NCERT Solutions for Class 12 Maths Chapter 1 – 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 the CBSE syllabus 2023-24. All exercise questions are solved using a step-by-step approach. Solving the questions from the Class 12 Maths NCERT textbook helps grasp the concepts correctly. Students can download and go through these NCERT Solutions for Class 12 Maths to sharpen their Maths skills.
Students should understand not only the basics of this chapter but also the advanced portions to get a command over the chapter Relations and Functions. Practising these NCERT Solutions for Class 12 Maths will help the students in their exam preparation in such a way that they will 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
| Also Access |
| NCERT Exemplar for Class 12 Maths Chapter 1 |
| CBSE Notes for Class 12 Maths Chapter 1 |
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 relations, 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 → Y is one-one (or injective) if f (x1) = f(x2) ⇒ x1 = x2 ∀ x1, x2 ∈ X.
- A function f: X → Y is onto (or surjective) if given any y ∈ Y, ∃ x ∈ X such that f(x) = y.
- A function f: X → Y is one-one and onto (or bijective), if f is both one-one and onto.
- A function f: X → 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)
Miscellaneous Exercise Solutions: 19 Questions (7 Long answers, 9 Short Answer Type, 3 MCQs)
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 is 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 board examinations apart from Mathematics. All the solutions are in accordance with the latest CBSE Syllabus and guidelines.
Disclaimer –
Dropped Topics – 1.4 Composition of Functions and Invertible Function (upto ‘This leads to the following definition’), Page 13-14 Full Pages, Page 15 Examples 24 and 25, Page 16-25 Full Pages, Page 26 Question 12 and 13, Page 27-28 Examples 45 and 49, Page 29-31 Ques. 1–3, 6–7, 9, 11–14, 18–19, Page 31-32 Summary points 11-13 and 15-19.
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