**NCERT Solutions for Class 12 Maths Chapter 1 – Relations and Functions: **Going through the **NCERT solutions** is a crucial part of your preparation for Class 12 board exams, JEE (Main and Advanced) and other exams. This will clear your doubts related to any question and improve your application skills. In this article, we will provide you with **NCERT Solutions for Class 12 Maths** – Chapter 1 – Relations and Functions. Read on to find out Relation and Function Class 12 solutions PDF.

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**CBSE NCERT Solutions For Class 12 Maths Chapter 1 PDF Download**

Candidates can download the NCERT Solutions for Class 12 Maths Chapter 1 PDF from this page for free to study in offline mode. Each and every question comes with a detailed, step-by-step solution that is solved by top academic experts of Embibe based on the CBSE Guidelines.

NCERT Solutions for Class 12 Maths Chapter 1 – Relations and Functions are available in the below section for free download. Before you download the Class 12 Maths Solution PDF, let’s have an overview:

Class | CBSE Class 12 |

Book Name | NCERT Class 12 Maths |

Solutions | Class 12 Maths Solutions Chapter 1 |

Available on | Embibe |

Price | Free |

**Download Relations and Functions NCERT Solutions PDF**

### NCERT Solutions For Class 12 Maths Relations & Functions: Important Questions

Some of the important questions from this chapter are as under:

Important 4 Mark Questions of Relations and Functions: Functions f ,g :R →R are defined, respectively, by f(x) = xQuestion 1 ^{2} + 3x +1, g(x) = 2x − 3, find(i) fog(ii) gof(iii) fof(iv) gog Question 2: Let * be the binary operation defined on Q. Find which of the following binary operations are commutative. Question 3: Let R be relation defined on the set of natural number N. Find the domain and range of the relation. Also verify whether R is reflexive, symmetric and transitive.Question 4: Given, A= {2,3,4} ; B= {2,5,6,7} . Construct an example of each of the following:(i) an injective mapping from a to B.(ii) a mapping from a to b which is not injective.(iii) a mapping from b to A. Question 5: Let a ={1, 2, 3, …,9} and R be the relation in A× a defined by (a , b) R (c , d) if a + d = b + c for (a , b), (c , d) in a × a Prove that R is an equivalence relation and also obtain the equivalent class [(2, 5)]. Question 6: Let A = [-1,1] , then, discuss whether the following functions defined on A are one-one onto or bijective.(i) f(x) = x/2(ii) g(x) = |x|(iii) h(x) = x |x|(iv) k(x) = x^{2} |

### NCERT Solutions For Class 12 Maths Chapter 1

NCERT Solutions for Class 12 Maths Chapter 1 – Relations and Functions as provided by India’s best teachers will give detailed and step-wise solutions to all the questions at the end of the chapter from the NCERT Maths book. The sections included in the Relations and Functions chapter are tabulated below:

Exercise 1.1 | Introduction |

Exercise 1.2 | Types of Relations |

Exercise 1.3 | Types of Functions |

Exercise 1.4 | Composition of Functions and Invertible Function |

Exercise 1.5 | Binary Operations |

** NCERT Solutions For Class 12 Maths Chapter 1: Relations And Functions Chapter Description**

The concept of the term ‘**relation**’ in Mathematics has been drawn from the meaning of ‘relation’ in the English language, according to which two objects or quantities are related (in a relation) if there is a recognizable connection or link between the two objects or quantities. Let **A** be the set of students of Class XII of a school and** B** be the set of students of Class XI of the same school. Then some of the examples of relations from **A to B** are

- {(a, b) ∈ A × B: a is brother of b},
- {(a, b) ∈ A × B: a is sister of b},
- {(a, b) ∈ A × B: age of a is greater than age of b},
- {(a, b) ∈ A × B: total marks obtained by a in the final examination is less than the total marks obtained by b in the final examination},
- {(a, b) ∈ A × B: a lives in the same locality as b}.

Abstracting from this, we define mathematically a relation R from A to B as an arbitrary subset of A × B. If (a, b) ∈ R, we say that a is related to b under the relation R and we write as **a** R **b**. In Class 11, you learned that the functions are special kind of relations whereas, in this Class 12 Chapter 1, you will learn about different types of relations and functions, the composition of functions, invertible functions, and binary operations.

## FAQs Related To Class 12 Maths Solutions Chapter 1

Some of the FAQs related to Ch 1 Maths Class 12 NCERT solutions/Class 12 Relations and Functions solutions and their answers are as under:

*Q: From where can I download Class 12 Maths Solutions for Chapter 1? *** A:** You can download the detailed NCERT Solutions for Class 12 Maths Chapter 1 from Embibe for free. All the exercise questions are solved by our expert academic teachers.

*Q: Are Class 12 Maths Solutions free to download? *** A:** On Embibe, we have provided correct and detailed solutions for all chapters of CBSE Class 12 Maths for absolutely free.

*Q: How to get 12th Grade Maths Solutions PDF? *** A:** You can download NCERT Class 12 Maths Solutions PDF in one-click from Embibe for free.

*Q: How many exercises are there in NCERT Class 12 Maths Chapter 1? *** A:** There are a total of 4 exercises in Class 12 Maths Chapter 1. Apart from that, there are some miscellaneous exercises at the end of the chapter. Embibe has provided comprehensive solutions for all exercises.

*Q: What are the concepts discussed in NCERT Solutions for Class 12 Maths Chapter 1?*** A:** The concepts covered in the NCERT Solutions for Class 12 Maths Relations and Functions are types of relations, types of functions, the composition of functions and invertible functions, and binary operations.

Download NCERT Solutions for Class 12 Maths for other chapters from the table below:

Class 12 Maths Chapter 2 Solutions | Class 12 Maths Chapter 3 Solutions | Class 12 Maths All Chapters Solutions |

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So, now you have all the Math 12 Class Chapter 1 solutions.

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