CBSE Class 11 Mathematics Chapter 2 Relations and Functions Worksheet with Answers

Before attempting the worksheet, refresh these core concepts from NCERT Class 11 Mathematics Chapter 2. A Cartesian product A × B is the set of all ordered pairs (a, b) where a belongs to A and b belongs to B. If A has m elements and B has n elements, then A × B contains exactly m×n ordered pairs. A relation R from set A to set B is any subset of A × B, while a function is a special relation where every element in the domain has exactly one image in the codomain. Relations are classified as reflexive when every element is related to itself, symmetric when aRb implies bRa, transitive when aRb and bRc together imply aRc, and equivalence when all three properties hold simultaneously. Functions are categorized as one-one (injective) when distinct elements have distinct images, onto (surjective) when every element in the codomain is an image of some element in the domain, and bijective when both properties hold. Understanding domain, codomain, and range is essential, as is the ability to compose functions and find inverse functions when they exist.

This worksheet is designed at a medium difficulty level, appropriate for students who have completed the NCERT Class 11 Mathematics Chapter 2 textbook exercises and are preparing for unit tests or term examinations. The suggested completion time is 90 minutes under exam conditions, though students may take longer during initial practice. Questions are distributed to mirror the actual CBSE marking scheme: Section A MCQs carry 1 mark each, Section B fill-in-the-blanks carry 1 mark each, Section C matching or true/false items carry 1 mark each, Section D short-answer questions carry 2-3 marks each, and Section E long-answer questions carry 5 marks each. The case-study question typically carries 4 marks split across sub-parts. Students should attempt all sections sequentially, managing approximately 30-35 minutes for Sections A through C combined, 25-30 minutes for Section D, and 30-35 minutes for Section E and the case study. Keep a calculator handy for complex Cartesian product calculations, though most problems focus on conceptual understanding rather than heavy computation.

This section contains six multiple-choice questions testing foundational understanding of Relations and Functions concepts from Class 11 Mathematics Chapter 2. Each question has four options with exactly one correct answer. These MCQs cover Cartesian products, relation properties like reflexivity and symmetry, function identification, domain and range determination, and basic function types. MCQs are a staple of CBSE Class 11 Mathematics assessments and typically appear in both term exams and competitive entrance tests. Students should read each question carefully, eliminate obviously incorrect options, and verify their chosen answer before moving to the next question. Working should be shown in the margin for questions involving calculation or verification of properties. While each MCQ carries only 1 mark, collectively they form 20 percent of most internal assessments, making accuracy crucial for overall performance in Mathematics examinations.

Section B comprises five fill-in-the-blank questions that require precise terminology and numerical accuracy. These questions test recall of definitions, standard results, and the ability to apply formulas from NCERT Class 11 Mathematics Chapter 2. Unlike MCQs where options provide hints, fill-in-the-blank questions demand exact knowledge of Relations and Functions vocabulary such as 'equivalence relation,' 'bijective,' 'Cartesian product,' 'codomain,' and 'inverse function.' Students must write answers clearly in the provided blanks, ensuring correct spelling of mathematical terms. Numerical answers should include all necessary working in the margin. These questions often appear in CBSE Mathematics board exams and school tests because they efficiently assess whether students have internalized fundamental definitions and properties. Partial credit is rarely awarded for fill-in-the-blank items, so accuracy is paramount. Review your NCERT textbook definitions before attempting this section to ensure precise mathematical language.

Section C contains four items combining match-the-following and true/false formats. Match-the-following questions present two columns — Column I listing mathematical statements or expressions and Column II listing properties, results, or classifications. Students must correctly pair each item in Column I with exactly one item from Column II. Write the pairing as 'A-P, B-Q' format clearly. True/false questions require you to determine the validity of a statement about Relations and Functions, writing 'True' or 'False' explicitly. For false statements in homework or self-study, you should also provide a brief correction or counterexample, though this is not always required in timed exams. This section tests your ability to distinguish between similar concepts like reflexive versus symmetric relations, one-one versus onto functions, and domain versus range. CBSE Class 11 Mathematics exams frequently use this format to assess conceptual clarity efficiently. Read each statement twice before committing to an answer, as small words like 'all,' 'some,' or 'if and only if' significantly change meaning.

Section D presents five short-answer questions, each carrying 2 to 3 marks and requiring 2-4 lines of working or explanation. These questions test your ability to verify relation properties, find domains and ranges, check injectivity or surjectivity, and solve simple problems involving Cartesian products and function composition. CBSE marking schemes for Class 11 Mathematics award marks for clear steps: stating the definition or property being used, substituting given values correctly, performing algebraic manipulation, and writing a concluding statement. For instance, when proving a relation is not transitive, you must find a specific counterexample showing (a,b) ∈ R and (b,c) ∈ R but (a,c) ∉ R. When finding the domain of a function, identify all restrictions such as denominators that cannot be zero or expressions under even roots that must be non-negative. Write each step on a separate line for clarity. Underline or box final answers. If asked to 'show' or 'verify,' you must provide logical reasoning, not just a yes/no answer. These short-answer questions form the bulk of internal assessments and carry significant weight in term exams.

Section E contains three long-answer or Higher Order Thinking Skills questions, each carrying 5 marks and demanding detailed solutions with formal mathematical reasoning. These questions assess your ability to prove properties of equivalence relations, analyze composite and inverse functions, construct examples and counterexamples, and apply Relations and Functions concepts to abstract problems. A typical 5-mark question in CBSE Class 11 Mathematics requires you to state relevant definitions, show all intermediate algebraic steps, justify each logical inference, and provide a clear concluding statement. For example, proving a relation is an equivalence relation requires three separate sub-proofs for reflexivity, symmetry, and transitivity, each worth approximately 1.5 marks. When finding the inverse of a function, you must first verify the function is bijective, then solve y = f(x) for x in terms of y, and finally write f⁻¹(y) with proper domain and codomain. HOTS questions may ask you to compare two functions, construct a relation satisfying specific properties, or interpret real-world scenarios using mathematical models of relations. Allocate roughly 10 minutes per question in this section. If stuck, move to the next question and return later rather than spending excessive time on one problem. These questions separate average performers from top scorers, so practice them thoroughly using NCERT exemplar and previous years' papers.

This case-study question simulates the format introduced in recent CBSE Class 11 Mathematics examinations, where a real-world or interdisciplinary scenario is described in a short paragraph, followed by 3-4 sub-questions of 1 mark each (MCQ or very short answer). Case studies test your ability to extract mathematical relationships from descriptive text and apply Relations and Functions concepts in context. Read the passage carefully, identify the sets involved, determine whether the relationship described is a relation or function, and analyze its properties. Such questions often involve real-life situations like student roll numbers mapped to marks (function), family relationships (symmetric relation), ordering of items (transitive relation), or database mappings. The passage below presents a scenario involving student registrations and course enrollments. After reading, answer the four sub-questions that follow. Each sub-question tests a specific aspect of Relations and Functions: identifying domain and codomain, checking function properties, counting ordered pairs, or interpreting range. This format encourages integrated learning and mirrors how mathematics appears in data science, computer science, and social sciences. CBSE marking schemes typically award full marks for correct answers with minimal working in case-study sub-questions, though clarity remains important.

Below is the complete answer key for all sections of this CBSE Class 11 Mathematics Chapter 2 Relations and Functions worksheet. Each answer includes the correct response along with a brief explanation or working to help you understand the reasoning. For MCQs, the correct option is highlighted with an explanation of why other options are incorrect. For numerical or algebraic answers, key steps are shown. For proof-type questions, the logical structure is outlined. Use this answer key for self-assessment after attempting the worksheet under timed conditions. If you get a question wrong, revisit the relevant section in your NCERT Class 11 Mathematics textbook or notes. Mark questions you found difficult and reattempt them after a day or two. Consistent practice with worksheets and answer verification is how top CBSE students build confidence and accuracy. If you need personalized doubt-solving, CBSETUTOR.ai offers 24×7 AI-powered tutoring where you can upload photos of problems and receive step-by-step solutions instantly, covering every chapter from Classes 6 to 12, all for a flat ₹999 per month with a 3-day free trial to experience the platform risk-free.

Effective use of this worksheet goes beyond simply checking answers. First, attempt the entire worksheet in one sitting under exam-like conditions without referring to notes or the NCERT textbook. This simulates real exam pressure and helps you identify knowledge gaps honestly. Time yourself strictly — 90 minutes total. Once complete, take a 10-minute break before reviewing your answers against the answer key. For each incorrect answer, do not just note the correct response; instead, identify why you went wrong. Was it a conceptual misunderstanding, a calculation error, misreading the question, or time pressure? Write these insights in the margin. For conceptual errors, immediately revise that topic from your Class 11 Mathematics notes or NCERT textbook, specifically the relevant subsections of Chapter 2. Reattempt all incorrect questions on a separate sheet the next day without looking at the answer key. Track your accuracy percentage by section — aim for 90 percent or higher in Sections A through C and at least 70 percent in Sections D and E before your exam. If you consistently struggle with long-answer questions, focus on writing more structured solutions: define terms, show all steps, and conclude clearly. For students who find self-study challenging, CBSETUTOR.ai provides an AI tutor available around the clock. Upload a photo of any difficult problem from this worksheet and receive instant, personalized, step-by-step explanations tailored to your level. The platform covers every CBSE subject and chapter for Classes 6-12 at a flat monthly fee of ₹999, making quality tutoring accessible without expensive coaching classes. Try the 3-day free trial to see how AI-powered learning can transform your Mathematics preparation.

Even strong students make recurring mistakes in Chapter 2 Relations and Functions. One frequent error is confusing the order in Cartesian products: A×B is not the same as B×A, and forgetting this costs marks in short-answer questions. Another common pitfall is incomplete verification when checking properties of relations; students often verify reflexivity and symmetry but skip checking transitivity, leading to incorrect conclusions about equivalence relations. In function problems, many students incorrectly assume every relation is a function without verifying that each element in the domain has exactly one image. When finding the domain of functions involving square roots or fractions, students sometimes write inequalities in the wrong direction or forget to exclude points where the denominator is zero. For composite functions, the order matters: (fog)(x) is not the same as (gof)(x), yet students often compute only one and assume commutativity. In inverse function questions, a typical mistake is attempting to find f⁻¹ without first verifying that f is bijective. Lastly, in proof-type questions, students write conclusions without showing steps, resulting in lost marks even when the final answer is correct. CBSE marking schemes award marks for method and reasoning, not just the answer. Avoid these pitfalls by writing every step clearly, double-checking definitions, and practicing a variety of problems from NCERT exercises, exemplar, and worksheets like this one. Consistent practice reveals patterns in your errors, allowing you to address them before exams.

After completing this worksheet, continue building mastery with additional resources aligned to CBSE Class 11 Mathematics Chapter 2 Relations and Functions. Start with the NCERT textbook exercises 2.1, 2.2, and 2.3, ensuring you can solve every problem confidently. Then move to the NCERT Exemplar book, which contains more challenging problems and HOTS questions similar to those in Section E of this worksheet. Previous years' CBSE board question papers (available on cbse.nic.in) give you exposure to actual exam phrasing and marking schemes. Many toppers recommend maintaining a separate notebook for Relations and Functions where you write down definitions, key properties, and standard results in your own words, along with 2-3 worked examples for each concept. Flashcards for definitions like reflexive, symmetric, transitive, equivalence, one-one, onto, bijective, domain, codomain, and range help with quick revision before exams. Practice drawing graphs of simple functions like identity, constant, polynomial, modulus, and signum to visualize their properties. Join study groups or online forums where you can discuss tricky problems with peers. If your school offers remedial classes or doubt-clearing sessions, attend them regularly. For personalized, on-demand help, CBSETUTOR.ai is a cost-effective solution: upload any question from NCERT, exemplar, or worksheets like this one, and receive instant step-by-step explanations tailored to the CBSE syllabus. Covering all subjects from Classes 6 to 12 for a flat ₹999 per month, with a 3-day free trial, it acts like a personal tutor available anytime you need help, without the recurring expense of traditional coaching.