# NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities (Ex 6.2) Exercise 6.2

The creation of Boards of Secondary Education across the country was carried out by the Calcutta University Commission. The original board of this kind was the U. P. Board of High School and Intermediate Education. But eventually the Board was unable to perform this extraterritorial role. The United Provinces government asked that applicants from regions outside the United Provinces not be permitted to sit for the Board’s test after 1927-1928 because it was felt that the United Provinces Board’s authority was too burdensome to maintain an efficient administration.

The Rajputana, Central India, and Gwalior princely realms were presented with two choices for their governance. A separate Board for each of the affected locations was an alternative to a single Board overseeing all the affected areas. The central board offered numerous advantages. Therefore, it was decided that a joint board should be established for all the territories. That is how the origin of the Central Board of Secondary Education, or CBSE, happened.

The NCERT syllabus is required for all schools that are affiliated to the CBSE. The NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 were developed with consideration for the NCERT curriculum.

Students can utilise the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 to help them with their preparation for the JEE Mains, BITSAT, VITEEE, and other undergraduate engineering admissions exams along with their Class 11 examinations. The students can appear for these exams once they are done with their Class 12 board examinations.

NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 are developed by the subject experts at the Extramarks website to aid in clear and accurate knowledge of the chapters. These NCERT Solutions Class 11 Maths Chapter 6 Exercise 6.2 provide comprehensive, step-by-step solutions to every question that appears in the NCERT textbook.

In 1969, a self-governing body known as the National Council of Educational Research and Training (NCERT) was established. It was established by the Indian government to aid and counsel the national and state governments on policies and initiatives aimed at boosting educational standards. The Extramarks website offers solutions to the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 these are answers to the book’s questions. The main goals of NCERT and the divisions that make up the organisation are to conduct, promote, and coordinate research in fields related to school education; to produce and publish model textbooks, supplemental materials, newsletters, journals, and educational kits; among other things, to provide these materials to the students of schools that follow the NCERT format.

NCERT books include practise questions at the end of each chapter for Class 11 students as well as students in other classes. The subjects covered in the preceding chapter’s form the basis for these questions. The answers to all of these questions from the NCERT books are accessible on Extramarks website as part of the NCERT Solutions.

The solutions are available for students to use in exam preparation, class test review, and other academic endeavours. These solutions include the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 .

The questions related to mathematical calculations are numerous and grouped into different exercises in subjects like Mathematics. In Mathematics, answering problems is just as crucial as understanding the theory. For the students to comprehend and practise applying the theory, each chapter has a number of exercises with various types of questions. These questions are based on the theory that’s taught in the previous chapter.

The NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 contain the answers to Exercise 6.2 Class 11 Mathematics. When doing their homework, students can refer to the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 and make the process quick and easy for themselves.

The fact that Mathematics requires a lot of practise is why many teachers like to assign some of the questions from each exercise as homework so that students can study independently and put their skills to use.

In this regard, the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 can be of great use. Instead of taking help from fellow students, the students can make use of the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 to complete their homework.

The significance of mastering each chapter’s conceptual basis must be made clear to the students. Without a firm grasp of the fundamentals of each chapter, students may struggle to finish their homework assignments, show up for tests with confidence, and take their final exam stress-free. When students use the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 , they have the chance to go through the expert-prepared solution in a detailed fashion. This can aid students in comprehending the proper methodology for answering questions and arriving at the correct answers.

Students have a higher chance of succeeding in the exams if they use the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 and the solutions to the other exercises in all the chapters of Class 11 Mathematics to try to comprehend the step-by-step solutions. The specialists at Extramarks have written the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 and other similar solutions with the needs of students in mind. Therefore, they are student-friendly.

The solutions provided by Extramarks’ mathematics experts, such as the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2, are only one set of solutions.Any of these solutions, including the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 , are accessible to all students through the Extramarks website and are very simple to use.

Students may easily access the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 and other useful resources by going to the Extramarks website. Other tools, in addition to the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2, are available on the Extramarks website for students to use.All these tools are prepared by Mathematics experts at Extramarks.

## NCERT Solutions for Class 11 Maths Chapter 6 Linear Inequalities (Ex 6.2) Exercise 6.2

The NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2, as well as the solutions to all of the other exercises in Class 11 Mathematics, can be one of the most effective ways for students to prepare for their exams.The students should not have a deadline for practising with the help of these solutions as many times as possible before their final examinations. The more time a student spends practising Mathematics solutions, the higher their chances are of understanding the topic thoroughly. Therefore, the students are advised to make maximum use of the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 and other similar resources that are easily available on the Extramarks website. The NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 and other tools can be accessed by the students by simply visiting the Extramarks website. The NCERT Solutions for Class 11 Maths, Chapter 6, Exercise 6.2 is an excellent resource that students should make full use of.

### Access NCERT Solutions for Class 11 Maths Chapter 6 – Linear Inequalities

Students are urged to begin focusing on their comprehensive, well-rounded education at a young age if they want to score well in their higher secondary studies. The specialists at Extramarks are aware that students need a solid foundation in the more basic ideas covered in lower-level classes in order to understand the more complicated subjects covered in higher education. The professionals at Extramarks have NCERT Solutions for the following classes, in addition to the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 .While keeping all of this in mind, Extramarks has NCERT Solutions for all the classes –

NCERT Solutions Class 12

NCERT Solutions Class 11

NCERT Solutions Class 10

NCERT Solutions Class 9

NCERT Solutions Class 8

NCERT Solutions Class 7

NCERT Solutions Class 6

NCERT Solutions Class 5

NCERT Solutions Class 4

NCERT Solutions Class 3

NCERT Solutions Class 2

NCERT Solutions Class 1

Many students find mathematics to be overwhelming, but if they are thorough with the fundamentals from the start, it can be a delightful subject. The NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 can aid students in understanding chapter 12’s fundamental ideas, in particular the ideas that are presented in the problems in Linear Inequalities Exercise 6.2 . Each subject has a subject specialist designated by Extramarks who is in charge of developing student-friendly tools that might lessen the stress of students studying for exams. Students can find other tools that can be useful, such as extra problems and previous years’ examinations, in addition to resources like the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 .

The NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 is a very useful tool for practising. Practice is the key to success in subjects like Mathematics. On the Extramarks website, students can easily acquire the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 .

Students can also get assistance with their homework from the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 . For students to fully grasp what they have learned in the classroom, homework is crucial. Some students might not require a lot of self-study, depending on their academic abilities. They can learn plenty in the classroom. Whereas some kids feel the need to spend a lot of time on independent study in order to score effectively. An aid for practising self-study is the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 . Everyone, regardless of the type of student, should revise when it comes to disciplines that involve formulae and equations, such as Mathematics, Physics, etc.

For revision, the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 can be extremely helpful. According to the CBSE syllabus, linear inequalities and related topics are covered in Class 11 Mathematics Chapter 6. Students can learn and understand these particular topics in preparation for their exams by using the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 . The NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 is just one of many resources available to help students understand the material in Chapter 6 of Class 11 Mathematics.

The usage of the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 and other similar solutions is not restricted to school education alone, but also for exams that happen for college admissions or higher studies. Students’ chances of succeeding in these crucial tests increase the more they practise using resources like the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 . Unlike other classes, Class 11 students must continue to pay attention after the final exams are over, since the board exams they take following the Class 11 exams are very important too.

The answers to the questions in the second exercise of this chapter can be found in the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 . There are more options when it comes to useful tools; than the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 . On the Extramarks website, students can also get the answers to every other exercise of Chapter 6. The answers to these questions may be found in NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 and the solutions to other exercises of Chapter 6. In addition, Class 11 students are instructed on a number of crucial topics related to linear identities. A few of those topics are –

- Introduction
- Inequalities
- Algebraic Solutions for Linear Inequalities in One Variable and its Graphical Representation
- Graphical Solution of Linear Inequalities in Two Variables

Each chapter is broken down into a variety of activities in the NCERT Mathematics books. The NCERT Solutions , which are offered on the Extramarks website, are similarly organised according to the same structure as the NCERT books. Facilitating the students’ ability to refer to these solutions. For instance, the answers to the problems from Exercise 6.2 of Chapter 6’s Mathematics Class 11 are in the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 .

In the period leading up to an exam, there isn’t a lot of time available to students. Finding a specific solution can be difficult if all the solutions to the problems from the NCERT books are compiled and offered in one document. Therefore, this method of division is very helpful for the students. The NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 is a part of all such solutions.

Along with the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 , other resources on the Extramarks website have also been created by specialists in Mathematics. The accessibility and usability of the solutions for the students are also taken into consideration when developing them. Although the majority of students are extremely tech-savvy,it is still crucial that the material be made accessible in a way that is very user-friendly. In order to prevent students from wasting valuable time hunting for information when they may be studying and improving their subject-matter knowledge instead. Along with all the solutions for Class 11 Mathematics, the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 are created by specialists keeping these points in mind.

The NCERT books follow a specific structure; hence, it is essential that students schedule their practise and revision in a similar fashion. Based on this design, the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 are also created. Planning the preparation in line with the NCERT structure and curriculum is crucial, since it may guarantee that the students understand all that was taught in the previous exercises completely and clearly before they move forward.

It’s imperative to understand the subject-matter of the previous chapter before going on to the following activity. Be it equations, formulas, or just anything pertaining to the themes. As NCERT Solutions For Class 11 Maths Chapter 6 Exercise 6.2 it facilitates progress that is effective. The NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 can help ensure this.

### Class 11 Maths Chapter 6- Linear Inequalities

Students are encouraged to practise and develop the very important skill of time management. All things considered, students who have effective time management techniques are more effective in their self study sessions and are more likely to do well on test day. The NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 and all other similar solutions are available on Extramarks, allowing students to make the most of their study time. The students can maintain their composure and confidence in their preparation by using time management. Before showing up for their final tests, the students are urged to master this additional crucial skill to help them perform better. Making use of the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 is advised to achieve this. The NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 can be used to assist students in making the most of the little time they have before final examinations. The likelihood that students will remember what they practised and learned increases if they can maintain their composure in pressure-filled situations like exams. This may enable these students to employ their acquired problem-solving techniques and strategies more effectively when needed.

The students can use the helpful resources created by Mathematics professionals and made available on Extramarks. If they want to schedule their preparation in an efficient manner. For example, the tools like the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2

### Introduction to Linear Inequalities

For every new topic that is covered in the Class 11 Mathematics NCERT books, start the chapter with an introduction to that topic. Some students might not consider this part of the chapter as important as its theory. There is a common misconception that mathematics does not require theory when it comes to preparation for examinations. The students are advised not to go along with this misconception. The theory in mathematics is exactly what forms the basis for the mathematical questions that the students are expected to answer in their examinations.From an examination standpoint, it is critical to thoroughly read the chapter’s introduction as well as the other theoretical sections of each chapter. The students can also take help from the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 to prepare for the examinations more effectively.

### Examples of Inequality in Daily Life H3 – Notations

Many students may find the subject of Mathematics to be intermediate, but if they look at it from the perspective of understanding daily life scenarios, it can be very interesting to study and understand. Our advice to the students is to go throughthe examples that are given in the chapter itself and look up other examples as well for each topic that is related to daily life scenarios. When the students understand the use of the formulas and equations of a particular chapter in everyday life, that chapter becomes easier to understand and more interesting to study.One of the many topics related to everyday life is linear inequalities.Speed limits on the roads, minimum payments on credit card bills, the number of text messages that can be sent each month from the cell phone of an individual, and the amount of time it will take a student to get from home to school. All of these can be represented as Mathematical inequalities.

### Types of Linear Inequalities

The theory part of Mathematics is equally important to the formulas and equations, as well as the Mathematical problems of the subject. The NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 other solutions to the Mathematical problems with there can be questions that can be asked from the theory part of the chapter as well. The questions that are formed based on Mathematical equations etc, can have higher weightage assigned to them. It is important to remember that even though questions that may be formed from the theoretical part can have one line carrying one mark answers, these questions are of great importance apart from just from the examination point of view.

It’s the theory that forms the base and helps the students understand each topic in depth. This is what enables the students to solve the Mathematical problems based on the theory. The NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 and the solutions to all the other questions can help students practice putting theory to use.

The NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 cannot be understood clearly by the students if they do not have a thorough understanding or knowledge of the theory that makes up the majority of the chapter.It is hence advised to make use of the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 for better preparation, but also keep in mind to have an in-depth knowledge of the theory of the chapter.

### Solutions for a Linear Inequality in One Variable Solution and Solution Set

The theory for each chapter is divided again into subtopics. The NCERT books follow this format in order to make the whole theory part of the subject easily understandable for the students of Class 11. The students are advised to be thorough with one topic before moving on to the next one. This can ensure there is minimum confusion when it comes to the problem-solving part. There are questions given for each topic in between the chapters as well as at the end of the chapters. The solutions to all those questions in the NCERT books are available on the website.

The NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 other solutions to only the second exercise of Chapter 6. The solutions to all the other exercises of Chapter 6 are also available on the website.

### Rules for Inequality

One of the many subtopics that are covered in Chapter 6 which talks about linear inequalities, is the rules of true inequality. This topic can be the basis for a number of questions.The answers to all such questions can be found on the website. NCERT Solutions for Class 11 Maths, Chapter 6, Exercise 6.2 is one of them.The questions that are formed from the different subtopics of Chapter 6 all have their solutions on the NCERT solutions part of the website. These solutions, including the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 are all prepared by experts who are thorough with the topics of Class 11 Mathematics.

The students are advised to make the most of these resourceful tools, like the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 to help them practise and excel in the Class 11 Mathematics examinations.

### Examples for Linear Inequalities in One Variable

Many real-world problems can be resolved by turning them into Mathematical equations, but other difficulties, such as those where the total height of your family is under 180 cm or where the maximum number of tables or chairs that can fit in an auditorium is 120, cannot be transformed into equations. Inequalities are statements that use the signs ” ‘>’ (greater than), ” (less than or equal), and (greater than or equal), ” (less than). The limitations are created using the inequality principle. Students can comprehend questions based on inequalities in one variable and two variables in the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 which is based on Linear Inequalities.

The NCERT Solutions for Class 11 Maths, Chapter 6, Exercise 6.2, can be extremely beneficial to students.The NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 are not only useful for exam preparation, but also for completing homework assignments based on Exercise 6.2 questions.

### Graphical Solutions of Linear Inequalities in 2 Variables

Many topics that are covered in mathematics have significance in everyday life. This makes the topic interesting and relatable for the students. With the help of the right tools, the students can master these topics. On the Extramarks website, the students can find examples that are related to everyday life based on such topics. These examples can help the students gain confidence in the subject-matter. When this approach is applied in preparing for the Mathematics examinations, the topic appears to be less intimidating and more interesting to the students. The students can take further help from the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 and the solutions to other such topics that are available on the Extramarks website to master the subject even more.

### Examples for Solving Linear Inequalities With Two Variables Using a Graphical Representation

Linear inequalities is a chapter that includes mathematical graphs as part of problem-solving tools. Many students may find graphs to be challenging, but with the help of the right tools like the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 they can acquire the skill to use them to their benefit.

The students are advised to remember that all of these tools make the chapter and the topic interesting, and looking at it that way can help them not get intimidated but instead master these tools.

The NCERT Solutions for Class 11 Maths, Chapter 6, Exercise 6.2, use graphical representations in each question, and students can look at the solutions and try to understand the graphical representations in depth in order to perform better in questions involving these.

### Exercises

There is a reason why the topics in Mathematics are divided into different exercises in the NCERT books. Every topic considered in mathematics is observed in nature, and thus the questions that can be formed from that topic can differ significantly from one another.To avoid getting the students confused between different equations and formulas that can be used to solve a question from the same topic, the topic is divided into different exercises. The NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 other solutions to only the second exercise of Chapter 6 Class 11 Mathematics.

The students can find the solutions to every exercise, not just for Chapter 6 Class 11 Mathematics, but for all the other chapters as well, on the Extramarks website.

The solutions that are available on the Extramarks website are also divided in a similar pattern by bifurcating the topic into different exercises. This helps the students follow the same flow that is followed in their classrooms. To avoid any confusion, the students should use the solutions, like the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 in the order that they are given.

With the help of the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 and other similar resources available for Chapter 6 of Class 11 Mathematics the students can revise the questions that are there in the NCERT books. The students can also use the solutions when they are preparing for their class tests or if they are required to make any assignments based on Chapter 6. The NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 are not the only useful resource available on the Extramarks website; there are other resources as well, such as important questions from this topic, questions based on this topic that have been asked in previous years, the Class 11 Mathematics syllabus, etc. About Extramarks

In today’s world, internet access and availability are very convenient and easily accessible to everyone.This can be a great advantage for the students preparing for their examinations, whether in class or in the morning, to complete their homework with the help of some externalStudents nowadays are very technologically advanced and can easily access various educational websites available on the internet.ernet. One major advantage of this situation is the abundance of educational websites available on the internet.

There is no formula for the students to ensure that the information provided on the internet is correct. So the students are advised to depend on a reliable source of information. The students can keep in mind a few points when doing so. The website that they decide to depend on for their preparations should be in sync with the curriculum and the guidelines that are issued by the CBSE and the NCERT.

Extramarks is one such website on which students can rely with confidence.Extramarks has subject specialistsfor each subject who are highly educated and experienced in their respective fields. .The experts are responsible for coming up with all the resourceful tools that can help the students prepare for their examinations. The tools, like the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 also prepared by experts, can be of great help to the students in anything related to Chapter 6 of Class 11 Mathematics.

The NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 is just one of many tools available to students on the Extramarks website.

There are various other resources available for the students to take help from.

**Q.1 ** x + y < 5

**Ans.**

Graph of x + y = 5 is given as dotted line in the figure.

This line divides the xy-plane in two half planes I and II.

We select a point (not on the line), say (0, 0), which lies in one of the half planes and determine if this point satisfies the given inequality, we note that

(0) + (0) < 5

or 0 < 5 , which is true.

Hence, half plane I is the solution region of the given inequality. Clearly, any point on the line does not satisfy the given strict inequality.

In other words, the shaded half plane I excluding the points on the line is the solution region of the inequality.

**Q.2 **

**Ans.**

Graph of 2x + y = 6 is given as line in the figure.

This line divides the xy-plane in two half planes I and II. We select a point (not on the line), say (0, 0), which lies in one of the half planes and determine if this point satisfies the given inequality, we note that 2(0) + (0) = 6 or 0 = 6 , which is false.

Hence, half plane II is the solution region of the given inequality including all the points on line.

In other words, the shaded half plane II excluding the points on the line is the solution region of the inequality.

This line divides the xy-plane in two half planes I and II. We select a point (not on the line), say (0, 0), which lies in one of the half planes and determine if this point satisfies the given inequality, we note that

2(0) + (0) ≥ 6

or 0 ≥ 6 , which is false.

Hence, half plane II is the solution region of the given inequality including all the points on line.

In other words, the shaded half plane II excluding the points on the line is the solution region of the inequality.

**Q.3 **

**Ans.**

Graph of 3x + 4y = 12 is given as line in the figure.

This line divides the xy-plane in two half planes I and II. We select a point (not on the line), say (0, 0), which lies in one of the half planes and determine if this point satisfies the given inequality, we note that

3(0) + 4(0) ≤ 12

or 0 ≤ 12, which is true.

Hence, half plane I is the solution region of the given inequality including all the points on line.

In other words, the shaded half plane I including the points on the line is the solution region of the inequality.

**Q.4 **

**Ans.**

Graph of y + 8 = 2x is given as line in the figure.

This line divides the xy-plane in two half planes I and II. We select a point (not on the line), say (0, 0), which lies in one of the half planes and determine if this point satisfies the given inequality, we note that

(0) + 8 ≥ 2(0)

or 8 ≥ 0, which is true.

Hence, half plane I is the solution region of the given inequality including all the points on line.

In other words, the shaded half plane I including the points on the line is the solution region of the inequality.

**Q.5 **

**Ans.**

Graph of x – y = 2 is given as line in the figure.

This line divides the xy-plane in two half planes I and II. We select a point (not on the line), say (0, 0), which lies in one of the half planes and determine if this point satisfies the given inequality, we note that

(0) – (0) ≤ 2

or 0 ≤ 2, which is true.

Hence, half plane I is the solution region of the given inequality including all the points on line.

In other words, the shaded half plane I including the points on the line is the solution region of the inequality.

**Q.6 **

**Ans.**

Graph of 2x – 3y = 6 is given as dotted line in the figure.

This line divides the xy-plane in two half planes I and II. We select a point (not on the line), say (0, 0), which lies in one of the half planes and determine if this point satisfies the given inequality, we note that

2(0) – 3(0) > 6

or 0 > 6, which is false.

Hence, half plane II is the solution region of the given inequality. Clearly, any point on the line does not satisfy the given strict inequality.

In other words, the shaded half plane II excluding the points on the line is the solution region of the inequality.

**Q.7 **

**Ans.**

Graph of –3x+2y = – 6 is given as line in the figure.

This line divides the xy-plane in two half planes I and II. We select a point (not on the line), say (0, 0),

which lies in one of the half planes and determine if this point satisfies the given inequality,

we note that

– 3 (0) + 2(0) ≥ – 6

or 0 ≥ – 6, which is true.

Hence, half plane I is the solution region of the given inequality including all the points on line.

In other words, the shaded half plane I including the points on the line is the solution region of the inequality.

**Q.8 **

**Ans.**

Graph of 3y – 5x = 30 is given as line in the figure.

This line divides the xy-plane in two half planes I and II. We select a point (not on the line), say (0, 0),

which lies in one of the half planes and determine if this point satisfies the given inequality,

we note that

3(0) – 5(0) < 30

or 0 < 30, which is true.

Hence, half plane I is the solution region of the given inequality. Clearly, any point on the line does not satisfy the given strict inequality.

In other words, the shaded half plane I excluding the points on the line is the solution region of the inequality.

**Q.9 ** y < – 2

**Ans.**

Graph of y = – 2 is given as line in the figure.

This line divides the xy-plane in two half planes I and II.

We select a point (not on the line), say (0, 0), which lies in one of the half planes and determine if this point satisfies the given inequality,

we note that

(0) < – 2, which is false.

Hence, half plane II is the solution region of the given inequality. Clearly, any point on the line does not satisfy the given strict inequality.

In other words, the shaded half plane II excluding the points on the line is the solution region of the inequality.

**Q.10 ** x > – 3

**Ans.**

Graph of x = – 3 is given as line in the figure.

This line divides the xy-plane in two half planes I and II.

We select a point (not on the line), say (0, 0),

which lies in one of the half planes and determine if this point satisfies the given inequality,

we note that

0 > – 2, which is true.

Hence, half plane I is the solution region of the given inequality.

Clearly, any point on the line does not satisfy the given strict inequality.

In other words, the shaded half plane I excluding the points on the line is the solution region of the inequality.

## FAQs (Frequently Asked Questions)

### 1. What is the importance of Class 11 in the academic life of a student?

Class 11 is as important as any other class in fact as important as Class 10 or 12 that have board examinations. The student sometime fail to remember this. Scoring low in Class 11 is a common trend that is seen among many students. Since the marks of Class 11 are not added in the final result for their board examinations many students take the class and its examinations slightly. The students are advised to not go with this trend.

The students are advised to make use of the helpful resources available on the Extramarks like the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 if they wish to be thorough with their Class 11 curriculum.

The topics that are taught in Class 11 be it Class 11 Mathematics or any other subject other topics that will only be taught to that extent in Class 11 exclusively. These are also so the topics that might be continued in Class 12 so to form a good base the students need to be thoro with the topics that are taught in Class 11. The results of Class 11 might not directly affect the marks of Class 12 but if the students failed to be thoro with the topics of Class 11 it can show in the results of Class 12. The NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 can be of great help for the students who wish to prepare sensory for the Class 11 examinations.

### 2. what is the importance of the questions that are given in the NCERT books of Class 11 Mathematics are they enough to prepare for the final examination?

The NCERT books are design in a way that the students are unable to revise what they are learning as they keep moving forward in the chapter. For this the books contain questions in the middle of the chapter as well as once the chapter ends there are more questions for the students to solve and revise what they are just taught. This questions are very important not just from a revision point of view but also from an examinations point of view.

The NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 are the answers to the questions that are asked in Chapter 6 of Class 11 Mathematics. With the help of these solutions the students can complete the homework related to this exercise, they can prepare for class test based on this exercise, as well as revise before the examinations; the questions that are from this exercise.

When the final examination paper are formed the reference is taken from these questions that are there in the NCERT books. The numeric value might change but the basic concept of the questions remains the same a lot of times and the students are advised to be thorough with these NCERT questions when preparing for their examinations.

### 3. Should the students solve extra questions that are not a part of the syllabus but are related to the topic that is there in the syllabus?

Mathematics is a subject that requires the students to practice everything that is being taught in the subject multiple times. The students should not hesitate from solving as many questions as they can find based on the topics that are a part of their syllabus. How so ever the confusion mein arise if the students are solving questions that are not directly apart of the syllabus. It can be a helpful practice for the students who aim to excel in their examinations for the next class. But are the same times it might end up students getting confused about the formulas and equations that are part of the syllabus of the current class.

Solving extra questions is never an issue if the students have a clear understanding of what is a part of the syllabus and what they need to be focusing on. The students are advised to go through the NCERT syllabus that is available on the Extramarks website for each class do not end up getting confused about what questions are a part of their curriculum for a particular class.

### 4. Who creates the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 ?

The NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 that are available on the Extramarks website were prepared by the experts at Extramarks. The students are advised to make use of NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 as it can be very beneficial for them when preparing for their final examinations. The subject expert at Extramarks is highly trained and experienced in the subject, which makes the NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 another similar tool or reliable source of information for the students to depend on when preparing for the examinations.The NCERT Solutions for Class 11 Maths Chapter 6 Exercise 6.2 I know that the only tools are formal letters from experts, but there are other helpful resources available on the Extramarks website as well.Like extra questions for all the chapters that are there in Class 11 Mathematics, along with the questions that are there in the NCERT book itself. There are also past years’ question papers that are available on the website for the students to use for practise.