s measurements, the semiperimeter of the triangular piece of land is: (a) 13 meters (b) 16 meters (c) 19 meters (d) 23 meters

Answer: (c) 19 meters

Q2. Using Neha’s measurements, the area of the triangular piece of land is: (a) 24 square meters (b) 26 square meters (c) 28 square meters (d) 30 square meters

Answer: (a) 24 square meters

Q3. Using Mohan’s measurements, the semiperimeter of the triangular piece of land is: (a) 16 meters (b) 18 meters (c) 21 meters (d) 25 meters

Answer: (c) 21 meters

Q4. Using Mohan’s measurements, the area of the triangular piece of land is: (a) 40 square meters (b) 42 square meters (c) 45 square meters (d) 48 square meters

Answer: (b) 42 square meters

Q5. The measurements taken by Neha represent a triangle that is: (a) Equilateral (b) Isosceles (c) Scalene (d) Right-angled

Hope the information shed above regarding Case Study and Passage Based Questions for Case Study Questions Class 9 Maths Chapter 12 Heron’s Formula with Answers Pdf free download has been useful to an extent. If you have any other queries about Case Study Questions Class 9 Maths Chapter 12 Heron’s Formula and Passage-Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible.

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Class 9 Maths Case Study Questions of Chapter 10 Circles PDF Download

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Case study Questions in Class 9 Mathematics Chapter 10  are very important to solve for your exam. Class 9 Maths Chapter 10 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving case study-based questions for Class 9 Maths Case Study Questions Chapter 10 Circles

Join our Telegram Channel, there you will get various e-books for CBSE 2024 Boards exams for Class 9th, 10th, 11th, and 12th.

These case study questions challenge students to apply their knowledge of quadrilaterals in practical scenarios, enhancing their problem-solving abilities. This article provides the Class 9 Maths Case Study Questions of Chapter 10 Circles, enabling students to practice and excel in their examinations.

Circles Case Study Questions With Answers

Here, we have provided case-based/passage-based questions for Class 9 Maths Chapter 10 Circles

Case Study/Passage-Based Questions

Case Study 2: Three friends Amit, Mayank, and Richa were playing with the ball by standing in a circle at A, B, and C points respectively. Richa throws a ball to Amit, Amit to Mayank, and Mayank to Richa. They all are equidistant from each other as shown in the figure.

Considering O as the centere of the circle, answer the following questions

Which type of ▲ABC is given in figure? (a) Right angled triangle (b) Equilateral triangle (c) Isosceles triangle (d) Scalene triangle

Answer: (b) Equilateral triangle

Measure of ∠ABC is (a) 45° (b) 60° (c) 30° (d) 90°

Answer: (b) 60°

If AB = 6 cm, then BC + CA is equal to (a) 12 cm (b) 14 cm (c) 15 cm (d) 18 cm

Answer: (a) 12 cm

Measure of ∠BOC is (a) 90° (b) 100° (c) 120° (d) 150°

Answer: (c) 120°

Value of ∠OBC + ∠OCB is (a) 30° (b) 45° (c) 90° (d) 60°

Answer: (d) 60°

Case Study 2: Rohan is a class 9th student. He did not attend school as his health is not fine for a few days. At home, he opens his Maths textbook and observes chapter circles. He was so much curious to know about the properties of circles. His father Mr. Raman, who is also a good Mathematician helps Rohan to understand all properties one by one. At last, he asks some questions to Rohan for quick revision. Help Rohan to answer the following questions.

A circle can circumscribe a (a) Rectangle (b) Trapezium (c) Triangle (d) All of these

Answer: (d) All of these

The perpendicular distance from the centre of the circle decreases when (a) the length of the chord increases (b) the length of the chord decreases (c) Radius of circle is decreased (d) Radius of circle is increased

Answer: (a) the length of the chord increases

The number of radii that can be drawn in a circle is (a) 10 (b) 100 (c) 1000 (d) infinite

Answer: (d) infinite

The distance from the centre of the circle to the longest chord is equal to (a) 22/7 units (b) 0 unit (c) 1 unit (d) 3 units

Answer: (b) 0 unit

Angle formed by the equal arcs on the circumference of the circle (a) are supplementary (b) are equal (c) are complimentary (d) None of these

Answer: (b) are equal

Hope the information shed above regarding Case Study and Passage Based Questions for Class 9 Mathematics Chapter 10 Circles with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 9 Maths Circles 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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Linear Inequalities Class 11 Notes CBSE Maths Chapter 6 (Free PDF Download)

Revision Notes for CBSE Class 11 Maths Chapter 6 (Linear Inequalities) - Free PDF Download

Class 11 Revision Notes For Linear Inequalities Of Chapter 6 are organized in an orderly manner which helps the students to get rid of confusion regarding the course content provided that CBSE keeps on updating the course every year. Notes of Class 11 revision notes Chapter 6 are inclusive of theory and formulas. The formulae list includes all important formulae that give the students an easy way to study and revise the chapter. Class 11 revision notes linear Inequalities offered by vedantu on this page in pdf format are sure to provide you with an effective preparation for your examinations.

Download CBSE Class 11 Maths Revision Notes 2024-25 PDF

Also, check CBSE Class 11 Maths revision notes for all chapters:

Linear Inequalities Chapter-Related Important Study Materials It is a curated compilation of relevant online resources that complement and expand upon the content covered in a specific chapter. Explore these links to access additional readings, explanatory videos, practice exercises, and other valuable materials that enhance your understanding of the chapter's subject matter.

Linear Inequalities Class 11 Notes Maths - Basic Subjective Questions

Section–A (1 Mark Questions)

1. Solve for real $ x: \frac{\left | x-2 \right |}{x-2}\geq 0$    

Ans. Since $\frac{|x-2|}{x-2} \geq 0$, for $x-2 \geq 0$, and

$$ \begin{aligned} & x-2 \neq 0 . \\ & \Rightarrow x \in(2, \infty) \end{aligned} $$

2. Solve for real x: -3x+17<-13 .

Ans. $$ \text {} \begin{aligned} & -3 x+17<-13 \\ & \Rightarrow-3 x<-30 \\ & \Rightarrow 3 x>30 \\ & \Rightarrow x>10 \\ & \Rightarrow x \in(10, \infty) \end{aligned} $$

3. Fill in the blanks with appropriate sign of inequality. If $x\geq -3$, then x+5……2. 

Ans. $x \geq-3$

$$ \begin{aligned} & \Rightarrow x+5 \geq-3+5 \\ & \Rightarrow x+5 \geq 2 . \end{aligned} $$

4. Fill in the blanks with appropriate sign of inequality. If p>0 and q<0, the (p+q).....p. 

Ans. Since, $p$ is positive and $q$ is negative, Therefore, $(p+q)$ is always smaller than $p$.

5. Fill in the blanks with appropriate sign of inequality. If $\frac{2}{x+2}>0$ , then x…..-2.

Ans. If $\frac{2}{x+2}>0$

$$\Rightarrow x>-2$$

Section–B (2 Marks Questions)

6. The length of a rectangle is three times the breadth. If the minimum perimeter of the rectangle is 160 cm, then find the possible breadth of rectangle.

Ans. Let $x$ be the breadth of rectangle Then, length of rectangle will be $3 x$ Therefore,

$$ \begin{aligned} \text { perimeter } & =2(\text { Length }+ \text { Breadth }) \\ & =2(3 x+x) \end{aligned} $$

Given, minimum perimeter $=160 \mathrm{~cm}$

$$ \begin{aligned} & \Rightarrow 2(3 x+x) \geq 160 \\ & \Rightarrow x \geq 20 \end{aligned} $$

Hence, breadth $\geq 20 \mathrm{~cm}$.

7. $C(x)=600+\frac{5}{2}x$ and $R(x)=4x$ are respectively, the cost and revenue function of a cassette company where x is the number of cassettes produced. Find the number of cassettes to be produced and sold so as to realize a profit. 

Ans. Profit $=P(x)=R(x)-C(x)$

Given: $P(x)>0$

$$ \begin{aligned} & \Rightarrow 4 x-600-\frac{5}{2} x>0 \\ & \Rightarrow \frac{3}{2} x-600>0 \\ & \Rightarrow \frac{3}{2} x-600>0 \\ & \Rightarrow \frac{3}{2} x>600 \Rightarrow x>400 \end{aligned} $$

The number of cassettes to be sold to earn some profit is greater than 400 .

8. Solve for x : $\frac{\left [ 2(x-1) \right ]}{5}\leq \frac{\left [ 3(2+x) \right ]}{7}$ .

Ans. Given: $\frac{[2(x-1)]}{5} \leq \frac{[3(2+x)]}{7}$

$$ \begin{aligned} & \Rightarrow \frac{(2 x-2)}{5} \leq \frac{(6+3 x)}{7} \\ & \Rightarrow 7(2 x-2) \leq 5(6+3 x) \\ & \Rightarrow 14 x-14 \leq 30+15 x \\ & \Rightarrow 14 x-15 x \leq 30+14 \\ & \Rightarrow-x \leq 44 \Rightarrow x \geq-44 \end{aligned} $$

$\therefore$ The solution of the given inequality is $[-44, \infty)$.

9. Solve the inequality: $\frac{x}{5}<\frac{(3 x-2)}{4}-\frac{(5 x-3)}{5}$.

Ans. $\frac{x}{5}<\frac{(3 x-2)}{4}-\frac{(5 x-3)}{5}$

$\Rightarrow \frac{x}{5}<\frac{(5(3 x-2)-4(5 x-3))}{4 \times 5}$

$\Rightarrow \frac{x}{5}<\frac{(15 x-10-20 x+12)}{20}$

$\Rightarrow \frac{x}{5}<\frac{(2-5 x)}{20}$

$\Rightarrow 4 x<2-5 x$

$\Rightarrow 9 x<2 \Rightarrow x<\frac{2}{9}$

$\therefore$ The solution of the given inequality is

$$\left(-\infty, \frac{2}{9}\right) \text {. }$$

10. The marks obtained by a student of Class XI in first and second terminal examination are 62 and 48, respectively. Find the minimum marks he should get in the annual examination to have an average of at least 60 marks.

Ans. Let $x$ be the marks obtained by student in the annual examination. Then,

$$\frac{62+48+x}{3} \geq 60 \text { or } 110+x \geq 180$$ or $x \geq 70$

Thus, the student must obtain a minimum of 70 marks to get an average of at least 60 marks.

11. A company manufactures cassettes, its cost and revenue functions are C(x)=26000+30x and R(x)=43x, respectively, where x is the number of cassettes produced and sold in week. How many cassettes must sold by the company to realize some profit.

Ans. Given that: Cost function, $C(x)=26000+30 x$

And revenue function $R(x)=43 x$

Now for profit

$$ \begin{aligned} & P(x)=R(x)-C(x)>0 \\ & \Rightarrow R(x)>C(x) \\ & \Rightarrow 43 x>26000+30 x \\ & \Rightarrow 43 x-30 x>26000 \\ & \Rightarrow 13 x>26000 \Rightarrow x>2000 \end{aligned} $$

Hence, the number of cassettes to be manufactured for some profit must be more than 2000 .

12. Solve the following system of equations in R 2x-7>5-x, 11-5x$\leq$1.

Ans. Given, 

$\Rightarrow 2x+x>5+7$

$\Rightarrow 3x>12\Rightarrow x>4$

$\therefore x\epsilon (4,\infty )$.....(1)

And 11-5x$\leq$ 1

$\Rightarrow -5x\leq 1-11$

$\Rightarrow -5x\leq - 10\Rightarrow x\geq 2$

$\therefore x\epsilon [2,\infty )$

From (1) and (2) we get $x\epsilon (4,\infty )$ 

PDF Summary - Class 11 Maths Linear Inequalities Notes (Chapter 6)

An inequality is a relationship that exists between two values that aren't equal.

For example, \[\text{x  >  9}\]. Here there is a relation between \[\text{x}\] & \[\text{9}\].

Any two algebraic expressions or real numbers related by symbol ‘\[\text{ < }\]’, ‘\[\text{ > }\]’, ‘\[\le \]’ or ‘\[\ge \]’ form inequality.

Inequalities can be used to solve problems in science, mathematics, statistics, economics, optimization problems, psychology, and other fields.

Example of Inequality in Daily Life: 

Rina and Samira have \[\text{Rs}\text{. 5,000}\] & wants to buy t-shirts and shoes for trekking. The cost price of t-shirt and shoes is \[\text{Rs}\text{. 250}\] and \[\text{Rs}\text{. 550}\] respectively. We can write the above statement mathematically using inequalities, as follows; 

Let the number of t-shirt they can buy be \[\text{x}\] & number of shoes be \[\text{y}\]. 

Then, the total amount spent by them is

\[\text{250x + 550y}\le 50\text{00}\]

Here, the total amount is upto  \[\text{Rs}\text{. 5,000}\].

The above given statement consists of two statements as,

\[\text{250x + 550y} < 50\text{00}\] which is an inequality and

\[\text{250x + 550y}=50\text{00}\] is an equation

The notation \[\text{a  <  b}\] means, \[\text{a}\] is less than \[\text{b}\].

The notation \[\text{a  >  b}\] means, \[\text{a}\] is greater than \[\text{b}\].

The notation \[\text{a }\ne \text{ b}\] means, \[\text{a}\] is not equal to \[\text{b}\].

The notation \[\text{a }\le \text{ b}\] means, \[\text{a}\] is less than or equal to \[\text{b}\].

The notation \[\text{a }\ge \text{ b}\] means, \[\text{a}\] is greater than or equal to \[\text{b}\].

Types of Inequalities: 

Numerical Inequalities: 

Relationship between numbers. 

For example, \[\text{8  <  19}\]

Literal or Variable Inequalities: 

Relationship between variables or between a variable and number. 

Example, \[\text{x  <  19}\]

Double Inequalities: 

Relationship from two side. 

For example, \[\text{19  <  x  <  25}\]

Strict Inequalities: 

An inequality that employs symbols  \[\text{ < }\] or \[\text{ > }\]

The symbols \[\le \] and  \[\ge \] are not used.

For example, \[\text{y  <  4}\]; \[\text{1 <  4}\]

Slack Inequalities. 

An inequality that employs symbols  \[\le \] or \[\ge \].

Example, \[\text{y }\le \text{ 7}\]

Linear Inequalities in One Variable: 

A one-variable inequality involving a linear function.

Example, \[\text{y  <  4}\]

Linear Inequalities in Two Variables: 

An inequality involving a two-variable linear function.

Example, \[\text{5x+ 7y  >  4}\]

Quadratic Inequalities: 

An inequality which employs a quadratic function.

Example, \[\text{7}{{\text{x}}^{2}}+3x\le \text{ 4}\] 

Solution for linear inequality in one variable:

Solution & solution set:.

Solution: 

Values of \[x\], which make inequality true statement. 

Example - \[5\] is a solution for \[x < 10\]

Solution Set: 

The set of values of x is known as its solution set.

Example - \[\left\{ 1,2,3,4 \right\}\] is solution set for \[x < 5\] where \[x\] is natural Number.

Rules of Inequality:

Both sides of an inequality can have equal numbers added to (or taken from) them without changing the sign of the inequality. 

For example, \[x < 5\] is same as \[x+2 < 5+2\]

Both sides of an inequality can be multiplied (or divided) by the same positive number without affecting the sign of inequality.

For example, \[x-y < 3\] is same as \[\left( x-y \right)\times 2 < 3\times 2\]

However, the sign of inequality is flipped or reversed when both sides are multiplied or divided by a negative value.

For example, \[x+y < 6\] is same as \[\left( x+y \right)\times \left( -2 \right) > 6\times \left( -2 \right)\]

Question: 

Solve \[30x < 160\] when

\[x\] is a natural number,

\[x\] is an integer,

\[x\] is real number

On dividing the inequality by \[30\]according to rule \[2\], we get

\[\dfrac{30x}{30} < \dfrac{160}{30}\] or

\[x < \dfrac{16}{3}\]

Case \[1\]: If \[x\] is a natural number, then the solution set is  \[\left\{ 1,2,3,4,5 \right\}\].

Case \[2\]: If \[x\] is an integer, then the solution set is \[\left\{ .....-4,-3,-2,-1,0,1,2,3,4,5 \right\}\].

Case \[3\]: If \[x\] is a real number, then the solution set is  \[\left( -\infty ,\dfrac{16}{3} \right)\]. 

By representing the case \[3\] solution on a number line, we get

Solve \[\mathbf{7x+2\le 5x+8}\]. Show the graph of the solutions on the number line.

By subtracting \[2\] from both side, we get \[7x\le 5x+6\]

By subtracting \[5x\] from both side, we get \[2x\le 6\]

On dividing \[2\] both side, we get \[x\le 3\]

We can represent this in the Number line below.

Graphical Solution of Linear Inequalities in \[2\] variables:

The Cartesian plane is divided into two equal sections by a line.

Each component is referred to as a half plane. 

A non-vertical line divides the plane into lower and upper half planes, while a vertical line divides it into left and right half planes.

In the Cartesian plane, a point will either lie on a line or in one of the half planes. 

The solution zone is the area that contains all of the solutions to an inequality.

To find the half plane represented by an inequality, simply choose any point \[\left( \text{a, b} \right)\] (not online) and see if it meets the inequality. 

If it does, the inequality represents the half plane and shades the region that contains the point; if it does not, the inequality represents the half plane that does not contain the point. 

For convenience, the point \[\left( 0,0 \right)\] is preferred.

Example: \[\text{x + 2y} > 9\]

Steps for find solution region for a linear inequality in \[2\] variables 

Substitute an equal sign for the inequality sign and plot the graph. Plot a graph for \[\text{x + 2y}=9\]. 

Red line represent \[\text{x + 2y}=9\].

Take any point on the graph. Here we took \[\left( 8,1 \right)\] and check if satisfies the linear inequality. 

In this case \[\text{x + 2y} > 9\]. 

If yes, then the region where this assumed point lies is the solution region.

When solving a Slack inequality \[\left( \ge \text{or}\le  \right)\] use solid line, since the points on the line are part of the solution set.

Use dotted line in the case of Strict inequality \[\left(  > \text{or }  < \right)\], since points on the line are not included in solution set. 

In the case of several linear inequalities, the solution region is the area that is shared by all of the inequalities.

Solve the following system of inequalities graphically \[\text{5x + 4y}\le 40\], \[\text{x} > 2\] and \[\text{y}\ge 3\]. 

Step \[1\]: Draw lines for \[\text{5x + 4y}=40\], \[\text{x}=2\] and \[\text{y}=3\].

Step \[2\]: For each of these linear inequalities, find the solution zone.

Step \[3\]: Locate a common area. The solution region is a common region. 

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Revision Notes for Class 11 Maths Chapter 6 Linear Inequalities

Mathematically, a linear inequality refers to inequality that includes a linear function. That being said, an inequality is called linear when each variable takes place in 1 st degree only and there is no term including the product of the variables. A linear inequality consists of one of the symbols of inequality ie: [> is greater than], [< is less than] or [≤ is less than or equal to]. There are certain types of linear Inequalities which are as follows:-

Linear inequalities in One Variable

An inequality which takes into account a linear function in one variable is called a linear inequality in one variable. For E.g. y < 5;

Linear inequalities in two variables

An inequality which typically includes a linear function in two variables is called a linear inequality in two variables. For E.g. 2x + 3y < 5

Quadratic inequalities

An inequality which takes into account a quadratic function is called a linear inequality in quadratic. E.g. y 3 + 3y ≤ 5

Note: You will learn more important elements about linear inequalities in Class 11 revision notes Maths Ch 6 designed by Vedantu experts. You will also learn Solutions and Graphical Solution of Linear Inequalities in your Class 11 Maths revision notes Chapter 6.

Solution of System of Linear Inequalities In Maths Class 11 Linear Inequalities Notes

Both sides of an inequality can be added to (or subtracted from) the equal numbers. The same positive number can be multiplied (or divided) on both sides of an inequality. However, when both sides are divided or multiplied by a negative number, then we see a reverse in inequality.

Solution of an Inequality

The value of x, which prompts an inequality to be a true statement, is known as solutions of the inequality.

In order to represent x > a (or x < a) on a number line, we need to put a circle on the number and outline it dark to the right (or left) of the number a.

To represent x ≥ a or x ≤ a on a number line, we have to put a dark circle on the number and outline it dark the line to the right (or left) of the number x.

If an inequality contains the symbol of ≤ or ≥, then the points on the line are also involved in the solutions of the inequality. Moreover, the graph of the inequality lies right (above) or left (below) the graph of the equality which is depicted by a dark line that satiates an arbitrary point in that part.

If an inequality consists of a < or > symbol, then the points on the line are not involved in the solutions of the inequality. In this case, the graph of the inequality lies to the left (below) or right (above) of the graph of the simultaneous equality denoted by a dotted line that satiates an arbitrary point in that part.

In order to eliminate the denominator when we are not known about the sign of the value of the denominator may be +ve or -ve:, then we have to multiply by the square of the denominator. Remember that the Square of the denominator is always positive. More so, the sign of inequality does not change, when we multiply an equation by a positive number.

To gain a brief information of all the topics covered in Chapter 6 Linear Inequalities, download Class 11 Revision Notes For Linear Inequalities of Chapter 6 now through the link provided. 

FAQs on Linear Inequalities Class 11 Notes CBSE Maths Chapter 6 (Free PDF Download)

1. How will I get benefited with the revision notes class 11 maths chapter 6?

Linear Inequalities Class 11 Maths Notes designed by Vedantu experts are CBSE quick revision notes which are very helpful to not just revise a particular chapter but the entire syllabus during exam days. The revision notes cover all important concepts and formulas provided in the chapter. Even if you seek to have a general overview of a chapter, quick revision notes will make you have a quick look through in a fraction of time. 

2. How do we find A Plane Containing Origin?

If the origin satiates the inequality of the half of the half plane, then the half plane consists of the origin. This inequality depicts the half plane consisting of an origin. On the other hand, if the origin does not satiate the inequality of the half of the half plane, then the half plane does not consist of the origin. This inequality denotes the half plane, which does not consist of the origin.

3. What is linear inequality according to Class 11 Maths Chapter 6?

According to Chapter 6 of Class 11 Maths , linear inequality is defined as:

The relation which is formed between two indifferent values is called an inequality.

Take, for example, t<4. In this, the relationship is between two values, t and 4 which are different.

The inequality relation between two real numbers is formed using comparison operators like <,>, etc.

In the field of mathematics, optimization problems, economics, science, psychology, etc the study of inequality is very useful.

4. Write the rules of inequality given in Chapter 6 of Class 11 Maths.

The rules of inequality mentioned in Chapter 6 of Class 11 Maths are as follows:

You can add or subtract the same number from both sides without affecting the sign of inequality.

Example –Z > 8

                 Z + 100 > 8 + 100

                 Z –3 > 8 – 1

Without affecting the sign of inequality, you can multiply or divide the same positive numbers on both sides.

Example –X < 6

                 X*2 <6*2

                 X ÷ 4 < 6 ÷ 4

The sign of inequality gets changed when both sides are divided or multiplied with the same negative number.

Example –W > 9

               S * (-300) < 4 * (-300) 

5. What are the various forms of inequality?

(a) Numerical Inequality – It is the relation between numbers.

Example- 5 > 4

(b) Double Inequality – One single value is related to the other two values. 

Example- 2 < y <4

(c) Variable Inequality – The relationship between numbers and variables. 

Examples- b > 1

(d) Slack Inequality – In this inequality relationship, more than equal to or less than equal to operators are used.

(e) Strict Inequality – This type of inequality uses the symbols of < or >.

Example- 6 >7 or y < 8

6. Explain quadratic inequality and linear inequality in one and two variables. Also, describe the terms solution set and solution.

Quadratic Inequality – It is the inequality that consists of a quadratic equation.

Linear Inequality in One Variable – The inequality which includes linear equations in one variable. Example- n > 5

Linear Inequality in Two Variables – This inequality has a linear equation in two variables. Example- y + z < 9

Solution Set – It is defined as the set of values for x which satisfies the inequality. Example- (6, 4, 2) is the solution set for x in inequality: x < 8

Solutions – These are values of x to make inequality a true statement. Example- for b > 5, 2 is a solution.

7. How should I prepare Chapter 6 for the Class 11 Maths examination?

Chapter 6 of Class 11 Maths is one of the easiest and scoring chapters. Students can prepare this chapter easily to score well in the Class 11 Maths examination. They can study from the NCERT book to understand the concepts or topics. By solving the exercises and examples, students can comprehend the chapter in a better way. Also, they should practice sample papers and previous years question papers to know about the type of questions asked in the exam.

If you want to understand these concepts more accurately then go through the given link CBSE Class 11 Chapter 6 . This link will redirect you to the official website of Vedantu where you can access the content related to Chapter 10 Straight lines for free. Additionally, you can also download its PDF if you want to study offline. 

CBSE Study Materials for Class 11