NCERT Solutions for Class 12 Maths Chapter 1 – Relations and Functions
Welcome to Myclass24's NCERT Solutions for Class 12 Maths Chapter 1 – Relations and Functions. These solutions are prepared to help Class 12 students understand each problem clearly and build the confidence needed for CBSE board examinations. Whether you're revising at the last minute or studying systematically, you'll find these solutions accurate, easy to follow, and aligned with the NCERT textbook.
Summary of Chapter 1 Relations and Functions
Relations and Functions-Relation: Definition, Domain, Range, Total number of relations, Composition & the inverse of relations, Types of relation, Reflexive, Symmetric, Transitive, Equivalence. Function: Domain, Range. Types of Functions: One-one, Many One, Onto, Into. Composite Function, Inverse of a Function. Even/odd Functions, Periodic function. Binary Operation and its Types.
Find the PDF of NCERT Solutions for Class 12 Maths Chapter 1 – Relations and Functions
The PDF of NCERT Solutions for Class 12 Maths Chapter 1 – Relations and Functions is available on Myclass24. Students can refer to it chapter-wise for quick revision or download it for offline use. The solutions in the PDF are written in a clear format that makes it easy to revise during exam preparation.
Chapter 1 – Relations and Functions: Quick Overview
| Detail | Information |
| Chapter Number | Chapter 1 |
| Chapter Name | Relations and Functions |
| Subject | Mathematics |
| Class | Class 12 |
| Board | CBSE (NCERT) |
| Total Exercises | 4 Exercises + Miscellaneous |
| Key Topics | Types of Relations, Types of Functions, Composition, Invertible Functions, Binary Operations |
| Difficulty Level | Moderate to High |
| Marks Weightage | Approx. 8-10 marks in board exams |
About NCERT Solutions for Class 12 Maths Chapter 1 – Relations and Functions
Chapter 1 of Class 12 Maths builds on what students studied in Class 11 and takes the concepts of relations and functions to a much deeper level. This chapter is foundational for many advanced topics in mathematics, and understanding it well makes the rest of the year significantly easier.
The chapter begins with a detailed look at types of relations. Students learn to distinguish between reflexive, symmetric, transitive, and equivalence relations. These distinctions might seem theoretical at first, but the exercises in this chapter make the ideas click through well-chosen examples and problems.
Key Concepts in Chapter 1
One of the most important topics here is the classification of functions. Students study one-one (injective) and onto (surjective) functions in this chapter, along with bijective functions. Understanding which function types are invertible is crucial, and Myclass24 solutions explain this with clear step-by-step reasoning so students don't just memorise but actually understand the logic.
Composition of functions is another area covered in depth. The chapter shows how two functions can be combined to form a new function, and the exercises test students on properties of this composition, such as whether it's commutative or associative. These are not always intuitive, and this is where good NCERT solutions make a real difference.
Binary operations are introduced toward the end of the chapter. Topics like commutativity, associativity, identity elements, and inverses of elements in binary operations are covered. The miscellaneous exercise at the end is particularly rich and challenges students with problems that require combining multiple concepts.
Exercise-wise Overview
Exercise 1.1 focuses on types of relations with 16 questions.
Exercise 1.2 deals with types of functions with 12 questions.
Exercise 1.3 covers composition of functions and invertible functions with 14 questions.
Exercise 1.4 is on binary operations with 13 questions. The Miscellaneous Exercise has 19 challenging problems that tie everything together.
Myclass24 provides solutions that walk through each problem clearly, showing the exact reasoning expected in board examinations. Students preparing for CBSE boards will find these solutions particularly useful since they match the expected answer format.
NCERT Solutions for Class 12 Maths Chapter 1 – Relations and Functions FAQs
One of the most common questions in this chapter is determining whether a given relation qualifies as a function. A relation becomes a function when every element of the domain is associated with exactly one element of the codomain. While solving questions, students should carefully check if any input value is connected to more than one output value. If even one element of the domain has multiple images, the relation is not a function. NCERT problems often present relations in set form, ordered pairs, or diagrams. Practising all formats helps develop a clear understanding of the concept and improves accuracy in examination-based questions.
A relation is a general connection between elements of two sets, whereas a function is a special type of relation. In a relation, one element of the first set may correspond to multiple elements of the second set. However, in a function, each element of the domain must have only one image in the codomain. This distinction is important because many NCERT questions ask students to classify mathematical statements as relations or functions. Understanding this difference helps in solving mapping, domain, range, and graphical representation questions more effectively and forms the foundation for advanced calculus topics studied later.
One-one and onto functions are important concepts frequently asked in board examinations. A one-one function assigns different outputs to different inputs, ensuring that no two distinct elements in the domain have the same image. An onto function covers every element of the codomain at least once. Students should learn to verify these properties through definitions, mappings, and algebraic methods. NCERT exercises provide several examples that illustrate both concepts clearly. Understanding one-one and onto functions is crucial because they help determine whether an inverse function exists, making them an important foundation for higher-level mathematical topics.
Composite functions are formed when one function operates on the result of another function. If two functions are represented as f(x) and g(x), then the composite function can be written as f(g(x)) or g(f(x)). Students often struggle because they substitute values incorrectly or overlook domain restrictions. The key is to first evaluate the inner function and then apply the outer function to the result. NCERT questions focus on evaluating composite functions, finding their domains, and simplifying expressions. Understanding the sequence of operations is essential because composite functions play an important role in later chapters involving inverse functions and calculus.
Finding the domain and range is a frequently tested concept in this chapter. The domain consists of all permissible input values for which the function is defined, while the range includes all possible output values obtained from those inputs. Students should examine restrictions carefully, especially in rational, square-root, and trigonometric functions. For example, a denominator cannot be zero, and the value inside a square root cannot be negative. NCERT exercises include various examples that help students understand these restrictions. Regular practice makes it easier to identify valid inputs and corresponding outputs quickly during examinations.