CBSE Class 12th Mathematics Chapter 1 - Relations and Functions Important Questions with Answers

You should focus on solving CBSE Class 12th Mathematics Chapter 1: Relations and Functions important questions, especially to help you score high marks. By solving CBSE Class 12th Mathematics 1 questions, you will be solving exam-oriented questions only.

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CBSE Class 12th Mathematics Chapter 1 - Relations and Functions Important Questions with Answers are provided here to help you score more marks. The CBSE Class 12 Mathematics exam 2025 has been scheduled on March 8, 2025. Before appearing for the exam, it is advisable for you to check out all the below mentioned important questions from Chapter 1 of CBSE Board 12th Math syllabus 2025. Relations and Functions in mathematics is a concept that refer to the relationship between elements of two sets, wherein a "relation" simply indicates a set of ordered pairs defining the connection between two sets, while a "function" is a special type of relation where each element of a domain is associated with exactly a single element in the codomain. This chapter is essentially about mapping inputs to outputs with a defined rule, where a function ensures each input has only one unique output. A relation may or may not be a function, however, functions are always relations.

There are a total of six units in the CBSE Class 12 Math syllabus 2024-25. In CBSE 12th Math, the theory exam is going to be conducted for 80 marks, and the remaining 20 marks will be evaluated on project. The syllabus is devoid of chapter-wise division of marks. Instead, the weightage is given based on the competencies which the questions from the chapters would evaluate. Relations and Functions is the first chapter in CBSE Class 12 Board Math syllabus 2025 which will carry 8 marks in total. Prepare thoroughly with the most important questions of CBSE Class 12th Mathematics Chapter 1 - Relations and Functions. You can first cover the CBSE Class 12th Mathematics syllabus to understand the key topics and then start solving the CBSE Class 12th Mathematics Chapter 1 - Relations and Functions Important Question to get a better understanding of your preparation level. Start practicing now.

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Check whether the relation R defined on the set A = {1, 2, 3, 4, 5, 6} as R = {(a, b): b = a + 1} is reflexive, symmetric or transitive. (All India 2019)

Question 2.

Let f : N ? Y be a function defined as f(x) = 4x + 3, where, Y = {y ? N : y = 4x + 3, for some x ? N}. Show that f is invertible. Find its inverse. (All India 2019)

Question 3.

Show that the relation R on IR defined as R = {(a, b) : (a ? b)}, is reflexive and transitive but not symmetric. (Delhi 2019)

Question 4.

Prove that the function, f : N ? N is defined by f(x) = x² + x + 1 is one-one but not onto. Find inverse of f : N ? S, where S is range of f. (Delhi 2019)

Question 5.

Let A = {x ? Z: 0 ? x ? 12}. Show that R = {(a, b): a, b ? A, |a – b| is divisible by 4} is an equivalence relation. Find the set of all elements related to 1. Also, write the equivalence class [2]. (CBSE 2018)

Question 6.

Show that the function f: R ? R defined by f(x) = \(\frac{x}{x^{2}+1}\), ? x ? R is neither one-one nor onto. Also, if g: R ? R is defined as g(x) = 2x – 1, find fog (x). (CBSE 2018)

Question 7.

Show that the relation R on the set Z of all integers defined by (x, y) ? R ? (x – y) is divisible by 3 is an equivalence relation. (CBSE 2018C)

Question 8.

Consider f: R⁺ ? [-5, ?) given by f(x) = 9x² + 6x – 5. Show that f is invertible with f^-1(y) = \(\left(\frac{\sqrt{y+6}-1}{3}\right)\). Hence find
(i) f^-1(10)
(ii) y if ^-1(y) = \(\frac{4}{3}\)
where R⁺ is the set of all non-negative real numbers. (Delhi 2017; Foreign 2010)

Question 9.

Consider f : R – \(\left\{-\frac{4}{3}\right\}\) ? R – \(\left\{\frac{4}{3}\right\}\) given by f(x) = \(\frac{4 x+3}{3 x+4}\). Show that f is bijective. Find the inverse of f and hence find f^-1(0) and x such that f^-1(x) = 2. (All India 2017)

Question 10.

Let f: N ? N be a function defined as f(x) – 9x² + 6% – 5. Show that f: N ? S, where S is the range of f, is invertible. Find the inverse of f and hence find f^-1(43) and f^-1(-3). (Delhi 2016)

Question 1.

If f, g: R ? R be two functions defined as f(x)= |x| + x and g(x)= |x| – x, ? x ? R. Then, find fog and gof. Hence find fog (-3), fog{ 5) and gof(-2). (Foreign 2016)

Question 2.

If N denotes the set of all natural numbers and R be the relation on N × N defined by (a, b) R (c, d), if ad(b + c) = bc(a + d). Show that R is an equivalence relation. (Delhi 2015)

Question 3.

Consider f: R⁺ ? [-9, ?) given by f(x) = 5x² + 6x – 9. Prove that f is invertible with f^-1(y) = \(\left(\frac{\sqrt{54+5 y}-3}{5}\right)\) [where, R⁺ is the set of all non-negative real numbers.] (All India 2015)

Question 4.

Let f: N ? R be a function defined as f(x) = 4x² + 12x + 15.Show that f:N ? S, where S is the range of f, is invertible. Also, find the inverse of f. (Foreign 2015)

Question 5.

Show that the relation R in the set A = {1, 2, 3, 4, 5} given by R = {(a, b): |a – b| is divisible by 2}, is an equivalence relation. Write all the equivalence classes of R. (All India 2015C)

Question 6.

If R = {(a, a³): a is a prime number less than 5} be a relation. Find the range of R . (Foreign 2014)

Question 7.

If f: {1,3, 4} ? {1, 2, 5} and g: {1,2, 5} ? {1, 3} given by f = {(1,2), (3, 5), (4,1)} and g = {(1,3), (2, 3), (5,1)}. Write down gof. (All India 2014C)

Question 8.

Let R is the equivalence relation in the set A = {0,1, 2, 3, 4, 5} given by R = {(a, b) : 2 divides (a – b)}. Write the equivalence class [0]. (Delhi 2014C)

Question 9.

If R = {(x, y): x + 2y = 8} is a relation on N, then write the range of R. (All India 2014)

Question 10.

If f: W ? W is defined as f(x) = x – 1, if x is odd and f(x) = x + 1, if x is even. Show that f is invertible. Find the inverse of f, where W is the set of all whole numbers. (Foreign 2014; All India 2011C)