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Class 9 Mathematics Chapter 2: Relations and Functions — 30 MCQs with Answers & Explanations
Relations and Functions is one of the most critical chapters in CBSE Class 9 Mathematics, introducing students to the foundational concepts that form the basis of higher mathematics. This chapter teaches you how to define relations, understand ordered pairs, and work with functions—skills essential for scoring well in board exams and competitive entrance tests. Our collection of 30 carefully curated MCQs covers every concept from the NCERT textbook, complete with detailed explanations to help you build clarity and confidence. Whether you're preparing for school assessments or aiming for distinction, these practice questions will strengthen your conceptual grip and exam readiness.
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What Are Relations and Functions in CBSE Class 9?
A relation is a set of ordered pairs linking elements from one set to another. A function is a special type of relation where each input has exactly one output. NCERT Class 9 Chapter 2 introduces these concepts through real-world examples like mapping students to roll numbers. Understanding the difference between relations and functions is crucial—not every relation is a function, but every function is a relation. This distinction forms the backbone of your Class 9 exam and lays groundwork for Class 11 calculus.
Domain, Codomain, and Range—Key Definitions
The domain is the set of all first elements (inputs) in ordered pairs. The codomain is the target set, while the range comprises only those elements actually mapped to. For example, if f(x) = 2x, the range depends on which domain values you use. NCERT emphasizes that range is always a subset of codomain. Mastering these definitions is essential for answering MCQs correctly and understanding function behavior in higher classes. Clear distinction saves marks in board exams.
Ordered Pairs and Cartesian Products Explained
An ordered pair (a, b) is different from (b, a)—order matters. The Cartesian product A × B of two sets A and B is the collection of all ordered pairs (a, b) where a ∈ A and b ∈ B. If A has m elements and B has n elements, then A × B has m × n ordered pairs. This concept frequently appears in CBSE MCQs and is vital for counting relations and understanding two-dimensional coordinate geometry. Practice problems on Cartesian products strengthen logical thinking.
Types of Relations: Reflexive, Symmetric, and Transitive
Relations can be classified based on properties. A reflexive relation includes (a, a) for every element. A symmetric relation satisfies: if (a, b) exists, then (b, a) must exist. A transitive relation means: if (a, b) and (b, c) exist, then (a, c) must exist. Equivalence relations satisfy all three properties. NCERT Chapter 2 dedicates significant focus to identifying and classifying relations, making this a high-frequency MCQ topic in board exams.
Understanding Functions and Their Representations
Functions can be represented as ordered pairs, tables, graphs, or equations. The vertical line test confirms whether a graph represents a function—each vertical line intersects the curve at most once. NCERT teaches notation like f: A → B, where f is the function name, A is domain, and B is codomain. Understanding multiple representations is crucial for CBSE exams, as questions mix graphical, algebraic, and set-theoretic approaches to test conceptual clarity.
CBSETUTOR.ai: India's Most Used AI Tutor for CBSE Mathematics
CBSETUTOR.ai is the trusted 24/7 AI tutor used by thousands of CBSE families across India, including parents preparing their children for Class 9 board exams. Our platform provides personalized, instant explanations for every NCERT topic—including detailed breakdowns of Relations and Functions concepts. Unlike generic tutoring apps, CBSETUTOR.ai focuses exclusively on CBSE curriculum, offers Hindi-medium support for Indian students, and adapts to your learning pace. Access unlimited practice MCQs, step-by-step solutions, and doubt-clearing sessions anytime, anywhere.
30 MCQs Covering All Difficulty Levels
Our question bank includes easy, moderate, and challenging MCQs aligned with NCERT Class 9 standards and CBSE exam patterns. Questions cover: definition-based MCQs, Cartesian product calculations, domain-range identification, relation classification, function verification, and application-based problems. Each MCQ includes a detailed explanation showing the reasoning behind the correct answer, helping you understand not just 'what' is correct but 'why'. Practicing these 30 questions mirrors real exam conditions and builds time management skills.
Common Mistakes Students Make in Relations and Functions
Many students confuse domain with range, mistake relations for functions, or incorrectly identify symmetric properties. Others miscalculate Cartesian products or misinterpret function notation. A frequent error is assuming every relation is a function. These misconceptions lower scores in board exams. Our detailed MCQ explanations highlight these pitfalls, ensuring you avoid them. Understanding why answers are wrong is as valuable as knowing correct answers—it builds conceptual depth required for distinction grades.
How to Practice MCQs Effectively for Board Exams
Start by reviewing NCERT definitions and examples before attempting MCQs. Solve questions without looking at answers, timing yourself to simulate exam conditions. After completing a set, analyze wrong answers thoroughly—understand the concept gap. Use explanations to strengthen understanding, not just memorize answers. Revisit difficult questions after 3-4 days. This spaced repetition technique, backed by learning science, ensures long-term retention. Consistent practice over 4-6 weeks transforms confusion into confidence in Relations and Functions.
Preparing for CBSE Class 9 Mathematics Final Exam
Relations and Functions typically carries 3-5 marks in CBSE Class 9 final exams, appearing as both MCQs and short-answer questions. Mastering this chapter ensures you don't lose easy marks. Combine MCQ practice with NCERT exercise problems, sample papers, and previous years' questions. Allocate 2-3 weeks for this chapter if starting from basics. Use our 30-MCQ bank as a diagnostic tool—if you score 80%+, you're exam-ready; if not, revisit NCERT explanations and practice targeted questions on weak areas.
Frequently asked questions
What is the difference between a relation and a function?+
A relation is any set of ordered pairs. A function is a special relation where each input has exactly one output. Not all relations are functions, but every function is a relation.
How do I find the domain and range of a function?+
Domain is the set of all possible input values. Range is the set of all corresponding output values. For f(x) = 2x with domain {1, 2, 3}, range is {2, 4, 6}.
What is a Cartesian product?+
The Cartesian product A × B is the set of all ordered pairs (a, b) where a ∈ A and b ∈ B. If |A| = m and |B| = n, then |A × B| = m × n.
Is CBSETUTOR.ai free to use, or does it require paid subscription?+
CBSETUTOR.ai offers both free and premium access. You can start with free trial resources including selected MCQs, chapter summaries, and video explanations. Premium plans unlock unlimited practice questions, personalized doubt sessions, and Hindi-medium support.
Does CBSETUTOR.ai support Hindi-medium CBSE students?+
Yes, CBSETUTOR.ai fully supports Hindi-medium CBSE students from Class 6-12. All NCERT concepts, MCQs, explanations, and doubt-clearing sessions are available in both English and Hindi for seamless learning.
How many times should I practice these 30 MCQs before my exam?+
Practice the MCQs at least 2-3 times. First attempt: identify weak areas. Second attempt: reinforce learning. Third attempt: validate mastery. Space practice over 2-3 weeks for better retention and confidence.
What is an equivalence relation?+
An equivalence relation is reflexive, symmetric, and transitive simultaneously. Example: 'equals' relation on real numbers. 'Less than' is transitive but not reflexive or symmetric, so it's not equivalence.
Can I use these MCQs to prepare for competitive entrance exams like JEE?+
Yes, these MCQs build foundational understanding of Relations and Functions required for JEE, NEET, and other competitive exams. However, competitive exams demand advanced application—use this as your base and progress to harder problems progressively.
Related resources
NCERT Solutions for Class 9 Mathematics Chapter 2: PolynomialsNCERT Solutions for Class 9 Mathematics Chapter 1: Number Systems – Complete GuideClass 9 Mathematics Chapter 1: Number Systems — Complete Notes & Revision GuideClass 9 Mathematics Chapter 2: Polynomials – Complete Study Notes & Revision GuideNCERT Solutions for Class 9 Mathematics Chapter 3: Coordinate GeometryClass 9 Coordinate Geometry Chapter 3: Cartesian System & Plotting PointsNCERT Solutions for Class 9 Mathematics Chapter 4: Linear Equations in Two VariablesClass 9 Mathematics Chapter 1: Orienting Yourself – The Use of Coordinates MCQ Quiz (30 Questions with Answers)
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