assignment class 11 maths

CBSE NCERT Solutions

NCERT and CBSE Solutions for free

Class 11 Mathematics Assignments

We have provided below free printable Class 11 Mathematics Assignments for Download in PDF. The Assignments have been designed based on the latest NCERT Book for Class 11 Mathematics . These Assignments for Grade 11 Mathematics cover all important topics which can come in your standard 11 tests and examinations. Free printable Assignments for CBSE Class 11 Mathematics , school and class assignments, and practice test papers have been designed by our highly experienced class 11 faculty. You can free download CBSE NCERT printable Assignments for Mathematics Class 11 with solutions and answers. All Assignments and test sheets have been prepared by expert teachers as per the latest Syllabus in Mathematics Class 11. Students can click on the links below and download all Pdf Assignments for Mathematics class 11 for free. All latest Kendriya Vidyalaya Class 11 Mathematics Assignments with Answers and test papers are given below.

Mathematics Class 11 Assignments Pdf Download

We have provided below the biggest collection of free CBSE NCERT KVS Assignments for Class 11 Mathematics . Students and teachers can download and save all free Mathematics assignments in Pdf for grade 11th. Our expert faculty have covered Class 11 important questions and answers for Mathematics as per the latest syllabus for the current academic year. All test papers and question banks for Class 11 Mathematics and CBSE Assignments for Mathematics Class 11 will be really helpful for standard 11th students to prepare for the class tests and school examinations. Class 11th students can easily free download in Pdf all printable practice worksheets given below.

Topicwise Assignments for Class 11 Mathematics Download in Pdf

More Assignments for Class 11 Mathematics

Advantages of Class 11 Mathematics Assignments

• As we have the best and largest collection of Mathematics assignments for Grade 11, you will be able to easily get full list of solved important questions which can come in your examinations.
• Students will be able to go through all important and critical topics given in your CBSE Mathematics textbooks for Class 11 .
• All Mathematics assignments for Class 11 have been designed with answers. Students should solve them yourself and then compare with the solutions provided by us.
• Class 11 Students studying in per CBSE, NCERT and KVS schools will be able to free download all Mathematics chapter wise worksheets and assignments for free in Pdf
• Class 11 Mathematics question bank will help to improve subject understanding which will help to get better rank in exams

Frequently Asked Questions by Class 11 Mathematics students

At https://www.cbsencertsolutions.com, we have provided the biggest database of free assignments for Mathematics Class 11 which you can download in Pdf

We provide here Standard 11 Mathematics chapter-wise assignments which can be easily downloaded in Pdf format for free.

You can click on the links above and get assignments for Mathematics in Grade 11, all topic-wise question banks with solutions have been provided here. You can click on the links to download in Pdf.

We have provided here topic-wise Mathematics Grade 11 question banks, revision notes and questions for all difficult topics, and other study material.

We have provided the best collection of question bank and practice tests for Class 11 for all subjects. You can download them all and use them offline without the internet.

Related Posts

Class 11 Assignments Download Pdf

Class 11 Sociology Assignments

Class 11 Mathematics Relations And Functions Assignments

WorkSheets Buddy

Download Math, Science, English and Many More WorkSheets

CBSE Worksheets for Class 11 Maths

CBSE Worksheets for Class 11 Maths: One of the best teaching strategies employed in most classrooms today is Worksheets. CBSE Class 11 Maths Worksheet for students has been used by teachers & students to develop logical, lingual, analytical, and problem-solving capabilities. So in order to help you with that, we at WorksheetsBuddy have come up with Kendriya Vidyalaya Class 11 Maths Worksheets for the students of Class 11. All our CBSE NCERT Class 11 Maths practice worksheets are designed for helping students to understand various topics, practice skills and improve their subject knowledge which in turn helps students to improve their academic performance. These chapter wise test papers for Class 11 Maths will be useful to test your conceptual understanding.

Board: Central Board of Secondary Education(www.cbse.nic.in) Subject: Class 11 Maths Number of Worksheets: 42

CBSE Class 11 Maths Worksheets PDF

All the CBSE Worksheets for Class 11 Maths provided in this page are provided for free which can be downloaded by students, teachers as well as by parents. We have covered all the Class 11 Maths important questions and answers in the worksheets which are included in CBSE NCERT Syllabus. Just click on the following link and download the CBSE Class 11 Maths Worksheet. CBSE Worksheets for Class 11 Math can also use like assignments for Class 11 Maths students.

Binomial Theorem

• CBSE Worksheets for Class 11 Mathematics Binomial Theorem Assignment 1
• CBSE Worksheets for Class 11 Mathematics Binomial Theorem Assignment 2

Complex Numbers and Quadratic Equation

• CBSE Worksheets for Class 11 Mathematics Complex Numbers and Quadratic Equation Assignment 1
• CBSE Worksheets for Class 11 Mathematics Complex Numbers and Quadratic Equation Assignment 2
• CBSE Worksheets for Class 11 Mathematics Complex Numbers and Quadratic Equation Assignment 3
• CBSE Worksheets for Class 11 Mathematics Complex Numbers and Quadratic Equation Assignment 4
• CBSE Worksheets for Class 11 Mathematics Complex Numbers and Quadratic Equation Assignment 5
• CBSE Worksheets for Class 11 Mathematics Complex Numbers and Quadratic Equation Assignment 6

Conic Sections

• CBSE Worksheets for Class 11 Mathematics Conic Sections Assignment 1
• CBSE Worksheets for Class 11 Mathematics Conic Sections Assignment 2

Introduction To 3Dimensional Geometry

• CBSE Worksheets for Class 11 Mathematics Introduction To 3Dimensional Geometry Assignment 1
• CBSE Worksheets for Class 11 Mathematics Introduction To 3Dimensional Geometry Assignment 2

Linear Inequalities

• CBSE Worksheets for Class 11 Mathematics Linear Inequalities Assignment 1
• CBSE Worksheets for Class 11 Mathematics Linear Inequalities Assignment 2

Permutations and Combinations

• CBSE Worksheets for Class 11 Mathematics Permutations and Combinations Assignment 1
• CBSE Worksheets for Class 11 Mathematics Permutations and Combinations Assignment 2

Principle of Mathematical Induction

• CBSE Worksheets for Class 11 Mathematics Principle of Mathematical Induction Assignment 1
• CBSE Worksheets for Class 11 Mathematics Principle of Mathematical Induction Assignment 2

Probability

• CBSE Worksheets for Class 11 Mathematics Probability Assignment 1
• CBSE Worksheets for Class 11 Mathematics Probability Assignment 2

Relations and Functions

• CBSE Worksheets for Class 11 Mathematics Relations and Functions Assignment

Sequences and Series

• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 1
• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 2
• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 3
• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 4
• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 5
• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 6
• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 7
• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 8
• CBSE Worksheets for Class 11 Mathematics Set Theory Assignment 1
• CBSE Worksheets for Class 11 Mathematics Set Theory Assignment 2
• CBSE Worksheets for Class 11 Mathematics Statistics Assignment 1
• CBSE Worksheets for Class 11 Mathematics Statistics Assignment 2

Straight Lines

• CBSE Worksheets for Class 11 Mathematics Straight Lines Assignment 1
• CBSE Worksheets for Class 11 Mathematics Straight Lines Assignment 2

Trigonometric Ratios

• CBSE Worksheets for Class 11 Mathematics Trigonometric Ratios Assignment 1
• CBSE Worksheets for Class 11 Mathematics Trigonometric Ratios Assignment 2
• CBSE Worksheets for Class 11 Mathematics Trigonometric Ratios Assignment 3
• CBSE Worksheets for Class 11 Mathematics Sample Paper 2014 Assignment 1
• CBSE Worksheets for Class 11 Mathematics Sample Paper 2014 Assignment 2
• CBSE Worksheets for Class 11 Mathematics Sample Paper 2014 Assignment 3
• CBSE Worksheets for Class 11 Mathematics Mathematical Reasoning Assignment

Advantages of CBSE Class 11 Maths Worksheets

• By practising NCERT CBSE Class 11 Maths Worksheet , students can improve their problem solving skills.
• Helps to develop the subject knowledge in a simple, fun and interactive way.
• No need for tuition or attend extra classes if students practise on worksheets daily.
• Working on CBSE worksheets are time-saving.
• Helps students to promote hands-on learning.
• One of the helpful resources used in classroom revision.
• CBSE Class 11 Maths Workbook Helps to improve subject-knowledge.
• CBSE Class 11 Math Worksheets encourages classroom activities.

Worksheets of CBSE Class 11 Maths are devised by experts of WorksheetsBuddy experts who have great experience and expertise in teaching Maths. So practising these worksheets will promote students problem-solving skills and subject knowledge in an interactive method. Students can also download CBSE Class 11 Maths Chapter wise question bank pdf and access it anytime, anywhere for free. Browse further to download free CBSE Class 11 Maths Worksheets PDF .

Now that you are provided all the necessary information regarding CBSE Class 11 Maths Worksheet and we hope this detailed article is helpful. So Students who are preparing for the exams must need to have great solving skills. And in order to have these skills, one must practice enough of Class 11 Math revision worksheets . And more importantly, students should need to follow through the worksheets after completing their syllabus.  Working on CBSE Class 11 Maths Worksheets will be a great help to secure good marks in the examination. So start working on Class 11 Math Worksheets to secure good score.

CBSE Worksheets For Class 11

Share this:.

• Click to share on Twitter (Opens in new window)
• Click to share on Facebook (Opens in new window)

Leave a Comment Cancel reply

Notify me of follow-up comments by email.

Notify me of new posts by email.

• Class 6 Maths
• Class 6 Science
• Class 6 Social Science
• Class 6 English
• Class 7 Maths
• Class 7 Science
• Class 7 Social Science
• Class 7 English
• Class 8 Maths
• Class 8 Science
• Class 8 Social Science
• Class 8 English
• Class 9 Maths
• Class 9 Science
• Class 9 Social Science
• Class 9 English
• Class 10 Maths
• Class 10 Science
• Class 10 Social Science
• Class 10 English
• Class 11 Maths
• Class 11 Computer Science (Python)
• Class 11 English
• Class 12 Maths
• Class 12 English
• Class 12 Economics
• Class 12 Accountancy
• Class 12 Physics
• Class 12 Chemistry
• Class 12 Biology
• Class 12 Computer Science (Python)
• Class 12 Physical Education
• GST and Accounting Course
• Excel Course
• Tally Course
• Finance and CMA Data Course
• Payroll Course

Interesting

• Learn English
• Learn Excel
• Learn Tally
• Learn GST (Goods and Services Tax)
• Learn Accounting and Finance
• GST Tax Invoice Format
• Accounts Tax Practical
• Tally Ledger List
• GSTR 2A - JSON to Excel

Are you in school ? Do you love Teachoo?

We would love to talk to you! Please fill this form so that we can contact you

You are learning...

Class 11 - Maths

Click on any of the links below to start learning from Teachoo ...

Updated according to new NCERT - 2023-24 NCERT Books.

Get NCERT solutions for Class 11 Maths Free with videos. All exercise questions, supplementary questions, examples and miscellaneous are solved with important questions marked.

Most of the chapters we will study in Class 11 forms a base of what we will study in Class 12. Forming a good base in Class 11 is important for good marks Class 12 Boards.

In each chapter, we have divided it into two parts - Serial Order Wise and Concept Wise. 

Serial Order Wise is studying the chapter from the NCERT Book. This is useful when you want to look for a particular question or example.

Concept Wise is the Teachoo (टीचू) way of doing the chapter. First a topic is explained, and then their questions of that topic - from easy to difficult.

We suggest you do all the chapters from Concept Wise, so that your concepts are cleared. Which is important in competitive exams like JEE, GRE, GMAT as well as in Class 12.

In this class, the chapters and their topics include 

• Chapter 1 Sets – What are sets, Roster & Set-builder form, Types of sets - Empty Set, Equal set, Finite & Infinite sets, Subsets, Universal Set, Power Set, Intervals, Venn Diagrams, Operation of sets - Intersection, Union, Complement, Difference
• Chapter 2 Relations and Functions – Cartesian Product of sets, Relation - domain, range, co-domain, number of relations, Functions - graph & algebra.
• Chapter 3 Trigonometric Functions – Degree to Radian conversion, Trigometric Functions, Sign of sin, cos, tan in Different Quadrants, Trigonometry Formulas, Trigonometric Equation - Principal & General Solutions.
• Chapter 4 Principle of Mathematical Induction – Proving P(1) true, then taking P(n) as true, we prove P(n+1) true.
• Chapter 5 Complex Numbers and Quadratic Equations – What is iota(i) - Square root of negative number, Finding roots of quadratic equations, Modulus & Conjugate of complex number and Polar Representation of Complex number.
• Chapter 6 Linear Inequalities – Algebraic & Graphical solution of Linear inequalities in one and two variables
• Chapter 7 Permutations and Combinations – Fundamental principle of counting, permutation - no repetition, repetition. Permuation formula, Factorial, Combination Formula
• Chapter 8 Binomial Theorem – Expanding terms, General term & Coefficient, Term independent of x, Middle term, Approximate numbers using first terms of expansion.
• Chapter 9 Sequences and Series – Arithmetic Progressions (AP), Geometric Progressions (GP), Arithmetic Mean (AM), Geometric Mean (GM), Inserting AP & GP between two numbers, Relationship between AM & GM. Sum of n terms, n 2 terms, n 3 terms,  Finding sum of series.
• Chapter 10 Straight Lines – Finding slope of line using angle and points, Finding angle between two lines, Proving lines perpendicular or parallel, Finding Equation of lines - Two point form, Slope-intercept form, Intercept form, General Form, Normal Form, Distance of point from line, Distance between two parallel lines 
• Chapter 11 Conic Sections – Finding equation, focus, directrix, center, vertex of Circle, Parabola, Ellipse, Hyperbola
• Chapter 12 Introduction to Three Dimensional Geometry – XYZ axis, octants and sign of co-ordinates in the octant, Distance between points and Section Formula
• Chapter 13 Limits and Derivatives – Limits of polynomial and trigonometric functions, Left Hand Limit & Right hand limit, Limit using formulas, Derivative by first principle,  Finding derivative of polynomial and trigonometric functions by formula
• Direct Method
• Contrapositive method
• Contradiction
• Using counter example
• Chapter 15 Statistics – Mean deviation about mean and median for raw, ungrouped & grouped data. Finding variance & standard deviation of discrete & continuous frequency distribution with Shortcut Method, Coefficient of Variation (CV)
• Chapter 16 Probability – Finding Sample space, Event & types of event - Impossible & sure events, simple event, compound event, Mutually Exclusive & Exhaustive events, Probability of event 'A or B',  'A and B', Probability of event not A

Click on a chapter link below to start doing the chapter. 

Chapter 1 Class 11 Sets

Chapter 2 class 11 relations and functions, chapter 3 class 11 trigonometric functions, mathematical induction, chapter 4 class 11 complex numbers, chapter 5 class 11 linear inequalities, chapter 6 class 11 permutations and combinations, chapter 7 class 11 binomial theorem, chapter 8 class 11 sequences and series, chapter 9 class 11 straight lines, chapter 10 class 11 conic sections, chapter 11 class 11 - intro to three dimensional geometry, chapter 12 class 11 limits and derivatives, mathematical reasoning, chapter 13 class 11 statistics, chapter 14 class 11 probability, important questions for exams class 11.

What's in it?

Hi, it looks like you're using AdBlock :(

Please login to view more pages. it's free :), solve all your doubts with teachoo black.

NCERT Solutions for Class 11 Maths Chapter 1 – Sets

Ncert solutions for class 11 maths chapter 1 – sets pdf.

Free PDF of NCERT Solutions for Class 11 Maths Chapter 1 – Sets includes all the questions provided in NCERT Books prepared by Mathematics expert teachers as per CBSE NCERT guidelines from Mathongo.com. To download our free pdf of Chapter 1 – Sets Maths NCERT Solutions for Class 11 to help you to score more marks in your board exams and as well as competitive exams.

Share with friends:

Talk to our experts

1800-120-456-456

Important Questions for CBSE Class 11 Maths Chapter 1 - Sets 2024-25

• Class 11 Important Question
• Chapter 1: Sets

Crucial Practice Problems for CBSE Class 11 Maths Chapter 1: Sets

Class 11th is quite important in making students understand the complex concepts of mathematics and preparing them for the JEE Main exams . Class 11th needs a significant amount of hard work from a student's point of view, and the same goes for the teachers as well. Vedantu is pushing the limits of education by helping students in their journey of making a strong foundation for the exams which they are going to give at the end of the year along with the entrance exams. Let's provide you with the briefing of the important questions for class 11 maths chapter 1 . 

In this chapter, students will be learning about the different types of sets and how to represent them. They will also get to know about empty sets, finite and infinite sets, equal sets, subsets, power sets, Universal sets, union and intersection of the given sets. Moreover, as the student studies the chapter and reaches its end, they will be able to solve the problems that use the formulas from the above topic and the difference of sets, a complement of sets, and properties of Complement. A lot of questions you are going to see in the competitive exams like JEE Main will use the concepts you have learned in class 11th as the competitive exams test you on your learning ability and come up with the answer constraint environment. 

Download CBSE Class 11 Maths Important Questions 2024-25 PDF

Also, check CBSE Class 11 Maths Important Questions for other chapters:

Boost Your Performance in CBSE Class 11 Mathematics Exam Chapter 1 with Important Questions

Very short questions and answers (1 marks questions).

Which of the following are sets? Justify your answer.

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

Ans: Set, because collection of certain and unique type of data is called a set.

2. The collection of difficult topics in Mathematics.

Ans: Not a set, because difficult topics differ person to person.

Let \[A=\{1,3,5,7,9\}\]. Insert the appropriate symbol in blank spaces:-(Question3,4) 

Ans: \[\in \]

4. 5-A                                                                                                                                                 

5. Write the set $A=\left\{ x:x\text{ is an integer},-1\le x \le 4 \right\}$ in roster form.

Ans: The elements in roster form is as shown

\[A=\{-1,0,1,2,3\}\]

6. List all the elements of the set, $A=\left\{ x:x \in Z,\dfrac{-1}{2}\le x\le \dfrac{11}{2} \right\}$                                                                                                 

Ans: All the elements are as shown 

\[A=\{0,1,2,3,4,5\}\]

7. Write the set $B=\left\{ 3,9,27,81 \right\}$ in set-builder form.

Ans: The above set in set builder form is as shown

\[B=\{x:x={{3}^{n}},n\in N\text{ and }1\le n\le 4\}\]

Which of the following are empty sets? Justify.

8. $A=\left\{ x:x\in N,3\le x \le 4 \right\}$

Ans: Empty set, because there is no natural number that lies between \[3\] and \[4\]

9. $B=\left\{ x:x\in N,{{x}^{2}}=x \right\}$                                                                                                            

Ans: Non-empty set, because there exist natural number which equals to square of itself. For example ${{1}^{2}}=1$ and so on.

Which of the sets are finite or infinite? Justify.

10. The set of all points on the circumference of a circle.                                     

Ans: Infinite set, because there are many points in the circumference of circle

11. $B=\left\{ x:x\in N\text{ and x is an even prime number} \right\}$

Ans: Finite set, because the only even prime number is two.

12. Are sets $A=\left\{ -2,2 \right\},B=\left\{ x:x\in R,{{x}^{2}}-4=0 \right\}$ equal? Why? 

Ans: Yes because the number of elements in A is equal to that of B 

13. Write $\left( -5,\left. 9 \right] \right.$in set-builder form

Ans: \[\left\{ x:x\in ,-5 \le x\le 9 \right\}\]

14. Write $A=\left\{ x:-3\le x \le 7 \right\}$ as interval

Ans: Clearly in interval the above set is written as

\[\left[ -3,\left. 7 \right) \right.\]

15. If $A=\left\{ 1,3,5 \right\}$ how many elements has P(A)? 

Ans: Clearly the number of elements in  \[P\left( A \right)={{2}^{3}}=8\]

16. Write all the possible subsets of $A=\left\{ 5,6 \right\}$.                                                        

Ans: Clearly the possible values of \[A=\left\{ 5,6, \right\}\]is given by

\[\left\{ \varphi ,\left\{ 5 \right\},\left\{ 6 \right\},\left\{ 5,6 \right\} \right\}\]

17. If  $A=\left\{ 2,3,4,5 \right\},B=\left\{ 3,5,6,7 \right\}$. Find $A\bigcup B$

Ans: Clearly \[A\bigcup B=\left\{ 2,3,4,5,6,7 \right\}\]

18.In above question find  $A\bigcap B$  

Ans: Clearly \[A\bigcap B=\left\{ 3,5 \right\}\]

19. If $A=\left\{ 1,2,3,6 \right\},B=\left\{ 1,2,4,8 \right\}$ find $B-A$

Ans: We are given with sets as shown

\[A=\left\{ 1,2,3,6 \right\}\]

\[B=\left\{ 1,2,4,8 \right\}\]

Hence \[B-A=\left\{ 4,8 \right\}\]

20. If $A=\left\{ p,q \right\},B=\left\{ p,q,r \right\}$, is B a superset of \[A\]? Why?

Ans: Yes, because A is a subset of B.

21. Are sets $A=\left\{ 1,2,3,4 \right\},B=\left\{ x:x\in N\text{ and 5}\le \text{x}\le \text{7} \right\}$ disjoint? Why?

Ans: The above mentioned sets are disjoint because  \[\left( A\bigcup B \right)=\varphi \].

22. If X and Y are two sets such that $n\left( X \right)=19,n\left( Y \right)=37,n\left( X\bigcap Y \right)=12$ find $n\left( X\bigcup Y \right)$.

Ans: We know that \[n\left( X\bigcup Y \right)\] is given by

\[n\left( X\bigcup Y \right)=n\left( X \right)+n\left( Y \right)-n\left( X\bigcap Y \right)\]

Hence we get \[n\left( X\bigcup Y \right)=44\]

23. Describe the set in Roster form.

$\left\{ x:\text{x is a two digit number such that the sum of its digits is 8 } \right\}$

Ans: The set in Roster form of above mentioned set is 

\[\left\{ 17,26,35,44,53,62,71,80 \right\}\]

24. Are the following pair of sets equal? Give reasons. 

$A=\left\{ x:\text{x is a letter in the word FOLLOW } \right\}$

$B=\left\{ x:\text{x is a letter in the word WOLF } \right\}$  

Ans: We can write above mentioned sets as shown

\[A=\left\{ F,O,L,W \right\}\]

\[n\left( A \right)=4\]

\[B=\left\{ W,O,L,F \right\}\]

\[n\left( B \right)=4\]

Hence  \[A=B\]

25. Write down all the subsets of the set $\left\{ 1,2,3 \right\}$

Ans: All the subsets of the set \[\{1,2,3\}\] is given below

\[\left\{ \varnothing ,\{1\},\{2\},\{3\},\{1,2\},\{1,3\},\{2,3\},\{1,2,3\} \right\}\]

26. Let $A=\left\{ 1,2,\left\{ 3,4 \right\},5 \right\}$ is $\left\{ \left\{ 3,4 \right\} \right\}\in A$ is incorrect. Give a reason.

Ans: Clearly \[\left\{ 3,4 \right\}\] is an element of set A, therefore \[\left\{ \left\{ 3,4 \right\} \right\}\] is a set containing element \[\left\{ 3,4 \right\}\] which belongs to A.

Hence, \[\left\{ \left\{ 3,4 \right\} \right\}\in A\] is correct.

27. Draw Venn diagram for $\left( A\bigcap B \right)'$

Ans: We know that 

\[\left( A\bigcap B \right)'=U-A\bigcap B\]

Hence the region is shown in the venn diagram below

                                           Fig: \[(A\cap B)'\]

28. Write the set in roster form A the set of letters in TRIGNOMETRY

Ans: The set of letters in TRIGNOMETRY in roster form is written as

\[A=\left\{ T,R,I,G,N,O,M,E,T,R,Y \right\}\]

29. Are the following pair of sets are equal? Give reasons    

A, the set of letters in “ALLOY” and B, the set of letters in “LOYAL”.

Ans: The set of letters in ALLOY is written as

\[A=\left\{ A,,L,O,Y \right\}\]

Similarly, the set of letters in LOYAL is written as

\[B=\left\{ L,O,Y,A \right\}\]

Hence \[A=B\]

30. Write down the power set of A, $A=\left\{ 1,2,3 \right\}$ 

Ans: We know that power set is written as shown

\[P(A)=\left\{ \varnothing ,\{1\},\{2\},\{3\},\{1,2\},\{1,3\},\{2,3\},\{1,2,3\} \right\}\]

31.  $A=\left\{ 1,2,\left\{ 3,4 \right\},5 \right\}$ which is incorrect and why.

 (i) \[\{3,4\}\subset A\]

Ans: Clearly we can see that \[\left\{ 3,4 \right\}\in A\] 

Hence \[\left\{ 3,4 \right\}\subset A\] is incorrect

(ii) \[\{3,4\}\in A\]

Hence \[\left\{ 3,4 \right\}\in A\] is correct

32. Fill in the blanks:

(i) $A\bigcup A'$

Ans: We know that \[A\bigcup A'=U\] where U is the universal set

(ii) $\left( A' \right)'$

Ans: We know that \[\left( A' \right)'=A\]

(iii) $A\bigcap A'$

Ans: We know that \[A\bigcap A'=\varphi \]where \[\varphi \] is the universal set.

33. Write the set $\left\{\dfrac{1}{2},\dfrac{2}{3},\dfrac{3}{4},\dfrac{4}{5},\dfrac{5}{6},\dfrac{6}{7} \right\}$ in the set builder form.

Ans: The set builder form of above set is given by

\[\left\{ \dfrac{n}{n+1}:n\text{ is a natural number less than or equal to 6} \right\}\]

34. Is set $C=\left\{ x:x-5=0 \right\}$ and

$E=\left\{ x:\text{x is an integral positive root of the equation }{{x}^{2}}-2x-15=0 \right\}$ are equal?

Ans: From set C we get

Hence \[C=\left\{ 5 \right\}\]

Also on solving the equation 

\[{{x}^{2}}-2x-15=0\]

We get the positive root as shown

Hence both the sets are equal

35. Write down all possible proper subsets of the set $\left\{ 1,\left\{ 2 \right\} \right\}$.                           

Ans: All possible proper subsets of the given set are

\[\varphi ,\left\{ 1 \right\},\left\{ 2 \right\},\left\{ 1,\left\{ 2 \right\} \right\}\]

36. State whether each of the following statements is true or false.

(i) $A=\left( 2,3,4,5 \right),B=\left\{ 3,6 \right\}$are disjoint sets.

Ans: Clearly we have

\[\left\{ 2,3,4,5 \right\}\bigcap \left\{ 3,6 \right\}=\left\{ 3 \right\}\ne \varphi \]

Hence the above statement is false

(ii) $A=\left( 2,6,10 \right),B=\left\{ 3,7,11 \right\}$are disjoint sets.

\[\left\{ 2,6,10 \right\}\bigcap \left\{ 3,7,11 \right\}=\varphi \]

Hence the above statement is true

37. Solve the followings:

(i) $\left( A\bigcup B \right)'$

Ans: By the properties we write

\[\left( A\bigcup B \right)'=A'\bigcap B'\]

(ii) $\left( A\bigcap B \right)'$

\[\left( A\bigcap B \right)'=A'\bigcup B'\]

38. Write the set of all vowels in the English alphabet which precede k in roster form.                        

Ans: The set of all vowels in the English alphabet which precede k in roster form is as shown

\[N=\left\{ a,e,i \right\}\]

39. Is pair of sets equal? Give reasons.

$A=\left( 2,3 \right),B=\left\{ x:\text{x is the solution of }{{x}^{2}}+5x+6=0 \right\}$

Ans: Given we have

\[A=\left\{ 2,3 \right\}\]

\[B=\left\{ x:x\text{ is the solution of }{{\text{x}}^{2}}+5x+6 \right\}\]

Now we can easily find the solution of  \[{{\text{x}}^{2}}+5x+6\] to be the set \[B=\left\{ -2,-3 \right\}\]

Hence  \[A\ne B\]

So the given pair of sets are not  equal

40. Write the following intervals in set builder form: $\left( -3,0 \right)$ and $\left[ \left( 6,12 \right) \right]$ 

Ans: The set builder form of above intervals is given by

\[\left\{ -3,0 \right\}\to \left\{ x:x\in R,-3\le x \le 0 \right\}\]

\[\left\{ 6,12 \right\}\to \left\{ x:x\in R,6\le x\le 12 \right\}\]  

41. If $X=\left\{ a,b,c,d \right\}$

$Y=\left\{ f,b,d,g \right\}$

Find $X-Y$ and $Y-X$

Ans: We are given with the following sets

\[X=\left\{ a,b,c,d \right\}\]

\[Y=\left\{ f,b,d,g \right\}\]

Hence \[X-Y=\left\{ a,c \right\}\]

Similarly, \[Y-X=\left\{ f,g \right\}\]

42. If A and B are two given sets, then represent the set $\left( A-B \right)'$, using the Venn diagram.

\[\left( A-B \right)'=U-\left( A-B \right)\] and hence the venn diagram is as shown

                                    Fig-\[(A-B)'\]

43. List all the element of the set $A=\left\{ x:x\text{ is an integer},{{x}^{2}}\le 4 \right\}$ 

Ans: The elements which we will get is as shown

\[\left\{ -2,-1,0,1,2 \right\}\]

44. From the sets given below pair the equivalent sets.

$A=\left\{ 1,2,3 \right\},B=\left\{ x,y,z,t \right\},C=\left\{ a,b,c \right\},D=\left\{ 0,a \right\}$

Ans: From the data given A and C are equivalent sets because the number of elements in each is same.

45. Write the following as interval                                                                              

(i) $\left\{ x:x\in R,-4 \le x\le 6 \right\}$

Ans : The interval form of above is given as shown

\[\left( -4,6 \right]\]

(ii) $\left\{ x:x\in R,3\le x\le 4 \right\}$

Ans: The interval form of above is given as shown

\[\left[ 3,4 \right]\]

46. If $A=\left\{ 3,5,7,9,11 \right\},B=\left\{ 7,9,11,13 \right\},C=\left\{ 11,13,15 \right\}$ Find $\left( A\bigcap B \right)\bigcap \left( B\bigcup C \right)$

Ans: From the data given we have

\[A=\left\{ 3,5,7,9,11 \right\}\]

\[B=\left\{ 7,9,11,13 \right\}\]

\[C=\left\{ 11,13,15 \right\}\]

Now \[A\bigcap B=\left\{ 7,9,11 \right\}\]

\[B\bigcup C=\left\{ 7,9,11,13,15 \right\}\]

Therefore \[\left( A\bigcap B \right)\bigcap \left( B\bigcup C \right)=\left\{ 7,9,11 \right\}\]

47. Write the set $\left\{ \dfrac{1}{3},\dfrac{3}{5},\dfrac{5}{7},\dfrac{7}{9},\dfrac{9}{11},\dfrac{11}{13} \right\}$in set builder form. 

Ans: \[\left\{ \dfrac{2n-1}{2n+1}:n\text{ is a natural number less than 7} \right\}\]

Long Questions and Answers (4 Marks Questions)

1. In a group of $800$ people, $500$ can speak Hindi and $320$ can speak English. Find

(i) How many can speak both Hindi and English?    

Ans: We will use following notation

H-People who can speak Hindi

E-People who can speak English

It is given in the question that

\[n\left( E\bigcup H \right)=800\]

\[n\left( E \right)=320\]

\[n\left( H \right)=500\]

Also we know that

\[n\left( E\bigcup H \right)=n\left( E \right)+n\left( H \right)-n\left( E\bigcap H \right)\]

800=320+500\[-n\left( E\bigcap H \right)\]

Hence on solving above we get \[20\] people can speak both Hindi and English

(ii) How many can speak Hindi only? 

Also we find that

\[n\left( E\bigcap H \right)=20\]

\[n\left( E'\bigcap H \right)=n\left( H \right)-n\left( E\bigcap H \right)\]

Hence on solving above we get \[480\] people can speak both Hindi and English

2. A survey shows that $84$ percent of Indians like grapes, whereas $45$ percent like pineapple. What percentage of Indians like both grapes and pineapple?                          

A-set of Indians who like grapes

O-set of Indians who like pineapple

\[n\left( A\bigcup O \right)=100\]

\[n\left( A \right)=84\]

\[n\left( O \right)=45\]

Now we know that 

\[n\left( A\bigcup O \right)=n\left( A \right)+n\left( O \right)-n\left( A\bigcap O \right)\]

Hence on solving the above we get 

\[n\left( A\bigcap O \right)=29\]

Therefore \[29\] percent of Indians like both apples and oranges 

3. In a survey of $450$ people, it was found that $110$ play cricket, $160$ play tennis and $70$ play both cricket as well as tennis. How many plays neither cricket nor tennis? 

S-set of surveyed people

A-set of people who play cricket

O- set of people who play tennis

\[n\left( A\bigcap O \right)=70\]

\[n\left( A \right)=110\]

\[n\left( O \right)=160\]

\[\Rightarrow n\left( A\bigcup O \right)=110+160-70=200\]

Therefore students who like neither cricket nor tennis is given by

\[n\left( A'\bigcap O' \right)=450-200=250\]

4. In a group of students, $225$ students know French, $100$ know Spanish and $45$ know both. Each student knows either French or Spanish. How many students are there in the group? 

A-set of students who know French

O- set of students who know Spanish

\[n\left( A\bigcap O \right)=45\]

\[n\left( O \right)=100\]

\[n\left( A \right)=225\]

 \[\Rightarrow n\left( A\bigcup O \right)=225+100-45=280\]

Hence there are 280 students in the group.

5. If $A=\left[ \left( -3,5 \right),B=\left( 0,6 \right) \right]$  then find 

(i) $A-B$, 

Ans: Given we have 

\[A=\left( -3,5 \right)\]

\[B=\left( 0,6 \right)\]

We know that \[A-B=A\bigcap B'\]

Hence \[A-B=\left[ -3,0 \right]\]

(ii) $A\bigcup B$

We know that \[A\bigcup B\] means occurrence of at least one 

Hence \[A\bigcup B=\left[ -3,6 \right]\]

6.  In a survey of $400$ students in a school, $100$ were listed as taking apple juice, $150$ as taking orange juice and $75$ were listed as taking both apple as well as orange juice. Find how many students were taking neither apple juice nor orange juice.

A-set of students who like apple juice

O- set of students who like orange juice

\[n\left( A\bigcap O \right)=75\]

\[n\left( A \right)=100\]

\[n\left( O \right)=150\]

\[\Rightarrow n\left( A\bigcup O \right)=100+150-75=175\]

Therefore students who take neither apple nor orange juice is given by

\[n\left( A'\bigcap O' \right)=400-175=225\]

7. A survey shows that $73$ percent of Indians like apples, whereas $65$ percent like oranges. What percent of Indians like both apples and oranges?

A-set of Indians who like apples

O-set of Indians who like oranges

\[n\left( A \right)=73\]

\[n\left( O \right)=65\]

\[n\left( A\bigcap O \right)=38\]

Therefore \[38\] percent of Indians like both apples and oranges 

8. In a school there are $20$ teachers who teach mathematics or physics. Of these $12$ teach mathematics and $4$ teach both physics and mathematics. How many teach physics?                                                                                                                          

Ans: We will use following notation 

P-Number of physics teachers

M- Number of mathematics teachers

We are given 

\[n\left( P\bigcup M \right)=20\]

\[n\left( M \right)=12\]

\[n\left( P\bigcap M \right)=4\]

\[n\left( P\bigcup M \right)=n\left( P \right)+n\left( M \right)-n\left( M\bigcap P \right)\]

On putting the respected values and solving we get

\[n\left( P \right)=12\]

9. Let $U=\left\{ 1,2,3,4,5,6 \right\},A=\left\{ 2,3 \right\},B=\left\{ 3,4,5 \right\}$. Find $A'\bigcap B',A\bigcup B$and hence show that $A\bigcup B=A'\bigcap B'$.               

Ans : We know that 

$=\left\{ 1,4,5,6 \right\}$

$=\left\{ 1,2,6 \right\}$

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

$\left( A'\bigcap B' \right)=\left\{ 1,6 \right\}$

Hence proved.

10. For any two sets A and B prove by using properties of sets that:

$\left( A\bigcap B \right)\bigcup \left( A-B \right)=A$

Ans: We write LHS and RHS as shown

 $LHS=\left( A\bigcap B \right)\bigcup \left( A-B \right)$

$=\left( A\bigcap B \right)\bigcup \left( A\bigcap {{B}^{'}} \right)$ (since $\left( A-B \right)=\left( A\bigcap {{B}^{'}} \right)$)

$=A\bigcap \left( B\bigcup {{B}^{'}} \right)$

$=A\bigcap \left( U \right)$

11. If A and B are two sets and $U$ is the universal set such that 

$n\left( U \right)=1000,n\left( A \right)=300,n\left( B \right)=300,n\left( A\bigcap B \right)=200$ find $n\left( {{A}^{'}}\bigcap {{B}^{'}} \right)$.

$n\left( {{A}^{'}}\bigcap {{B}^{'}} \right)=n{{\left( A\bigcup B \right)}^{'}}$

$\Rightarrow n\left( {{A}^{'}}\bigcap {{B}^{'}} \right)=n\left( U \right)-n\left( A\bigcup B \right)$

$\Rightarrow n\left( {{A}^{'}}\bigcap {{B}^{'}} \right)=n\left( U \right)-\left[ n\left( A \right)+n\left( B \right)-n\left( A\bigcap B \right) \right]$

$\Rightarrow n\left( {{A}^{'}}\bigcap {{B}^{'}} \right)=1000-\left[ 300+300-200 \right]=600$

12. There are $210$ members in a club. $100$ of them drink tea and $65$ drink tea but not coffee, each member drinks tea or coffee. Find how many drinks coffee. How many drink coffee, but not tea.             

Ans: Let us have following notation

S-total members in the club

T-members who drink tea

C- members who drink coffee

$n\left( T \right)=100$

$n\left( T-C \right)=65$

$n\left( T\bigcup C \right)=210=n\left( S \right)$(since $n\left( T\bigcap C \right)=0$

We know that

\[n\left( T-C \right)=n\left( T \right)-n\left( T\bigcap C \right)\]

\[\Rightarrow n\left( T\bigcap C \right)=35\]

$n\left( T\bigcup C \right)=n\left( T \right)+n\left( C \right)-n\left( T\bigcap C \right)$

$\Rightarrow n\left( C \right)=145$

Therefore $n\left( C-T \right)=110$

13. If $P\left( A \right)=P\left( B \right)$, Show that $A=B$

Ans: For every $a\in A$ 

$\left\{ a \right\}\subset A$

$\Rightarrow \left\{ a \right\}\in P\left( A \right)$

$\Rightarrow \left\{ a \right\}\in P\left( B \right)$ (since $P\left( A \right)=P\left( B \right)$)

$\Rightarrow \left\{ a \right\}\in B$

$\left\{ a \right\}\subset B$

$\Rightarrow A\subset B$

Similarly we can easily say $B\subset A$

Therefore $B=A$

14. In a class of $25$ students, $12$ have taken mathematics, $8$ have taken mathematics but not biology. Find the no. of students who have taken both mathematics and biology and the no. of those who have taken biology but not mathematics each student has taken either mathematics or biology or both.

T-total number of students

M- number of students who have taken mathematics

B- number of students who have taken biology

$n\left( M \right)=12$

$n\left( M-B \right)=8$

$n\left( M\bigcup B \right)=25$

$n\left( M\bigcup B \right)=n\left( M \right)+n\left( B-M \right)$

$\Rightarrow 25=12+n\left( B-M \right)$

$\Rightarrow n\left( B-M \right)=13$

\[n\left( M\bigcup B \right)=n\left( M-B \right)+n\left( B-M \right)+n\left( M\bigcap B \right)\]

Hence we get \[n\left( M\bigcap B \right)=4\]  

15. A and B are two sets such that $n\left( A-B \right)=14+x,n\left( B-A \right)=3x,n\left( A\bigcap B \right)=x$. Draw a Venn diagram to illustrate this information. If $n\left( A \right)=n\left( B \right)$, Find 

(i) the value of $x$ 

Ans: It is given in the question 

 $n\left( A-B \right)=14+x$

$n\left( B-A \right)=3x$

$n\left( A\bigcap B \right)=x$

The venn diagram is as shown

$n\left( A \right)=n\left( A-B \right)+n\left( A\bigcap B \right)$

$\Rightarrow n\left( A \right)=14+2x$

$n\left( A \right)=n\left( B-A \right)+n\left( A\bigcap B \right)$

$\Rightarrow n\left( B \right)=4x$

Also it is given that $n\left( B \right)=n\left( A \right)$

Hence $14+2x=4x$

$\Rightarrow x=7$

(ii) $n\left( A\bigcup B \right)$         

Ans: From the above data we have

$n\left( A\bigcup B \right)=n\left( A-B \right)+n\left( B-A \right)+n\left( A\bigcap B \right)$

$\Rightarrow n\left( A\bigcup B \right)=14+x+3x+x=14+5x$

Hence  $n\left( A\bigcup B \right)=49$ (since $x=7$)

16. If A and B are two sets such that $A\bigcup B=A\bigcap B$ , then prove that $A=B$. 

Ans: Let us have $a\in A\Rightarrow a\in A\bigcap B$ 

It is given that $A\bigcup B=A\bigcap B$

Since we have $a\in A\bigcap B$ 

Therefore $A\subset B$

And similarly $B\subset A$

Therefore $A=B$ proved

17. Prove that if $A\bigcup B=C$ and $A\bigcap B=\varphi $ then $A=C-B$ 

Ans: Given $\left( A\bigcup B \right)=C$and $\left( A\bigcap B \right)=\varphi $

$\left( A\bigcup B \right)-B=\left( A\bigcup B \right)\bigcap {{B}^{'}}$

$=\left( {{B}^{'}}\bigcap A \right)\bigcup \left( {{B}^{'}}\bigcap B \right)$

$=\left( {{B}^{'}}\bigcap A \right)$

$=A$(since $\left( A\bigcap B \right)=\varphi $)

Hence proved

18. In a group of $65$ people, $40$ like cricket, $10$ like both cricket and tennis. How many like tennis only and not cricket? How many like tennis? 

Ans: Let us have following denotion

C-the set of people who like cricket

T-the set of people who like tennis

$n\left( C\bigcup T \right)=65$

$n\left( C \right)=40$

$n\left( C\bigcap T \right)=10$

We know that 

$n\left( C\bigcup T \right)=n\left( C \right)+n\left( T \right)-n\left( C\bigcap T \right)$

$\Rightarrow 65=40+n\left( T \right)-10$

Hence we get people who like tennis as $n\left( T \right)=35$

Now people who like tennis only not cricket is given by

$n\left( T-C \right)=n\left( T \right)-n\left( C\bigcap T \right)$

$\Rightarrow n\left( T-C \right)=35-10=25$

19. Let A,B and C be three sets $A\bigcup B=A\bigcup C$ and $A\bigcap B=A\bigcap C$ show that $B=C$                                                                                                                                  

Ans: Let us have $b\in B\Rightarrow b\in A\bigcup B$

Also it is given $A\bigcup B=A\bigcup C$

Therefore $b\in A\bigcup C$

Hence we get $b\in A\text{ or }b\in C$

In both cases B is subset of C

Similarly in both cases C is subset of B

Therefore $B=C$

20. If $U=\left\{ a,e,i,o,u \right\}$

$A=\left\{ a,e,i \right\}$ and $B=\left\{ e,o,u \right\}$, $C=\left\{ a,e,i \right\}$

Then verify that \[A\bigcap \left( B-C \right)=A\bigcap B-A\bigcap C\]\[A\cap (B-C)=(A\cap B)-(A\cap C)\]

$B-C=\left\{ e,o \right\}$

$A\bigcap \left( B-C \right)=\left\{ e \right\}$

$A\bigcap B=\left\{ e,o \right\}$and

$A\bigcap C=\left\{ a \right\}$

Hence proved 

$A\bigcap \left( B-C \right)=\left( A\bigcap B \right)-\left( A\bigcap C \right)$

Very Long Questions and Answers (6 Marks Questions)

1. In a survey it is found that $21$ people like product A, $26$ people like product B   and $29$ like product C. If $14$ people like product A and B, $15$ people like product and C, $12$ people like product C and A, and $8$ people like all the three products. Find 

(i) How many people are surveyed in all? 

Ans : Let us have A, B, C denote respectively the set of people who like the products A, B, C.

Then we can have a venn diagram as shown

From the above diagram 

Total number of surveyed people is given by

$a+b+c+d+e+f+g$

$a=21,e=26,g=29,d=12,b=14,f=15,c=8$

Therefore total number of surveyed people is given by

$21+14+8+12+26+15+29=125$

(ii) How many like product C only?

Ans: The number of people who like product C only is $29$                                                                 

2. A college awarded $38$ medals in football, $15$ in basketball and $20$ in cricket. If these medals went to a total of $50$ men and only five men got medals in all the three sports, how many received medals in exactly two of the three sports?

Ans : Let us have a notation F, B, and C for medals in football, basketball, and cricket respectively

C is intersection of all A,B,C and a,e,g are intersections of A and not B, B and not C, A and not C respectively.

From the above venn diagram      

\[f=5\]                ……(a)

\[a+b+e+f=38\]……(b)

\[b+c+d+f=15\]……(c)

\[e+d+f+g=20\]……(d)

$a+b+c+d+e+f+g=50$ ……(e)

From equations (d), (e) we get as shown

$a+b+c=30$……(f)

Now from equation (b) and (f) we get as shown

$e-3=c$       …….(g)

put value of c in the equation € as shown

$a+e+g+b+e+d=50-5+3$

Also from equation (d) and (e) we get

Therefore the medals received in exactly 2 of three sports is given by solving above equations as shown

 \[b+e+d=13\]

3. There are 200 individuals with a skin disorder, $120$ had been exposed to the chemical ${{C}_{1}}$, 50 to chemical ${{C}_{2}}$, and 30 to both the chemicals ${{C}_{1}}$ and ${{C}_{2}}$. Find the number of individuals exposed to 

(i). Chemical ${{C}_{1}}$ but not chemical ${{C}_{2}}$

Ans: Let us have a following notation

A- Denote the set of individuals exposed to the chemical \[{{C}_{1}}\]

B- Denote the set of individuals exposed to the chemical \[{{C}_{2}}\]

Given 

\[n\left( S \right)=200\] 

\[n\left( A \right)=120\]

\[n\left( B \right)=50\]

\[n\left( A\bigcap B \right)=30\]

\[\therefore n\left( A\bigcap \overline{B} \right)=n\left( A \right)-n\left( A\bigcap B \right)\]

\[\Rightarrow n\left( A\bigcap \overline{B} \right)=120-30=90\]

Hence the number of individuals exposed to chemical \[{{C}_{1}}\] but not to \[{{C}_{2}}\] is \[90\]

(ii). Chemical ${{C}_{2}}$ but not chemical ${{C}_{1}}$

\[\therefore n\left( \overline{A}\bigcap B \right)=n\left( B \right)-n\left( A\bigcap B \right)\]

\[\Rightarrow n\left( \overline{A}\bigcap B \right)=50-30=20\]

Hence the number of individuals exposed to chemical \[{{C}_{2}}\] but not to \[{{C}_{1}}\]  is \[20\]

(iii). Chemical ${{C}_{1}}$ or chemical ${{C}_{2}}$

Ans : Let us have a following notation

\[\therefore n\left( A\bigcup B \right)=n\left( A \right)+n\left( B \right)-n\left( A\bigcap B \right)\]

\[\Rightarrow n\left( A\bigcup B \right)=120+50-30=140\]

Hence the number of individuals exposed to chemical \[{{C}_{2}}\]or \[{{C}_{1}}\]  is \[140\]

4. In a survey it was found that $21$ people liked product A, $26$ liked product B and $29$ liked product C. If $14$ people liked products A and B, $12$ people like C and A, $15$ people like B and C and $8$ liked all the three products. Find now many liked product C only.

Ans: Let us have a venn diagram of above information as shown

The followings are given in the question

$a+b+c+d=21$

$b+c+e+f=26$

$c+d+f+g=29$

Also it is given in the question 

$\therefore d=4$

$\therefore f=7$

Hence the number of people who like product C only is $g=10$ 

5. A college awarded $38$ medals in football, $15$ in basketball and $20$ in cricket. If these medals went to a total of $58$ men and only three men got medals in all the three sports, how many received medals in exactly two of the three sports?

Ans: Let us denote A, B and C as the sets of men who received medals in football, basketball and cricket respectively.

\[n\left( A \right)=38\]

\[n\left( B \right)=15\]

\[n\left( C \right)=20\]

\[n\left( A\bigcup B\bigcup C \right)=58\]

\[n\left( A\bigcap B\bigcap C \right)=3\]

\[\left( A\bigcup B\bigcup C \right)=n\left( A \right)+n\left( B \right)+n\left( C \right)-\left[ n\left( A\bigcap B \right)+n\left( B\bigcap C \right)+n\left( C\bigcap A \right) \right]+n\left( A\bigcap B\bigcap C \right)\]

\[\Rightarrow 58=38+15+20-\left( a+d \right)-\left( d+c \right)-\left( b+d \right)+3\]

\[\Rightarrow 18=a+b+c+3d\]

Hence we get \[a+b+c=9\]

6. In a survey of $60$ people, it was found that $25$ people read newspaper H, $26$ read newspaper T, $26$ read newspaper I, $9$ read both H and I, $11$ read both H and T, $8$ read both T and I, $3$ read all three newspapers. Find 

i) The no. of people who read at least one of the newspapers. 

Ans: Let us have a venn diagram as shown

We are given with the following data

\[a+b+c+d=25\]

\[b+c+e+f=26\]

\[d+c+g+f=26\]

And also it is given 

\[\therefore f=5\]

\[\therefore b=8\]

\[\therefore d=6\]

\[\therefore g=12\]

\[\therefore e=10\]

\[\therefore a=8\]

The no. of people who read at least one of the newspapers is \[a+b+c+d+e+f+g=52\]

ii) The no. of people who read exactly one newspaper

The no. of people who read exactly one newspaper is \[a+e+g=30\]

7. These are $20$ students in a chemistry class and $30$ students in a physics class. Find the number of students which are either in physics class or chemistry class in the following cases.

(i) Two classes meet at the same hour.

Ans: Let \[C\] be the set of students in chemistry class and \[P\] be the set of students in physics class.

\[n\left( P \right)=30\]

Now it is given that two classes meet at the same hour and hence

\[n\left( C\bigcap P \right)=0\]

\[\therefore n\left( C\bigcup P \right)=n\left( C \right)+n\left( P \right)-0\]

\[\Rightarrow n\left( C\bigcup P \right)=20+30=50\]

Hence the number of students which are either in physics class or chemistry class when classes are at the same time is \[50\].

(ii) The two classes met at different hours and ten students are enrolled in both the courses.

\[n\left( C\bigcap P \right)=10\]

\[\therefore n\left( C\bigcup P \right)=n\left( C \right)+n\left( P \right)-10\]

\[\Rightarrow n\left( C\bigcup P \right)=20+30-10=40\]

The number of students which are either in physics class or chemistry class when the two classes met at different hours and ten students are enrolled in both the courses is.

8. In a survey of $25$ students, it was found that $15$ had taken mathematics, $12$ had taken physics and $11$ had taken chemistry, $5$ had taken mathematics and chemistry, $9$ had taken mathematics and physics, $4$ had taken physics and chemistry and $3$ had taken all three subjects. 

Find the no. of students that had taken 

(i). only chemistry 

\[n\left( M \right)=a+b+d+e=15\]

\[n\left( P \right)=b+c+f+e=12\]

\[n\left( C \right)=d+e+f+g=11\]

\[n\left( M\bigcap P \right)=b+e=9\]

\[n\left( M\bigcap C \right)=d+e=5\]

\[n\left( P\bigcap C \right)=f+e=4\]

Also it is given that \[e=3\]

\[\therefore b=6,\therefore d=2,\therefore f=1\]

Also \[\therefore a=4,\therefore g=5,\therefore c=2\]

Therefore the number of students who had taken only chemistry is \[g=5\]

(ii). only mathematics 

Therefore the number of students who had taken only mathematics is \[a=4\]

(iii). only physics 

Therefore the number of students who had taken only physics is \[c=2\]

(iv). physics and chemistry but not  mathematics 

Therefore the number of students who had taken physics and chemistry but not mathematics is \[f=1\]

(v). mathematics and physics but not chemistry 

Therefore the number of students who had taken physics and mathematics but not chemistry is \[b=6\]

(vi). only one of the subjects 

Ans : Let us have a venn diagram of above information as shown

Therefore the number of students who had taken only one of the subjects is \[\therefore a+g+c=11\]

(vii). at least one of three subjects 

Therefore the number of students who had taken atleast one of the subjects is \[a+b+c+d+e+f+g=23\]

(viii). None of three subjects.

Therefore the number of students who had taken none of the subjects is \[25-\left( a+b+c+d+e+f+g \right)=2\]

9. In a survey of $100$ students, the no. of students studying the various languages were found to be English only $18$, English but not Hindi $23$, English and Sanskrit $8$, English $26$, Sanskrit $48$, Sanskrit and Hindi $8$, no language $24$. Find 

(i) How many students were studying Hindi? 

Ans: Let the total number of students be 

Let us have the venn diagram as shown

\[a+e+g+d=26\]

\[g+e+f+c=48\]

So we get 

\[e=5,g=3,d=0,f=5,c=35\]

Therefore the number of students studying Hindi is \[f+b+g+d=18\]

(ii) How many students were studying English and Hindi?

Therefore the number of students studying Hindi and English is \[g+d=3\] 

10. In a class of $50$ students, $30$ students like Hindi, $25$ like science and $16$ like both. Find the no. of students who like 

(i) Either Hindi or Science

Ans: Let the total number of students be

Let us denote number of students who like Hindi with H and who like science with S

\[n\left( H\bigcup S \right)=n\left( H \right)+n\left( S \right)-n\left( H\bigcap S \right)\]

\[\Rightarrow n\left( H\bigcup S \right)=30+25-16=39\]

Therefore the number of students who like either Hindi or Science is \[39\]

(ii) Neither Hindi nor Science.

\[n\left( {{H}^{'}}\bigcap {{S}^{'}} \right)=T-n\left( H\bigcup S \right)\]

\[\Rightarrow n\left( {{H}^{'}}\bigcap {{S}^{'}} \right)=50-39=11\]

Therefore the number of students who like either Hindi or Science is \[39\]  

11. In a town of 10,000 families, it was found that 40% of families buy newspaper A, 20% families buy newspaper B, and 10% of families buy newspaper C. 5% of families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three papers. Find the no. of families which buy

(i) A only 

Ans: Let the total number of families be 

\[T=10,000\]

Let us have the venn diagram of above information as shown

It is given in the question that 

\[x+a+c+d=4000\]

\[y+a+b+d=2000\]

\[z+b+c+d=1000\]

\[a+d=500\]

\[b+d=300\]

\[c+d=400\]

Hence on solving we get

\[a=300,b=100,c=200\]

Therefore the number of families who buy newspaper A only is \[x=4000-300-200-20=3380\]

(ii) B only

Ans : Let the total number of families be 

Let us have the venn diagram of above informations as shown

Therefore the number of families who buy newspaper B only is \[y=2000-300-200-100=1400\]

(iii) none of A, B, and C. 

From the above we get

\[z=1000-100-200-200=500\]

Therefore the number of families who buy newspaper none of A, B or C is 

\[10000-\left[ 3300+1400+500+300+100+200+200 \right]=5000\]

12. Two finite sets have m and n elements. The total no. of subsets of the first set is 56 more than the total no. of subsets of the second set. Find the value of m and n.      

Ans: Assume A and B be two sets having m and n elements respectively

Hence we know that number of subsets will be given as shown

Number of subsets of A is \[{{2}^{m}}\]

Number of subsets of B is \[{{2}^{n}}\]

According to the question 

\[{{2}^{m}}=56+{{2}^{n}}\]

\[\Rightarrow {{2}^{m}}-{{2}^{n}}=56\]

\[\Rightarrow {{2}^{n}}\left( {{2}^{m-n}}-1 \right)=56\]

On comparing we get

\[n=3,m-n=3\] \[\Rightarrow m=6\]

Sets Important Question PDF For Download

There is no doubt that we need help when we are solving something for the first time. The same goes for the important questions for class 11 maths chapter 1. Vedantu has provided its students with some tips in the pdf which can make their learning of sets in class 11 extra questions a bit less complicated and fun.

The chapter first of the 11th notebook is easy and has all the essential questions which make students test their formula-solving skills for sets. You can quickly check out the step-by-step solutions of this chapter's important questions in the pdf format and download it offline, so it can be viewed anytime even when the person is offline. 

Important Concepts Class 11 Maths Chapter 1 Related to Sets

Given below, we have breakdown of important concepts you will study in class 11 maths chapter 1. These will help you get a better grip of the formulas and the theorems which you need to use to solve the questions. 

Equal Sets 

For sets in class 11 important questions, one needs to know about sets as they are defined as a collection of well-defined, distinct objects. On the other hand, items which come together to form a set are called elements. The condition of two sets to become equal can happen when each set's element is also a part of the other set. Likewise, if both the sets are subsets of each other, you can even say these two sets are equal. 

Venn Diagram 

It is a diagram which is used by students and mathematicians to represent sets and their relation from each other. By seeing a Venn diagram, you can determine which operation has been done on the given two sets such as the intersection of the sets and their difference. Likewise, one can easily show the subsets of a given set using these diagrams. 

Union & Intersection of Sets

In class 11 sets important questions students will learn about the concept of a cardinal number of a set which is several distinct elements or members in a finite set. With the cardinality's help, we can define the size of a set if you want to denote the cardinal number of a set A you need to write it down like this n(A).

There are three properties of which you need to remember for the cardinal numbers and these are:

If A ∩ B = ∅, then, n(A ∪ B) = n(A) + n(B) this is a Union of disjoint sets.

If A and B are two finite sets, then n(A ∪ B) = n(A) + n(B) – n(A ∩ B) which is said to be a union of two sets.

If A, B and C are three finite sets, then; n(A ∪ B ∪ C) = n(A) + n(B) + n(C) – n(A ∩ B) – n(B ∩ C) – n(A ∩ C) + n(A ∩ B ∩ C) this shows the union of three sets. 

Sets Class 11 Extra Questions

Well, if you are preparing to give the exams this year or next year, one thing is sure you need to prepare for the additional questions which are a bit tricky, and you can't find them in your textbook as well. Students studying in 11th can prepare their academic and competitive exams by solving these additional questions from Sets class 11. 

Q.1 Which of the following sets. Explain your answer.

(a). A collection of all days which are present in a single week and starts with an alphabet S.

(b).  The collection of the ten most famous singers of India.

(c).  A group of best football strikers in the world.

(d).  The collection of all boys in your school.

(e).  The collection of all the possible odd numbers below 100.

(f).  A collection of poems which are penned down by the famous poet Shakespeare.

(g).  The collection of all prime numbers.

(h).  The collection of questions in a science book.

(i).  A collection of most dangerous reptiles in India.

Q.2: Let P = {2, 3, 4, 5, 6, 7}. Insert the correct symbol  inside the given blank spaces below:

(a).  2 . . . . . . . . . . P

(b).  9 . . . . . . . . . P

(c).  11 . . . . . . . . P

(d).  4 . . . . . . . . P

(e).  0 . . . . . . . . P

(f).  7 . . . . . . . . P

Q.3: List all the elements from the given set P = {y: y is even natural number}

Q.4: If A = {(x,y) : x² + y²= 25  where x, y ∈ W } write a set of all possible ordered pairs.

Q.5: If P(X) = P(Y) show that A = B.

Q.6: Let N  and M be sets ; if N∩M = M∩X = ∅ and N∪X = M∪X for some set X.Show that N=M.

Q.7: If X ={1,2,3,4,5}, then solve the question to find out the proper subsets of A.

Q.8: For this question Write a Roster form of the given set A={x: x ∈ R, 2x+10 =12}

Q.9 Let X and Y are the two sets which have 3 and 6 elements present in them respectively. Find the maximum and the minimum number of elements in X ∪ Y.

Q.10:  If X = {(a,b) : a² + b²= 25  where a, b ∈ W } write a set of all possible ordered pairs.

Practice Questions

Write the set {-2,7} in the set builder form.

If the set N = { 1,3,7), then how many elements have set P(N).

If the universal set (U) = { 1,2,3,4,5,6,7}, A = {2,4,6} , B= { 3,5} and C = { 1,2,4,7}, Find: A′ ∪ (B ∩ C′), and  (B – A) ∪ (A – C)

If X, Y, and Z are three sets, then X – (Y ∪ Z) is equal to.

If A = {x, y} and B = { x, y, z). Is Z a superset of Y? Why?

Chapterwise Links for CBSE Class 11 Maths

Chapter 2 - Relations and Functions

Chapter 3 - Trigonometric Functions

Chapter 4 - Principle of Mathematical Induction

Chapter 5 - Complex Numbers and Quadratic Equations

Chapter 6 - Linear Inequalities

Chapter 7 - Permutations and Combinations

Chapter 8 - Binomial Theorem

Chapter 9 - Sequences and Series

Chapter 10 - Straight Lines

Chapter 11 - Conic Sections

Chapter 12 - Introduction to Three Dimensional Geometry

Chapter 13 - Limits and Derivatives

Chapter 14 - Mathematical Reasoning

Chapter 15 - Statistics

Chapter 16 - Probability

Benefits of Solving Important Questions For Class 11 Maths Chapter 1

Let's try to find out why solving the important questions for class 11th maths chapters are pretty essential and need to be done as much as possible. 

Understanding the Formulae: many times, students might skip the derivation and keep on mugging the formula all along. Knowing your formulas is a good thing, but when you don't know which one to use to solve a question is when the problem comes. With our PDF of solved sets examples, you will be able to understand which formula will be suitable for solving the problem.

Makes Your Problem Solving Efficient: Once you get a good grip on how to solve the problem, you can easily find out which problem will take more time and start writing it before anything else. 

Covers Important Topics: With this Pdf designed by Vedantu students get to know about all the main concepts of Venn Diagrams and how to use them along with Complement's properties. As a result, students will understand every topic they need to learn for their upcoming exams. 

Confidence Booster: When you start solving a question, and it comes out that you managed to get the right answer, you feel uplifted as it boosts your morale. If you have an issue with the answer, you can find out the step by step solving of the union and intersection sets answers. 

Gives More Questions for Practise: A student needs to be solving different types of problems to sharpen their mind and test their knowledge of the subject, and these important questions do the same thing. 

There you have it, these are some of the basic concepts you are going to study in the class 11th maths chapter 1 based on Sets . The important questions are solved and were written down so that it will be easier for you to understand their language. You need to keep on practising even if you think you are done with the chapter and have enough understanding. Always revise the chapter by doing some questions before you finally appear in exams. For the important questions of class 11th maths chapter 1 , you need to put both your mind and heart to study its concepts and get them memorized.

Important Related Links for CBSE Class 11 

Important Questions for Class 11 Maths Chapter 1 - Sets offered by Vedantu is an excellent resource for students who want to excel in their mathematical studies. The questions cover all the important topics in the chapter, including the definition of sets, types of sets, operations on sets, and Venn diagrams, making it easier for students to understand and improve their mathematical skills. The questions are designed by subject matter experts according to the CBSE syllabus for Class 11 students and provide a comprehensive and detailed explanation of the concepts. Additionally, the questions offer practice exercises that help students test their understanding of the chapter and prepare for their exams. Vedantu also provides interactive live classes and doubt-solving sessions to help students clarify their doubts and improve their understanding of the chapter. Overall, the Important Questions for Class 11 Maths Chapter 1 - Sets offered by Vedantu are an essential resource for students who want to improve their mathematical skills and score well in their exams.

FAQs on Important Questions for CBSE Class 11 Maths Chapter 1 - Sets 2024-25

1. How to utilize Important Questions for CBSE Class 11 Maths Chapter 1 Sets to score well in exams?

Students can solve important questions for Class 11 Maths Chapter 1 Sets available online to score well in school exams as well as competitive exams. The extra questions provided by e-learning sites on the first chapter of Class 11 Maths can be utilized to understand what types of questions can be expected from exams. These questions are really helpful for practice and clearing the concepts related to the chapter. On platforms like Vedantu, these questions are solved by expert teachers. By referring to the PDF file of important questions for Class 11 Maths Chapter 1 Sets, students will be able to practice the chapter effectively. These questions will also help in revision.

2. Where can I find Important Questions for Class 11 Maths Chapter 1 Sets?

Vedantu caters to a well-prepared set of Important Questions for Class 11 Maths Chapter 1 Sets as well as other chapters. Vedantu is a well-known online learning site known for its top quality study materials. It selects questions for a chapter based on the exam pattern and most frequently asked questions. Vedantu provides a free PDF of Important Questions for Class 11 Maths Chapter 1 Sets. These solutions are also solved by subject matter experts to provide a clear cut understanding of the chapter. These are proven to be helpful in exam preparation and provide effective revision during exams.

3. What is the importance of Vedantu’s extra questions for Class 11 Maths Chapter 1 Sets?

Vedantu’s extra questions for CBSE Class 11 Maths Chapter 1 Sets is crucial during the exam preparation. The important questions for Class 11 Maths Chapter 1 Sets allow students to practice the chapter thoroughly. Working on these questions will make students familiar with all types of questions that can be asked in the exam. The important questions PDF file at Vedantu is designed to cover all the important topics of the chapters. These questions are based on the exam pattern and are added after referring to previous year question papers. The free PDF of CBSE Maths Class 11 Chapter 1 can be utilized at the time of revision. These are really helpful in scoring well in the paper and are a confidence booster during the exam time.

4. What are the important learning outcomes from Class 11 Maths Chapter 1 Sets?

From Class 11 Maths Chapter 1 Sets, students will learn what are sets and how to represent sets. Students will also learn about types of sets such as Empty Sets, Equal Sets and what are Subsets and how to identify them. Also, one will learn how to design Venn diagrams. The chapter also includes the knowledge of different operations on sets such as Union of sets, Intersection of sets, Difference of sets, Complement of a set, etc.  Students are also taught about practical problems on Union and Intersection of Two Sets .

5. What are the important topics of the Chapter-Sets of Class 11 Maths?

Chapter 1 'Sets' of Class 11 Maths is an entirely new concept that is quite significant for the Class 11 exams. The chapter 'Sets' consists of the following important topics that students must pay attention to:

What are sets?

Sets and their representations

Finite sets and infinite sets

Universal sets

Venn diagrams

Operation on sets: Union and intersection of sets

Complement of the sets and their properties

Practical problems of union and intersection of two sets

6. How many chapters are there in Class 11 Maths apart from Chapter 1-Sets?

Class 11 Maths has a total of 16 chapters. The following are the chapters prescribed in the NCERT textbook: 

Ch. 1: Sets

Ch. 2: Relations and Functions

Ch. 3: Trigonometric Functions

Ch. 4: Principle of Mathematical Induction

Ch. 5: Complex Numbers and Quadratic Equations

Ch. 6: Linear Inequalities

Ch. 7: Permutations and Combinations

Ch. 8: Binomial Theorem

Ch. 9: Sequence and Series

Ch. 10: Straight Lines

Ch. 11: Conic Sections

Ch. 12: Introduction to Three–dimensional Geometry

Ch. 13: Limits and Derivatives

Ch. 14: Mathematical Reasoning

Ch. 15: Statistics

Ch. 16: Probability

7. What should I keep in mind while solving Chapter 1 of Class 11 Maths?

It makes a lot of difference how you present your answers in your answer sheet. Especially when it's a subject like Maths, students should make sure that their answers look neat and tidy. There are marks allocated to the steps of any solution, therefore one should ensure that his answers are written step-wise. Don't forget to mention and highlight the formula or theorem you are using in the solution. Avoid making silly mistakes with operation signs and numbers. A single mistake can make your entire solution wrong.

8. Is Chapter Sets of Class 11 Maths an important chapter?

Sets is definitely an important chapter in Class 11 Maths. It holds a major part in the exam holding a pretty good enough weightage of marks. This chapter is a whole new chapter for any student who enters Class 11 and since it is a significant chapter, students must be very keen in comprehending this chapter thoroughly. This chapter explains various types of sets in detail and questions related to them. To study more about sets students can download the Important Questions free of cost from the Vedantu website or mobile app. 

9. How can I complete my Maths class test paper of Chapter 1 of Class 11 Maths on time?

Most of the students face the difficulty of not being able to finish their papers on time. The chief reason behind this is the lack of time management. If you waste too much time solving trivial questions, you may end up skipping some really important questions. Therefore, divide your time evenly on each question before you start the exam. Regular practice using NCERT solutions and Mock tests from Vedantu can help students learn to manage their time better. 

CBSE Class 11 Maths Important Questions

Cbse study materials.

Class 11 Maths NCERT Solutions

Cbse, karnataka board puc class 11 maths solutions guide.

Shaalaa.com provides the CBSE, Karnataka Board PUC Class 11 Maths Solutions Digest. Shaalaa is undoubtedly a site that most of your classmates are using to perform well in exams.

You can solve the Class 11 Maths Book Solutions CBSE, Karnataka Board PUC textbook questions by using Shaalaa.com to verify your answers, which will help you practise better and become more confident.

CBSE, Karnataka Board PUC Class 11 Maths Textbook Solutions

Questions and answers for the Class 11 Maths Textbook are on this page. NCERT Solutions for Class 11 Maths Digest CBSE, Karnataka Board PUC will help students understand the concepts better.

NCERT Solutions for Class 11 Maths Chapterwise List | Class 11 Maths Digest

The answers to the NCERT books are the best study material for students. Listed below are the chapter-wise NCERT Maths Class 11 Solutions CBSE, Karnataka Board PUC.

•  • Chapter 1: Sets
•  • Chapter 2: Relations and Functions
•  • Chapter 3: Trigonometric Functions
•  • Chapter 4: Principle of Mathematical Induction
•  • Chapter 5: Complex Numbers and Quadratic Equations
•  • Chapter 6: Linear Inequalities
•  • Chapter 7: Permutations and Combinations
•  • Chapter 8: Binomial Theorem
•  • Chapter 9: Sequences and Series
•  • Chapter 10: Straight Lines
•  • Chapter 11: Conic Sections
•  • Chapter 12: Introduction to Three Dimensional Geometry
•  • Chapter 13: Limits and Derivatives
•  • Chapter 14: Mathematical Reasoning
•  • Chapter 15: Statistics
•  • Chapter 16: Probability
• Commerce (English Medium) Class 11 CBSE
• Science (English Medium) Class 11 CBSE
• Arts (English Medium) Class 11 CBSE
• PUC Science Class 11 Karnataka Board PUC

Advertisements

NCERT Class 11 solutions for other subjects

• NCERT solutions for Biology Class 11
• NCERT solutions for Biology Class 11 [जीव विज्ञान ११ वीं कक्षा]
• NCERT solutions for Chemistry Part 1 and 2 Class 11
• NCERT solutions for Chemistry Part 1 and 2 Class 11 [रसायन विज्ञान भाग १ व २ कक्षा ११ वीं]
• NCERT solutions for Accountancy - Financial Accounting Class 11
• NCERT solutions for Ncert Class 11 Business Studies
• NCERT solutions for Computer Science Class 11
• NCERT solutions for Introductory Microeconomics - Textbook in Economics for Class 11
• NCERT solutions for Economics - Statistics for Economics Class 11
• NCERT solutions for Ncert Class 11 English (Core Course) - Hornbill
• NCERT solutions for Ncert Class 11 English (Core Course) - Snapshots
• NCERT solutions for Ncert Class 11 English (Elective Course) - Woven Words
• NCERT solutions for Geography - Fundamentals of Physical Geography Class 11
• NCERT solutions for Geography - India Physical Environment Class 11
• NCERT solutions for Geography - Practical Work in Geography Class 11
• NCERT solutions for Geography Class 11 [भूगोल - भौतिक भूगोल के मूल सिद्धांत ११ वीं कक्षा]
• NCERT solutions for Ncert Class 11 History - Themes in World History
• NCERT solutions for Ncert Class 11 Political Science - Indian Constitution at Work
• NCERT solutions for Ncert Class 11 Political Science - Political Theory
• NCERT solutions for Ncert Class 11 Psychology
• NCERT solutions for Ncert Class 11 Sociology - Introducing Sociology
• NCERT solutions for Ncert Class 11 Sociology - Understanding Society
• NCERT solutions for Economics Class 11 [अर्थशास्त्र - अर्थशास्त्र में सांख्यिकी ११ वीं कक्षा]
• NCERT solutions for Economics - Introductory Microeconomics Class 11 CBSE [अर्थशास्त्र - व्यष्टि अर्थशास्त्र एक परिचय परिचय ११ वीं कक्षा]
• NCERT solutions for Geography Class 11 [भूगोल - भारत: भौतिक पर्यावरण ११ वीं कक्षा]
• NCERT solutions for Geography Class 11 [भूगोल - भूगोल में प्रयोगात्मक कार्य ११ वीं कक्षा]
• NCERT solutions for Hindi - Aaroh Class 11 [हिंदी - आरोह ११ वीं कक्षा]
• NCERT solutions for Hindi - Antara Class 11 [हिंदी - अंतरा ११ वीं कक्षा]
• NCERT solutions for Hindi - Vitan Class 11 [हिंदी - वितान ११ वीं कक्षा]
• NCERT solutions for History Class 11 [इतिहास - विश्व इतिहास के कुछ विषय ११ वीं कक्षा]
• NCERT solutions for Mathematics Class 11 [गणित ११ वीं कक्षा]
• NCERT solutions for Physics Part 1 and 2 Class 11
• NCERT solutions for Physics Class 11 (Part 1 and 2) [भौतिकी भाग १ व २ कक्षा ११ वीं]
• NCERT solutions for Political Science Class 11 [राजनीति विज्ञान - भारत का संविधान सिद्धांत और व्यवहार ११ वीं कक्षा]
• NCERT solutions for Political Science Class 11 [राजनीति विज्ञान - राजनीतिक सिद्धांत ११ वीं कक्षा]
• NCERT solutions for Psychology Class 11 [मनोविज्ञान ११ वीं कक्षा]
• NCERT solutions for Sanskrit - Bhaswati Class 11 [संस्कृत - भास्वती कक्षा ११]
• NCERT solutions for Sanskrit - Sahitya Parichay Class 11 and 12 [संस्कृत - साहित्य परिचय कक्षा ११ एवं १२]
• NCERT solutions for Sanskrit - Shashwati Class 11 [संस्कृत - शाश्वत कक्षा ११]
• NCERT solutions for Sociology Class 11 [समाजशास्त्र - समाज का बोध ११ वीं कक्षा]
• NCERT solutions for Sociology Class 11 [समाजशास्त्र - समाजशास्त्र परिचय ११ वीं कक्षा]

Chapters covered in NCERT Solutions for Mathematics Class 11

Ncert solutions for class 11 mathematics (11th) chapter 1: sets, ncert class 11 mathematics (11th) chapter 1: sets exercises.

NCERT Solutions for Class 11 Mathematics (11th) Chapter 2: Relations and Functions

Ncert class 11 mathematics (11th) chapter 2: relations and functions exercises.

NCERT Solutions for Class 11 Mathematics (11th) Chapter 3: Trigonometric Functions

Ncert class 11 mathematics (11th) chapter 3: trigonometric functions exercises.

NCERT Solutions for Class 11 Mathematics (11th) Chapter 4: Principle of Mathematical Induction

Ncert class 11 mathematics (11th) chapter 4: principle of mathematical induction exercises.

NCERT Solutions for Class 11 Mathematics (11th) Chapter 5: Complex Numbers and Quadratic Equations

Ncert class 11 mathematics (11th) chapter 5: complex numbers and quadratic equations exercises.

NCERT Solutions for Class 11 Mathematics (11th) Chapter 6: Linear Inequalities

Ncert class 11 mathematics (11th) chapter 6: linear inequalities exercises.

NCERT Solutions for Class 11 Mathematics (11th) Chapter 7: Permutations and Combinations

Ncert class 11 mathematics (11th) chapter 7: permutations and combinations exercises.

NCERT Solutions for Class 11 Mathematics (11th) Chapter 8: Binomial Theorem

Ncert class 11 mathematics (11th) chapter 8: binomial theorem exercises.

NCERT Solutions for Class 11 Mathematics (11th) Chapter 9: Sequences and Series

Ncert class 11 mathematics (11th) chapter 9: sequences and series exercises.

NCERT Solutions for Class 11 Mathematics (11th) Chapter 10: Straight Lines

Ncert class 11 mathematics (11th) chapter 10: straight lines exercises.

NCERT Solutions for Class 11 Mathematics (11th) Chapter 11: Conic Sections

Ncert class 11 mathematics (11th) chapter 11: conic sections exercises.

NCERT Solutions for Class 11 Mathematics (11th) Chapter 12: Introduction to Three Dimensional Geometry

Ncert class 11 mathematics (11th) chapter 12: introduction to three dimensional geometry exercises.

NCERT Solutions for Class 11 Mathematics (11th) Chapter 13: Limits and Derivatives

Ncert class 11 mathematics (11th) chapter 13: limits and derivatives exercises.

NCERT Solutions for Class 11 Mathematics (11th) Chapter 14: Mathematical Reasoning

Ncert class 11 mathematics (11th) chapter 14: mathematical reasoning exercises.

NCERT Solutions for Class 11 Mathematics (11th) Chapter 15: Statistics

Ncert class 11 mathematics (11th) chapter 15: statistics exercises.

NCERT Solutions for Class 11 Mathematics (11th) Chapter 16: Probability

Ncert class 11 mathematics (11th) chapter 16: probability exercises.

Mathematics can be challenging for many, and missing a class or two can be detrimental and push you several weeks behind. As the saying goes, 'practice makes perfect', and the same applies to mathematics more than any other subject. Given how formulas, theorems, and equations work, getting all your doubts and questions answered while ensuring you make sufficient time to solve and practice the tough and challenging equations. To successfully ace the subject, you need to practice staying in touch with the subject constantly. It begins with finding reliable solutions for NCERT Mathematics Class 11 books.

NCERT Solutions for Mathematics Class 11

Class 11 NCERT solutions answers all the questions given in the NCERT textbooks in a step-by-step process. Our Maths tutors have helped us put together this for our Class 11 Students. The solutions on Shaalaa will help you solve all the NCERT Class 11 Maths questions without any problems. Every chapter has been broken down systematically for the students, which gives fast learning and easy retention.

Shaalaa provides free NCERT solutions for Mathematics Class 11. Shaalaa has carefully crafted NCERT solutions for Class 11 Maths that can help you understand the concepts and learn how to answer properly in your board exams. You can also share our link for free Class 11 Maths NCERT solutions with your classmates.

If you have any doubts while going through our Class 11 Maths NCERT solutions, then you can go through our Video Tutorials for Maths. The tutorials should help you better understand the concepts.

Frequently asked questions about NCERT Solutions for Mathematics Class 11

Why should you select class 11 maths ncert solutions.

It is essential to understand that mathematics needs a lot of practice, as it requires a good grasp of formulas and equations that need thorough understanding. Finding the correct sums to practice can be challenging from time to time. It is essential to understand that the only way you can successfully ace your NCERT Class 11 Maths is by finding a reliable source to refer to, and one such option is looking for NCERT Solutions Guide for Class 11 Maths, which will help you practice new and challenging sums and equations every single time.

How much should you practice for your NCERT Class 11 Maths?

While there may be no fixed time you should dedicate to practice equations, the time required to practice the same can vary from individual to individual, as some find mathematics challenging and complicated. In contrast, others can gain a firm command over the subject; picking and choosing complex sums and equations from your NCERT Answer Guide for Class 11 Maths books is advisable. Dedicating a few hours every week to practice those complex equations also becomes essential. This will help you prepare most effectively, thus keeping you well-prepared for the examinations you must appear for.

Why are NCERT Class 11 Maths the best option?

NCERT 11 Maths Solution is one of the most reputed and reliable sources for equations, and if you are someone that needs sums that can constantly challenge you and want to bring out the best in you, then referring to Shaalaa’s NCERT Mathematics Solution Guide is the right way to go, as we have a dedicated team of expert mathematicians, who constantly come up with challenging sums and equations, that will help you practice and get a better understanding of complex and complicated equations.

Why is a repeated practice from NCERT Mathematics Solution helpful?

As we are all aware that examinations need to be completed in the stipulated time, it becomes essential to time yourself well and to ensure that you do not leave out of vital marks and to ensure that you don’t fall victim to the same, constant practice from NCERT Answers Guide for Class 11 Maths books will ensure that you can solve the paper well within the stipulated time. One of the primary reasons you should constantly practice Class 11 Maths Solutions is that mathematics involves using various formulas, methods, and steps. If you ever happen to lose touch with the same, then chances are that the next time you come across a complex and complicated equation, you will struggle with solving with the same, and you may also have to spend more time per sum.   Mathematics is one subject that tends to make many students nervous and worried. Ensuring you have the best Class 11 Maths NCERT Solutions will help you better understand the equations and enable you to ace your exam while enjoying the subject.

NCERT Solutions for Class 11 Maths CBSE, Karnataka Board PUC

Class 11 NCERT Solutions answer all the questions in the NCERT textbooks in a step-by-step process. Our Maths tutors helped us assemble this for our Class 11 students. The solutions on Shaalaa will help you solve all the NCERT Class 11 Maths questions without any problems. Every chapter has been broken down systematically for the students, which gives them fast learning and easy retention.

Shaalaa provides a free NCERT answer guide for Maths Class 11, CBSE, Karnataka Board PUC. Shaalaa has carefully crafted NCERT solutions for the Class 11 Maths to help you understand the concepts and adequately answer questions in your board exams.

If you have any doubts while going through our Class 11 Maths NCERT solutions, you can go through our Video Tutorials for Maths. The tutorials help you better understand the concepts.

Finding the best Maths Class 11 NCERT Solutions Digest is significant if you want to prepare for the exam fully. It's crucial to ensure that you are fully prepared for any challenges that can arise, and that's why a heavy, professional focus can be an excellent idea. As you learn the answers, obtaining the desired results becomes much easier, and the experience can be staggering every time.

NCERT Class 11 Maths Guide Book Back Answers

The following CBSE, Karnataka Board PUC NCERT Class 11 Maths Book Answers Solutions Guide PDF Free Download in English Medium will be helpful to you. Answer material is developed per the latest exam pattern and is part of NCERT Class 11 Books Solutions. You will be aware of all topics or concepts discussed in the book and gain more conceptual knowledge from the study material. If you have any questions about the CBSE, Karnataka Board PUC New Syllabus Class 11 Maths Guide PDF of Text Book Back Questions and Answers, Notes, Chapter Wise Important Questions, Model Questions, etc., please get in touch with us.

Comprehensive NCERT Solutions for CBSE, Karnataka Board PUC Maths Class 11 Guide

The NCERT Maths Class 11 CBSE, Karnataka Board PUC solutions are essential as they can offer a good improvement guideline. You must push the boundaries and take things to the next level to improve. That certainly helps a lot and can bring tremendous benefits every time. It takes the experience to the next level, and the payoff alone can be extraordinary.

You want a lot of accuracy from the NCERT solution for Maths Class 11. With accurate answers, you'll have the results and value you want. That's why you want quality, reliability, and consistency with something like this. If you have it, things will undoubtedly be amazing, and you will get to pursue your dreams.

Proper Formatting

Suppose you acquire the Maths NCERT Class 11 solutions from this page. In that case, they are fully formatted and ready to use, helping make the experience simpler and more convenient while offering the results and value you need. That's what you want to pursue, a genuine focus on quality and value, and the payoff can be great thanks to that.

Our NCERT Maths Answer Guide for the Class 11 CBSE, Karnataka Board PUC covers all 16 chapters. As a result, you will be able to fully prepare for the exam without worrying about missing anything. You rarely get such a benefit, which makes the Maths Class 11 CBSE, Karnataka Board PUC NCERT solutions provided here such an extraordinary advantage that you can always rely on. Consider giving it a try for yourself, and you will find it very comprehensive, professional, and convenient at the same time.

Our CBSE, Karnataka Board PUC NCERT solutions for Maths Class 11 cover everything from Sets, Relations and Functions, Trigonometric Functions, Principle of Mathematical Induction, Complex Numbers and Quadratic Equations, Linear Inequalities, Permutations and Combinations, Binomial Theorem, Sequences and Series, Straight Lines, Conic Sections, Introduction to Three Dimensional Geometry, Limits and Derivatives, Mathematical Reasoning, Statistics, Probability and the other topics.

Yes, these are the best NCERT Class 11 Maths solution options on the market. You must check it out for yourself; the experience can be impressive. You get to prepare for the exam reliably, comprehensively, and thoroughly.

Please look at our Maths Class 11 CBSE, Karnataka Board PUC answer guide today if you'd like to handle this exam efficiently. Just browse our solutions right now, and you will master the NCERT exam questions in no time! It will offer an extraordinary experience every time, and you will not have to worry about any issues.

• Maharashtra Board Question Bank with Solutions (Official)
• Balbharati Solutions (Maharashtra)
• Samacheer Kalvi Solutions (Tamil Nadu)
• NCERT Solutions
• RD Sharma Solutions
• RD Sharma Class 10 Solutions
• RD Sharma Class 9 Solutions
• Lakhmir Singh Solutions
• TS Grewal Solutions
• ICSE Class 10 Solutions
• Selina ICSE Concise Solutions
• Frank ICSE Solutions
• ML Aggarwal Solutions
• NCERT Solutions for Class 12 Maths
• NCERT Solutions for Class 12 Physics
• NCERT Solutions for Class 12 Chemistry
• NCERT Solutions for Class 12 Biology
• NCERT Solutions for Class 11 Maths
• NCERT Solutions for Class 11 Physics
• NCERT Solutions for Class 11 Chemistry
• NCERT Solutions for Class 11 Biology
• NCERT Solutions for Class 10 Maths
• NCERT Solutions for Class 10 Science
• NCERT Solutions for Class 9 Maths
• NCERT Solutions for Class 9 Science
• CBSE Study Material
• Maharashtra State Board Study Material
• Tamil Nadu State Board Study Material
• CISCE ICSE / ISC Study Material
• Mumbai University Engineering Study Material
• CBSE Previous Year Question Paper With Solution for Class 12 Arts
• CBSE Previous Year Question Paper With Solution for Class 12 Commerce
• CBSE Previous Year Question Paper With Solution for Class 12 Science
• CBSE Previous Year Question Paper With Solution for Class 10
• Maharashtra State Board Previous Year Question Paper With Solution for Class 12 Arts
• Maharashtra State Board Previous Year Question Paper With Solution for Class 12 Commerce
• Maharashtra State Board Previous Year Question Paper With Solution for Class 12 Science
• Maharashtra State Board Previous Year Question Paper With Solution for Class 10
• CISCE ICSE / ISC Board Previous Year Question Paper With Solution for Class 12 Arts
• CISCE ICSE / ISC Board Previous Year Question Paper With Solution for Class 12 Commerce
• CISCE ICSE / ISC Board Previous Year Question Paper With Solution for Class 12 Science
• CISCE ICSE / ISC Board Previous Year Question Paper With Solution for Class 10
• Entrance Exams
• Video Tutorials
• Question Papers
• Question Bank Solutions
• Question Search (beta)
• More Quick Links
• Privacy Policy
• Terms and Conditions
• Shaalaa App
• Ad-free Subscriptions

Select a course

• Class 1 - 4
• Class 5 - 8
• Class 9 - 10
• Class 11 - 12
• Search by Text or Image
• Textbook Solutions
• Study Material
• Remove All Ads
• Change mode

• NCERT Solutions
• NCERT Class 11
• NCERT 11 Maths
• Chapter 5: Complex Numbers And Quadratic Equations

NCERT Solutions For Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations

Ncert solutions class 11 maths chapter 5 – free pdf download.

* According to the CBSE Syllabus 2023-24, this chapter has been renumbered as Chapter 4.

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations are prepared by the expert teachers at BYJU’S. These NCERT Solutions of Maths help students in solving problems quickly, accurately and efficiently. Also, BYJU’S provides step-by-step solutions for all NCERT problems, thereby ensuring students understand them and clear their board exams with flying colours. The chapter Complex Numbers and Quadratic Equations is categorised under the CBSE Syllabus for 2023-24 and includes different critical Mathematical theorems and formulae. The NCERT textbook has many practice problems to cover all these concepts, which would help students easily understand higher concepts in future. BYJU’S provides solutions for all these problems with proper explanations. These NCERT Solutions from BYJU’S help students who aim to clear their exams even with last-minute preparations. However, NCERT Solutions for Class 11 Maths are focused on mastering the concepts along with gaining broader knowledge.

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations

Access answers of maths ncert class 11 chapter 5 – complex numbers and quadratic equations.

carouselExampleControls112

Previous Next

Access the exercises of Maths NCERT Class 11 Chapter 5

Exercise 5.1 Solutions 14 Questions Exercise 5.2 Solutions 8 Questions Exercise 5.3 Solutions 10 Questions Miscellaneous Exercise on Chapter 5 Solutions 20 Questions; the summarisation of the topics discussed in Chapter 5 of the Class 11 NCERT curriculum is listed below.

Access NCERT Solutions for Class 11 Maths Chapter 5

Exercise 5.1 Page No: 103

Express each of the complex numbers given in Exercises 1 to 10 in the form a + ib.

1. (5i) (-3/5i)

(5i) (-3/5i) = 5 x (-3/5) x i 2

(5i) (-3/5i) = 3 + i0

2. i 9 + i 19

i 9 + i 19 = (i 2 ) 4 . i + (i 2 ) 9 . i

= (-1) 4 . i + (-1) 9 .i

= 1 x i + -1 x i

i 9 + i 19 = 0 + i0

Now, multiplying the numerator and denominator by i we get

i -39 = 1 x i / (-i x i)

i -39 = 0 + i

4. 3(7 +  i 7) +  i (7 +  i 7)

3(7 +  i 7) +  i (7 +  i 7) = 21 + i 21 + i 7 + i 2 7

= 14 + i 28

3(7 +  i 7) +  i (7 +  i 7) = 14 + i 28

5. (1 –  i ) – (–1 +  i 6)

(1 –  i ) – (–1 +  i 6) = 1 –  i + 1 –  i 6

(1 –  i ) – (–1 +  i 6) = 2 – i 7

8. (1 –  i ) 4

(1 –  i ) 4 = [(1 –  i ) 2 ] 2

= [1 + i 2 – 2 i ] 2

Hence, (1 –  i ) 4 = -4 + 0 i

9. (1/3 + 3 i ) 3

Hence, (1/3 + 3 i ) 3 = -242/27 – 26 i

10. (-2 – 1/3 i ) 3

(-2 – 1/3 i ) 3 = -22/3 – 107/27 i

Find the multiplicative inverse of each of the complex numbers given in Exercises 11 to 13.

Let’s consider z  = 4 – 3 i

= 4 + 3 i  and

|z| 2 = 4 2 + (-3) 2 = 16 + 9 = 25

Thus, the multiplicative inverse of 4 – 3 i  is given by z -1

12. √5 + 3 i

Let’s consider  z  = √5 + 3 i

|z| 2 = (√5) 2 + 3 2 = 5 + 9 = 14

Thus, the multiplicative inverse of √5 + 3 i is given by z -1

Let’s consider  z  = – i

Thus, the multiplicative inverse of – i  is given by z -1

14. Express the following expression in the form of a + ib:

Exercise 5.2 Page No: 108

Find the modulus and the arguments of each of the complex numbers in Exercises 1 to 2.

1. z = – 1 – i √3

2. z = -√3 + i

Convert each of the complex numbers given in Exercises 3 to 8 in the polar form:

Exercise 5.3 Page No: 109

Solve each of the following equations:

1. x 2 + 3 = 0

Given the quadratic equation,

x 2  + 3 = 0

On comparing it with  ax 2  +  bx  +  c  = 0, we have

a  = 1,  b  = 0, and  c  = 3

So, the discriminant of the given equation will be

D =  b 2  – 4 ac  = 0 2  – 4 × 1 × 3 = –12

Hence, the required solutions are

2. 2x 2 + x + 1 = 0

2 x 2  +  x  + 1 = 0

a  = 2,  b  = 1, and  c  = 1

D =  b 2  – 4 ac  = 1 2  – 4 × 2 × 1 = 1 – 8 = –7

3. x 2 + 3x + 9 = 0

x 2  + 3 x  + 9 = 0

a  = 1,  b  = 3, and  c  = 9

D =  b 2  – 4 ac  = 3 2  – 4 × 1 × 9 = 9 – 36 = –27

4. – x 2  +  x  – 2 = 0

– x 2  +  x  – 2 = 0

a  = –1,  b  = 1, and  c  = –2

D =  b 2  – 4 ac  = 1 2  – 4 × (–1) × (–2) = 1 – 8 = –7

5. x 2  + 3 x  + 5 = 0

x 2  + 3 x  + 5 = 0

a  = 1,  b  = 3, and  c  = 5

D =  b 2  – 4 ac  = 3 2  – 4 × 1 × 5 =9 – 20 = –11

6. x 2  –  x  + 2 = 0

x 2  –  x  + 2 = 0

a  = 1,  b  = –1, and  c  = 2

So, the discriminant of the given equation is

D =  b 2  – 4 ac  = (–1) 2  – 4 × 1 × 2 = 1 – 8 = –7

7. √2 x 2  + x  + √2 = 0

√2 x 2  + x  + √2 = 0

a  = √2,  b  = 1, and  c  = √2

D =  b 2  – 4 ac  = (1) 2  – 4 × √2 × √2 = 1 – 8 = –7

8. √3 x 2  – √2 x  + 3√3 = 0

√3 x 2  – √2 x  + 3√3 = 0

a  = √3,  b  = -√2, and  c  = 3√3

D =  b 2  – 4 ac  = (-√2) 2  – 4 × √3 × 3√3 = 2 – 36 = –34

9. x 2  + x  + 1/√2 = 0

x 2  + x  + 1/√2 = 0

It can be rewritten as,

√2 x 2  + √2 x  + 1 = 0

a  = √2,  b  = √2, and  c  = 1

D =  b 2  – 4 ac  = (√2) 2  – 4 × √2 × 1 = 2 – 4√2 = 2(1 – 2√2)

10. x 2  + x /√2 + 1 = 0

x 2  + x /√2 + 1 = 0

D =  b 2  – 4 ac  = (1) 2  – 4 × √2 × √2 = 1 – 8 = -7

Miscellaneous Exercise Page No: 112

2. For any two complex numbers   z 1  and z 2 , prove that

Re (z 1 z 2 )   = Re z 1  Re z 2  – Im z 1  Im z 2

3. Reduce to the standard form.

5. Convert the following into the polar form:

Solve each of the equations in Exercises 6 to 9.

6. 3x 2 – 4x + 20/3 = 0

Given the quadratic equation, 3x 2 – 4x + 20/3 = 0

It can be re-written as: 9x 2 – 12x + 20 = 0

On comparing it with  ax 2  +  bx  +  c  = 0, we get

a  = 9,  b  = –12, and  c  = 20

D =  b 2  – 4 ac  = (–12) 2  – 4 × 9 × 20 = 144 – 720 = –576

7. x 2 – 2x + 3/2 = 0

Given the quadratic equation, x 2 – 2x + 3/2 = 0

It can be re-written as 2x 2 – 4x + 3 = 0

a  = 2,  b  = –4, and  c  = 3

D =  b 2  – 4 ac  = (–4) 2  – 4 × 2 × 3 = 16 – 24 = –8

8. 27x 2 – 10x + 1 = 0

Given the quadratic equation, 27 x 2  – 10 x  + 1 = 0

a  = 27,  b  = –10, and  c  = 1

D =  b 2  – 4 ac  = (–10) 2  – 4 × 27 × 1 = 100 – 108 = –8

9. 21x 2 – 28x + 10 = 0

Given the quadratic equation, 21 x 2  – 28 x  + 10 = 0

On comparing it with  ax 2  +  bx  +  c  = 0, we have

a  = 21,  b  = –28, and  c  = 10

D =  b 2  – 4 ac  = (–28) 2  – 4 × 21 × 10 = 784 – 840 = –56

10. If z 1 = 2 – i , z 2 = 1 + i , find

Given, z 1 = 2 – i , z 2 = 1 + i

12. Let z 1 = 2 – i , z 2 = -2 + i . Find

13. Find the modulus and argument of the complex number.

14. Find the real numbers  x  and  y  if ( x  –  iy ) (3 + 5 i ) is the conjugate of – 6 – 24 i .

Let’s assume z = ( x  –  iy ) (3 + 5 i )

(3x + 5y) – i (5x – 3y) = -6 -24 i

On equating real and imaginary parts, we have

3x + 5y = -6 …… (i)

5x – 3y = 24 …… (ii)

Performing (i) x 3 + (ii) x 5, we get

(9x + 15y) + (25x – 15y) = -18 + 120

x = 102/34 = 3

Putting the value of  x  in equation (i), we get

3(3) + 5y = -6

5y = -6 – 9 = -15

Therefore, the values of  x  and  y are 3 and –3, respectively.

15. Find the modulus of

16. If ( x  +  iy ) 3  =  u  +  iv , then show that

17. If α and β are different complex numbers with |β| = 1, then find

18. Find the number of non-zero integral solutions of the equation |1 – i| x = 2 x.

Therefore, 0 is the only integral solution of the given equation.

Hence, the number of non-zero integral solutions of the given equation is 0.

19. If ( a  +  ib ) ( c  +  id ) ( e  +  if ) ( g  +  ih ) = A +  i B, then show that

( a 2  +  b 2 ) ( c 2  +  d 2 ) ( e 2  +  f 2 ) ( g 2  +  h 2 ) = A 2  + B 2

20. If, then find the least positive integral value of  m .

Thus, the least positive integer is 1.

Therefore, the least positive integral value of  m  is 4 (= 4 × 1).

NCERT Solutions for Class 11 Maths Chapter 5 – Complex Numbers and Quadratic Equations

Chapter 5 of Class 11 Complex Numbers and Quadratic Equations has 3 exercises and a miscellaneous exercise to help the students practise the required number of problems to understand all the concepts. The topics and sub-topics discussed in the PDF of NCERT Solutions for Class 11 of this chapter include 5.1 Introduction We know that some of the quadratic equations have no real solutions. That means the solution of such equations includes complex numbers. Here, we have found the solution of a quadratic equation ax 2 + bx + c = 0 where D = b 2 – 4ac < 0. 5.2 Complex Numbers Definition of complex numbers, examples and explanations about the real and imaginary parts of complex numbers have been discussed in this section. Class 11 Maths NCERT Supplementary Exercise Solutions PDF helps the students to understand the questions in detail. 5.3 Algebra of Complex Numbers 5.3.1 Addition of two complex numbers

5.3.2 Difference of two complex numbers

5.3.3 Multiplication of two complex numbers

5.3.4 Division of two complex number

5.3.5 Power of i

5.3.6 The square roots of a negative real number

5.3.7 Identities

After studying these exercises, students are able to understand the basic BODMAS operations on complex numbers, along with their properties, power of i, square root of a negative real number and identities of complex numbers. 5.4 The Modulus and the Conjugate of a Complex Number The detailed explanation provides the modulus and conjugate of a complex number with solved examples. 5.5 Argand Plane and Polar Representation 5.5.1 Polar representation of a complex number

In this section, it has been explained how to write the ordered pairs for the given complex numbers, the definition of a Complex plane or Argand plane and the polar representation of the ordered pairs in terms of complex numbers.

• A number of the form a + ib, where a and b are real numbers, is called a complex number, “ a” is called the real part, and “ b” is called the imaginary part of the complex number
• z 1 + z 2 = (a + c) + i (b + d)
• z 1 z 2 = (ac – bd) + i (ad + bc)
• For any non-zero complex number z = a + ib (a ≠ 0, b ≠ 0), there exists a complex number, denoted by 1/z or z–1, called the multiplicative inverse of z
• For any integer k, i 4k = 1, i 4k + 1 = i, i 4k + 2 = – 1, i 4k + 3 = – i
• The polar form of the complex number z = x + iy is r (cosθ + i sinθ)
• A polynomial equation of n degree has n roots.

Disclaimer – 

Dropped Topics – 

5.5.1 Polar Representation of a Complex Number 5.6 Quadratic Equation Example 11 and Exercise 5.3 Examples 13, 15, 16 Ques. 5–8, 9 and 13 (Miscellaneous Exercise) Last three points in the Summary 5.7 Square-root of a Complex Number

Frequently Asked Questions on NCERT Solutions for Class 11 Maths Chapter 5

What are the topics covered under each exercise of ncert solutions for class 11 maths chapter 5 complex numbers and quadratic equations, explain the marks distribution in ncert solutions for class 11 maths., does byju’s give the most reliable answers in chapter 5 of ncert solutions for class 11 maths, leave a comment cancel reply.

Your Mobile number and Email id will not be published. Required fields are marked *

Request OTP on Voice Call

Post My Comment

Register with BYJU'S & Download Free PDFs

Register with byju's & watch live videos.

Search This Blog

Cbse mathematics.

Basic concepts, definitions and formulas of mathematics, mathematics assignments for 9th standard to 10+2 standard, maths study material for 8th, 9th, 10th, 11th, 12th classes, Mathematics lesson plan for classes 8th,10th and 12th standard, Interesting maths riddles and maths magic, Class-wise mathematics study material for students from 8th to 12. A complete resource centre of mathematics for students and teachers

Featured Posts

Mathematics class 10 lab manual | 21 lab activities, math assignment class xi ch-3 | trigonometric functions, math assignment | class xi | chapter 3 ,   trigonometric functions.

Extra questions of chapter 3 class 11 Trigonometric Functions with answer and  hints to the difficult questions. Important and useful math. assignment for the students of class 11

For better results

• Students should learn all the basic points of Trigonometry up to 11th standard
• Student should revise NCERT book thoroughly with examples.
• Now revise this assignment. This assignment integrate the knowledge of the students.

ASSIGNMENT FOR XI  STANDARD TRIGONOMETRY

Find the degree measure for the following radian measure

Find the radian measure for the following degree measure

Find the magnitude, radian and degree, of the interior angles of a regular

Solution Hint:

Note:  Each interior angle of a regular polygon is given by : 

If sin  θ  =12/13 and  θ  lie in the second quadrant, then find the value of   sec θ  + tan θ.      Ans. [- 5]

Prove the followings

  i)   cos24 o  + cos 55 o  + cos 125 o  + cos 204 o  + cos 300 o  = 1/2

ii)  sin 600 o  tan(-690 o ) + sec 840 o  cot(-945 o ) = 3/2

  Solution Hint:

Evaluate the following :

Prove that : tan70 o  = tan20 o  + 2tan50 o

Now cross-multiply and simplify the above fraction we get the required result.

Solution Hint:  tan A = k tan B

  Now apply componendo and dividendo and using trigonometric formulas.

Solution Hint:  

Start from RHS and then putting the value of p and q then simplify and get the result.

An angle  α  is divided into two parts such that the ratio of the tangents of the two parts = k  and difference of two parts = x  then show that:  

Solution hint:

Let two parts of  α  are  p and q, Then

Now applying componendo and dividendo and simplify we get the required result.

Prove that :   cos20 o  cos40 o  cos60 o  cos80 o  = 1/16

Prove that :   sin20 o  sin40 o  sin60 o  sin80 o  = 3/16

Solution Hint :  

Use tan  θ  = sin θ/cos θ, then using AB and CD formulas

Applying componendo and dividendo  then applying CD formulas then simplify the fractions we get the required result.

Solution Hint

Taking LHS and convert these into cosine functions.

Multiply and divide by 2 and the apply AB formulas

Multiply and divide by 2 and then apply AB formulas

Find the value of sin18 o  

θ  = 18 o    ⇒  5  θ  = 90 o    ⇒    2 θ  + 3 θ = 90 o   ⇒    2 θ  = 90 o  - 3 θ

Now taking sin on both side we get

Sin (2 θ ) = Sin (90 o  - 3 θ)    Sin (2 θ) = Cos (3 θ)

2Sin θ  cos θ = 4Cos 3  θ – 3cos θ     2Sin θ  = 4Cos 2  θ – 3

2Sin θ   = 4(1-sin 2  θ) – 3

4 sin 2  θ  + 2sin θ – 1 = 0

Now using quadratic formula here and find the value of sin θ

Multiply numerator and denominator by 2

Applying AB formulas we get

Now applying CD formulas we get the required result.

Ans:    

Now simplify and then apply CD formula we get the required result

If tan x + tan y + tan x tan y = 1, find (x + y).

Ans: x + y = 45 o  

tan x + tan y  = 1-tan x tan y

Dividing on both side by 1-tanx tany we get

tan(x + y) = tan 45 o   ⇒ x + y = 45 o

Prove that: Cos6θ = 32cos 6  θ - 48cos 4  θ + 18cos 2  θ - 1

Solution Hint: Use cos6θ = cos3(2θ) = - 3cos2θ + 4cos 3  2θ and then proceed.

Prove that: cos6x = 1 - 18sin 2 x + 48sin 4 x - 32sin 6 x

Solution Hint: Use cos6θ = cos3(2θ) =  -3cos2θ + 4cos 3  2θ .

Now putting cos2 θ =  1 - 2sin 2 θ we get

cos6 θ = -3( 1 - 2sin 2 θ) +  4(1 - 2sin 2 θ) 3

Using tanθ = sinθ/cosθ in numerator and in denominator

Taking LCM then using the formula sin(A+B) and sin (A-B) in numerator and in denominator respectively.

Now using sin2θ = 2sinθcosθ in the numerator for two times.

Solution Hint: Expand sin3x and cos3x

Now multiply and divide by 2

Applying 2sinxcosx = sin2x for two times we get the required result.

Prove that: sin 2 α + sin 2 (α - β) - 2sinα cosβ sin(α - β) = sin 2 β

Solution Hint: 

LHS = sin 2 α + sin 2 (α - β) - [sin (α + β) + sin(α - β)]sin(α - β)

         =  sin 2 α + sin 2 (α - β) -  sin (α + β)sin(α - β) - sin 2 (α - β)

         =  sin 2 α - [sin 2 α - sin 2 β] ..... [Using sin(A+B)sin(A-B) = sin 2 A - sin 2 B ]

          = sin 2 β

Let all equations = k

Now find the value of x, y, z in terms of k

                                                                = xyz ×0 = 0

Question 38

Taking "-" common from numerator

Using this formula: sin3x = 3sinx – 4sin 3 x  

Using C, D formulas for the middle two terms we get

Find the general solution of the equation: cos x + cos 2x + cos 3x = 0.

Solution Hint:   

Dividing on both side by 

Find the general solution of: 2 cos 2 x + 3 sin x = 0.

Find general solution of  cos 2 x cosec x + 3sinx + 3 = 0

Convert all terms into sin x , we get a quadratic equation.

Solve the quadratic equations.

Post a Comment

Breaking news, popular post on this blog, lesson plan maths class 10 | for mathematics teacher.

Lesson Plan Math Class X (Ch-8) | Trigonometry

Lesson Plan Math Class X (Ch-7) | Coordinate Geometry

• Assignment 10 15
• Assignment 11 12
• Assignment 12 14
• Assignment 8 8
• Assignment 9 5
• Lesson plan 10 15
• Lesson Plan 12 14
• Lesson Plan 8 10
• Maths 10 20
• Maths 11 21
• Maths 12 17

SUBSCRIBE FOR NEW POSTS

Get new posts by email:.

AssignmentsBag.com

Assignments For Class 11 Mathematics Sequence And Series

Assignments for Class 11 Mathematics Sequence And Series have been developed for Standard 11 students based on the latest syllabus and textbooks applicable in CBSE, NCERT and KVS schools. Parents and students can download the full collection of class assignments for class 11 Mathematics Sequence And Series from our website as we have provided all topic wise assignments free in PDF format which can be downloaded easily. Students are recommended to do these assignments daily by taking printouts and going through the questions and answers for Grade 11 Mathematics Sequence And Series. You should try to do these test assignments on a daily basis so that you are able to understand the concepts and details of each chapter in your Mathematics Sequence And Series book and get good marks in class 11 exams.

Assignments for Class 11 Mathematics Sequence And Series as per CBSE NCERT pattern

All students studying in Grade 11 Mathematics Sequence And Series should download the assignments provided here and use them for their daily routine practice. This will help them to get better grades in Mathematics Sequence And Series exam for standard 11. We have made sure that all topics given in your textbook for Mathematics Sequence And Series which is suggested in Class 11 have been covered ad we have made assignments and test papers for all topics which your teacher has been teaching in your class. All chapter wise assignments have been made by our teachers after full research of each important topic in the textbooks so that you have enough questions and their solutions to help them practice so that they are able to get full practice and understanding of all important topics. Our teachers at https://www.assignmentsbag.com have made sure that all test papers have been designed as per CBSE, NCERT and KVS syllabus and examination pattern. These question banks have been recommended in various schools and have supported many students to practice and further enhance their scores in school and have also assisted them to appear in other school level tests and examinations. Its easy to take print of thee assignments as all are available in PDF format.

Some advantages of Free Assignments for Class 11 Mathematics Sequence And Series

• Solving Assignments for Mathematics Sequence And Series Class 11 helps to further enhance understanding of the topics given in your text book which will help you to get better marks
• By solving one assignment given in your class by Mathematics Sequence And Series teacher for class 11 will help you to keep in touch with the topic thus reducing dependence on last minute studies
• You will be able to understand the type of questions which are expected in your Mathematics Sequence And Series class test
• You will be able to revise all topics given in the ebook for Class 11 Mathematics Sequence And Series as all questions have been provided in the question banks
• NCERT Class 11 Mathematics Sequence And Series Workbooks will surely help you to make your concepts stronger and better than anyone else in your class.
• Parents will be able to take print out of the assignments and give to their child easily.

All free Printable practice assignments are in PDF single lick download format and have been prepared by Class 11 Mathematics Sequence And Series teachers after full study of all topics which have been given in each chapter so that the students are able to take complete benefit from the worksheets. The Chapter wise question bank and revision assignments can be accessed free and anywhere. Go ahead and click on the links above to download free CBSE Class 11 Mathematics Sequence And Series Assignments PDF.

You can download free assignments for class 11 Mathematics Sequence And Series from https://www.assignmentsbag.com

You can get free PDF downloadable assignments for Grade 11 Mathematics Sequence And Series from our website which has been developed by teachers after doing extensive research in each topic.

On our website we have provided assignments for all subjects in Grade 11, all topic wise test sheets have been provided in a logical manner so that you can scroll through the topics and download the worksheet that you want.

You can easily get question banks, topic wise notes and questions and other useful study material from https://www.assignmentsbag.com without any charge

Yes all test papers for Mathematics Sequence And Series Class 11 are available for free, no charge has been put so that the students can benefit from it. And offcourse all is available for download in PDF format and with a single click you can download all assignments.

https://www.assignmentsbag.com is the best portal to download all assignments for all classes without any charges.

Related Posts

Assignments For Class 7 Telegu

Assignments For Class 8 Mathematics Mensuration

Assignments For Class 4 Science

NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12

NCERT Exemplar Class 11 Maths Chapter 1 Sets

June 18, 2022 by Sastry CBSE

NCERT Exemplar Class 11 Maths Chapter 1 Sets are part of NCERT Exemplar Class 11 Maths . Here we have given NCERT Exemplar Class 11 Maths Chapter 1 Sets.

Short Answer Type Questions Q1. Write the following sets in the roaster from

Q3. If Y = {x\x is a positive factor of the number 2 P (2 P – 1), where 2 P – 1 is a prime number}. Write Y in the roaster form.

Sol: Y- {x | x is a positive factor of the number 2 P-1 (2 P – 1), where 2 P – 1 is a prime number}. So, the factors of 2 P-1 are 1,2,2 2 ,2 3 ,…, 2 P- 1 . Y= {1,2,2 2 ,2 3 , …,2 p-1 ,2 p -1}

Q4. State which of the following statements are true and which are false. Justify your answer. (i) 35 ∈ {x | x has exactly four positive factors}. (ii) 128 e {y | the sum of all the positive factorsofy is 2y} (iii) 3∉{x|x 4 -5x 3 + 2jc 2 -112x + 6 = 0} (iv) 496 ∉{y | the sum of all the positive factors of y is 2y}. Sol: (i) The factors of 35 are 1, 5, 7 and 35. So, 35 is an element of the set. Hence, statement is true.

(ii) The factors of 128 hre 1,2,4, 8, 16, 32, 64 and 128. Sum of factors = 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 = 255 * 2 x 128 Hence, statement is false.

(iii) We have, x 4 – 5x 3 + 2x 2 – 1 12jc + 6 = 0 Forx = 3, we have (3) 4 – 5(3) 3 + 2(3) 2 – 112(3) + 6 = 0 => 81 – 135 + 18-336 + 6 = 0 =>    -346 = 0, which is not true. So 3 is not an element of the set Hence, statement is true.

(iv) 496 = 2 4 x 31 So, the factors of 496 are 1,2,4, 8, 16,31,62, 124,248 and 496. Sum of factors = 1 +2 + 4 + 8+ 16 + 31+62+124 + 248 + 496 = 992 = 2(496) So, 496 is the element of the set Hence, statement is false

Q5. Given L, = {1,2, 3,4},M= {3,4, 5, 6} and N= {1,3,5} Verify that L-(M⋃N) = (L-M)⋂(L-N) Sol: Given L,= {1,2, 3,4}, M= {3,4,5,6} and N= {1,3,5} M⋃N= {1,3,4, 5,6} L – (M⋃N) = {2} Now, L-M= {1, 2} and L-N= {2,4} {L-M) ⋂{L-N)= {2} Hence, L-{M⋃N) = {L-M) ⋂ (L-N).

Q8. If X= {1, 2, 3}, if n represents any member of X, write the following sets containing all numbers represented by (i) 4n                      (ii) n + 6                  (iii) n/2 (iv) n-1 

Q11. Let U be the set of all boys and girls in a school, G be the set of all girls in the school, B be the set of all boys in the school, and S be the set of all students in the school who take swimming. Some, but not all, students in the school take swimming. Draw a Venn diagram showing one of the possible interrelationship among sets U, G, B and S.

Instruction for Exercises 13-17: Determine whether each of the statements in these exercises is true or false. Justify your answer.

Q13. For all sets A and B, (A – B)∪ (A∩ B) = A Sol: True L.H.S. = (A-B) ∪ (A∩B) = [(A-B) ∪A] ∩ [(A – B) ∪B] = A∩ (A-B) = A= R.H.S. Hence, given statement is true.

Q14. For all sets A, B and C, A – (B-C) = (A- B)-C Sol: False 

Q15. For all sets A, B and C, if A ⊂ B, then  A ∩C<⊂B ∩C

Q16. For all sets A, B and C, if A⊂ B, then A ∪ C⊂ B ∪ C Sol: True

Q17. For all sets A, B and C, if A⊂ C and B ⊂ C,then A∪ B ⊂ C

Instruction for Exercises 18-22: Using properties of sets prove the statements given in these exercises.

Q18. For all sets A and B, A ∪ (B -A) = A ∪ B

Q20. For all sets A and B, A – (A ∩ B) = A – B

Q21. For all sets A and B,(A ∪ B)- B = A-B

Long Answer Type Questions

From (i) and (ii), we get .                              . A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

Q24. Out of 100 students; 15 passed in English, 12 passed in Mathematics, 8 in Science,6 in English and Mathematics, 7 in Mathematics and Science; 4 in English and Science; 4 in all the three. Find how many passed (i) in English and Mathematics but not in Science (ii) in Mathematics and Science but not in English (iii) in Mathematics only (iv) in more than one subject only Sol. Let M be the set of students who passed in Mathematics, E be the set of students who passed in English and S be the set of students who passed in Science.

Given n (U) = 100, n(E) = 15, n(M) = 12, n(S) = 8, n(E ∩ M) = 6, n(M ∩S) = 7, n(E ∩ S) — 4, and n(E ∩M ∩ S) = 4,

Number of students passed in English and Mathematics but not in Science = b = 2 (ii) Number of students passed in Mathematics and Science but not in English = d = 3 (iii) Number of students passed in Mathematics only = e = 3 (iv) Number of students passed in more than one subject = a + b + c + d =4+2+0+3=9

Q25. In a class of 60 students, 25 students play cricket and 20 students play tennis, and 10 students play both the games. Find the number of students who play neither. Sol: Let C be the set of students who play cricket and T be the set of students who play tennis. n(U) = 60, n(C) = 25, n(T) = 20, and n(C ∩ T) = 10 n(C ∪ T) = n(C) + n(T) – n(C n T) = 25 + 20 – 10 = 35

Q26. In a survey of 200 students of a school, it was found that 120 study Mathematics, 90 study Physics and 70 study Chemistry, 40 study Mathematics and Physics, 30 study Physics and Chemistry, 50 study Chemistry and Mathematics and 20 none of these subjects. Find the number of students who study all the three subjects. Sol: Let M be the set of students who study Mathematics, P be the set of students who study E Physics and C be the set of students who study Chemistry

Q27. In a town of 10,000 families it was found that 40% families buy newspaper A, 20% families buy newspaper B, 10% families buy newspaper C, 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspapers. Find (a) The number of families which buy newspaper A only. (b) The number of families which buy none of A, B and C. Sol: Let A be the set of families which buy newspaper A, B be the set of families which buy newspaper B and C be the set of families which buy newspaper C. The

Number of families which buy none of A, B and C = 10000 x (40/100)

Q28. In a group of 50 students, the number of students studying French, English, Sanskrit were found to be as follows: French = 17, English = 13, Sanskrit = 15, French and English = 09, English and Sanskrit = 4,French and Sanskrit = 5, English, French and Sanskrit = 3. Find the number of students who study (i) French only  (ii) English only  (iii) Sanskrit only  (iv) English and Sanskrit  (v) French and  Sanskrit but not English (vi) French and  English but not Sanskrit (vii)     at least one  of the three languages (viii) none of the  three languages but not French

Sol: Let F be the set of students who study French, E be the set of students who study English and S be the set of students who study Sanskrit. Then, n{U) = 50, n(F) =17, n{E) = 13, and n{S) = 15, n(F ∩ E) = 9, n(E ∩ S) = 4, n(F ∩ S) = 5, n(F ∩ E ∩ S) = 3

(i) Number of students studying French only = e = 6 (ii) Number of students studying English only = g = 3 (iii) Number of students studying Sanskrit only =f= 9 (iv) Number of students studying English and Sanskrit but not French = c = 1 (v) Number of students studying French and Sanskrit but not English = d = 2 (vi) Number of students studying French and English but not Sanskrit = b = 6 (vii) Number of students studying at least one of the three languages = a + b + c + d + e+f+g = 30 (viii) Number of students studying none of the three languages but not French = 50-30 = 20

Q30. Two finite sets have m and n elements. The number of subsets of the first set is 112 more than that of the second set. The values of m and n are, respectively, (a) 4,7 (b) 7,4 (c) 4,4 (d) 7, 7

Q32. Let F 1 be the set of parallelograms, F 2 the set of rectangles, F 3 the set of rhombuses, F 4 the set of squares and F 5 the set of trapeziums in a plane. Then F 1 may be equal to (a) F 2 ∩F 3                                                (b) F 3 ∩F 4 (c) F 2 u F s (d) F 2 ∪ F 3 ∪ F 4 ∪ F 1 Sol: (d) Every rectangle, rhombus, square in a plane is a parallelogram but every trapezium is not a parallelogram. F 1 = F 2 ∪ F 3 ∪ F 4 ∪ F 1

NCERT Exemplar Class 11 Maths Solutions

• Chapter 1 Sets
• Chapter 2 Relations and Functions
• Chapter 3 Trigonometric Functions
• Chapter 4 Principle of Mathematical Induction
• Chapter 5 Complex Numbers and Quadratic Equations
• Chapter 6 Linear Inequalities
• Chapter 7 Permutations and Combinations
• Chapter 8 Binomial Theorem
• Chapter 9 Sequence and Series
• Chapter 10 Straight Lines
• Chapter 11 Conic Sections
• Chapter 12 Introduction to Three-Dimensional Geometry
• Chapter 13 Limits and Derivatives
• Chapter 14 Mathematical Reasoning
• Chapter 15 Statistics
• Chapter 16 Probability

NCERT Exemplar Problems Maths Physics Chemistry Biology

We hope the NCERT Exemplar Class 11 Maths Chapter 1 Sets help you. If you have any query regarding NCERT Exemplar Class 11 Maths Chapter 1 Sets, drop a comment below and we will get back to you at the earliest.

Free Resources

NCERT Solutions

Quick Resources