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NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions

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NCERT Solutions for Maths Chapter 1 Relations and Functions Class 12 - Free PDF Download

NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions contains answers to all the questions in the CBSE syllabus 2024-25. All exercise questions are solved in a step-by-step manner. Solving the questions in the Class 12 Maths NCERT textbook helps students understand the concept clearly. Students can download and study these NCERT Solutions for Class 12 Maths to improve their math skills.

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To master the chapter Relations and Functions, students must learn both the fundamentals and the advanced sections. Practicing these NCERT Solutions for Class 12 Maths will assist students in their test preparation in such a way that they will find even the toughest questions from this chapter extremely simple. Download the NCERT Solutions PDF for this chapter using the link provided below.


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NCERT Solutions for Maths Chapter 1 Relations and Functions Class 12

Chapter 1 of NCERT Class 12 Maths covers many forms of relations including equivalence relations, as well as function composition, invertible functions, and binary operations. Students can use relation and function class 12 NCERT Solutions as a quick reference to better understand complex topics.


This primary features of Chapter 1 include the following:


  • Empty relation

  • Universal relation

  • Reflexive relation

  • Symmetric relation

  • Transitive relation

  • Equivalence relation

  • A function $f: X \to Y$ is one-one (or injective) if $f(x_1) = f(x_2) \Rightarrow x_1 = x_2 \forall x_1, x_2 \in X$.

  • A function $f: X \to Y$ is onto (or surjective) if given any $y \in Y, \exists x \in X$ such that $f(x) = y$.

  • A function $f: X \to Y$ is one-one and onto (or bijective), if f is both one-one and onto.

  • A function $f: X \to Y$ is invertible if and only if f is one-one and onto.


Class 12 Maths Chapter 1: Exercise Breakdown

Exercise

Number of Questions

Exercise 1.1 Solutions

16 Questions (14 Short Answers, 2 MCQ)

Exercise 1.2 Solutions

12 Questions (10 Short Answers, 2 MCQ)

Miscellaneous Exercise Solutions

19 Questions (7 Long answers, 9 Short Answer Type, 3 MCQs)



Conclusion

NCERT Solutions for Class 12 Maths Chapter 1 - Relations and Functions are crucial for building a strong foundation in mathematics. It's important to focus on understanding the concepts of relations and functions thoroughly. Pay attention to the types of relations and functions, their properties, and how they are represented graphically. Practice solving various types of problems to grasp the application of these concepts effectively. In the previous year's question paper, typically 4-5 questions were asked from this chapter. Additionally, mastering this chapter will lay a solid groundwork for more advanced mathematical topics in higher classes. So, devote ample time and effort to ensure a clear understanding of relations and functions.




NCERT Solutions for Class 12 Maths | Chapter-wise List

Given below are the chapter-wise NCERT 12 Maths solutions PDF. Using these chapter-wise class 12th maths ncert solutions, you can get clear understanding of the concepts from all chapters.




Related Links for NCERT Class 12 Maths in Hindi

Explore these essential links for NCERT Class 12 Maths in Hindi, providing detailed solutions, explanations, and study resources to help students excel in their mathematics exams.




Important Related Links for NCERT Class 12 Maths

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FAQs on NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions

1. Where can I find the NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions in PDF format?

You can access stepwise NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions in PDF format from Vedantu, which provides CBSE 2025–26 approved solutions for all exercises including Exercise 1.1, Exercise 1.2, and Miscellaneous. The solutions follow the official NCERT textbook answer pattern, making them ideal for exam preparation.

2. How do I solve Exercise 1.1 of Class 12 Maths Chapter 1 as per NCERT guidelines?

To solve Exercise 1.1 of Class 12 Maths Chapter 1, follow the stepwise method as demonstrated in official NCERT Solutions: carefully read each question, identify the properties of relations, and answer using the correct CBSE format. Show every calculation and reasoning as per the updated 2025–26 NCERT textbook solutions for full marks.

3. Is it necessary to write stepwise answers in CBSE exams for Relations and Functions chapter?

Yes, it is essential to present your answers in a stepwise manner for chapters like Relations and Functions. The CBSE board values clarity and adherence to the NCERT answer format, which includes proper justification for each step, so you must show every stage of your calculation or reasoning as per the textbook.

4. Are these NCERT Solutions for Class 12 Maths Chapter 1 based on the latest CBSE 2025–26 syllabus?

All NCERT Solutions for Class 12 Maths Chapter 1 provided here strictly follow the latest CBSE 2025–26 syllabus and are aligned with the official NCERT textbooks. The solutions incorporate the most recent updates and are regularly reviewed to ensure accuracy as per current academic standards.

5. Can I download the NCERT Solutions for Class 12 Maths Chapter 1 in Hindi PDF?

Yes, the stepwise NCERT Solutions for Class 12 Maths Chapter 1 are also available in Hindi PDF on Vedantu, ensuring all students can study in their preferred language while maintaining full alignment with the CBSE 2025–26 NCERT answer key format.

6. What is the official method to solve Exercise 1.2 of Class 12 Maths Chapter 1 using NCERT solutions?

The official NCERT method for solving Exercise 1.2 involves analyzing each problem using set theory, mapping, and functions concepts in the sequence presented in the textbook. Stepwise justification, CBSE-approved terminologies, and structured reasoning as shown in the NCERT Solutions are important for securing complete marks in board exams.

7. How do stepwise NCERT Solutions help in solving intext and miscellaneous questions for Relations and Functions?

Stepwise NCERT Solutions break down each question into clear, logical steps, which helps you understand the process thoroughly—especially for Miscellaneous and intext questions. This approach, following the official NCERT answer format, also ensures that your solutions fulfill CBSE marking criteria and improve conceptual clarity.

8. Where can I get the CBSE-approved answer key for Class 12 Maths Chapter 1 all exercises?

The CBSE-approved answer key for Class 12 Maths Chapter 1 (Relations and Functions)—including Exercises 1.1, 1.2, and Miscellaneous—is available in the NCERT Solutions PDFs provided on Vedantu. These are structured exactly as per current NCERT and CBSE 2025–26 requirements for textbook-based answering.

9. Are the solutions for Class 12 Maths Chapter 1 Exercises 1.1 and 1.2 suitable for direct use in CBSE board exams?

Yes, the stepwise NCERT Solutions for Exercises 1.1 and 1.2 of Class 12 Maths Chapter 1 are suitable for direct use in CBSE board exams, as they strictly follow the official CBSE and NCERT answer structure and provide the correct answers accepted in 2025–26 assessments.

10. What common mistakes should students avoid while writing answers for Relations and Functions in Class 12 board exams?

Students should avoid skipping calculation steps, writing informal proofs, or using definitions outside the NCERT pattern. Always use stepwise reasoning as per the NCERT Solutions, clearly indicate domain, codomain, and range where asked, and format the answers as recommended in the CBSE 2025–26 guidelines for full marks.

11. How can I verify if my handwritten solution matches the NCERT answer key for Chapter 1?

After solving the exercise, cross-check your response with the stepwise explanations and official NCERT answer format provided in the CBSE-approved solutions. Ensure each step and justification matches the textbook logic to confirm accuracy as per current board requirements.

12. Why is following the NCERT answer format crucial for scoring in Class 12 Maths Chapter 1?

Following the NCERT answer format is crucial since CBSE examiners mark each step that adheres to official NCERT guidelines. This ensures clarity, avoids missing marks due to skipped steps, and aligns your answer with what is expected in the 2025–26 examinations for Relations and Functions.

13. Can stepwise solutions help in understanding the concept of functions versus relations in Chapter 1?

Yes, stepwise solutions in the NCERT answer key specifically break down problems involving functions and relations, making it easier to distinguish between the two, and mastering their properties as per the rigorous CBSE pattern.

14. Is there any difference between NCERT Solutions PDF and the answers written in the NCERT Maths textbook?

NCERT Solutions PDFs provide detailed, stepwise answers for every textbook question according to CBSE-approved format, which may include more expanded reasoning, structured steps, and explanations than the brief answers in the textbook's end or margin hints.