Important Questions: CBSE Class 11 Mathematics Chapter 2 Relations and Functions

Relations and Functions introduces ordered pairs, Cartesian product of sets, and the formal definition of a relation as a subset of A × B. You then learn to classify relations as reflexive (every element relates to itself), symmetric (if a R b then b R a), transitive (if a R b and b R c then a R c), and equivalence relations (all three properties). The second half defines a function as a special relation where each element in the domain maps to exactly one element in the co-domain, then distinguishes one-one (injective), onto (surjective), and bijective functions. CBSE typically allocates 6-8 marks across the Algebra unit for this chapter. Expect one 1-mark MCQ on Cartesian product or properties, one 2-3 mark question verifying relation types or finding domain-range, and one 4-5 mark case study or proof-based question. The 2024 CBSE sample paper included a 4-mark case on election data mapped as a function and a 2-mark question on equivalence relation verification.

These questions test recall of definitions, notation, and quick calculations on Cartesian product cardinality or identification of relation properties. CBSE sets 1-mark MCQs in the objective section (20 marks total) and VSA in the descriptive section. Practice speed and accuracy — these are scoring questions if you know the NCERT definitions verbatim. Below are six representative 1-mark questions with concise answers aligned to board marking schemes.

Two-mark questions require you to show working or provide brief reasoning. Typical tasks: verify one or two properties of a given relation, find domain or range of a function, or determine if a function is one-one or onto by counter-example or proof. CBSE marking schemes award 1 mark for correct method and 1 mark for final answer. Always write the definition you are applying, then demonstrate with the given data. Below are four standard 2-mark questions with step-by-step model answers.

Three-mark questions combine definition recall with multi-step reasoning. You may need to verify all three properties (reflexive, symmetric, transitive) for an equivalence relation, determine both one-one and onto for a function, or solve a word problem that models a real scenario as a relation or function. CBSE marking schemes typically allocate 1 mark for each sub-part or logical step. Always label your steps: 'Reflexive:', 'Symmetric:', 'Transitive:' or 'One-one test:', 'Onto test:'. Below are four representative 3-mark questions with detailed working.

Five-mark questions in CBSE Class 11 often come as case studies in the new competency-based format introduced in 2021. You are given a real-world scenario — election results, survey data, temperature readings — and asked to model it as a relation or function, then answer 3-4 sub-questions on properties, domain, range, or graph interpretation. Alternatively, a traditional 5-marker asks you to prove a function is bijective or to find the number of equivalence relations on a small set. Each sub-question carries 1-2 marks; show all working and cite definitions. Below are two complete 5-mark questions with structured answers.

CBSE question-setters follow a blueprint aligned to the revised 2021-22 pattern: 20 marks MCQ (Case-I and Case-II), 16 marks VSA/SA, and 44 marks LA (long answer). For Relations and Functions, you will see one MCQ in the objective section (often on Cartesian product cardinality or identifying non-functions from arrow diagrams), one 2-mark VSA verifying a single property (reflexive or symmetric), and one 3-5 mark case-based question embedding the concept in a table, graph, or survey data. The board loves equivalence relations because they test all three properties in one go. Function questions increasingly ask for domain and range of composite or real-world piecewise functions, linking to Chapter 3 Trigonometric Functions. Since 2020, CBSE has included at least one data-interpretation or graph-based sub-question under Case Study (5 marks), where you identify a relation from a Venn diagram or frequency table. To mirror actual exam style, always write 'Given:', 'To Prove/Find:', and 'Solution:' in long answers.

Even strong students lose 2-3 marks in this chapter due to terminology confusion and incomplete verification. The most frequent error is mixing up 'co-domain' with 'range': co-domain is the entire target set B in f: A → B, while range is the subset of B actually covered by f(A). Another pitfall is stating a function is not one-one without giving a counter-example — CBSE marking schemes deduct 0.5 marks for assertion without proof. For relations, students often check reflexivity on a few elements instead of all elements in the set, or forget the transitive property requires checking all chains (a,b), (b,c) ⇒ (a,c). In equivalence relation proofs on infinite sets like ℤ, write out the general case using variables (a, b, c) rather than numerical examples alone. Arrow diagrams can be tricky: ensure every element in the domain has exactly one outgoing arrow for a valid function. Finally, in case-based questions, underline keywords in the paragraph — 'each', 'at least one', 'exactly' — these hint at one-one or onto conditions.

In the 2024-25 CBSE Class 11 blueprint, Algebra accounts for 30 marks (out of 80) split across Sets, Relations and Functions, Trigonometric Functions, and Complex Numbers. Within that, Relations and Functions typically gets 6-8 marks. Your preparation should mirror this distribution: spend 40 per cent of time on Cartesian product and relation properties (scoring 3-4 marks via MCQ and one short answer), 40 per cent on function types and domain-range (3-4 marks), and 20 per cent on case-based integration (often combined with Sets or Real Functions). Practice previous year papers from 2020 onwards because the case-study format started then. Solve NCERT Exemplar Problems for Chapter 2 — the board lifts 1-2 questions almost verbatim. Make a one-page formula sheet listing: |A×B|=|A|×|B|, reflexive (∀a: (a,a)∈R), symmetric (∀a,b: (a,b)∈R ⇒ (b,a)∈R), transitive (∀a,b,c: (a,b),(b,c)∈R ⇒ (a,c)∈R), one-one (f(x₁)=f(x₂)⇒x₁=x₂), onto (∀y∈B ∃x∈A: f(x)=y). Revise this sheet weekly.

Relations and Functions is concept-dense: you need to internalize six definitions (reflexive, symmetric, transitive, one-one, onto, bijective) and apply them flawlessly under exam pressure. CBSETUTOR.ai gives your child a 24×7 AI tutor that explains each property with instant visual examples — upload a photo of any relation or function question from your textbook or worksheet, and the AI walks through the verification step-by-step in under 60 seconds. For example, ask 'Is R={(1,1),(2,2),(1,2)} symmetric on {1,2}?' and the AI replies with the definition, checks each pair, and highlights the missing (2,1). The platform includes 50+ practice questions for Chapter 2 tagged by difficulty and marks, auto-graded with worked solutions. At ₹999/month flat for classes 6-12 — one price, all subjects, unlimited asks — it is less than the cost of two tuition sessions yet available around-the-clock. Parents in Bengaluru, Delhi NCR, and Mumbai report a 15-20 per cent improvement in Algebra unit scores within one month of using the AI tutor for nightly doubt clearing. Try the 3-day free trial: upload today's homework, see the difference, then subscribe. No hidden fees, cancel anytime.

Two days before your unit test or board exam, run through this checklist to ensure no concept is left unrevised. Print this list and tick each box after a 10-minute focused review. Start with definitions: write out from memory the conditions for reflexive, symmetric, transitive, equivalence, one-one, onto, bijective — then cross-check with NCERT page 33-43. Next, solve one question of each type: a 1-mark Cartesian product MCQ, a 2-mark domain-range problem, a 3-mark relation verification, and a 5-mark equivalence relation proof. Time yourself; you should complete all four in under 25 minutes. Review your own error log — which property do you forget most often? Make a flashcard for it. Finally, skim the case-study paragraph from the 2023 sample paper and note keywords: these repeat every year in different contexts. On exam day, read the question twice, underline 'reflexive', 'symmetric', 'transitive', 'one-one', 'onto' as you encounter them, and tick them off as you verify. This prevents skipping a property and losing 1 mark.