A B f: A → B, one-one not onto
↦
Chapter 1  ·  Class XII Mathematics  ·  MCQ Practice

MCQ Practice Arena

Relations & Functions

Decode Every Relation — Master One-One, Onto and Invertible Functions

📋 50 MCQs ⭐ 28 PYQs ⏱ 90 sec/Q
🚀 Start Practising 📖 Revise Notes First

MCQ Bank Snapshot

50Total MCQs
18Easy
22Medium
10Hard
28PYQs
90 secAvg Time/Q
4Topics
Easy 36% Medium 44% Hard 20%

Why Practise These MCQs?

CBSE Class XIIJEE MainJEE Advanced

Relations & Functions opens Class XII by extending Class XI groundwork into proof-style objective questions. CBSE boards frequently test equivalence relations and bijection proofs as assertion-reason MCQs, while JEE Main asks 1–2 direct questions on invertibility and composition every year. This bank mirrors that mix so you build both proof intuition and calculation speed.

Topic-wise MCQ Breakdown

Types of Relations (Reflexive/Symmetric/Transitive)14 Q
Equivalence Relations & Classes10 Q
Types of Functions (One-One/Onto/Bijective)16 Q
Composition & Invertible Functions10 Q

Must-Know Formulae Before You Start

Recall these cold before attempting MCQs — they appear in >70% of questions.

$(g \circ f)(x) = g(f(x))$
$f^{-1} \text{ exists iff } f \text{ is bijective}$
$(g \circ f)^{-1} = f^{-1} \circ g^{-1}$
$R \text{ is equivalence iff reflexive, symmetric \& transitive}$

MCQ Solving Strategy

For relation MCQs, check all three properties one at a time and disprove with a single counterexample the moment one fails — don't verify every pair once you've found a break. For function-type questions, test one-one algebraically by assuming f(x₁)=f(x₂) and solving for x₁=x₂, and test onto by solving y=f(x) for x and confirming it lies in the domain. Invertibility MCQs almost always reduce to a bijectivity check first.

⚠ Common Traps & Errors

Difficulty Ladder

Work through each rung in order — do not jump to Hard before mastering Easy.

① Easy

Identify relation properties from a given set, evaluate f(x) and gof(x)

② Medium

Prove a relation is an equivalence relation, verify one-one/onto algebraically

③ Hard

Composition of piecewise functions, invertibility proofs with domain restrictions

★ PYQ

JEE Main — equivalence classes and bijection counts; CBSE — assertion-reason proofs

Continue Your Preparation

📖 Chapter Notes Revise concepts & theory 🧠 MCQ Practice Topic-wise Questions 🎯 PYQ Bank Previous year questions ✔️❌ True / False Concept-based True & False questions 📘✔️ Exercises Step by step Solutions to textbook exercises ➡ Next Chapter Inverse Trigonometric Functions MCQs
🎯 Knowledge Check

Mathematics — Relations And Functions

50 Questions Class 12 MCQs
1
Let \(A=\{1,2\}\) and \(B=\{a,b,c\}\). The number of relations from \(A\) to \(B\) is
2
If \(A=\{1,2,3\}\), then the number of ordered pairs in \(A\times A\) is
3
A relation from \(A\) to \(B\) is
4
The Cartesian product \(A\times B\) is
5
If \(|A|=4\) and \(|B|=5\), then \(|A\times B|=\)
6
A relation \(R\) on a set \(A\) is reflexive if
7
A relation is symmetric if
8
A relation is transitive if
9
A relation that is reflexive, symmetric and transitive is called
10
A function is
11
In a function \(f:A\to B\), every element of \(A\) has
12
The set of all first elements of a function is called
13
The set containing all outputs actually obtained is called
14
Which of the following is always true?
15
The function \(f(x)=2x+1\) is
16
The identity function on \(A\) is defined by
17
A constant function satisfies
18
Which function is one-one?
19
Which function is many-one on \(\mathbb{R}\)?
20
A function is onto if
21
Which function is bijective on \(\mathbb{R}\)?
22
If \(f(x)=3x-2\), then \(f(4)=\)
23
If \(f(x)=x^2+1\), then \(f(2)=\)
24
If \(f(x)=2x\) and \(g(x)=x+3\), then \((f+g)(x)=\)
25
If \(f(x)=x\) and \(g(x)=2x\), then \((fg)(x)=\)
26
If \(f(x)=x+2\) and \(g(x)=3x\), then \((f\circ g)(x)=\)
27
If \(f(x)=x+2\) and \(g(x)=3x\), then \((g\circ f)(x)=\)
28
Composition of functions is
29
If \(f(x)=2x+1\), then \(f^{-1}(x)=\)
30
An inverse function exists only if the function is
31
The domain of \(f(x)=\frac{1}{x}\) is
32
The domain of \(f(x)=\sqrt{x}\) is
33
The range of \(f(x)=x^2\) on \(\mathbb{R}\) is
34
If \(R=\{(1,2),(2,3),(3,4)\}\), then \(R\) is
35
The relation \(aRb\iff a=b\) is
36
The relation \(aRb\iff a\le b\) on \(\mathbb{R}\) is
37
Which is not a function?
38
If \(f(x)=5\), then the function is
39
If \(f(x)=x^3-1\), then \(f(-2)=\)
40
If \(f(x)=\frac{x-2}{3}\), then \(f(8)=\)
41
If \(f(x)=x^2+2x\), then \(f(-1)=\)
42
If \(f(x)=2x+1\) and \(g(x)=x-1\), then \((f\circ g)(5)=\)
43
If \(f(x)=x+4\), then \(f^{-1}(10)=\)
44
The relation \(R=\{(1,1),(2,2),(3,3)\}\) on \(\{1,2,3\}\) is
45
The number of functions from a set of 2 elements to a set of 3 elements is
46
The number of one-one functions from a set with 3 elements to a set with 4 elements is
47
The number of bijections from a set having 4 elements onto itself is
48
If \(f(x)=\frac{2x+3}{5}\), then \(f^{-1}(x)=\)
49
If \(f(x)=x^2,\;x\ge0\), then \(f^{-1}(16)=\)
50
Let \(f(x)=2x-3\) and \(g(x)=x^2\). Then \((g\circ f)(2)=\)
📚
ACADEMIA AETERNUM तमसो मा ज्योतिर्गमय · Est. 2025
Sharing this chapter
NCERT Class 12 Maths Chapter 1: Relations & Functions
NCERT Class 12 Maths Chapter 1: Relations & Functions — Complete Notes & Solutions · academia-aeternum.com
🎓 Class 12 📐 Mathematics 📖 NCERT ✅ Free Access 🏆 CBSE · JEE
Share on
WhatsApp
Telegram
X / Twitter
Facebook
Instagram
Threads
Pinterest
LinkedIn
Quora
Discord
Reddit
Email
academia-aeternum.com/class-12/mathematics/relations-and-functions/mcqs/ Copy link
💡
Exam tip: Sharing chapter notes with your study group creates a reinforcement loop. Teaching a concept is the fastest path to mastering it.

Frequently Asked Questions

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.

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

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.

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

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.

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.

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

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.

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.

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.

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.

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

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.

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

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

Recent Posts

    --:-- ⏱ Time
    ⚡ Progress 0 / 50 answered

    Relations and Functions — Learning Resources

    📄 Detailed Notes

    Get in Touch

    Let's Connect

    Questions, feedback, or suggestions?
    We'd love to hear from you.