Class 12 Mathematics Chapter 1 Relations and Functions MCQ

NCERT MCQ Solutions for Class 12 Mathematics Chapter 1 Relations and Functions serve as the foundation for understanding advanced mathematical concepts in set theory and algebraic structures. NCERT Detailed MCQ Solutions for Class 12 Maths Multiple Choice Questions (MCQs) provide a comprehensive resource with step-by-step derivations and detailed explanations for all exercises. MCQ solutions help students master concepts, improve problem-solving skills and prepare effectively for MCQ based assessments in board exams and competitive tests. NCERT Chapter 1 MCQ PDF ensures a structured approach to Relations and Functions, enhancing conceptual clarity and application.
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Class 12 Mathematics Chapter 1 Relations and Functions MCQ

Chapter 1 of Class 12 Mathematics, Relations and Functions, builds upon the fundamental concepts introduced in Class 11. The chapter begins by defining relations, which are connections between elements of two sets. It introduces different types of relations, such as empty relations, universal relations, reflexive, symmetric, transitive and equivalence relations. Functions, which are a special type of relation where each input has exactly one output, are also explored in detail. The chapter lays the foundation for understanding more advanced mathematical structures and their applications in calculus, algebra and real-world problem-solving.

Q1. Which of the following statements best describes the study of relations and functions in Class 12 Maths?

[A]. Relations connect elements of two sets and include functions, a special type of relation.

[B]. Relations are only defined for number sets, while functions are applicable to all mathematical operations.

[C]. Relations and functions have no connection to calculus or algebra.

[D]. Functions always have multiple outputs for a given input.

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Q2. A relation R is defined on N. Which of the following is the reflexive relation?

[A]. R = [(x, y) : x > y, x, y ∈ N]

[B]. R = [(x, y) : x + y = 10, x, y ∈ N]

[C]. R = [(x, y) : xy is the square number, x, y ∈ N]

[D]. R = [(x, y) : x + 4y = 10, x, y ∈ N]

Q3. The function f : R → R defined by f(x) = 4 + 3 cos x is

[A]. bijective

[B]. one-one but not onto

[C]. onto but not one-one

[D]. neither one-one nor onto

Types of Relations and their Properties in 12th Maths Chapter 1

A relation in a set is essentially a subset of the Cartesian product of the set with itself. The chapter introduces reflexive relations (where every element is related to itself), symmetric relations (where if 𝑎 is related to 𝑏, then 𝑏 is related to 𝑎) and transitive relations (if 𝑎 is related to 𝑏 and 𝑏 is related to 𝑐, then 𝑎 is related to 𝑐). A relation that satisfies all three properties is called an equivalence relation. Examples and practice problems in the chapter help students understand how to verify these properties using set theory and logic.

Q4. A relation R in a set A is called an equivalence relation if it satisfies which of the following properties?

[A]. Reflexive and symmetric only.

[B]. Symmetric and transitive only.

[C]. Reflexive, symmetric, and transitive.

[D]. None of the above.

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Q5. Let f : R → R be defined by f(x) = 1/x, for all x ∈ R. Then, f is

[A]. onto

[B]. one-one

[C]. bijective

[D]. not defined

Q6. A relation R is defined on Z as: aRb if and only if a² – 7ab + 6b² = 0, then, R is

[A]. reflexive and symmetric

[B]. transitive but not reflexive

[C]. symmetric but not reflexive

[D]. reflexive but not symmetric

Functions: One-One, Onto and Bijective

Functions are explored in depth, particularly one-one (injective) functions, where no two distinct inputs map to the same output, and onto (surjective) functions, where every element in the co-domain is mapped by at least one element in the domain. A function that is both injective and surjective is called a bijective function. The chapter also introduces the concept of an inverse function, which exists only for bijective functions. Understanding these concepts is essential for calculus, where functions play a critical role in differentiation and integration.

Q7. Which of the following statements is true about one-one and onto functions?

[A]. A one-one function ensures that each element of the co-domain has at least one pre-image.

[B]. An onto function ensures that each element of the domain maps to a unique element in the co-domain.

[C]. A function that is both one-one and onto is called bijective.

[D]. An onto function must always be one-one.

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Q8. Let the relation R in the set A = {x ∈ Z : 0 ≤ x ≤ 12}, given by R = {(a, b) : |a – b| is a multiple of 4}. Then [1], the equivalence class containing 1, is:

[A]. {1, 5, 9}

[B]. A

[C]. ϕ

[D]. {0, 1, 2, 5}

Q9. The function f R → R defined as f(x) = x³ is:

[A]. Neither one-one nor onto

[B]. One-one but not onto

[C]. Not one-one but onto

[D]. One-one and onto

Composition and Invertible Functions

The composition of functions is introduced as a method of combining two functions where the output of one function serves as the input of another. The notation 𝑔(𝑓(𝑥)), represents the composition of 𝑓 and 𝑔. The chapter also explains invertible functions, where a function has an inverse if and only if it is bijective. The process of finding the inverse of a function is explained through examples, illustrating how algebraic manipulation is used to determine the inverse function.

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Q10. For two functions 𝑓:X→Y and 𝑔:Y→Z, the composition g(f(x)) is defined as:

[A]. A function that applies g first and then 𝑓.

[B]. A function that applies 𝑓 first and then 𝑔.

[C]. A function that works only when f and 𝑔 are both one-one.

[D]. A function that is always non-invertible.

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Q11. Let R be the relation in the set N given by R = {(a, b) : a = b – 2, b – 2, b > 6}, then

[A]. (2, 4) ∈ R

[B]. (6, 8) ∈ R

[C]. (8,7) ∈ R

[D]. (3, 8) ∈ R

Q12. Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a function from A to B. Based on the given information, f is best defined as:

[A]. Surjective function

[B]. Injective function

[C]. Bijective function

[D]. None of these.

12th Maths Exam Preparation Strategies

To excel in Chapter 1 during exams, students should focus on thoroughly understanding definitions and properties of relations and functions. Solving NCERT examples and exercises is crucial. Practicing proof-based questions on reflexivity, symmetry and transitivity will strengthen conceptual clarity. For functions, mastering injective, surjective and bijective properties with examples is key. Students should also practice composition and inverse functions extensively, as these topics frequently appear in board exams. Using flowcharts or diagrams to understand function mappings can help in visualizing concepts more effectively. Regular revision and solving previous year’s questions will boost confidence and accuracy.

Q13. Which of the following is the most effective way to prepare for MCQs in Class 12 Maths Chapter 1?

[A]. Memorizing all function definitions without solving problems.

[B]. Understanding concepts, practicing proof-based questions, and solving previous year’s MCQs.

[C]. Skipping inverse function problems as they are rarely asked in exams.

[D]. Focusing only on definitions without checking function properties.

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Q14. Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set A = {1, 2, 3, 4}. Then relation R is

[A]. not symmetric

[B]. an odd function

[C]. transitive

[D]. reflexive

Q15. If a set A contains 5 elements and the set B contains 6 elements, then the number of one-one and onto mappings from A to B is

[A]. 120

[B]. 720

[C]. 0

[D]. none of these

What are the key concepts covered in Class 12 Maths Chapter 1 MCQs?

Class 12 Maths Chapter 1, Relations and Functions, focuses on fundamental concepts such as different types of relations (reflexive, symmetric, transitive and equivalence relations), types of functions (one-one, onto and bijective), composition of functions and invertible functions. MCQs in 12th Math chapter 1 test students’ understanding of these concepts through logical reasoning and problem-solving. To answer MCQs correctly, students must be clear about definitions, properties and problem-solving techniques. Questions require quick identification of function types, verifying relation properties and determining function compositions.

How can I quickly determine whether a function is one-one and onto in an MCQ?

To check if a function is one-one (injective) in an MCQ, verify whether different inputs produce different outputs. To check if a function is onto (surjective), see if every element in the co-domain has a corresponding pre-image in the domain. If some elements in the co-domain are missing outputs, the function is not onto. A function is bijective if it is both one-one and onto. Many MCQs provide function definitions and ask whether they satisfy these conditions.

What is the best approach to solving MCQs on equivalence relations?

Equivalence relations satisfy three properties: reflexivity, symmetry and transitivity. In an MCQ, you can quickly test these by checking if every element relates to itself (reflexivity), whether swapping elements maintains the relation (symmetry) and whether indirect relationships hold true (transitivity). If all three conditions are met, the relation is equivalence. If any condition fails, the relation is not equivalence. Practicing examples involving sets of numbers and algebraic expressions can help in answering these MCQs efficiently.

How to solve MCQs on composition of functions efficiently?

MCQs on composition of functions typically require evaluating expressions like g(f(x)). The best approach is to first solve for f(x), then substitute the result into g(x). If functions are given in table form, trace the mapping carefully. For inverse functions, remember that (f(x)) = x. Many MCQs also test whether composition is commutative (i.e., whether g(f(x)) = f(g(x))), which is not always true. Practicing different function compositions will help improve speed and accuracy in such questions.

What are some common mistakes students make while solving MCQs in 12th Maths chapter 1?

One common mistake is misidentifying function properties—students often confuse one-one with onto functions. Another error is not checking all properties for equivalence relations properly. In composition MCQs, students sometimes substitute incorrectly, leading to wrong answers. Calculation mistakes in determining inverse functions also occur frequently. To avoid these, students should carefully read questions, break them into steps and use logic instead of blindly memorizing formulas. Practicing previous years’ MCQs and mock tests can help in recognizing tricky patterns and improving accuracy.

NCERT MCQ Solutions for Class 12 Maths Chapter 1 Relations and Functions