NCERT Solutions for Exercise 1.1 Class 11 Maths Chapter 1 - Sets

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# NCERT Solutions for Exercise 1.1 Class 11 Maths Chapter 1 - Sets

Edited By Vishal kumar | Updated on Oct 31, 2023 07:20 AM IST

## NCERT Solutions for Class 11 Maths Chapter 1: Sets Exercise 1.1- Download Free PDF

NCERT Solutions for Class 11 Maths Chapter 1: Sets Exercise 1.1- The knowledge of sets is very important for the study of probability, geometry, sequences, etc. NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.1 consists of questions based on the basic definition of the set. The knowledge of sets is also required to define the concepts of relations and functions. Set is defined as a well-defined collection of objects like the set of all-natural numbers, a set of all integers, a set of positive real numbers, a set of positive integers, a set of real numbers, a set of positive rational numbers, etc. In exercise 1.1 Class 11 Maths, you will get questions related to representations of sets, which are written by subject experts of careers360. There are two methods to represent the sets i.e. roaster form and set-builder form. You can go through the Class 11 Maths chapter 1 exercise 1.1 solutions to get a detailed explanation of the sets and representation of sets. Check NCERT Solutions to get detailed solutions from Class 6 to Class 12 for Science and Maths.

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## Topics Covered in Class 11 maths ex 1.1

Class 11 ex 1.1 in NCERT Solutions for Class 11 Mathematics covers various topics related to sets. In class 11 maths chapter 1 exercise 1.1, you will find problems and exercises that primarily revolve around the following key concepts:

1. Introduction to Sets: Sets are introduced as a fundamental mathematical concept. A set is defined as a well-defined collection of objects or elements.

2. Sets and Their Representations: This section discusses how sets can be represented and described. It includes various methods of representing sets, such as:

• Roster or Tabular Form: Listing the elements of a set within curly braces.
• Set-Builder Form: Describing the properties that define the set's elements.

11th class maths exercise 1.1 answers likely contains questions and exercises related to these topics to help students understand and apply these fundamental concepts in set theory. Students may be asked to work with sets, represent them in different forms, and perform basic operations on sets as a part of their mathematics learning process.

## Access Sets Class 11 Chapter 1 Exercise: 1.1

The collection of all the months of a year beginning with the letter J.

The months starting with letter J are:

january

june

july

Hence,this is collection of well defined objects so it is a set.

The collection of ten most talented writers of India.

Ten most talented writers may be different depending on different criteria of determining talented writers.

Hence, this is not well defined so cannot be a set.

A team of eleven best-cricket batsmen of the world.

Eleven most talented cricketers may be different depending on criteria of determining talent of a player.

Hence,this is not well defined so it is not a set.

The collection of all boys in your class.

The collection of boys in a class are well defined and known.

Group of well defined objects is a set.

Hence, it is a set.

The collection of all natural numbers less than 100.

Natural numbers less than 100 has well defined and known collection of numbers.

that is S= {1,2,3............99}

Hence,it is a set.

A collection of novels written by the writer Munshi Prem Chand.

The collection of novels written by Munshi Prem Chand is well defined and known .

Hence,it is a set.

The collection of all even integers.

The collection of even intergers is well defined because we can get even integers till infinite. that is

Hence,it is a set.

The collection of questions in this Chapter.

Collection of questions in a chapter is well defined and known .

Hence ,it is a set.

A collection of most dangerous animals of the world.

A Collection of most dangerous animal is not well defined because the criteria of defining dangerousness of any animal can vary .

Hence,it is not a set.

(i) 5_____A

(ii) 8_____A

(iii) 0_____A

(iv) 4_____A

(v) 2_____A

(vi) 10____A

A = $\left \{ 1,2,3,4,5,6 \right \}$ ,the elements which lie in this set belongs to this set and others do not belong.

(i) 5 $\in$ A

(ii) 8 $\notin$ A

(iii) 0 $\notin$ A

(iv) 4 $\in$ A

(v) 2 $\in$ A

(vi) 10 $\notin$ A

Question:3(i) Write the following sets in roster form

$( i)\ A= \{x:x\ is \ an\ integer\ and\ -3\leq x< 7\}$

Elements of this set are:-3,-2,-1,0,1,2,3,4,5,6.

Hence ,this can be written as:

A = $\left \{ -3,-2,-1,0,1,2,3,4,5,6 \right \}$

Question:3(ii) Write the following sets in roster form

$\left ( ii \right )B= \left \{ x:x\, is \, a\, natural\, number\, less\, than\, 6 \right \}$

Natural numbers less than 6 are: 1,2,3,4,5.

This can be written as:

$B = \left \{ 1,2,3,4,5 \right \}$

Question:3(iii) Write the following sets in roster form

C = {x : x is a two-digit natural number such that the sum of its digits is 8}

The two digit numbers having sum equal to 8 are: 17,26,35,44,53,62,71,80.

This can be written as:

$C= \left \{ 17,26,35,44,53,62,71,80 \right \}$

Question:3(iv) Write the following sets in roster form

D = {x : x is a prime number which is divisor of 60}

$60= 2\ast 2\ast 3\ast 5$

Prime numbers which are divisor of 60 are:2,3,5.

This can be written as:

$D= \left \{ 2,3,5 \right \}$

Question:3(v) Write the following sets in roster form

E = The set of all letters in the word TRIGONOMETRY.

Letters of word TRIGONOMETRY are:T,R,I,G,N,O,M,E,Y.

This can be written as :

E = {T,R,I,G,N,O,M,E,Y}

Question:3(vi) Write the following sets in roster form

F = The set of all letters in the word BETTER.

The set of letters of word BETTER are: {B,E,T,R}

This can be written as:

F = {B,E,T,R}

Question:4(i) Write the following sets in the set builder form

{3, 6, 9, 12}

A = {3,6,9,12}

This can be written as : $\left \{ 3,6,9,12 \right \}= \left \{ x:x= 3n,n\in N\, \, and\,\, 1\leq n\leq 4 \right \}$

Question:4(ii) Write the following sets in the set builder form

{2,4,8,16,32}

$2 = 2^{1}$

$4 = 2^{2}$

$8= 2^{3}$

$16 = 2^{4}$

$32 = 2^{5}$

$\left \{ 2,4,8,16,32 \right \}$ can be written as $\left \{ x:x= 2^{n},n\in N and 1\leq n\leq 5 \right \}.$

Question:4(iii) Write the following sets in the set builder form:

{5, 25, 125, 625}

$5= 5^{1}$

$25= 5^{2}$

$125= 5^{3}$

$625= 5^{4}$

$\left \{ 5,25,125,625 \right \}$ can be written as $\left \{ x:x= 5^{n},n\in N and 1\leq n\leq 4 \right \}$

Question:4(iv) Write the following sets in the set builder form:

{2, 4, 6, . . .}

This is a set of all even natural numbers.

{2,4,6....} can be written as {x : x is an even natural number}

Question:4(v) Write the following sets in the set builder form :

{1,4,9, . . .,100}

$1= 1^{2}$

$4= 2^{2}$

$9= 3^{2}$

.

.

.

.

$100= 10^{2}$

$\left \{ 1,4,9.....100 \right \}$ can be written as $\left \{ x:x= n^{2} ,n\in N and \, 1\leq n\leq 10\right \}$

Question:5(i) List all the elements of the following sets:

A = {x : x is an odd natural number}.

A = { x : x is an odd natural number } = {1,3,5,7,9,11,13.............}

Question:5(ii) List all the elements of the following sets:

B= { x : x is an integer, $\frac{-1}{2} < x< \frac{9}{2}$ }

Intergers between $-\frac{1}{2}< x< \frac{9}{2}$ are 0,1,2,3,4.

Hence,B = {0,1,2,3,4}

Question:5(iii) List all the elements of the following sets:

C = {x : x is an integer, $x^{2}\leq 4$}

$\left ( -2 \right )^{2}= 4$

$\left ( -1 \right )^{2}= 1$

$\left ( 0 \right )^{2}= 0$

$\left ( 1\right )^{2}= 1$

$\left ( 2\right )^{2}= 4$

Integers whose square is less than or equal to 4 are : -2,-1,0,1,2.

Hence,it can be written as c = {-2,-1,0,1,2}.

Question:5(iv) List all the elements of the following sets:

D = {x : x is a letter in the word “LOYAL”}

LOYAL has letters L,O,Y,A.

D = {x : x is a letter in the word “LOYAL”} can be written as {L,O,Y,A}.

Question:5(v) List all the elements of the following sets:

E = {x : x is a month of a year not having 31 days}

The months not having 31 days are:

February

April

June

September

November

It can be written as {february,April,June,September,november}

Question:5(vi) List all the elements of the following sets :

F = {x : x is a consonant in the English alphabet which precedes k }.

The consonents in english which precedes K are : B,C,D,F,G,H,J

Hence, F = {B,C,D,F,G,H,J}.

(i) {1, 2, 3, 6} (a) {x : x is a prime number and a divisor of 6}

(ii) {2, 3} (b) {x : x is an odd natural number less than 10}

(iii) {M,A,T,H,E,I,C,S} (c) {x : x is natural number and divisor of 6}

(iv) {1, 3, 5, 7, 9} (d) {x : x is a letter of the word MATHEMATICS}.

(i) 1,2,3,6 all are natural numbers and also divisors of 6.

Hence,(i) matches with (c)

(ii) 2,3 are prime numbers and are divisors of 6.

Hence,(ii) matches with (a).

(iii) M,A,T,H,E,I,C,S are letters of word "MATHEMATICS".

Hence, (iii) matches with (d).

(iv) 1,3,5,7,9 are odd natural numbers less than 10.

Hence,(iv) matches with (b).

## More About NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.1:-

Class 11 Maths chapter 1 exercise 1.1 solutions consist of basic questions from the definition of sets and representation of sets. There are six questions in the NCERT book Class 11 Maths ch 1 ex 1.1 which you can solve by yourself. There are some examples given before this exercise that you must solve in order to get clarity of the concept. In exercise 1.1 Class 11 Maths there are some questions related to representing the set in the roaster form. In the roaster form, all the elements are enclosed in the braces and listed and separated by commas inside the braces.

Also Read| Sets Class 11th Notes

Benefits of NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.1:-

• In the NCERT syllabus Class 11th Maths chapter 1 exercise 1.1, you have learned about the methods of representing the set which is useful for the upcoming exercises of this chapter.
• Exercise 1.1 Class 11 Maths solutions are useful when you are not able to solve questions related to basic od sets.
• Class 11 Maths Chapter 1 Exercise 1.1 solutions are useful in the upcoming chapters like relations and functions, and trigonometric functions.

## Key Features of Class 11 Maths Chapter 1 Exercise 1.1

• Meticulously trained biology experts have meticulously crafted these class 11 maths chapter 1 exercise 1.1 solutions.
• These class 11 maths ex 1.1 solutions are meticulously accurate and devoid of errors, aligning perfectly with the latest CBSE Syllabus.
• Every vital concept of 11th class maths exercise 1.1 answers is thoughtfully and clearly explained in a way that is accessible to all students, making it easier for them to excel in their board exams.
• With the help of NCERT Solutions, students attain a comprehensive grasp of the fundamental concepts.
• PDFs of class 11 ex 1.1 solutions are also available, so students can use them offline.

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## Subject Wise NCERT Exampler Solutions

Happy learning!!!

1. What is set ?

Set is a well-defined collection of objects which is usually denoted by capital letters.

2. Write an example of a set ?

Set A = { 1,2,3,4,5,6}

3. What is the Roster from of set representation ?

In the Roster form of set representation, all the elements of the set are enclosed in the brace {} and separated by commas.

4. write an example of roster from of set representation ?

Set A = { 0,1,2,3,4}

5. What is the set builder form of set representation ?

In the set builder form, all the elements of a set possess a single property that is not possessed by any other elements outside the set.

6. Write the set {x : x is a positive integer and x < 10} in the roster form.

Required set = { 1,2,3,4,5,6,7,8,9}

7. If you have given set A = {1, 4, 9, 16, 25, . . . } then write set A in the set-builder form ?

A = { x : x is a square of natural number }

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##### Acrobat

Individuals who opt for a career as acrobats create and direct original routines for themselves, in addition to developing interpretations of existing routines. The work of circus acrobats can be seen in a variety of performance settings, including circus, reality shows, sports events like the Olympics, movies and commercials. Individuals who opt for a career as acrobats must be prepared to face rejections and intermittent periods of work. The creativity of acrobats may extend to other aspects of the performance. For example, acrobats in the circus may work with gym trainers, celebrities or collaborate with other professionals to enhance such performance elements as costume and or maybe at the teaching end of the career.

3 Jobs Available
##### Video Game Designer

Career as a video game designer is filled with excitement as well as responsibilities. A video game designer is someone who is involved in the process of creating a game from day one. He or she is responsible for fulfilling duties like designing the character of the game, the several levels involved, plot, art and similar other elements. Individuals who opt for a career as a video game designer may also write the codes for the game using different programming languages. Depending on the video game designer job description and experience they may also have to lead a team and do the early testing of the game in order to suggest changes and find loopholes.

3 Jobs Available
##### Talent Agent

The career as a Talent Agent is filled with responsibilities. A Talent Agent is someone who is involved in the pre-production process of the film. It is a very busy job for a Talent Agent but as and when an individual gains experience and progresses in the career he or she can have people assisting him or her in work. Depending on one’s responsibilities, number of clients and experience he or she may also have to lead a team and work with juniors under him or her in a talent agency. In order to know more about the job of a talent agent continue reading the article.

If you want to know more about talent agent meaning, how to become a Talent Agent, or Talent Agent job description then continue reading this article.

3 Jobs Available

Radio Jockey is an exciting, promising career and a great challenge for music lovers. If you are really interested in a career as radio jockey, then it is very important for an RJ to have an automatic, fun, and friendly personality. If you want to get a job done in this field, a strong command of the language and a good voice are always good things. Apart from this, in order to be a good radio jockey, you will also listen to good radio jockeys so that you can understand their style and later make your own by practicing.

A career as radio jockey has a lot to offer to deserving candidates. If you want to know more about a career as radio jockey, and how to become a radio jockey then continue reading the article.

3 Jobs Available
##### Talent Director

Individuals who opt for a career as a talent director are professionals who work in the entertainment industry. He or she is responsible for finding out the right talent through auditions for films, theatre productions, or shows. A talented director possesses strong knowledge of computer software used in filmmaking, CGI and animation. A talent acquisition director keeps himself or herself updated on various technical aspects such as lighting, camera angles and shots.

2 Jobs Available
##### Videographer

Careers in videography are art that can be defined as a creative and interpretive process that culminates in the authorship of an original work of art rather than a simple recording of a simple event. It would be wrong to portrait it as a subcategory of photography, rather photography is one of the crafts used in videographer jobs in addition to technical skills like organization, management, interpretation, and image-manipulation techniques. Students pursue Visual Media, Film, Television, Digital Video Production to opt for a videographer career path. The visual impacts of a film are driven by the creative decisions taken in videography jobs. Individuals who opt for a career as a videographer are involved in the entire lifecycle of a film and production.

2 Jobs Available
##### Multimedia Specialist

A multimedia specialist is a media professional who creates, audio, videos, graphic image files, computer animations for multimedia applications. He or she is responsible for planning, producing, and maintaining websites and applications.

2 Jobs Available
##### Copy Writer

In a career as a copywriter, one has to consult with the client and understand the brief well. A career as a copywriter has a lot to offer to deserving candidates. Several new mediums of advertising are opening therefore making it a lucrative career choice. Students can pursue various copywriter courses such as Journalism, Advertising, Marketing Management. Here, we have discussed how to become a freelance copywriter, copywriter career path, how to become a copywriter in India, and copywriting career outlook.

5 Jobs Available
##### Journalist

Careers in journalism are filled with excitement as well as responsibilities. One cannot afford to miss out on the details. As it is the small details that provide insights into a story. Depending on those insights a journalist goes about writing a news article. A journalism career can be stressful at times but if you are someone who is passionate about it then it is the right choice for you. If you want to know more about the media field and journalist career then continue reading this article.

3 Jobs Available
##### Publisher

For publishing books, newspapers, magazines and digital material, editorial and commercial strategies are set by publishers. Individuals in publishing career paths make choices about the markets their businesses will reach and the type of content that their audience will be served. Individuals in book publisher careers collaborate with editorial staff, designers, authors, and freelance contributors who develop and manage the creation of content.

3 Jobs Available
##### Vlogger

In a career as a vlogger, one generally works for himself or herself. However, once an individual has gained viewership there are several brands and companies that approach them for paid collaboration. It is one of those fields where an individual can earn well while following his or her passion. Ever since internet cost got reduced the viewership for these types of content has increased on a large scale. Therefore, the career as vlogger has a lot to offer. If you want to know more about the career as vlogger, how to become a vlogger, so on and so forth then continue reading the article. Students can visit Jamia Millia Islamia, Asian College of Journalism, Indian Institute of Mass Communication to pursue journalism degrees.

3 Jobs Available
##### Editor

Individuals in the editor career path is an unsung hero of the news industry who polishes the language of the news stories provided by stringers, reporters, copywriters and content writers and also news agencies. Individuals who opt for a career as an editor make it more persuasive, concise and clear for readers. In this article, we will discuss the details of the editor's career path such as how to become an editor in India, editor salary in India and editor skills and qualities.

3 Jobs Available

Advertising managers consult with the financial department to plan a marketing strategy schedule and cost estimates. We often see advertisements that attract us a lot, not every advertisement is just to promote a business but some of them provide a social message as well. There was an advertisement for a washing machine brand that implies a story that even a man can do household activities. And of course, how could we even forget those jingles which we often sing while working?

2 Jobs Available
##### Photographer

Photography is considered both a science and an art, an artistic means of expression in which the camera replaces the pen. In a career as a photographer, an individual is hired to capture the moments of public and private events, such as press conferences or weddings, or may also work inside a studio, where people go to get their picture clicked. Photography is divided into many streams each generating numerous career opportunities in photography. With the boom in advertising, media, and the fashion industry, photography has emerged as a lucrative and thrilling career option for many Indian youths.

2 Jobs Available
##### Social Media Manager

A career as social media manager involves implementing the company’s or brand’s marketing plan across all social media channels. Social media managers help in building or improving a brand’s or a company’s website traffic, build brand awareness, create and implement marketing and brand strategy. Social media managers are key to important social communication as well.

2 Jobs Available
##### Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.

3 Jobs Available
##### Quality Controller

A quality controller plays a crucial role in an organisation. He or she is responsible for performing quality checks on manufactured products. He or she identifies the defects in a product and rejects the product.

A quality controller records detailed information about products with defects and sends it to the supervisor or plant manager to take necessary actions to improve the production process.

3 Jobs Available
##### Production Manager

Production Manager Job Description: A Production Manager is responsible for ensuring smooth running of manufacturing processes in an efficient manner. He or she plans and organises production schedules. The role of Production Manager involves estimation, negotiation on budget and timescales with the clients and managers.

3 Jobs Available
##### QA Manager

Quality Assurance Manager Job Description: A QA Manager is an administrative professional responsible for overseeing the activity of the QA department and staff. It involves developing, implementing and maintaining a system that is qualified and reliable for testing to meet specifications of products of organisations as well as development processes.

2 Jobs Available

A QA Lead is in charge of the QA Team. The role of QA Lead comes with the responsibility of assessing services and products in order to determine that he or she meets the quality standards. He or she develops, implements and manages test plans.

2 Jobs Available
##### Reliability Engineer

Are you searching for a Reliability Engineer job description? A Reliability Engineer is responsible for ensuring long lasting and high quality products. He or she ensures that materials, manufacturing equipment, components and processes are error free. A Reliability Engineer role comes with the responsibility of minimising risks and effectiveness of processes and equipment.

2 Jobs Available
##### Safety Manager

A Safety Manager is a professional responsible for employee’s safety at work. He or she plans, implements and oversees the company’s employee safety. A Safety Manager ensures compliance and adherence to Occupational Health and Safety (OHS) guidelines.

2 Jobs Available
##### Corporate Executive

Are you searching for a Corporate Executive job description? A Corporate Executive role comes with administrative duties. He or she provides support to the leadership of the organisation. A Corporate Executive fulfils the business purpose and ensures its financial stability. In this article, we are going to discuss how to become corporate executive.

2 Jobs Available
##### Computer Programmer

Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.

3 Jobs Available
##### Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.

3 Jobs Available
##### ITSM Manager

ITSM Manager is a professional responsible for heading the ITSM (Information Technology Service Management) or (Information Technology Infrastructure Library) processes. He or she ensures that operation management provides appropriate resource levels for problem resolutions. The ITSM Manager oversees the level of prioritisation for the problems, critical incidents, planned as well as proactive tasks.

3 Jobs Available
##### Information Security Manager

Individuals in the information security manager career path involves in overseeing and controlling all aspects of computer security. The IT security manager job description includes planning and carrying out security measures to protect the business data and information from corruption, theft, unauthorised access, and deliberate attack

3 Jobs Available
##### Big Data Analytics Engineer

Big Data Analytics Engineer Job Description: A Big Data Analytics Engineer is responsible for collecting data from various sources. He or she has to sort the organised and chaotic data to find out patterns. The role of Big Data Engineer involves converting messy information into useful data that is clean, accurate and actionable.

2 Jobs Available
##### Cloud Solution Developer

A Cloud Solutions Developer is basically a Software Engineer with specialisation in cloud computing. He or she possesses a solid understanding of cloud systems including their operations, deployment with security and efficiency with no little downtime.

2 Jobs Available
##### CRM Technology Consultant

A Customer Relationship Management Technology Consultant or CRM Technology Consultant is responsible for monitoring and providing strategy for performance improvement with logged calls, performance metrics and revenue metrics. His or her role involves accessing data for team meetings, goal setting analytics as well as reporting to executives.

2 Jobs Available
##### IT Manager

Career as IT Manager  requires managing the various aspects of an organization's information technology systems. He or she is responsible for increasing productivity and solving problems related to software and hardware. While this role is typically one of the lower-level positions within an organisation, it comes with responsibilities related to people and ownership of systems.

2 Jobs Available