NCERT Solutions for Class 11 Maths Chapter 1 Miscellaneous Exercise

NCERT Solutions for Miscellaneous Exercise Chapter 1 Class 11 deals with various aspects of a Set and its detailed description under multiple cases. In miscellaneous exercise Class 11 chapter 1, students will learn about types of sets, explanations about subsets and their concepts, Venn Diagrams, etc. Class 11 Maths Chapter 1 miscellaneous solutions are essential, and students must be thorough with all the concepts to score well.

The NCERT Miscellaneous Exercise Chapter 1 Class 11 covers the important topics explained in the chapter to help students during the board exams. Class 11 students must keep practising the in-text questions and find areas where they need to improve for their betterment. Here at Embibe, everything is just a click away, so scroll down to download the solutions for miscellaneous exercises Chapter 1 Class 11.

NCERT Solutions for Miscellaneous Exercise Chapter 1 Class 11: Overview

CBSE NCERT Solutions for Miscellaneous Exercise Chapter 1 Class 11 acts as the best study material for students as it helps them in their board exam preparations. Moreover, the solutions for Class 11 Chapter 1 are presented step-by-step and detailedly, which allows students to gain a basic understanding of the chapter. They also learn the correct method to solve a problem in a time-bound manner. The Class 11 Maths Chapter 1 miscellaneous solutions are based on the concepts of sets and their representations, the intersection of sets, and practical problems on the union.

At Embibe, students can find the NCERT solutions for Miscellaneous Exercise Chapter 1 Class 11 for. The academic experts have solved all the Class 11 Maths Chapter 1 Miscellaneous Solutions to help students with their studies. The solutions have been explained in simple words that any student from Class 11 can easily understand. The subject experts have also provided in-depth solutions for students to understand the complex concepts.

NCERT Solutions for Miscellaneous Exercise Chapter 1 Class 11: PDF

A well-defined collection of objects is a set in NCERT Solutions for Class 11. A set is defined by an existing rule that can be used to determine whether an object is a part of a set and whether a collection is a set. This set’s problems and solutions teach us to determine whether a collection is set, different types of sets, algebra of sets, and power sets. This chapter will assist students in developing a solid foundation in Mathematics. It will assist students in understanding how sets are represented using symbols and Venn diagrams.

Students can check the solved exercises for Miscellaneous Exercise Chapter 1 Class 11 in the PDF below to better understand the level of questions asked during the exam. They can also download NCERT Solutions for Class 11 Chapter 1 Sets in PDF format to practice it offline:

Q.1. Decide, among the following sets, which sets are subsets of one and another:
A=x:x∈R and x satisfy x2-8x+12=0, B=2, 4, 6, C=2, 4, 6, 8…, D=6.

Solution: According to the question we have, A=x:x∈R and x satisfy x2-8x+12=0

Let us write set A in roster form,
x2-8x+12=0x2-6x-2x+12=0xx-6-2x-6=0x-6x-2=0x=2, x=6
∴A=2, 6
We are given, B=2, 4, 6, C=2, 4, 6, 8,…, D=6
If the elements of set A are present in the setB, then A⊂B else it will be A⊄B.
Therefore, we can write it as
D⊂A⊂B⊂C
Thus,
A⊂B, A⊂C, B⊂C, D⊂A, D⊂B and D⊂C.

Q.2. Show that A∩B=A∩C need not imply B=C.

Solution: 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 represent intersection.
Let A=0,1, B=0, 2, 3, and C=0, 4, 5
We can see that A∩B=0 and A∩C=0
Therefore, A∩B=A∩C
But, B≠C as 2∈B and 2∉C
Hence, proved

Q.3. Let A and B be sets. If A∩X=B∩X=φ and A∪X=B∪X for some set X, show that A=B.

Solution: Let A and B be two sets such that A∩X=B∩X=φ and A∪X=B∪X for some set X. We can see that A=A∩A∪X=A∩B∪X

=A∩B∪A∩X [Distributive Law]
=A∩B∪φ A∩X=φ
=A∩B
Thus, A=A∩B ……..1
Now, B=B∩B∪X
=B∩A∪X A∪X=B∪X
=B∩A∪B∩X [Distributive Law]
=B∩A∪φ B∩X=φ
=A∩B
Thus, B=A∩B ……….2
Therefore, from 1 and 2, we obtain A=B.

DOWNLOAD NCERT MISCELLANEOUS EXERCISE CHAPTER 1 CLASS 11 SOLUTIONS

NCERT Solutions for Miscellaneous Exercise Chapter 1 Class 11: Summary

The question from this exercise may seem a bit complicated at first, but with Embibe, you will learn more about this chapter and improve your problem-solving skills. Subject experts curate these NCERT Solutions as per the CBSE guidelines to provide a stress-environment to students during the board exams. Moreover, the NCERT Solutions for Miscellaneous Exercise Chapter 1 Class 11 contains 16 questions to improve students’ knowledge. The most important topics covered in this chapter are:

• Sets and their Representations
• The Empty Set, Finite and Infinite Sets, Equal Sets
• Subsets, Power Set, Universal Set
• Venn Diagrams
• Operations on Sets
• The complement of a Set
• Practical Problems on Union and Intersection of Two Sets

Below we have provided students with the number of questions present in each of the exercises of Chapter 1 to help them gain clarity over the topic:

Exercise 1.1 Solutions- 6 Questions

Exercise 1.2 Solutions- 6 Questions

Exercise 1.3 Solutions- 9 Questions

Exercise 1.4 Solutions- 12 Questions

Exercise 1.5 Solutions- 7 Questions

Exercise 1.6 Solutions- 8 Questions

Miscellaneous Exercise Solutions- 16 Questions

The topics and sub-topics included in this chapter are mentioned below:

Practice 11th CBSE Exam Questions

Benefits of NCERT Solutions for Miscellaneous Exercise Chapter 1 Class 11

The NCERT Textbook includes in-text and exercise questions for each chapter. Many students tend to dismiss these questions and focus on other components of the chapter. NCERT questions are significant not just for board exams but also for competitive tests. So, we provide you with some benefits of solving NCERT Solutions for Miscellaneous Exercise Chapter 1 Class 11 to help students understand the importance of the NCERT solutions:

1. The NCERT Solutions for Miscellaneous Exercise Chapter 1 Class 11 offers knowledge in simple language. After thorough research, experts prepare and design the NCERT books to help students understand the topic. The descriptions are exact and easy to understand.
2. NCERT solutions focus on offering in-depth knowledge about the topic. It helps students grasp the knowledge they require to help them in the future and the board exams.
3. The Class 11 Chapter 1 miscellaneous exercise has 16 questions which help students during practise. Students can quickly put their knowledge to the test by solving these questions to achieve higher grades. In this way, students can answer any tricky question like a pro.
4. The NCERT textbooks form the basis of examination. So, students must carefully go through them to score well in the board exams.
5. By practising the Class 11 Maths Chapter 1 miscellaneous solutions, students can analyse their mistakes and work on them to progress further. They can quickly rectify their mistakes on time through self-evaluation.
6. The NCERT books are the best for CBSE board exams, and they are formulated as per the CBSE guidelines. It will also help students develop a strong foundation in the chapter Sets.

FAQs on NCERT Solutions for Miscellaneous Exercise Chapter 1 Class 11

Some of the frequently asked questions on NCERT Solutions for Miscellaneous Exercise Chapter 1 Class 11 are mentioned below:

Q.1. Where can I find the NCERT Solutions for Class 11 Sets for? 
Ans. CBSE Class 11 can find the NCERT Solutions for Sets for on Embibe and start solving them.

Q.2. Are NCERT Solutions for Miscellaneous Exercise Chapter 1 Class 11 difficult to solve? 
Ans. No questions are difficult to solve if you have the basic knowledge of the topic and practise well. If you are practising the sums on a regular basis, then it may not seem difficult to understand or solve.

Q.3. Is Class 11 Maths Chapter 1 Miscellaneous Solutions good enough to score well in the exams? 
Ans. If a student practises the Class 11 Maths Chapter 1 miscellaneous solutions and is thorough with the chapter, they can easily score good marks during the exam.

Q.4. Can I download the NCERT Solutions for Miscellaneous Exercise Chapter 1 Class 11 for? 
Ans. Students can easily access the PDFs on Embibe and download them to keep practising them offline to score well in the board exams.

Q.5. How can I solve the Miscellaneous Exercise Chapter 1 Class 11 questions? 
Ans. Students must be clear with the chapter’s concepts before beginning to solve the in-text questions present in the exercise. This will help them in enhancing their problem-solving skills and achieve higher grades.

Attempt 11th CBSE Exam Mock Tests

You now have access to all of the information you require about the the Miscellaneous Exercise in Class 11 Maths Chapter 1. To reap the rewards, attempt to answer the questions on your own first. Only use the NCERT Solutions if you are unable to solve. Understand how the professionals arrived at the solution and then try again. On Embibe, students in Class 11 can take Class 11 Sets Mock Tests. The practise questions will undoubtedly aid students in their exam preparation.

We hope this detailed article on NCERT Solutions for Class 11 Maths Chapter 1 Miscellaneous Exercise helps you. Refer to the solutions that we have provided in this article. If you have any queries, feel to ask in the comment section below and we will get back to you at the earliest.