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Class 11 Mathematics Case Study Questions

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Download the app to get CBSE Sample Papers 2023-24, NCERT Solutions (Revised), Most Important Questions, Previous Year Question Bank, Mock Tests, and Detailed Notes.

If you’re seeking a comprehensive and dependable study resource with Class 11 mathematics case study questions for CBSE, myCBSEguide is the place to be. It has a wide range of study notes, case study questions, previous year question papers, and practice questions to help you ace your examinations. Furthermore, it is routinely updated to bring you up to speed with the newest CBSE syllabus. So, why delay? Begin your path to success with myCBSEguide now!

The rationale behind teaching Mathematics

The general rationale to teach Mathematics at the senior secondary level is to assist students:

• In knowledge acquisition and cognitive understanding of basic ideas, words, principles, symbols, and mastery of underlying processes and abilities, notably through motivation and visualization.
• To experience the flow of arguments while demonstrating a point or addressing an issue.
• To use the information and skills gained to address issues using several methods wherever possible.
• To cultivate a good mentality in order to think, evaluate, and explain coherently.
• To spark interest in the subject by taking part in relevant tournaments.
• To familiarise pupils with many areas of mathematics utilized in daily life.
• To pique students’ interest in studying mathematics as a discipline.

Case studies in Class 11 Mathematics

A case study in mathematics is a comprehensive examination of a specific mathematical topic or scenario. Case studies are frequently used to investigate the link between theory and practise, as well as the connections between different fields of mathematics. A case study will frequently focus on a specific topic or circumstance and will investigate it using a range of methodologies. These approaches may incorporate algebraic, geometric, and/or statistical analysis.

Sample Class 11 Mathematics case study questions

When it comes to preparing for Class 11 Mathematics, one of the best things Class 11 Mathematics students can do is to look at some Class 11 Mathematics sample case study questions. Class 11 Mathematics sample case study questions will give you a good idea of the types of Class 11 Mathematics sample case study questions that will be asked in the exam and help you to prepare more effectively.

Looking at sample questions is also a good way to identify any areas of weakness in your knowledge. If you find that you struggle with a particular topic, you can then focus your revision on that area.

myCBSEguide offers ample Class 11 Mathematics case study questions, so there is no excuse. With a little bit of preparation, Class 11 Mathematics students can boost their chances of getting the grade they deserve.

Some samples of Class 11 Mathematics case study questions are as follows:

Class 11 Mathematics case study question 1

• 9 km and 13 km
• 9.8 km and 13.8 km
• 9.5 km and 13.5 km
• 10 km and 14 km
• x  ≤   −1913
• x <  −1613
• −1613  < x <  −1913
• There are no solution.
• y  ≤   12 x+2
• y >  12 x+2
• y  ≥   12 x+2
• y <  12 x+2

Answer Key:

• (b) 9.8 km and 13.8 km
• (a) −1913   ≤  x 
• (b)  y >  12 x+2
• (d) (-5, 5)

Class 11 Mathematics case study question 2

• 2 C 1 × 13 C 10
• 2 C 1 × 10 C 13
• 1 C 2 × 13 C 10
• 2 C 10 × 13 C 10
• 6 C 2​ × 3 C 4   × 11 C 5 ​
• 6 C 2​ × 3 C 4   × 11 C 5
• 6 C 2​ × 3 C 5 × 11 C 4 ​
• 6 C 2 ​  ×   3 C 1 ​  × 11 C 5 ​
• (b) (13) 4  ways
• (c) 2860 ways.

Class 11 Mathematics case study question 3

Read the Case study given below and attempt any 4 sub parts: Father of Ashok is a builder, He planned a 12 story building in Gurgaon sector 5. For this, he bought a plot of 500 square yards at the rate of Rs 1000 /yard². The builder planned ground floor of 5 m height, first floor of 4.75 m and so on each floor is 0.25 m less than its previous floor.

Class 11 Mathematics case study question 4

Read the Case study given below and attempt any 4 sub parts: villages of Shanu and Arun’s are 50km apart and are situated on Delhi Agra highway as shown in the following picture. Another highway YY’ crosses Agra Delhi highway at O(0,0). A small local road PQ crosses both the highways at pints A and B such that OA=10 km and OB =12 km. Also, the villages of Barun and Jeetu are on the smaller high way YY’. Barun’s village B is 12km from O and that of Jeetu is 15 km from O.

Now answer the following questions:

• 5x + 6y = 60
• 6x + 5y = 60
• (a) (10, 0)
• (b) 6x + 5y = 60
• (b) 60/√ 61 km
• (d) 2√61 km

A peek at the Class 11 Mathematics curriculum

The Mathematics Syllabus has evolved over time in response to the subject’s expansion and developing societal requirements. The Senior Secondary stage serves as a springboard for students to pursue higher academic education in Mathematics or professional subjects such as Engineering, Physical and Biological Science, Commerce, or Computer Applications. The current updated curriculum has been prepared in compliance with the National Curriculum Framework 2005 and the instructions provided by the Focus Group on Teaching Mathematics 2005 in order to satisfy the rising demands of all student groups. Greater focus has been placed on the application of various principles by motivating the themes from real-life events and other subject areas.

Class 11 Mathematics (Code No. 041)

Design of Class 11 Mathematics exam paper

CBSE Class 11 mathematics question paper is designed to assess students’ understanding of the subject’s essential concepts. Class 11 mathematics question paper will assess their problem-solving and analytical abilities. Before beginning their test preparations, students in Class 11 maths should properly review the question paper format. This will assist Class 11 mathematics students in better understanding the paper and achieving optimum scores. Refer to the Class 11 Mathematics question paper design provided.

 Class 11 Mathematics Question Paper Design

• No chapter-wise weightage. Care to be taken to cover all the chapters.
• Suitable internal variations may be made for generating various templates keeping the overall weightage to different forms of questions and typology of questions the same.  

Choice(s): There will be no overall choice in the question paper. However, 33% of internal choices will be given in all the sections.

  Prescribed Books:

• Mathematics Textbook for Class XI, NCERT Publications
• Mathematics Exemplar Problem for Class XI, Published by NCERT
• Mathematics Lab Manual class XI, published by NCERT

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CBSE Case Study Questions for Class 11 Maths Sets Free PDF

Mere Bacchon, you must practice the CBSE Case Study Questions Class 11 Maths Sets in order to fully complete your preparation . They are very very important from exam point of view. These tricky Case Study Based Questions can act as a villain in your heroic exams!

I have made sure the questions (along with the solutions) prepare you fully for the upcoming exams. To download the latest CBSE Case Study Questions , just click ‘ Download PDF ’.

CBSE Case Study Questions for Class 11 Maths Sets PDF

Checkout our case study questions for other chapters.

• Chapter 2 Relations and Functions Case Study Questions
• Chapter 3 Trigonometric Functions Case Study Questions
• Chapter 4 Principle of Mathematical Induction Case Study Questions
• Chapter 5 Complex Numbers and Quadratic Equations Case Study Questions

How should I study for my upcoming exams?

First, learn to sit for at least 2 hours at a stretch

Solve every question of NCERT by hand, without looking at the solution.

Solve NCERT Exemplar (if available)

Sit through chapter wise FULLY INVIGILATED TESTS

Practice MCQ Questions (Very Important)

Practice Assertion Reason & Case Study Based Questions

Sit through FULLY INVIGILATED TESTS involving MCQs. Assertion reason & Case Study Based Questions

After Completing everything mentioned above, Sit for atleast 6 full syllabus TESTS.

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NCERT Solutions Class 11 Maths Chapter 1 Sets

NCERT Solutions for Class 11 Maths Chapter 1 Sets explains the most fundamental math concepts based on sets, their types, and applications. A set is a collection of well-defined objects such as a set of players in a team, a pack of cards, etc. Sets are often used to represent and define relations and functions. This knowledge of sets is also crucial for studying many related math topics, including geometry , sequences , probability , etc. With the help of NCERT Solutions Class 11 Maths Chapter 1, students will get well-versed with this topic and its applications in real-world situations.

The topic of Sets is not only fundamental for maths, but it is also helpful for other subjects. Learning about elements of sets and operations performed on them is vital for every student. With the regular practice of Class 11 Maths NCERT Solutions Chapter 1, students will easily attain this knowledge to perform operations on sets. The sample problems and examples included in these solutions are proficient in promoting a step-by-step understanding of this topic. To learn and practice with NCERT Solutions Chapter 1 Sets, download the exercises provided in the links below.

• NCERT Solutions Class 11 Maths Chapter 1 Ex 1.1
• NCERT Solutions Class 11 Maths Chapter 1 Ex 1.2
• NCERT Solutions Class 11 Maths Chapter 1 Ex 1.3
• NCERT Solutions Class 11 Maths Chapter 1 Ex 1.4
• NCERT Solutions Class 11 Maths Chapter 1 Ex 1.5
• NCERT Solutions Class 11 Maths Chapter 1 Ex 1.6
• NCERT Solutions Class 11 Maths Chapter 1 Miscellaneous Exercise

NCERT Solutions for Class 11 Maths Chapter 1 PDF

NCERT Solutions for Class 11 Maths Chapter 1 are designed by experts to aid effective math learning for higher grades. These comprehensively structured resources are beneficial to enhance the problem-solving abilities of students. Sets can be a confusing topic if not prepared well hence, it is necessary to revisit the theories under this topic. To practice with these solutions, click on the links of the pdf files given below.

☛ Download Class 11 Maths NCERT Solutions Chapter 1 Sets

NCERT Class 11 Maths Chapter 1   Download PDF

NCERT Solutions for Class 11 Maths Chapter 1 Sets

NCERT solutions Class 11 Maths Chapter 1 Sets are highly efficient to strengthen the reasoning skills in students. These well-structured resources offer a simplistic learning approach with the help of interesting illustrations. The gradually placed examples provided in these solutions are helpful for strategic learning of each and every concept. To practice the exercise-wise NCERT Solutions Class 11 Maths Sets, try the links given below.

• Class 11 Maths Chapter 1 Ex 1.1 - 6 Questions
• Class 11 Maths Chapter 1 Ex 1.2 - 6 Questions
• Class 11 Maths Chapter 1 Ex 1.3 - 9 Questions
• Class 11 Maths Chapter 1 Ex 1.4 - 12 Questions
• Class 11 Maths Chapter 1 Ex 1.5 - 7 Questions
• Class 11 Maths Chapter 1 Ex 1.6 - 8 Questions
• Class 11 Maths Chapter 1 Miscellaneous Ex - 16 Questions

☛  Download Class 11 Maths Chapter 1 NCERT Book

Topics Covered: NCERT solutions Class 11 Maths Chapter 1 briefly introduces sets, their representation, and applications. The important topics covered in these solutions are an introduction to sets , finite infinite sets , equal sets, subsets , power sets , universal sets , Venn diagram , operations on sets including union, intersection , difference, and complement of a set.

Total Questions: Class 11 Maths Chapter 1 Sets has 48 questions in 6 exercises plus 16 questions in one miscellaneous exercise. These questions are primarily based on the representation of sets and their basic operations.

List of Formulas in NCERT Solutions Class 11 Maths Chapter 1

Having a clear understanding of all the terms and operations performed on sets is vital for every student. NCERT Solutions Class 11 Maths Chapter 1 will help gain this knowledge quickly with the help of suitable examples. Each concept in these solutions is well-explained to promote this understanding. Some of the important terms, formulas , and concepts related to sets explained in these solutions are listed below:

• Union of Sets: If A and B are two finite sets, then their union is the sum of all elements present in A and B.

Union of two sets can be represented using the formulas:

A U B = {x: x ∈ A (or) x ∈ B} which implies any element present in A U B is either an element of set A or set B.

• Intersection of Sets: If A and B are two finite sets then their intersection is the collection of all elements present in both A and B.

The intersection of two sets can be represented using the formulas:

A ∩ B = {x: x ∈ A (and) x ∈ B} which implies any element present in A∩B is present in both A and B.

• Venn Diagram: A Venn diagram is used to represents the logical relationship between sets.

FAQs on NCERT Solutions Class 11 Maths Chapter 1

What is the importance of ncert solutions for class 11 maths chapter 1 sets.

NCERT Solutions for Class 11 Maths Chapter 1 Sets are written as per the CBSE guidelines to promote efficient learning of each and every concept. The questions provided in these solutions are competent to deliver an in-depth understanding of sets and their relations. The practical examples included in these solutions are apt to promote math proficiency in students. With thorough practice, students will also gain the right approach for scoring well in exams.

What are the Important Topics Covered in Class 11 Maths NCERT Solutions Chapter 1?

The important topics covered in the NCERT Solutions Class 11 Maths Chapter 1 are the introduction to sets, their representation, types of sets, including finite infinite sets, equal sets, subsets, power sets, and universal sets. Other important topics included in these solutions are based on operations on sets and their Venn diagrams.

Do I Need to Practice all Questions Provided in NCERT Solutions Class 11 Maths Sets?

Every question included in NCERT Solutions Class 11 Maths Sets is well-framed to facilitate the formation of crystal clear concepts. By practicing all questions available in these solutions, students can easily master the fundamentals of sets and their applications. These solutions help in getting well-versed with sets, their representations, and operations. Additionally, regular practice helps kids recall concepts within seconds when required.

How Many Questions are there in Class 11 Maths NCERT Solutions Chapter 1 Sets?

NCERT Solutions for Class 11 Maths Chapter 1 Sets has 48 questions in 6 exercises. These exercises succinctly provide a holistic understanding of the whole topic, including important terms, formulas, and operations based on sets and their applications. The simple format of these solutions is suitable for acquiring a step-by-step understanding of sets.

What are the Important Formulas in NCERT Solutions Class 11 Maths Chapter 1?

NCERT Solutions Class 11 Maths Chapter 1 explains the representation of sets and their operations. Some of the important concepts explained in these solutions are based on the relations and functions of sets. These topics are elaborately detailed with the help of examples and illustrations. This chapter is majorly based on intuition rather than simply on formulas thus, requiring students to make use of their cognitive abilities.

Why Should I Practice NCERT Solutions for Class 11 Maths Chapter 1 Sets?

NCERT Solutions for Class 11 Maths Chapter 1 Sets is a competent learning resource that offers complete guidance and practice of core concepts for higher-level studies. These solutions cover the whole syllabus of CBSE Class 11 Maths Chapter 1 to provide comprehensive learning of all topics. The format of these solutions is simple and easy for students to grasp all complex concepts. Regular practice of these resources will ensure the best results in exams.

CBSE Class 11 Maths – Chapter 1 Sets- Study Materials

NCERT Solutions Class 11 All Subjects Sample Papers Past Years Papers

Sets : Notes and Study Materials -pdf

• Concepts of  Sets
• Sets Master File
• Sets Revision Notes
• R D Sharma Solution : Sets
• NCERT Solution  Sets
• NCERT  Exemplar Solution Sets
• Sets : Solved Example 1

CBSE Class 11 Maths Notes Chapter 1 Sets

Set A set is a well-defined collection of objects.

Representation of Sets There are two methods of representing a set

• Roster or Tabular form In the roster form, we list all the members of the set within braces { } and separate by commas.
• Set-builder form In the set-builder form, we list the property or properties satisfied by all the elements of the sets.

Types of Sets – Class 11 Maths Notes

• Empty Sets:  A set which does not contain any element is called an empty set or the void set or null set and it is denoted by {} or Φ.
• Singleton Set:  A set consists of a single element, is called a singleton set.
• Finite and infinite Set:  A set which consists of a finite number of elements, is called a finite set, otherwise the set is called an infinite set.
• Equal Sets:  Two sets A and 6 are said to be equal, if every element of A is also an element of B or vice-versa, i.e. two equal sets will have exactly the same element.
• Equivalent Sets:  Two finite sets A and 6 are said to be equal if the number of elements are equal, i.e. n(A) = n(B)

Subset – Class 11 Maths Notes

A set A is said to be a subset of set B if every element of set A belongs to set B. In symbols, we write A ⊆ B, if x ∈ A ⇒ x ∈ B

• Every set is o subset of itself.
• The empty set is a subset of every set.
• The total number of subsets of a finite set containing n elements is 2 n .

Intervals as Subsets of R Let a and b be two given real numbers such that a < b, then

• an open interval denoted by (a, b) is the set of real numbers {x : a < x < b}.
• a closed interval denoted by [a, b] is the set of real numbers {x : a ≤ x ≤ b}.
• intervals closed at one end and open at the others are known as semi-open or semi-closed interval and denoted by (a, b] is the set of real numbers {x : a < x ≤ b} or [a, b) is the set of real numbers {x : a ≤ x < b}.

Power Set The collection of all subsets of a set A is called the power set of A. It is denoted by P(A). If the number of elements in A i.e. n(A) = n, then the number of elements in P(A) = 2 n .

Universal Set A set that contains all sets in a given context is called the universal set.

Venn-Diagrams Venn diagrams are the diagrams, which represent the relationship between sets. In Venn-diagrams the universal set U is represented by point within a rectangle and its subsets are represented by points in closed curves (usually circles) within the rectangle.

Operations of Sets Union of sets: The union of two sets A and B, denoted by A ∪ B is the set of all those elements which are either in A or in B or in both A and B. Thus, A ∪ B = {x : x ∈ A or x ∈ B}.

Intersection of sets:  The intersection of two sets A and B, denoted by A ∩ B, is the set of all elements which are common to both A and B. Thus, A ∩ B = {x : x ∈ A and x ∈ B}

Disjoint sets:  Two sets Aand Bare said to be disjoint, if A ∩ B = Φ.

Intersecting or Overlapping sets:  Two sets A and B are said to be intersecting or overlapping if A ∩ B ≠ Φ

Difference of sets:  For any sets A and B, their difference (A – B) is defined as a set of elements, which belong to A but not to B. Thus, A – B = {x : x ∈ A and x ∉ B} also, B – A = {x : x ∈ B and x ∉ A}

Complement of a set:  Let U be the universal set and A is a subset of U. Then, the complement of A is the set of all elements of U which are not the element of A. Thus, A’ = U – A = {x : x ∈ U and x ∉ A}

Some Properties of Complement of Sets

Symmetric difference of two sets:  For any set A and B, their symmetric difference (A – B) ∪ (B – A) (A – B) ∪ (B – A) defined as set of elements which do not belong to both A and B. It is denoted by A ∆ B. Thus, A ∆ B = (A – B) ∪ (B – A) = {x : x ∉ A ∩ B}.

Laws of Algebra of Sets – Class 11 Maths Notes

Idempotent Laws:  For any set A, we have

Identity Laws:  For any set A, we have

Commutative Laws:  For any two sets A and B, we have

• A ∪ B = B ∪ A
• A ∩ B = B ∩ A

Associative Laws:  For any three sets A, B and C, we have

• A ∪ (B ∪ C) = (A ∪ B) ∪ C
• A ∩ (B ∩ C) = (A ∩ B) ∩ C

Distributive Laws:  If A, B and Care three sets, then

• A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
• A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

De-Morgan’s Laws:  If A and B are two sets, then

• (A ∪ B)’ = A’ ∩ B’
• (A ∩ B)’ = A’ ∪ B’

Formulae to Solve Practical Problems on Union and Intersection of Two Sets Let A, B and C be any three finite sets, then

• n(A ∪ B) = n(A) + n (B) – n(A ∩ B)
• If (A ∩ B) = Φ, then n (A ∪ B) = n(A) + n(B)
• n(A – B) = n(A) – n(A ∩ B)
• n(A ∪ B ∪ C) = n(A) + n(B) + n(C) – n(A ∩ B) – n(B ∩ C) – n(A ∩ C) + n(A ∩ B ∩ C)

Sets Class 11 MCQs Questions with Answers

Question 1. If A, B and C are any three sets, then A – (B ∪ C) is equal to (a) (A – B) ∪ (A – C) (b) (A – B) ∪ C (c) (A – B) ∩ C (d) (A – B) ∩ (A – C)

Answer: (d) (A – B) ∩ (A – C) Hint: Given A, B and C are any three sets. Now, A – (B ∪ C) = (A – B) ∩ (A – C)

Question 2. (A’)’ = ? (a) ∪ – A (b) A’ (c) ∪ (d) A

Answer: (d) A Hint: (A’)’ = A

Question 3. A – B is read as? (a) Difference of A and B of B and A (b) None of the above (c) Difference of B and A (d) Both a and b

Answer: (a) Difference of A and B of B and A Hint: A – B will read as difference of A and B of B and A Ex: Let A = {1, 2, 3, 4, 5} and B = {1, 3, 5, 7} Now, A – B = {2, 4}

Question 4. If A, B and C are any three sets, then A × (B ∪ C) is equal to (a) (A × B) ∪ (A × C) (b) (A ∪ B) × (A ∪ C) (c) None of these (d) (A × B) ∩ (A × C)

Answer: (a) (A × B) ∪ (A × C) Hint: Given A, B and C are any three sets. Now, A × (B ∪ C) = (A × B) ∪ (A × C)

Question 5. IF A = [5, 6, 7] and B = [7, 8, 9] then A ∪ B is equal to (a) [5, 6, 7, 8, 9] (b) [5, 6, 7] (c) [7, 8, 9] (d) None of these

Answer: (a) [5, 6, 7, 8, 9] Hint: Given A = [5, 6, 7] and B = [7, 8, 9] then A ∪ B = [5, 6, 7, 8, 9]

Question 6. Which of the following sets are null sets (a) {x: |x |< -4, x ?N} (b) 2 and 3 (c) Set of all prime numbers between 15 and 19 (d) {x: x < 5, x > 6}

Answer: (b) 2 and 3 Hint: 2 and 3 is the null set.

Question 7. IF R = {(2, 1),(4, 3),(4, 5)}, then range of the function is? (a) Range R = {2, 4} (b) Range R = {1, 3, 5} (c) Range R = {2, 3, 4, 5} (d) Range R {1, 1, 4, 5}

Answer: (b) Range R = {1, 3, 5} Hint: Given R = {(2, 1),(4, 3),(4, 5)} then Range(R) = {1, 3, 5}

Question 8. The members of the set S = {x | x is the square of an integer and x < 100} is (a) {0, 2, 4, 5, 9, 58, 49, 56, 99, 12} (b) {0, 1, 4, 9, 16, 25, 36, 49, 64, 81} (c) {1, 4, 9, 16, 25, 36, 64, 81, 85, 99} (d) {0, 1, 4, 9, 16, 25, 36, 49, 64, 121}

Answer: (b) {0, 1, 4, 9, 16, 25, 36, 49, 64, 81} Hint: The set S consists of the square of an integer less than 100 So, S = {0, 1, 4, 9, 16, 25, 36, 49, 64, 81}

Question 9. In a class of 120 students numbered 1 to 120, all even numbered students opt for Physics, whose numbers are divisible by 5 opt for Chemistry and those whose numbers are divisible by 7 opt for Math. How many opt for none of the three subjects? (a) 19 (b) 41 (c) 21 (d) 57

Answer: (b) 41 Hint: The number of students who took at least one of the three subjects can be found by finding out A ∪ B ∪ C, where A is the set of those who took Physics, B the set of those who took Chemistry and C the set of those who opted for Math. Now, A ∪ B ∪ C = A + B + C – (A ∩ B + B ∩ C + C ∩ A) + (A ∩ B ∩ C) A is the set of those who opted for Physics = 120/2 = 60 students B is the set of those who opted for Chemistry = 120/5 = 24 C is the set of those who opted for Math = 120/7 = 17 The 10th, 20th, 30th….. numbered students would have opted for both Physics and Chemistry. Therefore, A ∩ B = 120/10 = 12 The 14th, 28th, 42nd….. Numbered students would have opted for Physics and Math. Therefore, C ∩ A = 120/14 = 8 The 35th, 70th…. numbered students would have opted for Chemistry and Math. Therefore, B ∩ C = 120/35 = 3 And the 70th numbered student would have opted for all three subjects. Therefore, A ∪ B ∪ C = 60 + 24 + 17 – (12 + 8 + 3) + 1 = 79 Number of students who opted for none of the three subjects = 120 – 79 = 41

Question 10. { (A, B) : A² +B² = 1} on the sets has the following relation (a) reflexive (b) symmetric (c) none (d) reflexive and transitive

Answer: (b) symmetric Hint: Given {(a, b) : a² + b² = 1} on the set S. Now a² +b² = b² + a² = 1 So, the given relation is symmetric.

Question 11. Two finite sets have N and M elements. The number of elements in the power set of first set is 48 more than the total number of elements in power set of the second test. Then the value of M and N are (a) 7, 6 (b) 6, 4 (c) 7, 4 (d) 6, 3

Answer: (b) 6, 4 Hint: Let A and B be two sets having m and n numbers of elements respectively Number of subsets of A = 2m Number of subsets of B = 2n Now, according to question 2m – 2n = 48 ⇒ 2n(2m – n – 1) = 24(22 – 1) So, n = 4 and m – n = 2 ⇒ m – 4 = 2 ⇒ m = 2 + 4 ⇒ m = 6

Question 12. The range of the function f(x) = 3x – 2‚ is (a) (- ∞, ∞) (b) R – {3} (c) (- ∞, 0) (d) (0, – ∞)

Answer: (a) (- ∞, ∞) Hint: Let the given function is y = 3x – 2 ⇒ y + 2 = 3x ⇒ x = (y + 2)/3 Now x is saisfied by all values. So, Range{f(x)} = R = (-∞, ∞)

Question 13. If A, B, C be three sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C, then, (a) B = C (b) A = C (c) A = B = C (d) A = B

Answer: (a) B = C Hint: Given A, B, C be three sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C then B = C

Question 14. In 2nd quadrant? (a) X < 0, Y < 0 (b) X < 0, Y > 0 (c) X > 0, Y > 0 (d) X > 0, Y < 0

Question 15. How many rational and irrational numbers are possible between 0 and 1? (a) 0 (b) Finite (c) Infinite (d) 1

Answer: (c) Infinite Hint: There are infinite many rational and irrational numbers are possible between 0 and 1 This is because between any two numbers, there are infinite numbers.

Question 16. Empty set is a? (a) Finite Set (b) Invalid Set (c) None of the above (d) Infinite Set

Answer: (a) Finite Set Hint: In mathematics, and more specifically set theory, the empty set is the unique set having no elements and its size or cardinality (count of elements in a set) is zero. So, an empty set is a finite set.

Question 17. If A = [5, 6, 7] and B = [7, 8, 9] then A U B is equal to (a) [5, 6, 7, 8, 9] (b) [5, 6, 7] (c) [7, 8, 9] (d) None of these

Answer: (a) [5, 6, 7, 8, 9] Hint: Given A = [5, 6, 7] and B = [7, 8, 9] then A U B = [5, 6, 7, 8, 9]

Question 18. Which of the following two sets are equal? (a) A = {1, 2} and B = {1} (b) A = {1, 2} and B = {1, 2, 3} (c) A = {1, 2, 3} and B = {2, 1, 3} (d) A = {1, 2, 4} and B = {1, 2, 3}

Answer: (c) A = {1, 2, 3} and B = {2, 1, 3} Hint: Two sets are equal if and only if they have the same elements. So, A = {1, 2, 3} and B = {2, 1, 3} are equal sets.

Question 19. In a class of 50 students, 10 did not opt for math, 15 did not opt for science and 2 did not opt for either. How many students of the class opted for both math and science. (a) 24 (b) 25 (c) 26 (d) 27

Answer: (d) 27 Hint: Total students = 50 Students who did not opt for math = 10 Students who did not opt for Science = 15 Students who did not opt for either maths or science = 2 Total of 40 students in math and 13 did not opt for science but did for math = 40 – 13 = 27 So, students of the class opted for both math and science is 27

Question 20. In last quadrant? (a) X < 0, Y > 0 (b) X < 0, Y < 0 (c) X > 0, Y < 0 (d) X > 0, Y > 0

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

NCERT Solutions for Class 11 Maths Chapter 1 are now easily accessible for students on Vedantu. The Class 11 NCERT Solutions are prepared in detail by our well-learned experts with years of experience in teaching. With our online solutions, you can be able to understand the basics of sets along with some shortcut techniques and build a strong foundation for the subject. The best part of our high-quality NCERT Solutions for Class 11 Maths chapter 1 sets is that they are available for download in PDF format.

Access NCERT solutions for Class 11 Math Chapter 1 – Sets

Exercise (1.1)

1. Which of the following are sets? Justify your answer.

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

To determine if the given statement is a set

A set is a collection of well-defined objects.

We can definitely identify the collection of months beginning with a letter J.

Thus, the collection of all months of a year beginning with the letter J is the set.

ii. The collection of ten most talented writers of India

The criteria for identifying the collection of ten most talented writers of India may vary from person to person. So it is not a well-defined object.

Thus, the collection of ten most talented writers of India is not a set.

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

The criteria for determining the eleven best cricket batsmen may vary from person to person. So it is not a well-defined object.

Thus, a team of eleven best cricket batsmen in the world is not a set.

iv. The collection of all boys in your class.

We can definitely identify the boys who are all studying in the class. So it is a well-defined object.

Thus, the collection of all boys in your class is a set.

v. The collection of all natural numbers less than $100$.

We can identify the natural numbers less than $100$ can easily be identified. So it is a well-defined object.

Thus, the collection of all natural numbers less than $100$ is a set.

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

We can identify the books that belong to the writer Munshi Prem Chand. So it is a well-defined object.

Thus, a collection of novels written by the writer Munshi Prem Chand is a set.

vii. The collection of all even integers.

We can identify integers that are all the collection of even integers. So it is not a well-defined object.

Thus, the collection of all even integers is a set.

viii. The collection of questions in this chapter.

We can easily identify the questions that are in this chapter. So it is a well-defined object.

Thus, the collection of questions in this chapter is a set.

ix. A collection of the most dangerous animals in the world.

The criteria for determining the most dangerous animals may vary according to the person. So it is not a well-defined object.

Thus, the collection of the most dangerous animals in the world is a set.

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

Given that,

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

To insert the appropriate symbol $\in $ or $\notin $

The number $5$ is in the set.

$\therefore 5\in A$

ii. $8...A$

The number $8$ is not in the set.

$\therefore 8\notin A$

iii. $0...A$

The number $0$ is not in the set.

$\therefore 0\notin A$

iv. $4...A$

The number $4$ is in the set.

$\therefore 4\in A$

The number $2$ is in the set.

$\therefore 2\in A$

vi. $10...A$

The number $10$ is not in the set.

$\therefore 10\notin A$

3. Write the following sets in roster form:

i. $A=\left\{ x:x\text{ is an integer and -3x7} \right\}$

$A=\left\{ x:x\text{ is an integer and -3x7} \right\}$

To write the above expression in its roaster form

In roaster form, the order in which the elements are listed is immaterial.

The elements of the set are $-2,-1,0,1,2,3,4,5,6$.

$\therefore $ The roaster form of the set $A=\left\{ x:x\text{ is an integer and -3x7} \right\}$ is $A=\left\{ -2,-1,0,1,2,3,4,5,6 \right\}$.

ii. $B=\left\{ x:x\text{ is a natural number less than 6} \right\}$

$B=\left\{ x:x\text{ is a natural number less than 6} \right\}$

The elements of the set are $1,2,3,4,5$.

$\therefore$ The roaster form of the set $B=\left\{ x:x\text{ is a natural number less than 6} \right\}$ is $B=\left\{ 1,2,3,4,5 \right\}$.

iii. $C=\left\{ x:x\text{ is a two-digit natural number such that sum of its digits is 8} \right\}$

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

The elements of the set are $17,26,35,44,53,62,71,80$ such that their sum is $8$

$\therefore $ The roaster form of the set $C=\left\{ x:x\text{ is a two-digit natural number such that sum of its digits is 8} \right\}$ is $\left\{ 17,26,35,44,53,62,71,80 \right\}$.

iv. $D=\left\{ x:x\text{ is a prime number which is divisor of 60} \right\}$

$D=\left\{ x:x\text{ is a prime number which is divisor of 60} \right\}$

The divisors of $60$ are $2,3,4,5,6$. Among these the prime numbers are $2,3,5$

The elements of the set are $2,3,5$.

$\therefore $ The roaster form of the set $D=\left\{ x:x\text{ is a prime number which is divisor of 60} \right\}$ is $D=\left\{ 2,3,5 \right\}$.

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

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

There are $12$ letters in the word TRIGONOMETRY out of which T, R and O gets repeated.

The elements of the set are T, R, I G, O, N, M, E, Y.

$\therefore $ The roaster form of the set $E=$The set of all letters in the word TRIGONOMETRY is $E=\left\{ T,R,I,G,O,N,M,E,Y \right\}$.

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

$F=$The set of all letters in the word BTTER

There are $6$ letters in the word BETTER out of which E and T are repeated.

The elements of the set are B, E, T, R.

$\therefore $ The roaster form of the set $F=$The set of all letters in the word BTTER

 is $F=\left\{ B,E,T,R \right\}$.

4. Write the following sets in the set builder form:

i. $\left( 3,6,9,12 \right)$

$\left\{ 3,6,9,12 \right\}$

To represent the given set in the set builder form

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

From the given set, we observe that the numbers in the set are multiple of $3$ from $1$ to $4$ such that $\left\{ x:x=3n,n\in N\text{ and 1}\le \text{n}\le \text{4} \right\}$

$\therefore \left\{ 3,6,9,12 \right\}=\left\{ x:x=3n,n\in N\text{ and 1}\le \text{n}\le \text{4} \right\}$

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

{2,4,8,16,32}

From the given set, we observe that the numbers in the set are powers of $2$ from $1$ to $5$ such that $\left\{ x:x={{2}^{n}},n\in N\text{ and 1}\le \text{n}\le 5 \right\}$

$\therefore \left\{ 2,4,8,16,32 \right\}=\left\{ x:x={{2}^{n}},n\in N\text{ and 1}\le \text{n}\le 5 \right\}$

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

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

From the given set, we observe that the numbers in the set are powers of $5$ from $1$ to $4$ such that $\left\{ x:x={{5}^{n}},n\in N\text{ and 1}\le \text{n}\le \text{4} \right\}$

$\therefore \left\{ 5,25,125,625 \right\}=\left\{ x:x={{5}^{n}},n\in N\text{ and 1}\le \text{n}\le \text{4} \right\}$

iv. $\left\{ 2,4,6,... \right\}$

$\left\{ 2,4,6,... \right\}$

From the given set, we observe that the numbers are the set of all even natural numbers.

$\therefore \left\{ 2,4,6,... \right\}=\left\{ x:x\text{ is an even natural number} \right\}$

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

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

From the given set, we observe that the numbers in the set squares of numbers form $1$ to $10$ such that $\left\{ x:x={{n}^{2}},n\in N\text{ and 1}\le \text{n}\le 10 \right\}$

$\therefore \left\{ 1,4,9,...100 \right\}=\left\{ x:x={{n}^{2}},n\in N\text{ and 1}\le \text{n}\le 10 \right\}$

5. List all the elements of the following sets:

i. $A=\left\{ x:x\text{ is an odd natural number} \right\}$

$A=\left\{ x:x\text{ is an odd natural number} \right\}$

To list the elements of the given set

The odd natural numbers are $1,3,5,...$

$\therefore $ The set $A=\left\{ x:x\text{ is an odd natural number} \right\}$ has the odd natural numbers that are $\left\{ 1,3,5,... \right\}$

ii. $B=\left\{ x:x\text{ is an integer;-}\frac{1}{2}<x<\frac{9}{2} \right\}$

$B=\left\{ x:x\text{ is an integer;-}\frac{1}{2}<x<\frac{1}{2} \right\}$

$-\frac{1}{2}=-0.5$ and $\frac{9}{2}=4.5$

So the integers between $-0.5$ and $4.5$ are $0,1,2,3,4$

$\therefore $ The set $B=\left\{ x:x\text{ is an integer;-}\frac{1}{2}<x<\frac{1}{2} \right\}$ has an integers that are between $\left\{ 0,1,2,3,4 \right\}$

iii. $C=\left\{ x:x\text{ is an integer;}{{\text{x}}^{2}}\le 4 \right\}$

$C=\left\{ x:x\text{ is an integer;}{{\text{x}}^{2}}\le 4 \right\}$

It is observed that,

${{x}^{2}}\le 4$

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

${{\left( -1 \right)}^{2}}=1\le 4$

${{\left( 0 \right)}^{2}}=0\le 4$

${{\left( 1 \right)}^{2}}=1\le 4$

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

$\therefore $The set $C=\left\{ x:x\text{ is an integer;}{{\text{x}}^{2}}\le 4 \right\}$ contains elements such as $\left\{ -2,-1,0,1,2 \right\}$

iv. $D=\left\{ x:x\text{ is a letter in the word ''LOYAL''} \right\}$

$D=\left\{ x:x\text{ is a letter in the word ''LOYAL''} \right\}$

There are $5$ total letters in the given word in which L gets repeated two times.

So the elements in the set are $\left\{ L,O,Y,A \right\}$

$\therefore $The set $D=\left\{ x:x\text{ is a letter in the word ''LOYAL''} \right\}$ consists the elements $\left\{ L,O,Y,A \right\}$.

v. $E=\left\{ x:x\text{ is a month of a year not having 31 days} \right\}$

$E=\left\{ x:x\text{ is a month of a year not having 31 days} \right\}$

The months that don’t have $31$ are as follows:

February, April, June, September, November

$\therefore $The set $E=\left\{ x:x\text{ is a month of a year not having 31 days} \right\}$ consist of the elements such that $\left\{ \text{February, April, June, September, November} \right\}$

vi. $F=\left\{ x:x\text{ is a consonant in the English alphabet which precedes k} \right\}$

$F=\left\{ x:x\text{ is a consonant in the English alphabet which precedes k} \right\}$

The consonants are letters in English alphabet other than vowels such as a, e, i, o, u and the consonants that precedes k include b, c, d, f, g, h, j

$\therefore $The set $F=\left\{ x:x\text{ is a consonant in the English alphabet which precedes k} \right\}$ consists of the set $\left\{ b,c,d,f,g,h,j \right\}$

6. Match each of the sets on the left in the roaster form with the same set on the right described inn set-builder form.

i. $\left\{ 1,2,3,6 \right\}$

$\left\{ 1,2,3,6 \right\}$

To match the roaster form in the left with the set builder form in the right

It has been observed from the set that these set of numbers are the set of natural numbers which are also the divisors of $6$

Thus, $\left\{ 1,2,3,6 \right\}=\left\{ x:x\text{ is a natural number and is a divisor of 6} \right\}$ is the correct option which is option.

ii. $\left\{ 2,3 \right\}$

$\left\{ 2,3 \right\}$

It has been observed from the set that these set of numbers are the set of prime numbers which are also the divisors of $6$

Thus, $\left\{ 2,3 \right\}=\left\{ x:x\text{ is a prime number and is a divisor of 6} \right\}$ is the correct option which is option (a)

iii. $\left\{ M,A,T,H,E,I,C,S \right\}$

$\left\{ M,A,T,H,E,I,C,S \right\}$

It has been observed from the set of these letters of word MATHEMATICS.

Thus, $\left\{ M,A,T,H,E,I,C,S \right\}=\left\{ x:x\text{ is a letter of the word MATHEMATICS} \right\}$ is the correct option which is option (d)

iv. $\left\{ 1,3,5,7,9 \right\}$

$\left\{ 1,3,5,7,9 \right\}$

It has been observed from the set that these sets of numbers are the set of odd numbers that are less than $10$.

Thus, $\left\{ 1,3,5,7,9 \right\}=\left\{ x:x\text{ is a odd number less than 10} \right\}$ is the correct option which is option (b)

Topics Covered in Exercise 1.1 Class 11 Maths NCERT

Exercise 1.1 is based on the following topics:

A. Introduction to Sets

In mathematics, Sets are simply a collection of distinct objects that form a group. A set can contain any number of items, such as numbers, days of the week, car types, and so on. An element of the set refers to each object in the set. When writing a set, curly brackets are used.

B. Sets and their Representations

Set: A set is called a well-defined collection of objects.

Representation of Sets

There are 2 methods to represent a set:

Roster or Tabular Form: In this form, we list all the members of the set within braces { } and separate them by commas.

Set-builder Form: In the set-builder form, we list the property or properties satisfied by all the elements of the sets.

Importance of Sets for Class 11 Maths

Sets is a topic that is not only important in math but also useful in other subjects. Every student should learn about the elements of sets and the operations that can be performed on them. Students can quickly learn to execute operations on sets if they practise Class 11 Maths NCERT Solutions Chapter 1 on a regular practice. These solutions' sample problems and examples are effective at promoting a step-by-step grasp of this topic.

Class 11 Maths Chapter 1 – Exercise 1.1

In mathematics, a 'set' is a collection of distinct and well-defined objects. These objects are referred to like elements and these can be anything: people, numbers, alphabet, subsets, and so on. Sets are a significant part of mathematics as every field of it uses sets in some way. Sets can have topological or algebraic properties that are useful. If you want to pursue a career in the field of mathematics, then you must have a deep understanding of sets. It will help you in developing mathematical theories. It may sound a bit tricky here but our knowledgeable teachers ensure that you get every bit of this chapter and hold a strong command on sets. With Vedantu’s NCERT Solutions for Class 11 Maths Chapter 1, you can learn all the concepts of sets and their applications. With their smart learning methods, our experts have made the learning so simple that students won’t feel boredom while studying maths.

Coming on to the NCERT maths chapter 1, there are seven exercises in it including the miscellaneous one. Each one of them covers a crucial concept of sets. For your better understanding, a brief of every exercise is given below:-

Exercise 1.1

Exercise 1.1 of NCERT Class 11 Maths provides a basic introduction to sets and their representation. The students will learn about the difference between roaster form or builder form of sets. The knowledge gained from this exercise may help them in understanding other exercises and concepts discussed in this chapter. The students of class 11 will learn about recognizing a particular set type from a given cluster of data. This can only be done with a great understanding of appropriate concepts and knowledge. In addition to this, they will gain an understanding of forms of sets and one set to other alternative forms of the set. Exercise 1.1 of NCERT Class 11 is crucial as it tests the basic understanding of students. Moreover, they get to learn about various elements of a set through the question given in the Class 11 ex 1.1. Furthermore, the last question in exercise 1.1 asks students to match identical sets in various forms. The overall Exercise 1.1 of Class 11 NCERT Maths demands students to have knowledge of recognizing a set, determining appropriate symbols, transforming the forms, listing of set elements, etc. With the help of NCERT Solutions for Exercise 1.1 Class 11 Maths prepared by the experts of Vedantu, you can be able to solve every question with detailed reasons.

Exercise 1.2

Talking about exercise 1.2 of the chapter, it comprises many problems that will help you in gaining a thorough understanding of the null set. For instance, the first question asks whether a set of odd natural number divisible by 2 is a null set or not. As per the solutions prepared by our experts, it is a null set because no odd number is divisible by 2. In addition to this, you will get to learn about the finite and infinite sets. For example, a set of months of the year is a finite set because such a set will have only 12 elements only. On the other hand, a set of natural numbers is an infinite set. Furthermore, one will also learn about equal sets and their properties. The experts of Vedantu has prepared the solutions with detailed explanation and student-friendly content. These will help you in providing in-depth reasoning for every question and getting good marks in the exam.

Exercise 1.3

In this exercise, the primary motive of the NCERT is to build an understanding of equations and putting the right symbol in students studying in class 11. For that purpose, a few questions on forms of sets are placed in exercise 1.3 of class 11 maths. There are many symbols that have their own meaning in the set theory. It has been seen that students do not have a clear understanding of using the right symbol in the problems. This results in the deduction of marks in the exam. However, with our detailed NCERT Solutions for Class 11 Maths Chapter 1, you can get the highest marks as our experts have detailed out the exact meaning of each symbol with their proper usage in the problem. In exercise 1.3, you will also learn about a part of a set called 'subset' with the help of some problems mentioned in the exercise. For instance, a set of vowels is a subset of a set consisting of the English alphabets.

Exercise 1.4

This exercise covers the most crucial aspect of the set theory i.e., the union of two or more sets. The whole exercise consists of different types of questions on the union of sets. As a student, you will learn about the symbol of the 'union' which is 'U' and various properties of the union set. For example, you will learn that the commutative properties, associative properties, identity properties, distributive and intersection properties of a union set. For a better understanding of this concept, one needs to have a stronghold of these properties and their application. Many students get confused about these properties and their usage. With the tips given by Vedantu's experts, one can have a strong understanding of the aforementioned properties. Our detailed NCERT Solutions for Class 11 Maths Chapter 1 will assist you in getting the answers for all your doubts and that too in a very simple language.

Exercise 1.5

Coming on to the exercise 1.5 of class 11 maths, a lot of complex problems are given on the usage of union set. This exercise tests the overall knowledge and clarity of concepts of students they have gained till the previous exercise. The problems in exercise 1.5 are framed in such a way that only those students will be able to solve them those have a strong command over the properties of a Union and their applications. For instance, the value of the union is provided and you are asked to work out the value of different sections of the set. This requires a great understanding of the Venn diagram, complementary sets, and universal sets. However, you need not worry as our experts have solved each and every problem with a step-by-step explanation. They have prepared a solution for every question from scratch.

Exercise 1.6

The exercise 1.6 of class 11 maths introduces another aspect of sets which is called ‘intersection’ of two or more sets. It is denoted by ‘∩’ and represents the common elements between two or more sets. In this exercise, you will learn about the properties of an intersection set, such as commutative properties, associative properties, identity properties, distributive and intersection properties along with their application. Also, some complex problems that require the use of properties of a union and intersection are placed in exercise 1.6 of class 11 maths. A large number of students face difficulties in solving questions given in this exercise as it requires a strong understanding of all the concepts of sets. Remembering each concept is quite difficult but with our expert’s tips given in Class 11 Maths NCERT Solutions Chapter 1, you will be able to remember every concept in no time.

Miscellaneous Exercise

As a student of class 11, it is important for you to figure out whether you have learned all the concepts covered in the chapter. Miscellaneous exercise is the best way to revise and prepare for the exams. It covers complex problems on every concept you have learned in the whole chapter. It will help in making you more confident on sets. It has been seen that students usually skip miscellaneous exercise but our experts advise them not to do so. Just give it a try and in case, they face any difficulty, do refer Vedantu's NCERT Solutions for Class 11 Chapter 1. These will assist in getting a detailed explanation for each complex miscellaneous problem. Our solutions are comprehensive and well explained with the proper reasoning for the usage of any concept or theory. These solutions provide step-by-step guidance to students and assist them in solving their doubts in no time. 

Apart from the aforementioned concepts, there are other topics also on which our subject experts can assist you and clear your doubts. You can always reach them in case you face any problem and they will provide you with the best assistance related to your problems.

Access other exercise solutions of Class 11 Maths Chapter 1- Sets

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NCERT Solutions for Class 11 Maths Chapter 1 Sets PDF Download

NCERT Solutions are essential for all students who want to score well in their exams. Our subject matter experts have developed these solutions to help the students score good marks in their examinations. These solutions are well-explained and include each and every topic. Another essential benefit of NCERT Solutions for Class 11 Maths Chapter 1 Sets is that it is created as per the latest pattern of CBSE (Central Board of Secondary Education). These solutions also ensure that a student gets a clear understanding of each and every concept. 

In the Class 11 Maths Chapter 1 Sets Miscellaneous Solutions, each and every type of question is included. From easy to hard, the students will get an idea of all the types of questions which can appear in the exam. Also, apart from this, the students will also get to know about the most common questions which have a high chance of appearing in the exam. 

It can be assumed that a student will score good marks in their exams if they will study the Maths Class 11 Chapter 1 Sets PDF NCERT Solution on a regular basis. Our subject matter experts at Selfstudys have invested a good amount of time in creating them so that the students do not find any difficulty studying from these solutions. As the experts have been in the education line for quite some time, they are aware of the learning potential of every student, which is why they have created these solutions in a simple way so that no student faces any difficulty studying from them. Students can also use these solutions at the time of revision. 

The NCERT Solutions for Class 11 Maths Chapter 1 Sets can be easily downloaded from the website of Selfstudys i.e. Selfstudys.com. 

NCERT Solutions for Class 11 Maths Chapter 1 Sets PDF 

The NCERT Solutions for Class 11 Maths Chapter 1 Sets PDF can be easily downloaded from the website of Selfstudys. As they are in PDF format, it becomes easier for the students to access them. They are also mobile-friendly. 

How to Download the NCERT Solutions for Class 11 Maths Chapter 1 Sets? 

Downloading the NCERT Solutions for Class 11 Maths Chapter 1 Sets is if you know the right steps. The steps to download them are as follows: 

• Visit the official website of Selfstudys i.e. Selfstudys.com.

• Once the website is completely loaded, you need to click on the three lines which you will find on the upper left side. Following that, you have to click on the ‘NCERT Books and Solutions’ column. 

• After clicking on the option of ‘NCERT Books and Solutions’, a new list will open where you need to select the option of ‘NCERT Solutions’. 

• Following that, you will be redirected to a page where you need to select the class and the subject for which you want to download the NCERT Solutions. 
• In this case, you need to select class 10 and the subject Maths to download the NCERT Solutions for Class 11 Maths Chapter 1 Sets. 

What are the Features of the Maths Class 11 Chapter 1 Sets PDF NCERT Solution? 

There are many features of the NCERT Solutions for Class 11 Maths Chapter 1 Sets which can be very beneficial for all the students. The most important features include: 

• Well-Elaborated: The NCERT Solutions for Class 11 Maths Chapter 1 Sets is well-elaborated to make it easier for the students to understand all the concepts with in-depth knowledge. 
• Includes every topic: Every important topic is covered in the Class 11 Maths Chapter 1 Sets Miscellaneous Solutions which increases the confidence of the students as they feel that they know every topic and will eventually score good marks in their exams. 
• 24*7 Online Availability: One more feature of the NCERT Solutions for Class 11 Maths Chapter 1 Sets is that it is available 24*7. This is very beneficial for all the students as they can access these notes anytime either day or night. 
• Simple Language Used: The language which is used in the Class 11 Maths Chapter 1 Sets Miscellaneous Solutions is very easy. As we have mentioned earlier that our subject matter experts are aware of the learning power of all the students, so they have intentionally used the easiest language in these solutions so that no student faces any difficulty in learning them. 
• Well-organized Format: One thing which makes our Maths Class 11 Chapter 1 Sets PDF NCERT Solution different from other solutions is that they are developed in a well-structured format. These solutions are organized systematically, following the order of the chapters and topics in the textbooks. 
• Accuracy and reliability: Our subject matter experts have invested a good amount of time in developing these NCERT Solutions for Class 11 Maths Chapter 1 Sets. They are accurate and reliable for the preparation of exams. These notes can also be helpful for the students who do self-study. 

What are the Benefits of the NCERT Solutions for Class 11 Maths Chapter 1 Sets? 

The NCERT Solutions for Class 11 Maths Chapter 1 Sets has several benefits to offer to the students. Some of the most important of them are 

• Clear Understanding of the Topic: The Class 11 Maths Chapter 1 Sets Miscellaneous Solutions provides in-depth knowledge of each and every topic which is present in the syllabus. Each chapter is explained in detail in a step-by-step process. To make learning easier and more interesting for all the students, diagrams and examples are also given. 
• Authentic Solutions: The Maths Class 11 Chapter 1 Sets PDF NCERT Solution are completely authentic and can be trusted 100%. The highly qualified subject matter experts at Selfstudys have created these solutions in an authentic way which makes it simple for all the students to learn all the concepts. 
• Improved Problem-Solving Skills: By regularly practicing the NCERT Solutions for Class 11 Maths Chapter 1 Sets, students can improve their problem-solving skills. They get the idea of the techniques and methods which are used to solve various types of maths problems. 
• Conceptual Clarity: The NCERT Solutions for Class 11 Maths Chapter 1 Sets focuses on building a strong foundation for all the students. Students can get a deep understanding of the fundamental principles of maths formulas, which serve as a basis for further mathematical topics. 
• Boosts Confidence: If a student regularly goes through the NCERT Solutions for Class 11 Maths Chapter 1 Sets, there is no doubt that the students will gain confidence in their maths power. This confidence can motivate them to explore more difficult topics and make a strong base for all of them. 

What are the tips to study from the NCERT Solutions for Class 11 Maths Chapter 1 Sets? 

There are various tips that can help the students to study effectively from the NCERT Solutions for Class 11 Maths Chapter 1 Sets: 

• Go through the chapter thoroughly: It is very important for all the students to first go through the chapter as it will help them to understand the basics. If their basics will get strong, they will automatically be able to grasp the other concepts in a better way. 
• Practice Problem solving step-by-step: It is advisable for all the students to solve the problems step-by-step which are present in the Class 11 Maths Chapter 1 Sets Miscellaneous Solutions without looking at the answers. This will allow them to develop problem-solving skills and test their understanding of the concepts. 
• Create a study schedule: It is important for students to create a study schedule and follow it consistently to stay focused. Devote at least 45 minutes to grasp the concepts thoroughly. Give enough time to each topic covered in NCERT Solutions for Class 11 Maths Chapter 1 Sets and review them daily. Sticking to the schedule is recommended to ensure timely completion of all the topics. 
• Do not get distracted: All the students should stay focused to concentrate better and should not get distracted. They should stay away from their mobile phones and other electronic gadgets, for example, TV, etc. to avoid all the distractions while studying Maths Class 11 Chapter 1 Sets PDF NCERT Solution. 
• Practice Time Management: While doing exam preparation from the NCERT Solutions for Class 11 Maths Chapter 1 Sets, it is advisable for all the students to practice time management by setting a time duration for solving problems. This will help you develop efficiency and improve your speed in solving problems accurately. 

How to Master the Maths Class 11 Chapter 1 Sets PDF NCERT Solution ?

There are various ways to master NCERT Solutions for Class 11 Maths Chapter 1 Sets. Some of the most important of them are: 

• Study the NCERT Solutions: The students can start by studying the Class 11 Maths Chapter 1 Sets Miscellaneous Solutions. It is advisable for them to read the solutions carefully and understand them stepwise manner used to solve each problem. They should use them regularly as it will help them to understand the concepts in a clear manner. 
• Do regular practice of these solutions: It is advisable for all the students to regularly practice these NCERT Solutions for Class 11 Maths Chapter 1 Sets as it helps the students to do effective preparation for their exams. The conceptual knowledge of the students is also boosted by regularly practicing these solutions. 
• Do group discussions with your peers: It is advisable for all the students to do group discussions with their peers as discussing the concepts, problem-solving techniques, and solutions with others can help you understand them in a better way. Teaching and explaining concepts to others can deepen your understanding of all the concepts. 
• Revise regularly: Regularly revise the concepts and solutions from NCERT Solutions for Class 11 Maths Chapter 1 Sets. Review your notes, summaries, and solved problems. Revisit the solutions and attempt to solve them again without referring to the provided solutions. This revision will help reinforce your understanding and improve retention. 
• Take note of your mistakes and work on them: It is advisable for all the students to take note of their mistakes while solving the Maths Class 11 Chapter 1 Sets PDF NCERT Solution and work on them. Find your weaknesses and identify the specific concepts or steps that caused confusion. This will help you improve your problem-solving skills. 

How to Maximise Your Learning Potential While Solving the NCERT Solutions for Class 11 Maths Chapter 1 Sets? 

To maximize your learning potential while solving the NCERT Solutions for Class 11 Maths Chapter 1 Sets, here are the tips which can help you: 

• Do a thorough reading of the chapter: All the students should read Maths Class 11 Chapter 1 Sets PDF NCERT Solution thoroughly to maximize their learning potential as it will help them to understand the basic concepts which will make it easier for them to grasp all the concepts. 
• Practice regularly: One of the most important tips which every student should follow in order to maximize their learning potential is to practice these NCERT Solutions for Class 11 Maths Chapter 1 Sets regularly. It includes practicing the questions regularly in the Class 11 Maths Chapter 1 Sets Miscellaneous Solutions. This will help them in understanding the concepts with a deep understanding which can help them to score high marks in their exams. 
• Revise the concepts on a regular basis: It is very important for all the students to Revise all the concepts from the NCERT Solutions for Class 11 Maths Chapter 1 Sets as it helps to recall all the information which they have studied during the preparation for the exam. You can also use different methods to revise the concepts on a regular basis, for example, making flashcards, notes, etc. 

What Are the Methods To Study From NCERT Solutions for Class 11 Maths Chapter 1 Sets? 

Studying for the exam requires focus and concentration. Below we will discuss various methods of how students can study for an Exam with the help of NCERT Solutions for Class 11 Maths Chapter 1 Sets: 

• Making a strong grip of basics: It is very important for all students to create a strong base for basics and learn them for NCERT Solutions for Class 11 Maths Chapter 1 Sets as it helps a student to get a clear understanding of the concepts. This makes it easier for the students to learn them fast. 
• Study the NCERT Solutions for Class 11 Maths Chapter 1 Sets on a regular basis: It is advisable for all the students to study Class 11 Maths Chapter 1 Sets Miscellaneous Solutions on a regular basis as it will help them to do effective preparation for their exams and also increases the chances of the students to score good marks in their exams. 
• Always read the summary of your textbook: It is advisable for all students to always read the summary which is included in the Maths Class 11 Chapter 1 Sets PDF NCERT Solution. The students should read them on a regular basis as it will help them to get a thorough knowledge of all the topics and will also help them to prepare well for the exams. This will increase their chances of scoring good marks in the exams. 
• Identify your strong and weak areas: It is very important for all the students to identify their strong and weak areas as it will help them to understand where they need to put more effort in order to do well in their exams. 
• Do timely revision: All the students should do timely revision from the NCERT Solutions for Class 11 Maths Chapter 1 Sets if they want to do extremely well in their exams as it will ensure that you have created a strong base of all the topics in their minds. 

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NCERT Solutions for Class 11 Maths Chapter 1 Sets

Class 11 Maths Chapter 1 Solutions in English Medium Class 11 Maths Exercise 1.1 Solutions in English Class 11 Maths Exercise 1.2 Solutions in English Class 11 Maths Exercise 1.3 Solutions in English Class 11 Maths Exercise 1.4 Solutions in English Class 11 Maths Exercise 1.5 Solutions in English Class 11 Maths Chapter 1 Miscellaneous Exercise Class 11 Maths Chapter 1 Solutions in Hindi Medium Class 11 Maths Exercise 1.1 Solutions in Hindi Class 11 Maths Exercise 1.2 Solutions in Hindi Class 11 Maths Exercise 1.3 Solutions in Hindi Class 11 Maths Exercise 1.4 Solutions in Hindi Class 11 Maths Exercise 1.5 Solutions in Hindi Class 11 Maths Chapter 1 Miscellaneous in Hindi

NCERT Solutions for Class 11 Maths Chapter 1 Sets in Hindi and English Medium updated for academic session 2024-25. As per the rationalised NCERT textbooks and new syllabus there are only five exercises and a miscellaneous exercise in chapter 1 of 11th mathematics. Related Links Class 11 Maths all Chapters Solutions Class 11 all Subjects NCERT Solutions

Class 11 Maths Chapter 1 Solutions are useful for CBSE, UP Board, MP Board, Gujrat Board and other board’s students following CBSE curriculum 2024-25. NCERT Solutions and Offline Apps are based on latest Books from NCERT (https://ncert.nic.in/) website and Latest CBSE Syllabus for their final exams. Download UP Board Solutions for Class 11 Maths Chapter 1 in PDF format free.

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NCERT Solutions for Class 11 Maths Chapter 1 Sets in English Medium is given below to free download. These solutions and Offline apps are based on latest textbook by NCERT for all students who are following new Syllabus.

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 play neither cricket nor tennis? [Answer: 23]

In a town of 10,000 families it was found that 40% families buy newspaper A, 20% families buy newspaper B and 10% families by 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 the no of families which buy(1) A only (2) B only (3) none of A, B and C (4) exactly two newspapers (5) exactly one newspaper (6) A and C but not B (7) at least one of A,B, C. [Answer: {2, 3, 5}]

Two finite sets have m and n elements. The total number of subsets of first set is 56 more than the total number of subsets of the second set. Find the value of m and n. [Answer: m = 6 and n = 3]

In a group of 84 persons, each plays at least one game out of three viz. tennis, badminton and cricket. 28 of them play cricket, 40 play tennis and 48 play badminton. If 6 play both cricket and badminton and 4 play tennis and badminton and no one plays all the three games, find the number of persons who play cricket but not tennis.

Important Questions on 11th Maths Chapter 1

Write the following sets in the set-builder form: (3, 6, 9, 12)..

Set builder form of {3, 6, 9, 12} = {x: x = 3n, n∈ N and 1 ≤ n ≤ 4}

List all the elements of the following set: A = {x: x is an odd natural number}.

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

Write down all the subsets of the following set: {1, 2, 3}.

The subsets of {1, 2, 3} are Φ, {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3} {1, 2, 3}

Let A = {a, b}, B = {a, b, c}. Is A ⊂ B? What is A ∪ B?

Here, A = {a, b} and B = {a, b, c} Yes, A ⊂ B. A ∪ B = {a, b, c} = B

In a group of 400 people, 250 can speak Hindi and 200 can speak English. How many people can speak both Hindi and English?

Let H be the set of people who speak Hindi, and E be the set of people who speak English ∴ n(H ∪ E) = 400, n(H) = 250, n(E) = 200 n(H ∩ E) = ? We know that: n(H ∪ E) = n(H) + n(E) – n(H ∩ E) ∴ 400 = 250 + 200 – n(H ∩ E) ⇒ 400 = 450 – n(H ∩ E) ⇒ n(H ∩ E) = 450 – 400 ∴ n(H ∩ E) = 50 Thus, 50 people can speak both Hindi and English.

If S and T are two sets such that S has 21 elements, T has 32 elements and S ∩ T has 11 elements, how many elements does S ∪ T have?

It is given that: n(S) = 21, n(T) = 32, n(S ∩ T) = 11 We know that: n (S ∪ T) = n (S) + n (T) – n (S ∩ T) ∴ n (S ∪ T) = 21 + 32 – 11 = 42 Thus, the set (S ∪ T) has 42 elements.

If X and Y are two sets such that X has 40 elements, X ∪Y has 60 elements and X ∩Y has 10 elements, how many elements does Y have?

It is given that: n(X) = 40, n(X ∪ Y) = 60, n(X ∩ Y) = 10 We know that: n(X ∪ Y) = n(X) + n(Y) – n(X ∩ Y) ∴ 60 = 40 + n(Y) – 10 ∴ n(Y) = 60 – (40 – 10) = 30 Thus, the set Y has 30 elements.

In a group of 70 people, 37 like coffee, 52 like tea, and each person likes at least one of the two drinks. How many people like both coffee and tea?

Let C denote the set of people who like coffee, and T denote the set of people who like tea n(C ∪ T) = 70, n(C) = 37, n(T) = 52 We know that: n(C ∪ T) = n(C) + n(T) – n(C ∩ T) ∴ 70 = 37 + 52 – n(C ∩ T) ⇒ 70 = 89 – n(C ∩ T) ⇒ n(C ∩ T) = 89 – 70 = 19 Thus, 19 people like both coffee and tea.

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?

Let C denote the set of people who like cricket, and T denote the set of people who like tennis ∴ n(C ∪ T) = 65, n(C) = 40, n(C ∩ T) = 10 We know that: n(C ∪ T) = n(C) + n(T) – n(C ∩ T) ∴ 65 = 40 + n(T) – 10 ⇒ 65 = 30 + n(T) ⇒ n(T) = 65 – 30 = 35 Therefore, 35 people like tennis. Now, (T – C) ∪ (T ∩ C) = T Also, (T – C) ∩ (T ∩ C) = Φ ∴ n (T) = n (T – C) + n (T ∩ C) ⇒ 35 = n (T – C) + 10 ⇒ n (T – C) = 35 – 10 = 25 Thus, 25 people like only tennis.

In a committee, 50 people speak French, 20 speak Spanish and 10 speak both Spanish and French. How many speak at least one of these two languages?

Let F be the set of people in the committee who speak French and S be the set of people in the committee who speak Spanish ∴ n(F) = 50, n(S) = 20, n(S ∩ F) = 10 We know that: n(S ∪ F) = n(S) + n(F) – n(S ∩ F) = 20 + 50 – 10 = 70 – 10 = 60 Thus, 60 people in the committee speak at least one of the two languages.

In a survey of 600 students in a school, 150 students were found to be taking tea and 225 taking coffee, 100 were taking both tea and coffee. Find how many students were taking neither tea nor coffee?

Let U be the set of all students who took part in the survey. Let T be the set of students taking tea. Let C be the set of students taking coffee. Accordingly, n(U) = 600, n(T) = 150, n(C) = 225, n(T ∩ C) = 100 To find: Number of student taking neither tea nor coffee i.e., we have to find n(T’ ∩ C’). n(T’ ∩ C’) = n(T ∪ C)’ = n(U) – n(T ∪ C) = n(U) – [n(T) + n(C) – n(T ∩ C)] = 600 – [150 + 225 – 100] = 600 – 275 = 325 Hence, 325 students were taking neither tea nor coffee.

In a group of students 100 students know Hindi, 50 know English and 25 know both. Each of the students knows either Hindi or English. How many students are there in the group?

Let U be the set of all students in the group. Let E be the set of all students who know English. Let H be the set of all students who know Hindi. ∴ H ∪ E = U Accordingly, n(H) = 100 and n(E) = 50 n( H U E ) = n(H) + n(E) – n(H ∩ E) = 100 + 50 – 25 = 125 Hence, there are 125 students in the group.

2. In a class, 18 students took Physics, 23 students took Chemistry and 24 students took Mathematics of these 13 took both Chemistry and Mathematics, 12 took both Physics and Chemistry and 11 took both Physics and Mathematics. If 6 students offered all the three subjects, find: (1) The total number of students. (2) How many took Maths but not Chemistry. (3) How many took exactly one of the three subjects.

How many exercises, questions, and examples are there in class 11 Maths Chapter 1?

There are six exercises in class 11 Maths Chapter 1 (Sets). In the first exercise (Ex 1.1), there are six questions. In the second exercise (Ex 1.2), there are six questions. In the third exercise (Ex 1.3), there are 9 questions. In the fourth exercise (Ex 1.4), there are 12 questions. In the fifth exercise (Ex 1.5), there are seven questions. In the last exercise (Miscellaneous), there are 16 questions. So, there are in all 54 questions in class 11 Maths Chapter 1. There are in all 34 examples in class 11 Maths Chapter 1.

• Examples 1, 2, 3, 4, 5 are in Ex 1.1.
• Examples 6, 7, 8 are in Ex 1.2.
• Examples 9, 10, 11 are in Ex 1.3.
• Examples 12, 13, 14, 15, 16, 17, 18, 19 are based on Ex 1.4.
• Examples 20, 21, 22 are in Ex 1.5.
• Examples 23, 24, 25, 26, 27 are in Ex 1.6.
• Examples 28, 29, 30, 31, 32, 33, 34 are based on Miscellaneous exercise.

Which problems of chapter 1 of class 11th Maths are most important for the terminal exams?

Problems of chapter 1 of class 11th Maths that are most important for the exams are: 1. Questions 2, 3, 4, and 5 of exercise 1.1. 2. Questions 1 and 6 of exercise 1.2. 3. Questions 1, 3, 4, 5, 6, 7, and 9 of exercise 1.3. 4. Questions 3, 4, 5, 9, and 12 of exercise 1.4. 5. Questions 1, 3, 4, 5, and 7 of exercise 1.5. 6. Questions 2, 7, and 8 of exercise 1.6. 7. Questions 2, 4, 5, 6, 7, 8, 9, 11, 12, 13, 15, 16 of miscellaneous exercise on chapter 1. 8. Examples 5, 6, 9, 11, 13, 18, 22, 24, 25, 27, 29, 30, 31, 32, 33, 34.

Are there any books other than NCERT from which students can practice extra questions of chapter 1 of class 11th Maths?

Yes, there are some books other than NCERT from which students can practice extra questions of chapter 1 of class 11th Maths. The names of these books are NCERT Exemplar, R.L. Arora, R.D. Sharma, R.S. Aggarwal. These books are the best books after NCERT and NCERT Exemplar. The languages of these books are students friendly. Students can easily prepare chapter 1 of class 11th Maths from these books. Students can also see the previous year’s question papers.

Is chapter 1 of class 11 Maths easy to solve?

Chapter 1 of class 11th mathematics is not easy and not complicated. It lies in the middle of easy and hard because some examples and questions of this chapter are easy, and some are difficult. But difficulty level of any chapter varies from student to student. So, Chapter 1 of class 11th mathematics is easy or not depends on students also. Some students find it complex, some find it simple, and some find it in the middle of simple and complex.

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NCERT Solutions for Class 11 Maths Chapter 1

Ncert solutions for class 11 maths chapter 1 sets.

Are you searching for the best NCERT Solutions for Class 11 Maths Chapter 1 Sets? Here in this article, Study Path has provided what you need exactly. NCERT Solutions for Class 11 Maths Chapter 1 Sets includes all the questions of the NCERT textbook that are solved and explained beautifully using Vann diagrams, images etc. Here you can get complete NCERT Solutions for Class 11 Maths Chapter 1 Sets in one place.

NCERT Solutions for Class 11 Maths Chapter 1 Set solved by expert teachers at Study Path. The Solutions to the questions of Chapter 1 Sets Maths Class 11 have been solved in a very logical, step-by-step manner. It is as prepared per the latest Syllabus and NCERT Guidelines.

Download PDF of NCERT Solutions for Class 11 Maths Chapter 1 Sets

In this section, we have provided the links of different exercises of the chapter. Click on the appropriate links to access the solutions we want.

• Exercise 1.1
• Exercise 1.2
• Exercise 1.3
• Exercise 1.4
• Exercise 1.5
• Exercise 1.6
• Miscellaneous Exercise

NCERT Solutions for Class 11 Maths Chapter 1 Sets – A Brief Discussion

Chapter Overview:  In the above section, we have listed the major concepts of Maths covered in Chapter 1- Sets of NCERT Solutions for Class 11. In this section, we will explain some important terms that you must know to understand the concepts of sets easily. 

Set:  A set is a well-defined collection of objects.

Null set: A set which does not contain any element is called the empty set or the null set or the void set.

Finite and Infinite Set:  A set which is empty or consists of a definite number of elements is called finite otherwise, the set is called infinite set.

Equal and Unequal Sets: Two sets A and B are said to be equal if they have exactly the same elements and we write A = B. Otherwise, the sets are said to be unequal and we write A ≠ B.

Subset: A set A is said to be a subset of a set B if every element of A is also an element of B. In other words, A ⊂ B if whenever a ∈ A, then a ∈ B. It is often convenient to use the symbol “⇒” which means implies. Using this symbol, we can write the definiton of subset as : A ⊂ B if a ∈ A ⇒ a ∈ B

Power Set:  The collection of all subsets of a set A is called the power set of A. It is denoted by P(A).

Venn Diagrams:  Most of the relationships between sets can be represented by means of diagrams which are known as Venn diagrams.

Union of Sets: Let A and B be any two sets. The union of A and B is the set which consists of all the elements of A and all the elements of B, the common elements being taken only once. The symbol ‘∪’ is used to denote the union. Symbolically, we write A ∪ B and usually read as ‘A union B’

Intersection of sets:  The intersection of sets A and B is the set of all elements which are common to both A and B. The symbol ‘∩’is used to denote the intersection. The intersection of two sets A and B is the set of all those elements which belong to both A and B. Symbolically, we write A ∩ B = {x : x ∈ A and x ∈ B}

Difference of sets: The difference of the sets A and B in this order is the set of elements which belong to A but not to B. Symbolically, we write A – B and read as “ A minus B”.

De Morgan,s Law:  The complement of the union of two sets is the intersection of their complements and the complement of the intersection of two sets is the union of their complements. These are called De Morgan’s laws.

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• NCERT Solutions for Class 11 Maths Chapter 1: Sets - Exercise 1.6
• NCERT Solutions

NCERT Solutions for Class 11 Maths Chapter 1 Sets

NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.6 provided by Vedantu is a very reliable study material. Our Class 11 Maths Exercise 1.6 Solutions have been prepared under the guidance of qualified maths experts. Also, our latest Class 11 Maths Ex 1.6 Solutions strictly follows the latest  CBSE syllabus . To ensure quality exam preparation get the NCERT Solution PDF for Maths available as free PDF downloads for enhanced exam preparation.

Access NCERT Solutions for Class 11 Maths Chapter 1 – Sets

Exercise 1.6

1. If $X$ and $Y$ are two sets such that $n\left( X \right) = 17$, $n\left( Y \right) = 23$ and $n\left( {X \cup Y} \right) = 38$, find $n\left( {X \cap Y} \right)$.

Ans: For two sets $X$ and $Y$ , using the formula $n\left( {X \cup Y} \right) = n\left( X \right) + n\left( Y \right) - n\left( {X \cap Y} \right)$ and substituting the values $n\left( X \right) = 17$ , $n\left( Y \right) = 23$ and $n\left( {X \cup Y} \right) = 38$ ,

$\Rightarrow 38 = 17 + 23 - n\left( {X \cap Y} \right)$

$\Rightarrow n\left( {X \cap Y} \right) = 17 + 23 - 38$

$\Rightarrow n\left( {X \cap Y} \right) = 2$ 

2. If $X$ and $Y$ are two sets such that $\left( {X \cup Y} \right)$ has $18$ elements, $X$ has $8$ elements and $Y$ has $15$ elements. How many elements does $\left( {X \cap Y} \right)$ have?

Ans: For two sets $X$ and $Y$ , using the formula $n\left( {X \cup Y} \right) = n\left( X \right) + n\left( Y \right) - n\left( {X \cap Y} \right)$ and substituting the values $n\left( X \right) = 8$ , $n\left( Y \right) = 15$ and $n\left( {X \cup Y} \right) = 18$ ,

$\Rightarrow 18 = 8 + 15 - n\left( {X \cap Y} \right)$

$\Rightarrow n\left( {X \cap Y} \right) = 8 + 15 - 18$

$\Rightarrow n\left( {X \cap Y} \right) = 5$ 

3. In a group of $400$ people, $250$ can speak Hindi and 200 can speak English. How many people can speak both Hindi and English?

Ans: Assume the set people who can speak English as $A$ and set of people who can speak Hindi as $B$ . Therefore the set of total people is denoted by $\left( {A \cup B} \right)$ . According to the question the values given are,

$n\left( {A \cup B} \right) = 400$ , $n\left( B \right) = 250$ and $n\left( A \right) = 200$

Using the formula $n\left( {A \cup B} \right) = n\left( A \right) + n\left( B \right) - n\left( {A \cap B} \right)$ , where the set $\left( {A \cap B} \right)$ represents the people who can speak both English and Hindi,

$\Rightarrow 400 = 200 + 250 - n\left( {A \cap B} \right)$

 $\Rightarrow n\left( {A \cap B} \right) = 200 + 250 - 400$

 $\Rightarrow n\left( {A \cap B} \right) = 50$ 

4. If $S$ and $T$ are two sets such that $S$ has $21$ elements, $T$ has $32$ elements and $\left( {S \cap T} \right)$ has $11$ elements. How many elements does $\left( {S \cup T} \right)$ have?

Ans: For two sets $S$ and $T$ , using the formula $n\left( {S \cup T} \right) = n\left( S \right) + n\left( T \right) - n\left( {S \cap T} \right)$ and substituting the values $n\left( S \right) = 21$ , $n\left( T \right) = 32$ and $n\left( {S \cap T} \right) = 11$ ,

$\Rightarrow n\left( {S \cup T} \right) = 21 + 32 - 11$

$\Rightarrow n\left( {S \cup T} \right) = 42$ 

5. If $X$ and $Y$ are two sets such that $X$ has $40$ elements, $\left( {X \cup Y} \right)$ has $60$ elements and $\left( {X \cap Y} \right)$ has $10$ elements. How many elements does $Y$ have?

Ans: For two sets $X$ and $Y$ , using the formula $n\left( {X \cup Y} \right) = n\left( X \right) + n\left( Y \right) - n\left( {X \cap Y} \right)$ and substituting the values $n\left( X \right) = 40$ , $n\left( {X \cap Y} \right) = 10$ and $n\left( {X \cup Y} \right) = 60$ ,

$\Rightarrow 60 = 40 + n\left( Y \right) - 10$

$\Rightarrow n\left( Y \right) = 60 + 10 - 40$

$\Rightarrow n\left( Y \right) = 30$ 

6. In a group of $70$ people, $37$ like coffee, $52$ like tea and each person likes at least one of the two drinks. How many people like both coffee and tea?

Ans: Assume the set people who like coffee as $A$ and set of people who like tea as $B$ . Therefore the set of people who like at least one of two drinks is denoted by $\left( {A \cup B} \right)$ . According to the question the values given are,

$n\left( {A \cup B} \right) = 70$ , $n\left( A \right) = 37$ and $n\left( B \right) = 52$

Using the formula $n\left( {A \cup B} \right) = n\left( A \right) + n\left( B \right) - n\left( {A \cap B} \right)$ , where the set $\left( {A \cap B} \right)$ represents the people who like both tea and coffee,

$\Rightarrow 70 = 37 + 52 - n\left( {A \cap B} \right)$

$\Rightarrow n\left( {A \cap B} \right) = 37 + 52 - 70$

$\Rightarrow n\left( {A \cap B} \right) = 19$ 

7. 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: Assume the set people who like cricket as $A$ and set of people who like tennis as $B$ . Therefore the set of total people is denoted by $\left( {A \cup B} \right)$ and the set of people who like both cricket and tennis is denoted by $\left( {A \cap B} \right)$ . According to the question the values given are,

$n\left( {A \cup B} \right) = 65$ , $n\left( A \right) = 40$ and $n\left( {A \cap B} \right) = 10$

Using the formula $n\left( {A \cup B} \right) = n\left( A \right) + n\left( B \right) - n\left( {A \cap B} \right)$ ,

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

$\Rightarrow n\left( B \right) = 35$ 

Hence, $35$ people like tennis.

Now, the number of people who like tennis only and not cricket is,

$= n\left( B \right) - n\left( {A \cap B} \right)$

$= 35 - 10$

8. In a committee, $50$ people speak French, $20$ speak Spanish and $10$ speak both Spanish and French. How many speak at least one of the two languages?

Ans: Assume the set people who speak French as $A$ and set of people who speak Spanish as $B$ . Therefore the set of people who speak either of the two languages is denoted by $\left( {A \cup B} \right)$ and the set of people who speak both the languages is denoted by $\left( {A \cap B} \right)$ . According to the question the values given are,

$n\left( A \right) = 50$ , $n\left( B \right) = 20$ and $n\left( {A \cap B} \right) = 10$

$\Rightarrow n\left( {A \cup B} \right) = 50 + 20 - 10$

$\Rightarrow n\left( {A \cup B} \right) = 60$ Class 11 Maths NCERT Solutions Chapter 1 – An Overview of Sets

Sets being one of the most crucial and fundamental concepts of Mathematics finds its application across all the branches of the other subjects too. With the help of fundamentals of sets, the concept of Union and Intersection of sets can be defined easily. The concept of Sets has also found its application in the study of geometry, sequences and several other fields.

In this particular chapter, you will learn about various representation of sets and you will also become familiar with its various operations.

To elaborate, this chapter touches upon the following concepts:

Introduction to the concept and functionality of sets.

Representation of sets.

The empty set.

Finite and Infinite sets.

Equal sets.

Subsets of a set of real numbers.

Intervals as subsets of R.

Power set as a universal set.

Venn diagram.

Operations on sets.

Differences in sets.

A complement of a set.

Union and intersection of two sets.

A fair idea of these concepts will prove useful for you in higher classes and will also help you to apply them in various other kinds of sums also. Also, make it a point to get all your doubts cleared in advance before you delve into the chapters in details.

To facilitate the same, you can download our study material like NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.6. This prepared solution will help you to pick up shortcut techniques to solve sums and will also help you to clear your chapter-related doubts.

Our exercise-based notes material in the form of Class 11 Maths Ex 1.6 Solutions provides a proper step by step explanation for each answer. It also helps to obtain a fair understanding of the step by step approach that goes into solving each question of this chapter. Now, let us take a look at the questions included in our NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.6 to have a proper understanding of how our study material can help you score better grades.

NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.6 – All Questions

Let us take an example of Ex. 1.6 Class 11 Maths and figure out how our updated NCERT Solutions for Class 11 Maths Chapter 1 benefits your revisions for exam preparation. It comprises a total of 8 questions, each of which is based on the essential concepts of Sets.

Exercise 1.6 Class 11 Maths – Question 1

To begin with, the first question of this exercise provides you with two sets, namely X and Y. The objective of this question is to test your knowledge of sets and their operation. For example, this question requires you to find the intersection of sets X and Y by using the Union of sets X and Y.

To solve these questions effectively, you would first need to learn how to find the intersection of a given set. You also need an understanding of how to find the union of two separate sets which will give you an upper hand in solving such questions more accurately in exams. With a quick reference of our Class 11 Maths NCERT Solutions Chapter 1, you will learn not just how to solve such sums but will pick up smart techniques of approaching these kinds of questions.

Additionally, our NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.6 provides essential insight into the steps that should be applied to solve sums of these kinds. The said question requires you to find the Union and intersection of sets X and Y.

You will find out the step by step method to find the Union of sets X and Y while going through our solutions, This will further show how to find out the intersection of these two sets.

Our solutions will provide you with useful insight to allow you to solve similar problems in this exercise with more confidence and will also directly benefit your exam preparation. Regardless, make it a point to go for multiple revisions of this chapter so that the various methods and laws that come in handy while solving these kinds of sums are instilled in your mind.

Subsequently, include our Class 11 Maths Exercise 1.6 Solutions into your revision plan to take your exam preparation to the next level. Such inclusion will prove to be immensely beneficial and will help you gain the confidence you always needed to ace all your exams.

Class 11 Maths NCERT Solutions Chapter 1 Exercise 1.6 – Question 2

Based on the similar concept and approach as above, this particular sum in Ex 1.6 Class 11 Maths requires you to the number of intersections of different sets respectively. Two sets are provided in the same, which serves as a reference point for the students.

Solving these questions at a go, and then figure out if the answers you have received are correct or not. You can use our NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.6 as a guide to check the accuracy of your answers as well as the effectiveness of your method.

Nonetheless, it must be noted that these sums are quite easy to solve and require a simple approach. That being said, students are more likely to make careless mistakes while solving them quickly. With proper practice, you can solve the sums accurately and quickly.

Thus, to ensure that you do not commit minute errors while rushing through these sums, you need to adopt a few smart shortcut techniques. For instance, our Class 11 Maths Chapter 1 Exercise 1.6 Solutions offer you several easy techniques and help you to solve these sums quite early, thus saving time.

Since our solutions are updated frequently, the tips and techniques we share with your timely revision will give you improved efficiency. It directly benefits the quality of your exam preparation and helps you to upgrade your approach towards planning for it.

Download our NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.6 from Vedantu, and go through all the latest tips and techniques that can help you to take your learning experience to the next level.

Class 11 Maths Exercise 1.6 Solutions – Question 3

Before discussing this particular question, it is essential to look into other vital aspects of Sets that will facilitate the process of solving the remaining questions of this exercise.

Through the course of this chapter, students will be introduced to several new methods and touches upon the different rules of sets in details. Possessing a basic idea of these laws simplifies the concepts of this chapter to a great extent. It also provides you with a fair understanding of the approach to different sums required to get an accurate result.

Which is why, before moving ahead in this exercise, you must make it a point to go through these following in details –

Commutative law

Associative law

Law of identity

Idempotent law

Universal law

Distributive law

De Morgan’s law

Complements law

Law of double complementation

Laws of empty set and universal set

Once you gain a substantial idea of these laws of set operations, you can move onto solving the remaining questions of Class 11 Maths Chapter 1 Exercise 1.6 effectively. As for the third question of this exercise, it is quite similar to the previous two questions. However, to solve it correctly, you need to be equipped with the idea and concept of Sets in more depth.

To elaborate, you are to use apply the idea of union and intersection of sets in real-life problems.

Consequently, you need to be aware of a few things to ensure the accuracy of their solution. To begin with, you need to know a Natural Set and a Universal Set.

Similarly, you must also know about the following.

Odd natural numbers.

Even natural numbers.

Positive multiples of three.

Prime numbers.

Divisibility of natural numbers.

Characteristics of a perfect square.

Characteristics of a perfect cube.

Equip yourself with the basic idea of these concepts and then proceed to approach other problems of the same kind. Reach out to the accurate answers for this unique question by referring to our NCERT Solutions for Class 11 Maths Chapter 1 that we have made available for you online. You can access the free PDF downloads of such solutions for free and go through them as per your convenience.

Ex. 1.6 Class 11 Maths – Question 4 

To solve this particular question from NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.6 effectively, you need to have a fair understanding of the concepts that were touched upon in the previous exercises. For instance, refresh your knowledge of how to form the union of one set with the other. Also, while at it, make sure to go through the steps that have to be applied to create an intersection set.

These basics will help you solve this particular sum with more confidence and ease. To elaborate, this question requires you to verify that the union of two sets (S and T) by using the intersection of the two given sets.

When it comes to proving sums, the right approach is essential to get accurate answers. Make it a point to be familiar with the accurate approach and know the step by step method of solving similar problems.

Regardless of your ability to answer this type of questions; you can follow the approach that our subject experts have adopted to solve all these questions. By doing so, you will not only gain a significant idea of the steps that will into solving such sums but it will also further help you to pick up effective shortcut techniques.

As qualified teaching professionals cross-check them, you need not worry about the accuracy of the methods in our Ex. 1.6 Class 11 NCERT Solutions. With the incorporation of shortcut techniques, we have shared with you our solutions, to help you improve your problem-solving skills significantly.

Also, a familiarity with the use of such techniques and a working knowledge of the same will help you to solve similar problems in exams quite efficiently. Over time, it will sharpen your skills to solve problems with a few steps and will also come in handy in your CBSE Class 12 Board Examination.

Avail more of such revision-friendly tips and tricks from us to take your exam preparation a level up and make the entire revision process smooth and convenient. Just visit our online platform and choose from a world of learning options like never before.

Class 11 Maths Chapter 1 Exercise 1.6 – Question 5

How proficient are you when it comes to finding Union of sets by using formula? It is recommended that you get your basics cleared when it comes to using formula before the beginning of this question. It requires you to draw an accurate representation of the relation between the number of union and intersection of different sets.

For example, this question gives you the number of elements in set X and the number of elements in set Y. It also gives you the number of elements in the intersection of the sets X and Y. Thus, By using these pieces of information, you have to find the number of elements present in the union of the set X and Y.

Also, you need to refresh your memory of three basics concepts to solve these and other similar questions accurately –

Practical problems of Union and Intersection of two sets.

The meaning of intersection and union of sets.

The difference between intersection and complement of sets.

Figure out why you need to be familiar with these three by following the answer format of our expert-approved solutions. With a quick look, you will be able to figure out how these come in to play while solving related questions.

You can use our NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.6 as a learning guide and cross-check your methods as well as answers with a quick reference. To make it effective immediately, download our latest chapter-wise solutions from our official website and begin your revision for complete preparation. Also, by including our study guide into your revision plan, you will be able to keep track of your improvement. It will further help you systematically plan your exam revision and make changes to it as and when deemed necessary.

Ex 1.6 Class 11 NCERT Solutions – Question 6

Word problems are always fun to solve. They do not just gauge your ability to understand the question but also test how well you approach them. The next question on sets maintains the same spirit and is represented as an interesting word problem.

Nonetheless, it must be noted that to solve this problem; you need to have a clear idea of the fundamentals of both Sets and its applications. Only if you have mastered the two; you will be able to solve problems like this one in no time.

Also, if you need to figure out the accurate answer for this particular problem and more, you can download our NCERT Solutions Class 11 Maths Chapter 1 Exercise 1.6. It will provide you with all the answers and effective shortcut techniques that can be used effectively to solve not just this sum but other similar problems as well.

Class 11 Maths Exercise 1.6 – Question 7

The highlight of this question is that it is represented in the format of application of sets. You are provided with a structural break down of the solution to for a clear explanation.

To effectively solve them, you need to be familiar with the functioning of –

The formula of the number of elements in the union and intersection of sets.

Complement sets.

Additionally, you should also have a fair idea of how two sets can be related to each other. Since it is a unique way of approaching this type of question, you will gain a better insight into how to solve it with the help of Ex 1.6 Class 11 NCERT Solutions. A quick look at the same will help you to solve the questions more effectively. Also, the scope of making any errors will considerably reduce.

Nonetheless, you must dedicate ample time and attention to the solution of this chapter to be able to retain it for a long time. Also, with regular revision, you will be able to boost your confidence level and perform well in exams.

Class 11 Maths Exercise 1.6 – Other Exercise of Sets

There are a total of 6 exercises of this chapter namely –

Exercise 1.1

Exercise 1.2

Exercise 1.3

Exercise 1.4

Other than these, one miscellaneous exercise is also included that touches upon all the topics of sets and consists of different types of questions.

The following will offer you a fair idea of all the exercises mentioned above. It will further tell you how our NCERT Solutions for Class 11 Maths Chapter 1 proves beneficial in solving each one of them.

Exercise 1.1 of Sets 

In this exercise, you will be solving a total of 6 questions; each of which tends to test your basic knowledge of Sets.

For example, the first question comprising nine problems requires you to figure out which of the given collections qualify as a set. Once identified, you will further be required to justify your answer for the same.

Though it may be easy to identify which of the collections form a set, students often falter at providing a suitable justification. You can avoid such unwarranted problem by simply following our latest NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.6. Our solution will not only help you to justify your answer but will also enable you to solve similar problems with minimum assistance.

Besides, the other question of this exercise requires you to have a substantial idea of the following –

The symbols of set theory.

The roster format.

The set builder format.

Elements of sets.

With a clear idea of these pointers, you will be able to solve the remaining questions quite effectively. Also, take note of the key pointers that are shared in our CBSE NCERT Books free PDF downloads. They are highlighted in blue and represented in boxes to make it easier for you to spot them.

Having a fair hold of them will help you solve the sums quite easily. For example, one of the key pointers preceding the first exercise states: “The order in which the elements are listed in the roster form is immaterial.” While going through the same, you will also learn that all elements in the roster form are considered to be distinct.

In case you want to have more of such learning tips and shortcut techniques of solving problems, you can refer to our study materials available online. Subject experts have formulated our study solutions like Class 11 Maths NCERT Solutions Chapter 1 Ex 1.6. Their years of experience and thorough knowledge have helped us to come up with brilliant shortcut techniques and prompt learning tips. All of these facilitate an effective learning process and allow you to prepare for your upcoming exams better.

Exercise 1.2 of Sets

When you move onto the next question of this exercise, you will find that it consists of 6 questions, all of which are entirely based on concepts of finite, infinite and empty sets.

To elaborate, the first one of the lot requires you to state which one of the given sets can be deemed as null sets. The following two questions also direct you to pick up the finite and infinite set from the sets provided.

However, as you move on to the fourth question, you will notice that you need to state if the two specific sets are similar to one another. Though question 5 and 6 are also on the same line and requires a similar approach, you have to offer suitable reasons for your choice of answer.

Here are two potent tips for you to solve these and other similar questions easily –

Go through the solved examples that precede the exercise.

Practice our compact NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.6.

A perfect blend of both will come a long way and allow you to polish your understanding of the chapter significantly. Similarly, it will offer a functional idea of which approach to adopt for solving these types of questions.

By incorporating this blend into your study regime, you will benefit your exam revision and will improve your scope of performing exceptionally well in your upcoming exam. To facilitate the same at the earliest, access our study solutions now and take your exam preparation to the next level.

Exercise 1.3 of Sets

How well-acquainted are you are with concepts like – subsets, power sets and universal sets? In case you are not well-versed with them, it is recommended that you improve your knowledge about them before moving on to this exercise. As all nine questions of this exercise are largely based on these concepts mentioned above, brushing up your memory of the same will prove immensely helpful.

That being said; let us take a quick look at how the questions are based on these concepts. For example, the first question tests your knowledge of subsets. First, you have to identify if the two given set of elements are subsets or not. Then, based on your identification, you have to fill in the accurate symbol for each case.

The following question in NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.6 is also based on the same concepts. Here, you need to figure out if the following statements are true or false. Subsequently, you need to provide a suitable explanation for your choice of answer.

While you are at your revision, pay close attention to provide subsets of given sets and the steps to compute the number of elements in a given set. All these techniques and information will allow you to solve the remaining exercises quite efficiently.

Regardless of your comfort level with these concepts of sets, you can access the latest PDF free downloads of our study guides for further assistance. As they are formulated by subject experts, you would not have to guess the accuracy of our solutions, and the methods applied.

Also, you can access all the accurate answers and accompanying explanations in our chapter guides like Class 11 Maths Exercise 1.6 study solutions. Take a cue from the question-answering approach we have shared in our study materials to improve on your question-answering skills.

Exercise 1.4 of Sets

The exercise carries a total of 12 questions, and each of them is designed to test your familiarity with the operations of sets.

To refresh your memory, these are the operations that you need to know in details to offer the accurate step by step solution for each question –

Union of Sets – In this case, the union of two sets (A and B) would consist of all the elements of both sets. The union between the two sets is denoted by the symbol ‘U’.

Also, the operation of the union has these following properties –

As per Commutative law, A ∪ B = B ∪ A ()

As per Associative law, (A ∪ B) ∪ C = A ∪ ( B ∪ C) 

As per the Law of identity element, φ is the identity of ∪ A ∪ φ = A 

As per Idempotent law A ∪ A = A 

As per Law of U (v) U ∪ A = U

Intersections of Sets – In this case, the intersection of two sets (A and B) would consist of those elements that are common to both sets. An intersection between the two sets is denoted by the symbol ‘∩’

             Also, operation of the intersection has these following properties –

As per Commutative law, A ∩ B = B ∩ A.

As per Associative law, (A ∩ B) ∩ C = A ∩ (B ∩ C).

As per Law of φ and U, φ ∩ A = φ, U ∩ A = A (U).

As per Idempotent law, A ∩ A = A 

As per Distributive law, A ∩ ( B ∪ C ) = ( A ∩ B ) ∪ ( A ∩ C ) 

The difference of Sets – In this case, the set elements which belong to A do not belong to B. The same would be denoted as A – B.

With the help of this information, you would be able to solve 12 questions of NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.6 quickly and accurately. Also, a close reference to the solved exercises provided at the beginning of this exercise will help you understand how these laws are applied in each case. Simultaneously, follow the step by step problem-solving methods shown in our NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.6 to understand the application of these laws better.

Exercise 1.6 of Sets

How good are you at solving word problems? Put your skills to test by solving the practical problems on the union and intersection of two sets. The section preceding the exercise will provide you with ample information on how to solve word problems based on sets. You will also gain potential insight into why a particular step was applied for solving a problem.

Subsequently, try the eight-word problems of this exercise to figure out how well you have understood the requisite approach for solving similar problems. If you still think you would require a little more assistance to solve them properly, you can take a quick look at our previous exercise Ex 1.6 Class 11 NCERT Solutions online. Doing so, you will not only figure the accurate answer for each question but will also be able to pick up the best techniques of solving them.

Nonetheless, to be able to attempt these questions in the first place, you need to be thorough with the topics covered in previous exercises. A firm understanding of those will pave your way for solving it correctly.

Hence, make it a point to practice the chapter and our study guides like Exercise 1.6 Class 11 Maths Solutions frequently and give your exam preparation the much-required boost.

Miscellaneous Exercise of Sets

Once you have solved all the exercises of this chapter, you can easily move on to the miscellaneous exercises. The thing about this particular exercise is that it is based on all the important concepts of this chapter. It is why you must be thorough with them for successfully solving all the questions of NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.6 correctly.

To get the hang of it, you can go through the solved miscellaneous examples that are provided in the chapter and pick up the necessary pointers from them. Once you have glanced through them, you can move on to solving the chapter-based questions with confidence. 

Regardless, you need to know that the problems mostly require you –

To identify subsets.

To determine the accuracy of the statement and to provide a suitable explanation for the same.

To prove the equivalence between two conditions.

Other than these, you would also be tested on your previous knowledge of solving practical problems based on sets. Additionally, a firm idea of the operation of sets and their properties will help you solve most of the sums with greater ease. 

Once you are done solving the miscellaneous exercise, you can use our updated learning tools like NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.6 to cross-check your answers. It will also serve as a potent tool for your last-minute exam revision and make the learning process smooth. It will further directly help you plan your revision systematically and allow you to obtain higher scores in exams. 

Vedantu – The Best Place to Get Your Doubts Cleared

Vedantu is one of the most popular eLearning platform. Our team of qualified professionals have years of experience in the academic field. It thus enhances the quality of our study materials and helps us create study guides that are not just reliable but also effective for exam preparation.

Students can access our chapter-based study materials like NCERT Solutions for Class 11 Maths Chapter 1 Set Exercise 1.6 for free by simply downloading them. Since all our solutions are updated regularly, they include all the latest shortcut techniques and methods. All of such new inclusions are as per the syllabus and help provide answers that match the quality standard of CBSE Board.

We also extend study solutions for subjects like English, Science, Commerce, Economics, Social Science, etc. for all standards. You can access them at any time to take your exam preparation to the next level. Join us at Vedantu now to get all your doubts cleared instantly!

FAQs on NCERT Solutions for Class 11 Maths Chapter 1: Sets - Exercise 1.6

1. What is NCERT Solutions for class 11 Maths Chapter 1?

NCERT solutions for class 11 Maths Chapter 1 is equivalent to Encyclopedia for you. It is a complete solution of all your worries regarding your studies. Maths is a complicated subject and most of us find it difficult to understand the concepts. But with NCERT Solutions for class 11 Maths Chapter 1, Maths will become a child play. WIth the help of NCERT Solutions, you can become a pro in Maths. Its a complete package of all solutions of chapter 1 Maths class 11 and all the concepts are discussed in detail. 

2. Where can I find Vedantu’s NCERT Solutions for class 11 Maths Chapter 1 Sets Exercise 1.6?

Vedantu’s NCERT Solutions for class 11 Maths Chapter 1 Sets Exercise 1.6 is very easy to find and download. Visit Vedantu’s website and click on “NCERT Solutions” and you will be able to download Vedantu's NCERT Solutions. You can select the class, subject and chapter from the list and download as per your requirement. You can also download from Vedantu’s official app. 

3. What is a Set in Mathematics?

A set in mathematics is a collection of objects that are well defined and distinct. Set theory is founded by Georg Cantor. He defined a set as “ A set is a gathering together into a whole of definite, distinct objects of our perception and of our thought - which are called elements of the set.” 

4. How many Types of Sets are there?

There are many types of sets such as - 

Empty/Null/Void Sets - 

A set is said to be a null set if it has no element. 

Finite Sets - 

A set is called finite when it has a countable number of elements.

Infinite Sets - 

A set is called infinite when it has an uncountable number of elements.

Equal Sets - 

Two sets X and Y are said to be equal if they have equal elements.

Unequal Sets - 

Two sets X and Y are said to be unequal if they have at least one uncommon element.

Equivalent Sets - 

Two sets X and Y are said to be equivalent if they have the same number of elements irrespective of what elements are. 

Singleton Set - 

A set which contains only one element is called a singleton set. 

Universal Set - 

A set that contains all elements and of which all other sets are subsets, is called universal set.

5. Where will I get the NCERT Solutions for Class 11 Maths PDF?

When we talk about board exams, the most vital study material is NCERT textbooks. NCERT Solutions for Class 11 Maths PDF is available on Vedantu. You can visit the site and avail all the solutions online and use them offline as well. The exciting part is that NCERT Solutions for Class 10 Maths PDF can be downloaded for free. Vedantu offers solutions for all the questions in the NCERT Class 11 Maths .

6. How can I make a Study Plan for Class 11?

For the desired result in the board exam, one must read every topic from the NCERT textbooks. Going through the books and making notes will help you in your preparation. You should look at all the topics and focus on the important ones. You can easily solve sample papers after going through these books thoroughly. Use the Vedantu Mobile app to study anytime.

7. What are the main points explained in the solutions of NCERT Class 11 Maths Textbook?

If you look at the Solutions of NCERT Class 11 Maths Textbook on Vedantu, you can find reasons and validations for all the concepts. The solutions for questions from all the chapters in the NCERT Class 11 Maths textbook are provided in the solutions PDF. The solutions are prepared by experts in a very clear and concise manner after substantial research so that you can understand the concepts well.

8. Is 11th standard easier than previous classes?

In Class 11, students will learn more advanced concepts. Hence, it can be challenging for some students. However, by studying properly and referring to the right study materials, students can easily score well in their Class 11 exams. Students must understand and learn all the concepts thoroughly, as that will set their foundation for Class 12. They can find several study materials such as NCERT Solutions, revision notes, formulas, and important questions on Vedantu.

9. How to master Class 11 Maths CBSE?

Practice makes a man perfect. This saying applies to students as well. To clearly understand the topics covered in Class 11 Maths, students should go through all the topics in their NCERT Maths textbook. To do this, they must solve each question from the examples and exercises given in their NCERT Class 11 Maths textbook. They can find the NCERT Solutions for Class 11 Maths for these exercises on Vedantu’s website and on the Vedantu Mobile app as well.

NCERT Solutions for Class 11 Maths Chapter 1 Miscellaneous

Ncert solutions for class 11 maths chapter 1 sets miscellaneous examples.

Free PDF download of NCERT Solutions for Class 11 Maths Chapter 1 miscellaneous prepared by expert Mathematics teacher at Mathongo.com as per CBSE (NCERT) books guidelines. Download our Class 11 Maths Chapter 1 Sets miscellaneous Questions with Solutions to help you to revise complete Syllabus and Score More marks in your exams.

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• Chapter 1: Sets

Sets Class 11 Notes - Chapter 1

Sets are defined as a well-defined collection of objects. A set without any element is termed an empty set. A set comprising of definite elements is termed as a finite set, whereas if the set has an indefinite number of elements, it is termed an infinite set. Two sets, P and Q are equal if they have exactly the same number of elements. A set P is a subset of a set Q if all the elements of P are also an element of Q. A power set [A(P)] of a set P comprising of all subsets of P. The union of sets P and Q is a set comprising of all elements which are either in sets P or Q. The intersection of sets P and Q is a set comprising of all common elements of sets P and Q. Similarly, the difference of sets P and Q in the same order is a set comprising of elements belonging to P but not Q.

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Important Equations

• For any two sets P and Q,
• (P ∪ Q)′ = P′ ∩ Q′
• (P ∩ Q)′ = P′ ∪ Q′
• If P and Q are finite sets such that P ∩ Q = φ, then n (P ∪ Q) = n (P) + n (Q).
• If P ∩ Q ≠ φ, then

n (P ∪ Q) = n (P) + n (Q) – n (P ∩ Q)

• n (P ∪ Q ∪ R) = n(P) + n(Q) + n(R) – n(P ∩ Q) – n(P ∩ Q) – n(P ∩ Q ) + n(P ∩ Q ∩ R)
• If P is a subset of set U (Universal Set), then its complement (P′) is also a subset of Universal Set (U).

Also Read :  NCERT Solutions for Class 11 Maths Chapter 1

Some Properties of Operation of Intersection

• P ∩ Q = Q ∩ P (Commutative law).
• (P ∩ Q) ∩ R = P ∩ (Q ∩ R) (Associative law).
• φ ∩ P = φ, U ∩ P = P.
• P ∩ P = P (Idempotent law).
• P ∩ (Q ∪ R) = (P ∩ Q) ∪ (P ∩ Q) (Distributive law).

Also Read:  Set Theory

Some Properties of the Operation of Union

• P ∪ Q = Q ∪ P (Commutative law).
• (P ∪ Q) ∪ R = P ∪ ( Q ∪ R) (Associative law).
• P ∪ φ = P (Law of the identity element).
• U ∪ P = U (Law of U).

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Sets Class 11 Practice Questions

• For any set P and Q, Show that P = (P ∩ Q) ∪ (P – Q) and P ∪ (Q – P) = (P ∪ Q)
• Using the properties of sets, Prove
• P ∪ ( P ∩ Q) = P
• P ∩ (P ∪ Q) = P
• Prove that P ∩ Q = P ∩ R need not imply Q = R.
• If P and Q are two sets and P ∩ Z = Q ∩ Z = φ and P ∪ Z = Q ∪ Z for some set Z, Prove that P = Q.
• Find sets M, N and O such that M ∩ N, N ∩ O, and M ∩ O are non-empty sets and M ∩ N ∩ O = φ.
• Let M, N, and O be three sets such that M ∪ N = M ∪ O and M ∩ N = M ∩ O. Prove that N = O.
• If P ⊂ Q, then prove that R – Q ⊂ Q – P.
• If A(n) = A(m), then prove that m = n.

Also refer:    NCERT Exemplar for Class 11 Maths Chapter 1

Related Links:

• Types of Sets
• Sets For Class 11
• Component of a Set
• Subset and Superset

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Frequently Asked Questions on CBSE Class 11 Maths Notes Chapter 1 Sets

What is a powerset.

In set theory, the power set (or power set) of a Set A is defined as the set of all subsets of the Set A, including the Set itself and the null or empty set.

What is a Subset?

A set A is said to be a subset of another set B if all elements of the set A are elements of the set B.

What is a Singleton set?

A singleton set is a set containing only one element.

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