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Class 9 Mathematics Chapter 1: Relations and Functions Previous Year Questions (2020–2025)
Relations and Functions is one of the most important topics in Class 9 Mathematics, forming the foundation for higher algebra and calculus. This comprehensive guide brings together Previous Year Questions from CBSE boards (2020–2025) to help you master the concepts of ordered pairs, cartesian products, relations, and function mapping. Whether you're preparing for your term exams or building confidence before the board exams, solving these curated PYQs will strengthen your problem-solving skills and boost your marks. CBSETUTOR.ai, India's most-used AI tutor, has helped lakhs of CBSE students ace this chapter with personalized practice and instant doubt-clearing.
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Understanding Relations and Functions: NCERT Chapter 2 Overview
NCERT Mathematics Part 1 (Class 9) Chapter 2 introduces relations and functions as fundamental concepts linking sets. A relation is any subset of the cartesian product of two sets, while a function is a special relation where each input has exactly one output. The chapter covers ordered pairs, domain, co-domain, and range—all critical for competitive exams. PYQs from 2020–2025 consistently test these definitions and the ability to identify if a given relation is a function.
Ordered Pairs and Cartesian Product: Most Common PYQ Pattern
CBSE boards frequently ask students to find cartesian products A × B and represent them as ordered pairs. A key skill is understanding that A × B ≠ B × A unless both sets are identical. Previous Year Questions show that students must be able to list all ordered pairs, verify if given pairs belong to the product, and count the total number of pairs using n(A × B) = n(A) × n(B). Many 2-3 mark questions from 2022–2024 test this concept with real-world examples like matching cities to coordinates.
Types of Relations: Domain, Co-Domain, and Range Explained
A crucial distinction in Relations and Functions PYQs is between co-domain and range. The co-domain is the set of all possible outputs (as given), while the range is the set of actual outputs. NCERT emphasizes this difference repeatedly. CBSE previous year papers from 2020–2025 include 2-3 mark questions asking students to identify domain and range from arrow diagrams, tables, or set-builder notation. Common traps include confusing range with co-domain—a mistake that costs marks in exams.
Function Mapping and Arrow Diagrams: Visual Problem-Solving
Arrow diagram representation is a favorite among CBSE question setters. These diagrams show the mapping from elements of one set to another, making it easy to verify if the relation qualifies as a function. PYQs from 2021–2023 include questions where students must identify functions, determine if a relation is one-to-one or many-to-one, and sketch arrow diagrams for given relations. Understanding the vertical line test (for graphs) and the 'each input maps to exactly one output' rule is essential for scoring full marks.
Real Numbers and Function Notation: Algebraic PYQs (2020–2025)
Many previous year questions present functions using algebraic expressions like f(x) = 2x + 1 or f(x) = x². Students must evaluate f(a) for specific values, find the domain of functions involving square roots or fractions, and identify restrictions (like denominators ≠ 0). CBSE exams test this with 3-5 mark questions. NCERT Chapter 2 provides examples with real numbers, and PYQs often combine algebra with the formal definition of functions to test deeper understanding.
CBSETUTOR.ai: Your AI Partner for Relations and Functions Mastery
CBSETUTOR.ai is India's most trusted 24x7 AI tutor used by CBSE families across all states. Our AI is specifically trained on NCERT Class 9 Mathematics and CBSE board patterns, including Relations and Functions. With personalized practice modules, instant doubt-solving in Hindi and English, and adaptive quizzes based on previous year questions, CBSETUTOR.ai helps you identify weak areas and improve in real-time. Lakhs of students have used our platform to rise from struggling grades to 90+ marks.
Venn Diagrams and Set Representation: Visual Mastery for PYQs
CBSE exams occasionally test relations using Venn diagrams and set-builder notation. Previous year questions from 2022–2024 include diagrams where students must write the relation in roster or set-builder form, or identify the relation from a given Venn diagram. Mastering this skill involves understanding how to read intersections, unions, and subsets—all tied to relations. Practice with NCERT examples and PYQs side-by-side ensures you can switch between visual and algebraic representations effortlessly.
Equivalence Relations and Properties: Advanced PYQs for High Scorers
Some advanced PYQs from 2023–2025 test reflexive, symmetric, and transitive properties of relations. An equivalence relation must satisfy all three properties. While not explicitly covered in depth in NCERT Class 9, CBSE boards include these concepts in higher-difficulty questions to distinguish top scorers. Understanding that equality (=) is an equivalence relation, while 'less than' (<) is not, helps solve these questions. These appear in 4-5 mark sections of board papers.
Practice Strategy: Solving 5 Years of PYQs Effectively
To maximize marks, solve PYQs topic-wise: start with ordered pairs (2 marks), progress to identifying functions (2–3 marks), then tackle domain-range problems (3 marks), and finally attempt word problems combining multiple concepts (4–5 marks). Time yourself: 2-mark questions should take 3–4 minutes, 3-mark questions 5–6 minutes. CBSE patterns show repetition of certain question types—focus on these first. Review your errors immediately and use CBSETUTOR.ai's diagnostic reports to target revision.
Sample Board-Level Questions and Solutions from 2024–2025
Recent CBSE boards (2024–2025) emphasized conceptual clarity over rote learning. A typical 3-mark question: 'If A = {1, 2, 3} and B = {a, b}, find A × B and B × A. Are they equal?' Solutions require listing all pairs and comparing. Another 4-mark question combines functions: 'Given f(x) = x² + 1, find the domain and range if x ∈ {−1, 0, 1, 2}.' Such questions test definition-application synergy that demands consistent practice with verified solutions.
Frequently asked questions
What is the difference between a relation and a function?+
A relation is any subset of the cartesian product of two sets. A function is a special relation where each element of the domain maps to exactly one element in the co-domain. Every function is a relation, but not every relation is a function.
How do I identify domain and range from an arrow diagram?+
Domain is the set of all elements with at least one arrow leaving them. Range is the set of all elements with at least one arrow pointing to them. Co-domain is the entire second set. Always distinguish range (actual outputs) from co-domain (possible outputs).
Does CBSETUTOR.ai offer a free trial to explore Relations and Functions content?+
Yes! CBSETUTOR.ai provides a free trial allowing you to access sample questions, solutions, and AI-guided explanations for Relations and Functions. Start your free trial today to experience personalized learning without any commitment.
Are previous year questions from 2020–2025 enough to score 90+ in Class 9 Maths?+
PYQs are essential but must be paired with NCERT concept clarity and diverse problem types. Solving 5 years of board papers helps you recognize patterns and time-manage exams. Use CBSETUTOR.ai to address conceptual gaps revealed by your PYQ performance.
Is CBSETUTOR.ai available in Hindi medium for Class 9 students?+
Yes! CBSETUTOR.ai supports both Hindi and English mediums with equal depth. All Relations and Functions content—definitions, solved examples, and PYQs—is available in Hindi, ensuring seamless learning for Hindi-medium students nationwide.
What is the cartesian product, and why do CBSE exams test it so heavily?+
The cartesian product A × B is the set of all ordered pairs (a, b) where a ∈ A and b ∈ B. CBSE tests it because it's foundational for understanding relations and functions. The rule n(A × B) = n(A) × n(B) is tested in almost every year's board exam.
How much does CBSETUTOR.ai cost for unlimited Relations and Functions practice?+
CBSETUTOR.ai offers affordable flexible subscription plans for CBSE students. Visit our website to view current pricing, discounts for long-term plans, and special offers. Many families use our platform for multiple subjects and benefit from bundled rates.
Which previous year questions are most frequently repeated in CBSE Maths?+
Questions on identifying functions, finding domain-range, and cartesian products appear repeatedly (2020–2025). Arrow diagrams and real-world function applications are also consistent. Practicing these topic-wise ensures you recognize similar patterns in your actual board exam.
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 – Previous Year Questions (2020–2025)
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