NCERT Solutions for Exercise 1.1 Class 11 Maths Chapter 1

Q: What is set ?

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

Q: 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.

Q: 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.

Q: 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}

Q: 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 }

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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NCERT Solutions for Class 11 Maths Chapter 1: Sets Exercise 1.1- Download Free PDF
Topics Covered in Class 11 maths ex 1.1
NCERT Solutions for Class 11 Maths Chapter 1 – Sets Exercise 1.1
Access Sets Class 11 Chapter 1 Exercise: 1.1
More About NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.1:-
Key Features of Class 11 Maths Chapter 1 Exercise 1.1
NCERT Solutions of Class 11 Subject Wise
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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:

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

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

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Access Sets Class 11 Chapter 1 Exercise: 1.1

Question:1(i) Which of the following are sets ?justify your answer

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

Answer:

The months starting with letter J are:

january

june

july

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

Question:1(ii) Which of the following are sets ?justify your answer

The collection of ten most talented writers of India.

Answer:

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.

Question:1(iii) Which of the following are sets ?justify your answer

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

Answer:

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.

Question:1(iv) Which of the following are sets ?justify your answer

The collection of all boys in your class.

Answer:

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.

Question:1(v) Which of the following are sets? Justify your answer

The collection of all natural numbers less than 100.

Answer:

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.

Question:1(vi) Which of the following are sets? Justify your answer

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

Answer:

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

Hence,it is a set.

Question:1(vii) Which of the following are sets? Justify your answer

The collection of all even integers.

Answer:

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

Hence,it is a set.

Question:1(viii) Which of the following are sets? Justify your answer

The collection of questions in this Chapter.

Answer:

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

Hence ,it is a set.

Question:1(ix) Which of the following are sets? Justify your answer

A collection of most dangerous animals of the world.

Answer:

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.

Question:2 $\, Let A = \left \{ 1,2,3,4,5,6 \right \}.Insert\, the\, appropriate\, symbol \in or\notin in\, the\, blank\, space :$

(i) 5_____A

(ii) 8_____A

(iii) 0_____A

(iv) 4_____A

(v) 2_____A

(vi) 10____A

Answer:

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

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

Answer:

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

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

Answer:

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}

Answer:

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}

Answer:

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

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.

Answer:

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.

Answer:

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}

Answer:

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}

Answer:

$2 = 2^{1}$

$4 = 2^{2}$

$8= 2^{3}$

$16 = 2^{4}$

$32 = 2^{5}$

$\left \{ 2,4,8,16,32 \right \}$ 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}

Answer:

$5= 5^{1}$

$25= 5^{2}$

$125= 5^{3}$

$625= 5^{4}$

$\left \{ 5,25,125,625 \right \}$ 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, . . .}

Answer:

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}

Answer:

$1= 1^{2}$

$4= 2^{2}$

$9= 3^{2}$

$100= 10^{2}$

$\left \{ 1,4,9.....100 \right \}$ 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}.

Answer:

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, $\frac{-1}{2} < x< \frac{9}{2}$ }

Answer:

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, $x^{2}\leq 4$ }

Answer:

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

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

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

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

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

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”}

Answer:

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}

Answer:

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 }.

Answer:

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

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

Question:6 Match each of the set on the left in the roster form with the same set on the right described in set-builder form:

(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}.

Answer:

(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).

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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NCERT Solutions of Class 11 Subject Wise

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Frequently Asked Questions (FAQs)

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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