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Class 9 Mathematics Chapter 2: Relations and Functions – Solved Previous Year Questions (2020–2025)
Relations and Functions is a foundational concept in Class 9 Mathematics that bridges arithmetic and algebra. This chapter, part of NCERT 2024-25 syllabus, teaches students how to represent mathematical relationships and understand functional behaviour—skills essential for higher mathematics. Our comprehensive collection of solved previous year questions (2020–2025) helps Class 9 students master this topic through real CBSE exam patterns. Whether you're preparing for half-yearly, final exams, or competitive entrance tests, these solutions provide clarity on domain, range, mapping, and function notation with step-by-step explanations.
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Understanding Relations and Functions: NCERT Chapter 2 Overview
Relations and Functions (Chapter 2, NCERT Class 9 Mathematics) introduces the concept of ordered pairs, Cartesian products, and functional relationships. A relation is a set of ordered pairs, while a function is a special relation where each input has exactly one output. The chapter covers domain (input values), codomain (possible outputs), and range (actual outputs). Understanding these definitions is critical because they appear in every CBSE board paper. Students must recognize when a relation qualifies as a function and represent it using diagrams, tables, or algebraic notation.
2020–2025 CBSE Board Question Patterns on Relations and Functions
CBSE Class 9 Mathematics board papers consistently test three key areas: identifying functions from relations (1–2 marks), finding domain and range (2–3 marks), and applying functions to real-world scenarios (3–5 marks). Previous year questions reveal that examiners favour arrow diagrams, set-builder notation, and piecewise function representation. Short-answer questions dominate the board paper, requiring concise reasoning rather than lengthy derivations. By studying solved papers from 2020–2025, students develop familiarity with expected answer formats and can predict question types. This pattern recognition dramatically improves exam confidence and accuracy.
How to Find Domain and Range: Solved Step-by-Step Solutions
Finding domain and range requires careful analysis of the given function or relation. For a function f(x) = √(x – 2), the domain is x ≥ 2 (values that make the expression valid), and the range is f(x) ≥ 0 (all possible outputs). Previous year CBSE questions test this skill through multiple representations—verbal descriptions, graphs, and algebraic expressions. Solving these systematically teaches students to identify restrictions (denominators ≠ 0, radicands ≥ 0) and logical constraints. Our solved solutions model the exact reasoning CBSE examiners expect, helping students avoid common errors like confusing domain with range or omitting boundary values.
Arrow Diagrams and Cartesian Graphs: Visual Representation Methods
CBSE Class 9 students must master two visual methods for representing relations and functions. Arrow diagrams show connections between input and output sets, making it easy to verify the function property (each input maps to exactly one output). Cartesian graphs plot ordered pairs on the coordinate plane, with the vertical line test confirming functionality—a vertical line crosses the graph at most once. Previous year solutions demonstrate how to sketch these diagrams accurately, label them properly, and use them to communicate mathematical ideas. Visual literacy is rewarded in board exams because it shows conceptual understanding beyond memorisation.
Real-World Applications: Functions in Daily Life Examples
CBSE examiners increasingly include real-world function problems to test application skills. Examples include: cost as a function of quantity, temperature as a function of time, and profit as a function of sales. Solved previous year questions (2020–2025) show how to translate word problems into functional notation, identify variables, and interpret results in context. A student might determine that delivery cost C(x) = 100 + 5x (where x is distance in km) and find the cost for a 20 km delivery. These applied problems develop mathematical reasoning beyond abstract theory, preparing students for competitive exams and real-world problem-solving.
Why CBSETUTOR.ai Is India's Trusted AI Tutor for Relations and Functions
CBSETUTOR.ai is used by lakhs of Class 6–12 CBSE students across India for personalised AI-driven tutoring. Our platform offers instant 24/7 solutions for Relations and Functions, with step-by-step explanations aligned to NCERT 2024-25. Unlike static textbooks or generic videos, CBSETUTOR.ai adapts to each student's pace and learning style, explaining concepts in Hindi or English. Thousands of Indian families trust us because we focus on CBSE board patterns, not unrelated content. Our AI identifies knowledge gaps in domain-range problems or function recognition and provides targeted practice until mastery. Students using CBSETUTOR.ai report significantly improved exam scores in relations and functions topics.
Common Mistakes in Relations and Functions Questions
Class 9 students frequently misidentify functions because they confuse one-to-one relations with functions—many-to-one is allowed, but one-to-many is not. Another error: writing domain as a single number instead of a set or interval. Students also forget that domain depends on the function's context—f(x) = 1/x has domain ℝ – {0}, excluding zero. A third mistake involves calculating range without considering all possible outputs, especially for piecewise or restricted functions. Previous year CBSE solutions highlight these pitfalls explicitly, training students to double-check their answers. Recognising and avoiding these errors is the difference between board pass marks and distinction.
Preparing for Class 9 Board Exams: Study Plan Using Previous Year Papers
Effective exam preparation combines NCERT theory with solved previous year questions. Week 1–2: master definitions, domain, and range using NCERT examples. Week 3: solve 2020–2022 CBSE questions topic-wise (relations, then functions, then applications). Week 4: attempt mixed papers from 2023–2025 under timed conditions. Week 5: review mistakes and weak areas using detailed solutions. This progressive approach builds confidence gradually. Previous year papers reveal that examiners repeat certain concepts (e.g., identifying functions from diagrams) while varying difficulty. Students who follow this structured plan develop both conceptual clarity and exam-technique, maximising their board exam score.
Practice Exercises: Sample Questions with Detailed Solutions
Sample Q1: If f(x) = 2x + 3, find f(0), f(–1), and f(2). Solution: f(0) = 3, f(–1) = 1, f(2) = 7. (Shows function evaluation). Q2: State which relation is a function: (i) {(1,2), (1,3), (2,4)} – Not a function (1 maps to 2 and 3). (ii) {(1,2), (2,4), (3,6)} – Is a function (each input has one output). Q3: Find domain and range of f(x) = √(4 – x²). Domain: –2 ≤ x ≤ 2 (from 4 – x² ≥ 0). Range: 0 ≤ f(x) ≤ 2. These representative problems, based on CBSE patterns, help students practice and self-assess before exams.
Key Formulas and Theorems for Relations and Functions
Essential concepts include: (1) Ordered pair (a, b) where order matters. (2) Cartesian product A × B = {(a, b) : a ∈ A, b ∈ B}. (3) Function notation f: A → B, read 'f from A to B'. (4) Domain = input set, Range = output set ⊆ Codomain. (5) Vertical line test: a graph is a function if every vertical line intersects it at most once. (6) One-to-one (injective): different inputs give different outputs. (7) Onto (surjective): every codomain element is mapped. These definitions appear verbatim in NCERT and feature in every board paper—memorising and applying them is non-negotiable for success.
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 (domain element) maps to exactly one output. For example, {(1,2), (1,3)} is a relation but not a function because 1 maps to both 2 and 3.
How do I find domain and range from an algebraic function?+
Domain: identify all x-values that make the function defined (avoid division by zero, negative radicands). Range: determine all possible output y-values the function can produce. For f(x) = √x, domain is x ≥ 0, range is f(x) ≥ 0.
Is CBSETUTOR.ai available for free trial or low-cost access?+
Yes! CBSETUTOR.ai offers a free trial period so students can explore AI-tutored lessons on Relations and Functions before subscribing. Our flexible pricing ensures access for all Indian families. Check our website for current offers and trial eligibility.
Does CBSETUTOR.ai support Hindi-medium CBSE students?+
Absolutely. CBSETUTOR.ai provides bilingual support in English and Hindi for all CBSE classes and chapters, including Relations and Functions. Students can toggle language preference anytime for seamless learning in their comfort language.
Which previous year papers should I prioritise for Relations and Functions?+
Start with 2023–2025 CBSE board papers because recent patterns closely resemble current exams. Then solve 2020–2022 papers to build deeper understanding. Focus on questions that require domain-range calculations and function identification—these are highest-frequency topics.
How much time should I spend on Class 9 Relations and Functions?+
Allocate 4–5 weeks: Week 1–2 for NCERT theory and examples, Week 3 for topic-wise previous year questions, Week 4 for mixed practice papers, Week 5 for revision. Daily 45–60 minutes of focused study is ideal for mastery before board exams.
What marks are typically allocated to Relations and Functions in CBSE Class 9 boards?+
Relations and Functions usually carry 6–8 marks in the Class 9 board paper (both Part A short-answers and Part B long-answers combined). Expect 1–2 definition questions, 2–3 domain-range problems, and 1–2 application-based questions across the full paper.
How do arrow diagrams help in understanding functions?+
Arrow diagrams visually show how each input maps to outputs. If every input has exactly one arrow pointing to an output, it's a function. If any input has multiple arrows, it's not. This visual method makes function identification intuitive, especially for Class 9 learners new to the concept.
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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