In NCERT Class 12 Mathematics Chapter 1, titled Relations and Functions, students are introduced to the fundamental concepts of relations and functions. The chapter explores various types of relations, including reflexive, symmetric, and transitive relations. It also covers the important concept of functions, including one-to-one, onto, and bijective functions. The concepts of domain, co-domain, and range are explained in depth. Additionally, students learn how to work with the composition and inverse of functions, which are essential topics in higher mathematics.
This article provides a comprehensive resource for exam preparation. It includes sample MCQs and subjective questions for CBSE and CUET, alongside downloadable PDFs of Class 12 Mathematics Chapter 1 MCQs and previous year questions for detailed practice of NCERT Class 12 Relations and Functions.
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NCERT Class 12 Mathematics Chapters
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Class 12 Mathematics Chapter 1 MCQs
This question bank includes previous years' CUET and CBSE MCQs, along with questions curated by subject experts. Below are 5 sample multiple-choice questions (MCQs) for Class 12 Mathematics Chapter 1: Relations and Functions. For the full set of 50 questions, download the PDF using the link provided below.
1. If the domain of function f(x) = x2 – 6x + 7 is (–∞,∞), then the range of function is
A) (–∞,∞) B) [–2, ∞) C) ( –2, 3) D) (–∞,–2)
2. Let A = {x : -1 ≤ x ≤ 1} and f : A → A is a function defined by f(x) = x |x| then f is
A) a bijection B) injection but not surjection
C) surjection but not injection D) neither injection nor surjection
3. The domain of the function
is
A) [–4, ∞) B) [- 4,4] C) [0, 4] D) [0, 1]
4. Let A = {1, 2, 3, 4, 5, 6} and B = {p, q, r, s}.Then number of one-one functions from A to B are
A) 0 B) 2 C) 24 D) 6
5. Let S be the set of all real numbers and R be the relation in set S defined by aRb ⇔ a2 + b2 = 5 then R is
A) only reflexive B) only transitive C) only symmetric D) equivalence
CUET Free Master Classes:
Class 12 Mathematics Chapter 1 Subjective Questions Without Solutions
This question bank includes previous years' CBSE subjective questions (2 marks and above) without solutions, along with expert-curated questions. Below are 5 sample subjective questions for Class 12 Mathematics Chapter 1: Relations and Functions. To access all questions, download the PDF from the link provided below.
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1.
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Check if the relation R in the set of real numbers defined as R = {(a, b): a < b} is (i) symmetric,
(ii) transitive
(CBSE 2020, 2M)
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2.
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Check if the relation R on the set A = { 1, 2, 3, 4, 5, 6 } defined as R = { (x, y): y is divisible by x} is (i) symmetric (ii) transitive.
(CBSE 2020, 2M)
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Let N be the set of natural numbers and R be the relation on N × N defined by (a, b) R (c, d) iff ad = bc for all a, b, c, d ∈ N. Show that R is an equivalence relation.
(CBSE 2020, 4M)
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4.
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Check whether the relation R in the set N of natural numbers given by R = {(a, b): a is divisor of b} is reflexive, symmetric or transitive. Also determine whether R is an equivalence relation.
(CBSE 2020, 4M)
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5.
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Show that the relation R in the set A = {1, 2, 3, 4, 5, 6} given by R = {(a, b): |a – b| is divisible by 2} is an equivalence relation.
(CBSE 2020, 4M)
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NCERT Mathematics Topics
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Chapter Name
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Sub Topics
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Chapter 1: Relations and Functions
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1.1 Introduction
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1.2 Relations
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1.3 Types of Relations
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1.4 Functions
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1.5 Domain, Co-domain, and Range
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1.6 Types of Functions
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1.7 One-to-One, Onto, and Bijective Functions
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1.8 Composition of Functions
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1.9 Inverse of a Function
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Review of NCERT Class 12 Mathematics Chapter 1
NCERT Class 12 Mathematics Chapter 1, Relations and Functions, introduces the basic concepts that lay the foundation for more advanced studies in mathematics. The chapter explores relations and their types, including equivalence relations and partial orders, as well as functions, including injective, surjective, and bijective functions. These concepts are crucial for solving complex problems in algebra and calculus.
Mastering this chapter is essential for a deeper understanding of the mathematical structure and its real-world applications. By practicing the concepts of relations and functions, students will be better prepared for exams like CBSE, CUET, and other competitive exams.
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