NCERT Solutions for Class 12 Maths Chapter 1 Miscellaneous Exercise Relations and Functions

Class 12 Maths Chapter 1 Miscellaneous Exercise Solutions: Class 12 Maths Chapter 1 Solutions contains information regarding the concept of Relations and Functions. There are solutions provided in this article that cover the essential concepts of Maths Class 12 Chapter 1. Embibe’s subject expert faculty created Class 12 Maths solutions to assist students with their exam preparations.

Latest Update and NCERT 12 Maths Solutions for

• CBSE Class 12 Maths Exam Date
• CBSE Class 12 Maths Exam Notes
• CBSE Class 12 Maths Sample Papers
• CBSE Class 12 Maths Mock Test Series
• List of Best Books for Maths CBSE Class 12

Students can also refer to the solutions for the competitive exams such as JEE Main, JEE Advanced, BITSAT etc. Practicing the Class 12 Maths Chapter 1 Miscellaneous Exercise Solutions will help the candidates prepare for the Term I and Term II exams. Read this article to learn more. Continue reading this article to know more.

Class 12 Maths Chapter 1 Miscellaneous Exercise Solutions: Important Topics

Students taking the board examinations must ensure they adequately prepare for the exams. Therefore they must practise the questions found on the Embibe platform in order to achieve better exam results. The fundamental ideas of Relations and Functions are already known to the students from earlier classes. Simply said, this chapter offers in-depth knowledge that can be useful both before and after competitive exams.

For exam preparation, students can benefit from practising the Relations and Function questions from Embibe. Since this is the first chapter, students should consult all related Embibe materials, including the explainer and 3D videos. These resources not only make learning simple but enjoyable as well.

NCERT Solutions for Class 12 Maths Chapter 1 Miscellaneous Exercise: Important Points to Remember

Students can go through some of the important points of Class 12 Maths Chapter 1 to learn more about the topics:

• A binary operation ** on a set SS associates any two elements a,b∈Sa,b∈S to a unique element a*b∈Sa*b∈S.
• Distributive over a binary operation∘∘on SS, if a*(b∘c)=(a*b)∘(a*c)a*(b∘c)=(a*b)∘(a*c) and (b∘c)*a=(b*a)∘(c*a)(b∘c)*a=(b*a)∘(c*a) for all a,b∈S
• Commutative, ifa*b=b*aa*b=b*a for all a,b∈S
• Types of relations
  • (i) The identity relation, if every element of AA is related to itself only.
  • (ii) Reflexive, if (a,a)∈R(a,a)∈R for all a∈Aa∈A
  • (iii) Symmetric, if (a,b)∈R⇒(b, a)∈R(a,b)∈R⇒(b, a)∈R for all a,b∈Aa,b∈A
  • (iv) Transitive, if (a,b)∈R(a,b)∈R and (b, c)∈R⇒(a,c)∈R(b, c)∈R⇒(a,c)∈R for all a,b,c∈A
• Composition of functions and Invertible functions
  • (i) If f:A→Bf:A→B is a bijection, then g:B→Ag:B→A is inverse of ff if f(x)=y⇒g(y)=xf(x)=y⇒g(y)=x or gof=IAgof=IA and fog=IBfog=IB
  • (ii) Let f:A→Bf:A→B and g:B→Ag:B→A be two functions, If gof=IAgof=IA and ff is an injection, then gg is a surjection. And  if fog=IBfog=IB and ff is a surjection, then gg is an injection.
  • (iii) Let f:A→Bf:A→B and g:B→Cg:B→C be two functions, If gof: A→Cgof: A→C is onto, then g:B→Cg:B→C is onto And if gof:A→Cgof:A→C is one-one, then f: A→Bf: A→B is one-one.

FAQs on NCERT Solutions Maths Chapter 1

Q.1: From where can I download Class 12 Maths Solutions for Chapter 1 in PDF structure?
Ans: You can download the complete NCERT Solutions for Class 12 Maths Chapter 1 from Embibe for nothing. Our master scholarly educators settle all the activity questions.

Q.2. Do NCERT questions come in the board exams?
Ans: If your board follows the NCERT schedule, then there’s a more substantial likelihood that most of the questions will be from NCERT course books. Ensure you cover every one of the sections thoroughly.

Q.3. How many activities are there in NCERT Class 12 Maths Chapter 1?
Ans: There are 4 practices in Class 12 Maths Chapter 1. Aside from that, there are a few various activities toward the finish of the section. Embibe has given extensive answers for all activities.

Q.4. What is the use of the NCERT models?
Ans: The NCERT books and arrangements are extra course materials for grades 6-12. They are centred around Maths and Science subjects and belong to a more difficult level.

Q.5. How to get the twelfth Grade Maths Solutions PDF?
Ans: You can download NCERT Class 12 Maths Solutions PDF with a single click from Embibe.