## NCERT Solutions for Class 12 Maths Chapter 1 â€“ Free PDF Download

**NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions** provides solutions for all the questions enlisted under the chapter which is included in term â€“ I of CBSE syllabus 2021-22. All exercise questions are solved using step by step approach. Solving the questions from the Class 12 Maths NCERT textbook helps in grasping the concepts correctly. Students can download and go through theseÂ NCERT Solutions for Class 12 MathsÂ to sharpen their Maths skills.

Students should understand not only the basics of this chapter but also the advanced portions to create a command over the chapter Relations and Functions. Practising these **NCERT Solutions for Class 12 Maths**Â will help the students in their first exam preparation in such a way that they would find even the difficult questions from this chapter to be extremely easy. Download the NCERT Solutions PDF of this chapter from the link provided below.

## Download PDF of NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions

### Access Answers of Class 12 NCERT Maths Chapter 1 Relations and Functions

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### NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions

In NCERT Class 12 Maths Chapter 1, students study different types of relations and equivalence relation, composition of functions, invertible functions and binary operations. Students can utilise the **NCERT Solutions for Class 12 Maths Chapter 1** for any quick reference to comprehend complex topics.

**The main features of this chapter are as follows:**

- Empty relation
- Universal relation
- Reflexive relation
- Symmetric relation
- Transitive relation
- Equivalence relation
- A function f : X â†’ Y is one-one (or injective) if f (x
_{1}) = f(x_{2}) â‡’ x_{1}= x_{2}âˆ€ x_{1}, x_{2}âˆˆ X. - A function f : X â†’ Y is onto (or surjective) if given any y âˆˆ Y, âˆƒ x âˆˆ X such that f(x) = y.
- A function f : X â†’ Y is one-one and onto (or bijective), if f is both one-one and onto.
- A function f : X â†’ Y is invertible if and only if f is one-one and onto.

**NCERT Solutions For Class 12 Maths Chapter 1 Exercises:**

Get detailed solutions for all the questions listed under the below exercises:

Exercise 1.1 Solutions : 16 Questions (14 Short Answers, 2 MCQ)

Exercise 1.2 Solutions : 12 Questions (10 Short Answers, 2 MCQ)

Exercise 1.3 Solutions : 14 Questions (12 Short Answers, 2 MCQ)

Exercise 1.4 Solutions : 13 Questions (12 Short Answers, 1 MCQ)

**The main topics covered in this chapter include:**

Exercise |
Topic |

1.1 | Introduction |

1.2 | Types of Relations |

1.3 | Types of Functions |

1.4 | Composition of Functions and Invertible Function |

1.5 | Binary Operations |

Others | Miscellaneous Q&A |

### Key Features of NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions

- These NCERT exercises are meticulously solved by subject experts.
- Simple and easy language used.
- All questions are solved with the best possible explanations given.
- These NCERT Solutions are a valuable help to students in their assignments and competitive exams.

Students can also access the NCERT Solutions for Class 12 of any subject while preparing for the first and second term examinations apart from Mathematics. All the solutions are in accordance with the latest term-wise CBSE Syllabus and guidelines.