What is a relation in Class 12 Mathematics?

A relation is a subset of the Cartesian product of two sets. It defines how elements of one set are associated with elements of another set.

What are the different types of relations?

The main types are empty relation, universal relation, reflexive relation, symmetric relation, transitive relation, and equivalence relation.

What is the difference between a relation and a function?

A relation can associate one element with multiple elements, whereas a function assigns exactly one image in the codomain to every element of the domain.

What is an equivalence relation?

An equivalence relation is a relation that is simultaneously reflexive, symmetric, and transitive.

What are injective, surjective, and bijective functions?

An injective function maps distinct elements to distinct images, a surjective function covers every element of the codomain, and a bijective function is both injective and surjective.

What is the composition of functions?

The composition of functions combines two functions into one and is defined as \((g\circ f)(x)=g(f(x))\), where the output of the first function becomes the input of the second.

What is an invertible function?

An invertible function is a bijective function that has an inverse function \(f^{-1}\), satisfying \(f^{-1}\circ f=I_X\) and \(f\circ f^{-1}=I_Y\).

Why is the chapter 'Relations and Functions' important for CBSE and competitive exams?

It is the foundation for inverse trigonometric functions, calculus, matrices, probability, and advanced algebra, making it highly important for CBSE Boards, JEE Main, CUET, NDA, and other entrance examinations.

How can I determine whether a function is invertible?

A function is invertible if and only if it is both one-one (injective) and onto (surjective). This means every output has a unique pre-image.

What are the most important formulas in Relations and Functions?

Key formulas include \(R\subseteq A\times B\), \((g\circ f)(x)=g(f(x))\), \(f^{-1}\circ f=I_X\), \(f\circ f^{-1}=I_Y\), and the conditions for injective, surjective, bijective, and equivalence relations.

What are Relations and Functions in NCERT Class 12 Mathematics?

Relations describe associations between elements of two sets, while functions are special relations in which every element of the domain has exactly one image in the codomain.

How many MCQs are included in this Relations and Functions practice set?

This practice set contains 50 carefully selected MCQs with answers and concise explanations arranged from basic to advanced difficulty.

Which topics are covered in these Class 12 Relations and Functions MCQs?

The MCQs cover Cartesian products, relations, types of relations, equivalence relations, functions, one-one and onto functions, bijections, composition of functions, inverse functions, and domains and ranges.

Are these MCQs based on the latest NCERT and CBSE syllabus?

Yes, all questions are prepared according to the latest NCERT textbook and CBSE Class 12 Mathematics syllabus.

Do these MCQs include detailed explanations?

Yes, every question is followed by the correct answer and a concise explanation to help students understand the underlying concept.

NCERT Class 12 Maths Chapter 1: Relations & Functions

8 CBSE Marks

★★★★★ Difficulty

8 Topics

Medium JEE Weight

Topics Covered

8 key topics in this chapter

Types of Relations: Reflexive, Symmetric, Transitive

Equivalence Relations

Equivalence Classes

One-One (Injective) Functions

Onto (Surjective) Functions

Bijective Functions

Composition of Functions

Invertible Functions

Study Resources

📖 NCERT Notes ✏️ MCQ Practice 🏆 JEE / CBSE PYQs 📝 Exercise Solutions ✅ True / False Quiz

𝑓 Key Formulae

Essential mathematical expressions for this chapter — understand derivations, not just results.

Reflexive

\[(a,a) \in R \;\; \forall\, a \in A\]

📌 Every element related to itself

Symmetric

\[(a,b) \in R \implies (b,a) \in R\]

📌 Relation works both ways

Transitive

\[(a,b)\in R,\,(b,c)\in R \implies (a,c)\in R\]

📌 Chains carry through

Invertibility

\[f^{-1} \text{ exists} \iff f \text{ is bijective}\]

📌 One-one AND onto, both required

Composition

\[g\circ f = I_A,\; f \circ g = I_B \iff f \text{ invertible}\]

📌 Two-sided inverse test

🎯 Exam-Ready Insights

Important points to remember — curated from CBSE Board question patterns.

CBSE loves "show R is an equivalence relation" — always verify reflexive, symmetric, and transitive separately, never assume.

Equivalence classes partition the set completely — no element is left out and no two classes overlap.

One-one and onto must both be shown with full working; stating "clearly one-one" without proof loses marks.

A function and its inverse are reflections of each other across y = x — useful for quick sketch-based checks.

🏆 Competitive Exam Strategy

Targeted tips for JEE Main, JEE Advanced, NEET, BITSAT, and CBSE Boards.

JEE Main

Counting equivalence relations on small finite sets is a favourite MCQ — list partitions systematically rather than guessing.

JEE Main

Checking bijectivity of piecewise functions requires testing continuity of the one-one/onto property at breakpoints.

BITSAT

Quick composition evaluation (f∘g)(x) at a specific value is common — substitute innermost function first.

⚠️ Common Mistakes to Avoid

Proving only reflexivity and symmetry while skipping transitivity — all three are mandatory for equivalence.

Assuming a graph "looks" one-one without the algebraic f(x₁)=f(x₂) ⟹ x₁=x₂ argument.

Writing f⁻¹(x) for a non-invertible function — the inverse simply does not exist.

💡 Key Takeaways

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A relation is any subset of A×A; an equivalence relation additionally needs all three properties together.

◆

Only bijective functions possess an inverse function.

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Composition of functions is associative but not commutative in general.

Relations and Functions