NCERT Solutions for Class 11 Maths Chapter 1 Sets (Ex 1.5)

One of India’s most recognised and highly esteemed educational bodies is the CBSE. There are schools associated with CBSE that are spread out over the nation. When it comes to educating its students, the CBSE board takes an impartial stance. The curriculum used by CBSE requires students to examine the subject and the ideas being taught in it in depth. The entire curriculum is developed by CBSE with the goal of ensuring that all of its students comprehend the complex ideas taught at the upper secondary level. In addition to encouraging students to think critically and analytically, CBSE encourages them to look at subjects outside of the box. Students’ understanding of the concepts from the curriculum must be so complete that they can quickly visualise all the fundamentals they were taught. It is emphasised to students that regular recapitulation and active recall are more important than memorisation. Students are well aware of CBSE’s extensive syllabus. Students must therefore be able to sort through the knowledge that is redundant and not needed for the exams. Teachers at Extramarks have expressed empathy for the kids’ struggles and have given helpful strategies for overcoming them. Every student has been informed by teachers that there is nothing to be concerned about with the CBSE curriculum. Teachers encourage their students to take their studies seriously and to make small adjustments to their daily routines.

The National Council of Educational Research and Training (NCERT) is a centralised managed organisation. In 1961, the Indian government founded NCERT. NCERT assists the Indian Government in making decisions on the nation’s educational system. In order to make choices regarding all issues pertaining to the country’s educational growth, NCERT offers assistance to both the Central Government and the State Governments. NCERT and CBSE have a very synergistic connection in which they collaborate closely. NCERT offers their own set of principles and regulations. If students want to perform well on the tests, students must adhere to the norms and guidelines that have been set forth.

NCERT books are considered essential books for CBSE students, and their benefits will help build the foundation for academic examinations or competitive examinations. NCERT books are very helpful for students as they build a strong base for them and enhance their knowledge. NCERT books are more than enough to cover and develop the understanding of basic fundamentals in every subject in an easy language. An important fact of NCERT books is that students get their concepts clear by just going through NCERT books. Students must focus on understanding concepts rather than just memorising them. When students understand the topics, then they will be easily able to solve any question concerning that very concept. The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 will help the students to understand even the complex and complicated topics of the given chapter. With the help of the  Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5, students will be able to solve the difficult questions of that exercise. Mathematics may seem like a complex subject for students, but NCERT books have been designed in easy and understanding language. After studying from NCERT books, students may not understand NCERT exercise questions at times, then Extramarks’ website provides them with the easiest and most understanding solution to solve the questions of the NCERT textbook by downloading  Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5.

It is important to remember that NCERT books are the roots, even though there are plenty of other books available on the market. Its architecture is formed by designated expert educators who design them according to the age of students and how much they can grasp. Since the NCERT books are formulated for every Class of students from Class 1 to Class 12, and Extramarks makes all the solutions of NCERT books for students so that their conceptual understanding of topics gets crystal clear. The  Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 will help students in getting their concepts clear. To ensure that students have no difficulties answering questions, Extramarks concentrates on the NCERT books while also offering solutions to a variety of other books. NCERT textbooks comply with all CBSE guidelines. NCERT is the nation’s top management and research organisation. As a result, students who follow the CBSE board curriculum should be aware that they can pass the CBSE exams with good grades by only studying the NCERT textbooks. The wise thing to do would be to focus on NCERT books while preparing for their annual examinations. Extramarks has followed the CBSE pattern. Practising the Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 will help the students gain a thorough understanding of the chapter.

Further NCERT books will prepare students well for their examinations. At the end of every chapter, there is an exercise for students to solve. If students fail to solve exercise questions then Extramarks has prepared the solutions of every exercise so that no stone will be left unturned in students’ development. The  Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 will help out students to get their concepts clear for their competitive examinations as well. The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 have been compiled by experts with years of experience and can be relied upon

Students will face no issues if they follow the NCERT books, as they are written in lucid language. The  Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 try to resolve the issues of students regarding NCERT exercise questions and other questions too. Students must focus on NCERT books’ given patterns so that they would not get baffled in the examination. A few students claim sometimes after the examination that the question was out of the syllabus but the question creator had just made the question complex following the base pattern of NCERT books. A student with a sharp understanding of questions can easily solve any question that will be asked in examinations. Hence, it is important to know the pattern of NCERT books and study it minutely with the help of  Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5. NCERT books focus on making concepts clear for students, so those who try to learn without understanding them properly may face issues while solving questions in their annual examinations or competitive examinations. Students must know the application of the concepts in NCERT books so that they will understand the questions and be able to solve any question concerning that very concept. Hence, it is important to know how to apply the concepts to certain questions.

Important Class 11 questions have also been solved by Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5. Since the level of difficulty in the topic has suddenly increased then students too must increase their hard work. The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 will ease the queries for students. They can learn more about the various question formats that can be used to solve questions in the test. Daily practice is essential to ace any Mathematics test. It is anticipated that most of the questions in the examination will be asked from the NCERT textbook only. Practice is the key in Mathematics so students must solve several questions from a certain topic only and then pursue another topic.

Class 11 is usually vast compared to Class 10, and those who plan to pursue science after Class 10 may face complexities, but  Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 will solve all those complexities for students. There are three streams for students, and they have to choose one of three: Science, Arts and Commerce. Students must know what interests them so that they can pursue their careers effectively. As Class 10 syllabus is quite easy in comparison with Class 11 and the Science stream, in general, gets hectic for students. Class 10 gives a generalised idea of every subject but, after Class 10, subjects get specific. So those who plan to give competitive examinations like Joint Entrance Exam (JEE) or National Eligibility Entrance Exam (NEET) or Central Universities Entrance Tests (CUET) just after Class 12 must know the importance of Class 11 and Class 12. Those who study minutely get their competitive examinations qualified in one go. Class 11 must be taken with utmost importance as it builds students’ morale. If a student scores well in Class 11 it is obvious that the concepts of the students are quite clear and that they are preparing quite well for the upcoming Class 12 board examinations too. Students must stay focused and reach out to Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 whenever they are in doubt. Class 11 plays a crucial role in making students choose the right path. Students can consider Class 11 as a morale booster that will raise their confidence if they will study properly and score well in the examinations. The clarity of concepts will undoubtedly help them out in their competitive examinations. The  Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 will make understanding easy for students in the time of their need. Class 11 is a crucial time, and students must get decisive and make major decisions in their lives. They need to know the gravity of the choices they are going to make after choosing the Science stream. Students must get sincere about Class 11 and start to studying and Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 will always be there to help them.

NCERT Solutions for Class 11 Maths Chapter 1 Sets (Ex 1.5) Exercise 1.5

CBSE students of Class 11 can easily download solutions of Maths 1.5 Class 11. They can download the Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 from Extramarks’ website or mobile application in PDF format so that they can study Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 even in offline mode.

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Mathematics out of all subjects, plays an important role in students’ lives. Therefore, they must focus on mathematics. Mathematics is one of the most complex subjects of all because it is concept based. Learning Mathematics is indeed good for the development of minds, and students must practice Mathematics daily to make their minds sharp and fast. From students’ early age to their Class 11, Mathematics has played a significant role in students’ development. Starting from Class 1 or Class 2, Mathematics starts teaching them basic things like learning to see a Watch, Addition, Subtraction, Multiplication, and Division which will help them in doing finances from a young age only. Mathematics not just provides the students with knowledge but also builds their personalities. They become good at problem-solving because of their sharp minds, as their minds will become good at analytical approaches and reasoning. Therefore, Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 will also help them perform better in under-pressure situations.

Class 11 Mathematics is quite different from Class 10 Mathematics as Class 10 is just basic Mathematics and Class 11 is a vast version of it and very few chapters are related to each other. Therefore, Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 is here to help students out in a time of their transition from basic to advanced level. Class 10 Mathematics is easier than Class 11 which is why students’ pressure is less. That pressure can be eased by the Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5. After choosing the Science stream some students still try to figure out what to do next. Students find that the Science stream has wider options and they choose it. They may face problems in the beginning but after a few months, Mathematics will be easier with the assistance of Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5.  Students must download the PDF format of these solutions from Extramarks’ website or mobile application for a better understanding of Mathematics. As it is very helpful for students and their development.

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Access NCERT Solutions for Class 11 Mathematics Chapter 1 – Sets

Students can get access to the NCERT Solutions for Class 11 Mathematics Chapter 1- Sets from Extramarks’ website or mobile application and they can download the answers from Extramarks in PDF format so that they can use the answers even in offline mode when they would not be connected to the internet.

There are a total of 7 questions in the Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5,and each question has been solved in the easiest method by the experts in Mathematics. There are a total of six exercises, and at the end of chapter 1, there are 16 questions of miscellaneous exercises.

Class 11 is significant for laying the groundwork for the Class 12 Board Examination and also for preparing students’ minds for what course they will choose for them. Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 could be very useful for students preparing for the Joint Entrance Exam (JEE) who aspire to get into the Indian Institute of Technology (IIT) or the National Institute of Technology (NIT). The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 are designed in such a way that if students read it carefully, they will understand which topics have how much weightage based according to marks. It gives students a clear perspective on which topics should be prioritised more. The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 includes a plethora of sample papers and past years’ papers to assist students in preparing for the Class 11 annual examination. Students can use the Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 methods to assess and evaluate their performance for upcoming examinations. The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 provides accurate answers and methods. As a result, the Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 are reliable for the students’ learning. Extramarks is an excellent resource for students who have started to prepare for the Central Universities Entrance Test (CUET). The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 from Extramarks will help students qualify for competitive examinations. It will provide students with a broad understanding of the subject matter, allowing them to perform well even in Multiple Choice Questions (MCQs).

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Mathematics makes students disciplined and always stimulates logical reasoning. The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 have been solved with smart reasoning and easy steps. The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 gives students an idea of how to solve questions faster. The use of Mathematics has spread out to other subjects too such as Physics, Chemistry, Economics, Engineering etc. These subjects require the basics of  Mathematics to understand and the certain topics of their curriculum. The presentation of easy solutions can be seen in the Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5. Mathematics is around us in different forms, shapes, sizes, degrees, temperatures, finance, and time. Mathematics is offered as an ‘instrumental subject’ in some curricula to supplement the study of other school subjects, while in others, integrated courses that combine Mathematics and other fields are offered.

Extramarks is a learning platform where students can learn about every subject. It is not limited to mathematics or any other subject, students can access the study materials for every subject. The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 are prepared by the expert faculty at Extramarks according to the latest CBSE Syllabus for 2022-23. The NCERT Solutions of Mathematics help the students in solving problems efficiently. Also, Extramarks focuses on building step-by-step solutions for all NCERT problems in such a way that it will be simple for the students to understand. Sets are used to define the concepts of functions and relations, some of which are covered in Chapter 1 of the NCERT textbook. The Class 11 Maths Chapter 1 of NCERT are categorized under the CBSE syllabus and also has some basic definitions and operations involving the Sets. It is necessary to get fundamental knowledge of Sets since the study of Sequences, Geometry, and Probability requires it. However, this is an easy chapter among all the chapters of NCERT Class 11 Mathematics for scoring maximum marks in the annual examination. The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 help the students who are looking for a quick and easy way of learning.

The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 have easy questions concerning the essential operations involving Sets. Students will be able to solve the stepwise solutions to all of the necessary questions of this chapter with these NCERT Solutions as they have been solved with new tips and guidelines of CBSE and cover all the ideas of the NCERT curriculum. Rooster forms, Venn diagrams, and sets are important topics of Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5. There are 16 total chapters in Mathematics Class 11 syllabus from Chapter 1- Sets to Chapter 16 – Probability.

The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5, can clear any doubts a student may have. The Extramarks’ website and mobile application are extremely helpful for students because of the study materials. The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 are also available in Hindi. So those students who have issues understanding the English language can get their issues solved with Hindi solutions as well. Extramarks also offers study materials for the CBSE, ICSE, and other state boards as well. This will benefit students of all boards who want to learn. Extramarks is constantly updated with new syllabi and examination patterns so that students do not have to suffer. There is no room for error or confusion because a professional educator with subject knowledge framed has the Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5. Language should never be a barrier to learning. As a result, learning is simplified when students fully comprehend everything due to language accessibility. A student can study online or in PDF format by downloading the Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 from Extramarks’ website or mobile application.

There are numerous books for Class 11 learning, but the NCERT book is critical in shaping students’ fundamentals. Extramarks has primarily focused on NCERT Books but gives solutions like  Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5. The NCERT book already contains so much information, and all of these solutions have been created following the NCERT question pattern. As a result, students will find it easier to solve NCERT questions if the correct solutions are also available when they encounter problems. The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 have effectively singled out every student’s problem on the Extramarks’ website and mobile application. The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5, are easily accessible to students. This is well prepared and thoroughly covered for students so that they do not encounter any challenges while studying the topics. Students should not rush into a subject or chapter, but rather focus on each one and complete them one by one. This way, they will have an understanding that will stay with them for the rest of their lives. When students simply go over the topics before the examination and solve the Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5, they will outperform in their examination.

The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5, are based on sets. And sets are an organised collection of objects in Mathematics that can be represented in set-builder or roster form. Sets are typically represented by curly braces{}; for example, A = {1,2,3,4} is a set. Sets and their properties will be covered in set theory. It was created to describe a group of objects. The Set theory defines the various types of sets, symbols, and operations. Every detail of Sets has been mentioned in Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 by the experts in Mathematics at Extramarks.

To practice the exercise questions based on Class 11 Mathematics, all of the important topics must be thoroughly understood. Sets are the topic of Chapter 1. The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 is essential for achieving higher grades in Mathematics. Students should read the concepts of Sets from the NCERT textbook regularly. Sets are extremely important from the standpoint of competitive exams. After reviewing the topics, students must complete the exercises in Chapter 1. Class 11 Maths topics are broad but simple, and it is necessary to gain a deeper understanding of the topics to answer questions in the annual Mathematics examination. The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 can be used to practice writing answers for the Mathematics examination. Online resources are extremely beneficial for enhancing exam preparation levels. To effectively prepare for the annual exams, it is necessary to obtain study materials from reliable sources. All of the useful resources are available to students via the Extramarks’ website and mobile application.

Mathematics can be a challenging subject to master. Students in Class 11 must understand the Mathematics topics from an examination perspective. Class 11 students can use Extramarks’ website and mobile application to solve Chapter 1 questions by accessing the Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5. The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 can also be used to review the concepts of the questions. Many Mathematics questions require the use of Venn diagrams to be answered. Students should practice drawing Venn diagrams for Mathematics topics. The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 can also help students to learn how to draw appropriate diagrams while answering questions.

Extramarks eliminates all of the difficulties that students face in an instant. The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 must be accessed by students. To access the  Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 students can visit the Extramarks’ website or download the mobile application, which contains the PDF format of these solutions. Even if students do not have access to the internet, the PDF format of these solutions can be useful. Extramarks has made students’ lives easier by creating short notes and simple sentences that are easy to understand.

Numerous significant topics are a crucial component of the overall higher-level mathematics concepts covered in the Class 11 mathematics curriculum. Many concepts introduced in the mathematics curriculum for Class 8 are crucial for the Class 11 exam as well as Engineering entrance exams like the Joint Entrance Exam (JEE). Students studying for the Class 11 Mathematics examination should consult the Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5. With the use of resources like sample answers to problems, quick hints, summaries, notes, etc. The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 can allow students to understand the exercise questions. Students must be comfortable with all the Mathematics Class 11 principles because even in Class 12 mathematics, higher level concepts from Class 11 chapters are incorporated. The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 would be helpful to students in Class 12 as well.

Class 11 Maths NCERT Solutions Chapter 1 – An Overview of Sets

Every chapter in Class 11 must be covered with meticulous planning and distinctive strategies. There are seven exercises in Chapter 1 and one miscellaneous exercise. Each of them contains questions based on theories and formulas presented in Chapter 1 of the NCERT Mathematics textbook for Class 11. While textbook solutions are helpful when completing these exercises, students may encounter difficulties with certain questions. In that case, students can go to the Extramarks’ website and download detailed and step-by-step solutions to all of the questions in the Exercise. Students should download the Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 to get detailed solutions and cover Class 11 Maths Chapter 1 Exercise 1.5. The Extramarks solutions are of the highest quality.

Chapter 1 is very easy if the student is studying properly. Every Chapter of Class 11 has an important role if a student is planning to appear in the Joint Entrance Exam (JEE). The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 has provided every important formula that is needed to solve questions. The different elements of a Set are generally described by a capital letter. Thus, A is the set, and 1, 2, 3, 4, and 5 are the set’s elements or members. The Set’s elements can be written in any order but cannot be repeated. In the case of alphabets, all of the elements of the Set are represented in small letters. We can also write it as 1 A, 2 A, and so on. The set’s cardinal number is 5. The following are some examples of commonly used sets:

N: the set of all-natural numbers.

Z: Set of all integers

Q: the set of all rational numbers

R: the set of all real numbers.

Z+: the set of all positive integers.

This chapter is a building foundation for the development of students, and that foundation will be strong with the support of the Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5. Those students who will stay focused on their studies from the very beginning will score better in their examinations and even do well in their competitive examinations, like JEE or CUET.

This chapter builds the basic understanding of Sets and questions in JEE also arise from this. Though the chapter is not that complex, its application could be tough at times. Just mugging up NCERT Solutions will not help students in the long run. Therefore, they must understand the concepts and know the application of each concept because Mathematics is all about concepts and practice.

Then another topic that has been mentioned in the Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5, the order of a set determines how many elements it contains. It describes the size of a set. The order of the set is also known as cardinality. The size of a set, whether finite or infinite, is referred to as a set of finite or infinite order.

Initially, students must practice Sets topic-wise only and then go ahead. Students must not rush into things that will cause them confusion in the future when they appear in their examinations. So, to understand certain topics and chapters Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 is always there to help students. The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 are a safe tool for students as it covers each question of the exercise and that will eventually make the work of students easier.

The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 gives an explanation of the types of Sets. There are several types of sets in Mathematics- Empty Sets, Singleton Sets,  Finite Sets, Infinite Sets, Equivalent Sets, Equal Sets, Disjoint Sets, Subsets, Proper Subsets, Supersets, and Universal Sets. After understanding the concepts, students must practice them themselves to understand them properly. Each one of the topics has been discussed in  Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5.

The Chapter after Sets is interrelated to each other. Therefore, to understand the next chapter of the NCERT Mathematics book students must focus from the very beginning of the chapter and study topic-wise.

NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.5 – All Questions

Students can download NCERT Solutions in English and Hindi Medium for Class 11 Maths Chapter 1 Sets Ex 1.5 in PDF format. The Maths Class 11 Exercise 1.5 is solved by experienced experts from Extramarks who produced these NCERT solutions. All the questions in Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 have thorough explanations from the NCERT Textbook. Not only Ex 1.5 but all other exercises from Chapter 1 are available in NCERT Solutions for Class 11 Maths Chapter 1. The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5  were created with the help of competent topic specialists, which increases their dependability and accuracy. The NCERT Solutions Class 11 Maths Chapter 1 Exercise 1.5 are available in PDF format for offline access.There are a total of seven questions in the exercise -1.5 and each of them is solved from the point of view of getting step marking. Hence, the students should never try to memorise the questions but rather try to understand them. Even if the students find something complex while studying,they should read it again and again until they understand the whole concept. The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 are solved with the easiest step and in the easiest language. Students are advised to do their work honestly so that they will not suffer in their examinations.

Extramarks – The Best Place to Get Your Doubts Cleared

Extramarks is a learning platform specially designed for students who rely on NCERT books. Extramarks is a platform where specific subject experts such as educators, make solutions for the NCERT books. Then they make sample paper questions for students to revise and retain the topics they have already read. The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5, give clarity to the students, and they will be able to solve any question. So, to download Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5, students should go to Extramarks’ website and mobile application, which will be easily available in PDF format.

Apart from the Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5, students can also access other study materials like live classes, past years’ papers, sample papers, complete syllabus etc.

The Extramarks’ website or mobile application is very reliable to students as it makes answers and sample questions with accuracy so that no issue arises for the students who are preparing for JEE or other competitive exams. The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5, will make sure that no problem will occur to students in the time of their need. If students will prepare minutely and practice Mathematics rigorously, then they can compete in any examination and do well.

Extramarks is always there for students to improve their skills. The Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.5 will improve their skills in answering questions. Students are indeed already-intelligent but Extramarks brushes them up and makes them understand the Chapter in a vivid and specific manner. Extramarks makes its own questions for students to practice over. It will be quite evident to students that they can understand the topics and chapters better when they get help from Extramarks and practice them.

Every chapter of Class 11 solutions has been solved by Extramarks experts, students can also search for others chapters as well.

NCERT Solutions Class 11 Chapter 2 – Relations and Functions

NCERT Solutions Class 11 Chapter 3- Trigonometric Functions

NCERT Solutions Class 11 Chapter 4- Principle of Mathematical Induction

NCERT Solutions Class 11 Chapter 5- Complex Numbers and Quadratic Equations

NCERT Solutions Class 11 Chapter 6- Linear Inequalities

NCERT Solutions Class 11 Chapter 7- Permutations and Combinations

NCERT Solutions Class 11 Chapter 8- Binomial Theorem

NCERT Solutions Class 11 Chapter 9- Sequences and Series

NCERT Solutions Class 11 Chapter 10- Straight Lines

NCERT Solutions Class 11 Chapter 11- Conic Sections

NCERT Solutions Class 11 Chapter 12- Introduction to Three Dimensional Geometry

NCERT Solutions Class 11 Chapter 13- Limits and Derivatives

NCERT Solutions Class 11 Chapter 14- Mathematical Reasoning

NCERT Solutions Class 11 Chapter 15- Statistics

NCERT Solutions Class 11 Chapter 16- Probability

Students can also download NCERT Solutions for other classes by clicking the links given below-

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

Q.1 Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9},
A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find

(i) A′
(ii) B′
(iii) (A ∪ C)′
(iv) (A ∪ B)′
(v) (A′)′
(vi) (B – C)’

Ans.
(i) A’ = U – A = {5, 6, 7, 8, 9}
(ii) B’ = U – B = {1, 3, 5, 7, 9}
(iii) A ∪ C = {1, 2, 3, 4, 5, 6}
(A ∪ C)’ = U – (A ∪ C)
= {7, 8, 9}
(iv) A ∪ B = {1, 2, 3, 4, 6, 8}
(A ∪ B)’ = U – (A∪B)
= {5, 7, 9}
(v) (A’)’ = U – (A’)
= {1, 2, 3, 4}
(vi) B – C = {2, 8}
(B – C)’ = U – (B – C)
= {1, 3, 4, 5, 6, 7, 9}

Q.2 If U = {a, b, c, d, e, f, g, h}, find the complements of the following sets:
(i) A = {a, b, c}
(ii) B = {d, e, f, g}
(iii) C = {a, c, e, g}
(iv) D = {f, g, h, a}

Ans.
(i) A = {a, b, c}
A’ = U – A
= {d, e, f, g, h}

(ii) B = {d, e, f, g}
B’ = U – B
= {a, b, c, h}

(iii) C = {a, c, e, g}
C’ = U – C
= {b, d, f, h}

(iv) D = {f, g, h, a}
D’ = U – D
= {b, c, d, e}

Q.3 Taking the set of natural numbers as the universal set, write down the complements of the following sets:

(i) {x: x is an even natural number}
(ii) {x: x is an odd natural number}
(iii) {x: x is a positive multiple of 3}
(iv) {x: x is a prime number}
(v) {x: x is a natural number divisible by 3 and 5}
(vi) {x: x is a perfect square}
(vii) {x: x is a perfect cube}
(viii) {x: x + 5 = 8}
(ix) {x: 2x + 5 = 9}
(x) { x : x ≥ 7 }
(xi) { x : x ∈ N and 2x + 1 > 10 }

Ans.
Here, U = N = {1, 2, 3, 4, 5, …}

(i) Let A = {x: x is an even natural number}
A’ = U – A
= {1, 3, 5, 7, …}
= {x: x is an odd natural number}

(ii) Let B = {x: x is an odd natural number}
B’ = U – B
= {2, 4, 6, 8, …}
= {x : x is an even natural number}

(iii) Let C = {x: x is a positive multiple of 3}
C’ = U – C
= {1, 3, 4, 5, 7, …}
= {x : x is a natural number but not a multiple of 3}

(iv) Let D = {x: x is a prime number}
D’ = U – D
= {x : x is composite number and 1}

(v) Let E = {x: x is a natural number divisible by 3 and 5}
E’ = U – E
= {x: x is a natural number neither divisible by 3 nor by 5}

(vi) Let F = {x: x is a perfect square}
F’ = U – F
= {x : x is not a perfect square}

(vii) Let G = {x: x is a perfect cube}
G’ = U – G
= {x : x is not a perfect cube}

(viii) Let H = {x: x + 5 = 8}
= {3}
H’ = U – H
= {x : x is a natural number except 3}

(ix) Let I = {x: 2x + 5 = 9}
= {2}
I’ = U – I
= {x : x is a natural number except 2}

(x) Let J = { x:x ≥ 7}
J’ = U – J
= {1, 2, 3, 4, 5, 6}

(xi) Let K = {x : x ∈ N and 2x + 1 > 10}
= { x : x ∈ N and x > 9/2}
= {5, 6, 7, 8, …}
K’ = U – K
= {1, 2, 3, 4}

Q.4 If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that

(i) (A ∪ B)′ = A′ ∩ B′
(ii) (A ∩ B)′ = A′ ∪ B′

Ans.
A ∪ B = {2, 3, 4, 5, 6, 7, 8}
A ∩ B = {2}
(i) L.H.S.:
(A ∪ B)′ = U – (A ∪ B)
= {1, 9}
R.H.S.:
A′ ∩ B′ =(U – A) ∩ ( U – B)
= {1, 3, 5, 7, 9}∩{1, 4, 6, 8, 9}
= {1, 9}
Thus,
(A ∪ B)′ = A′ ∩ B′

(ii) L.H.S.:
(A ∩ B)′ = U – (A ∩ B)
= {1, 3, 4, 5, 6, 7, 8, 9}
R.H.S.:
A′ ∪ B′=(U – A) ∪ ( U – B)
= {1, 3, 5, 7, 9} ∪ {1, 4, 6, 8, 9}
= {1, 3, 4, 5, 6, 7, 8, 9}
Thus,
(A ∩ B)’ = A′ ∪ B′

Q.5 Draw appropriate Venn diagram for each of the following :

(i) (A ∪ B)’, (ii) A′ ∩ B′,
(iii) (A ∩ B)′, (iv) A′ ∪ B′

Ans.
(i) (A ∪ B)’

(ii) A′ ∩ B′=(A ∪ B)’ [By De Morgan’s Law]

(iii) (A ∩ B)′

(iv) A′ ∪ B′ = (A ∩ B)′ [By De Morgan’s Law]

Q.6 Let U be the set of all triangles in a plane. If A is the set of all triangles with at least one angle different from 60°, what is A′?

Ans.
Here, U = set of all triangles in a plane,
A = set of all triangles with at least one angle different from 60°
A’ = set of all triangles with each angle 60° i.e., set of all equilateral triangles.

Q.7 Fill in the blanks to make each of the following a true statement:
(i) A ∪ A′ = . . .
(ii) Φ′ ∩ A = . . .
(iii) A ∩ A′ = . . .
(iv) U′ ∩ A = . . .

Ans.
(i) A ∪ A′ = U
(ii) Φ′ ∩ A = A
(iii) A ∩ A′ = Φ
(iv) U′ ∩ A = Φ

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