Last Updated on July 29, 2025 by XAM CONTENT
To succeed in Class 12 Maths exams, a strong grasp of Chapter 1 – Relations and Functions is essential. Our comprehensive collection of chapterwise MCQ questions with answers for Class 12 Maths is designed according to the latest syllabus and exam guidelines, ensuring targeted preparation and better performance. It is a part of MCQ Questions for CBSE Class 12 Maths Series.
These multiple-choice questions will help you assess your knowledge, improve accuracy, and boost confidence for your exams. Whether you are preparing for school tests, online tests or competitive exams, these Relations and Functions MCQs will strengthen your conceptual clarity.
| Chapter | Relations and Functions |
| Book | Maths for Class 12 |
| Type of Questions | MCQ Questions |
| Nature of Questions | Competency Based Questions |
| Board | CBSE |
| Class | 12 |
| Subject | Maths |
| Useful for | Class 12 Studying Students |
| Answers provided | Yes |
| Difficulty level | Mentioned |
| Important Link | Class 12 Maths Chapterwise MCQ Questions |
MCQ Questions on Relations and Functions Class 12 Maths (PDF Download)
Show Answer
Answer: (a) SymmetricExplanation: A relation $R$ is symmetric if for every $(a_1,a_2)$ in $R$, $(a_2,a_1)$ is also in $R$.
2. Let $R$ be a relation on the set $\mathbb{N}$ defined by $nRm$ if $n$ divides $m$. Then $R$ is
Show Answer
Answer: (d) Reflexive, transitive but not symmetricExplanation: The relation is reflexive and transitive, but dividing is not symmetric, as $n$ divides $m$ does not mean $m$ divides $n$.
3. The function $f : A \to B$ defined by $f(x) = 4x + 7$, $x \in \mathbb{R}$ is
Show Answer
Answer: (a) One-oneExplanation: $f(x) = 4x + 7$ is linear with non-zero slope, hence one-one (injective).
4. The smallest integer function $f(x) = [x]$ is
Show Answer
Answer: (b) Many-oneExplanation: The greatest integer (floor) function assigns the same value to all $x$ in $[n, n+1)$.
5. The function $f : \mathbb{R} \to \mathbb{R}$ defined by $f(x) = 3 – 4x$ is
Show Answer
Answer: (a) OntoExplanation: For any $y \in \mathbb{R}$, $x = \frac{3 – y}{4}$ exists in $\mathbb{R}$ such that $f(x) = y$.
6. Which of these is not a type of relation?
Show Answer
Answer: (b) SurjectiveExplanation: Surjective describes a function’s property, not a relation.
7. An Equivalence Relation is always symmetric.
Show Answer
Answer: (a) TrueExplanation: Equivalence relations are reflexive, symmetric, and transitive.
8. The number of possible relations on a set $A$ with $n$ elements is
Show Answer
Answer: (c) $2^{n^2}$Explanation: Number of relations on $A$ is the number of subsets of $A \times A$, i.e., $2^{n^2}$.
9. The number of bijective functions from a set with 3 elements to itself is
Show Answer
Answer: (b) 6Explanation: Number of bijections = $3! = 6$.
10. Which of the following is a function?
Show Answer
Answer: (b) $\{(1,2), (2,3), (3,4)\}$Explanation: Each element from the domain must have exactly one image. Only option (b) satisfies this.
11. Let $f : A \to B$ and $g : B \to C$ be invertible functions. Then $(g \circ f)^{-1}$ equals
Show Answer
Answer: (b) $g^{-1} \circ f^{-1}$Explanation: The inverse of the composition is the composition of the inverses in reverse, i.e., $(g \circ f)^{-1} = f^{-1} \circ g^{-1}$.
12. Let $A = \{1,2,3\}$ and
Show Answer
Answer: (a) ReflexiveExplanation: All $(a, a)$ for $a \in A$ are present, but $R$ is not symmetric.
13. Let $f(x) = x^2$. Which of the following is true?
Show Answer
Answer: (c) $f$ is neither one-one nor ontoExplanation: $f:\mathbb{R} \to \mathbb{R}$, $f(x) = x^2$ is not one-one ($f(2)=f(-2)$), nor onto (negatives not obtained).
14. If $f: X \to Y$ and $g: Y \to Z$ are functions, what is the domain of $g \circ f$?
Show Answer
Answer: (a) $X$Explanation: The composition $g \circ f$ is defined on the domain of $f$.
15. If $f: \mathbb{R} \to \mathbb{R}$ is defined as $f(x) = |x|$, then the function is
Show Answer
Answer: (b) Many-oneExplanation: $f(1) = f(-1) = 1$, so it is many-one; not onto since negatives are not possible as outputs.
We hope the given mcq questions with Answers for Relations and Functions Class 12 helps you in your learning.
🚀 Boost Your Exam Prep: Get MCQ Questions for all subjects (Class 6-12) now!
👉 Explore more resources on CBSE Class 12
Also check
- Inverse Trigonometric Functions – Class 12 Maths Chapter 2 MCQ Questions with Answers (Updated)
- Relations and Functions – Class 12 Maths Chapter 1 MCQ Questions with Answers (Updated)
Topics from which mcq questions may be asked
- Types of relations
- Types of functions
- Composition and inverse
Functions and relations describe the core structure of mathematical logic.
Frequently Asked Questions (FAQs) on Relations and Functions MCQ Questions
Q1: What types of questions are most commonly asked in MCQs for Relations and Functions?
A1: The most common types include proving whether a relation is an equivalence relation, identifying types of relations (reflexive, symmetric, transitive), checking if a function is one-one (injective), onto (surjective), or bijective, and questions about domain, range, and the composition/inverse of functions
Q2: What concepts from Relations and Functions must I master for scoring well in MCQs?
A2: Key concepts include the definitions and properties of relations and functions, types of relations (reflexive, symmetric, transitive, equivalence), types of functions (one-one, many-one, onto, into, bijective), composition and inverse of functions, binary operations, and solving problems on domain and range
Q3: How are marks typically distributed for questions from Chapter 1 in the CBSE Class 12 Maths exam?
A3: Usually, there are a mix of 1-mark questions (definitions or identification), 2-3 mark questions (verifying properties, computing domains/ranges), and 4-5 mark HOTS/application-based or proof questions, as per the latest CBSE marking scheme
Q4: What are the common mistakes students make while solving MCQs on Relations and Functions?
A4: Frequent errors include misidentifying the type of relation/function without formal proof, ignoring all cases for domain and range, misunderstanding onto (surjective) functions, and overlooking properties like composition and inverse
Q5: Why is practising MCQs important for Chapter 1 of Class 12 Maths, and what are the best resources?
A5: Practising MCQs builds conceptual clarity, improves speed and accuracy, and prepares students for the format of the CBSE exam, which increasingly emphasizes objective-type questions. Recommended resources include chapter-wise MCQ compilations and explanations from leading educational platforms such as Physics Gurukul, EbookPublisher, and Xam Content.
