Relations and Functions

87 CBSE Class 12 Mathematics past-year questions from 4 papers, 2023 to 2026, with answers and worked solutions.

Difficulty: 20 easy · 42 moderate · 25 hard.
Most-asked subtopics: One-One and Onto Functions (43), Types of Relations (28), Equivalence Relations and Classes (15).
Updated 19 August 2026.

Filter all 87 in the question bank

#1Types of Relations
A school wants the students of class XII to do a project on ‘Sustainability’ keeping the world environment in mind. They select the student participants on the basis of an essay writing competition. 7 students out of 80 are selected for the project and are categorized into two sets such that : Girl students belong to Set $A = \{G_1,\ G_2,\ G_3,\ G_4\}$ , Boy students belong to Set $B = \{B_1,\ B_2,\ B_3\}$ . Based on the above information, answer the following questions :
#2Types of Relations
#3Types of Relations
#4Types of Relations
#5Types of Relations
Done a few? Here’s your next move
- Filter all 87 by year or level
#6Types of Relations
#7Types of Relations
#8Types of Relations
Students of a school are taken to a railway museum to learn about railways heritage and its history. An exhibit in the museum depicted many rail lines on the track near the railway station. Let L be the set of all rail lines on the railway track and R be the relation on L defined by R = $\{(l_1, l_2) : l_1$ is parallel to $l_2\}$ On the basis of the above information, answer the following questions :
#9Types of Relations
Students of a school are taken to a railway museum to learn about railways heritage and its history. An exhibit in the museum depicted many rail lines on the track near the railway station. Let L be the set of all rail lines on the railway track and R be the relation on L defined by R = $\{(l_1, l_2) : l_1$ is parallel to $l_2\}$ On the basis of the above information, answer the following questions :
#10Types of Relations
Students of a school are taken to a railway museum to learn about railways heritage and its history. An exhibit in the museum depicted many rail lines on the track near the railway station. Let L be the set of all rail lines on the railway track and R be the relation on L defined by R = $\{(l_1, l_2) : l_1$ is parallel to $l_2\}$ On the basis of the above information, answer the following questions :
#11Types of Relations
#12Types of Relations
Questions No. 19 & 20, are Assertion (A) and Reason (R) based questions carrying 1 mark each. Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below :
#13Types of Relations
#14Types of Relations
#15Types of Relations
An organization conducted bike race under two different categories – Boys and Girls. There were 28 participants in all. Among all of them, finally three from category 1 and two from category 2 were selected for the final race. Ravi forms two sets B and G with these participants for his college project. Let B = $\{b_1, b_2, b_3\}$ and G = $\{g_1, g_2\}$ , where B represents the set of Boys selected and G the set of Girls selected for the final race. Based on the above information, answer the following questions :
#16Types of Relations
#17Types of Relations
#18Types of Relations
#19Types of Relations
#20Types of Relations
#21Types of Relations
A school is organizing a debate competition with participants as speakers $S = \{S_1, S_2, S_3, S_4\}$ and these are judged by judges $J = \{J_1, J_2, J_3\}$ . Each speaker can be assigned one judge. Let R be a relation from set S to J defined as $R = \{(x, y) : \text{speaker } x \text{ is judged by judge } y,\ x \in S,\ y \in J\}$ . Based on the above, answer the following :
#22Types of Relations
A school is organizing a debate competition with participants as speakers $S = \{S_1, S_2, S_3, S_4\}$ and these are judged by judges $J = \{J_1, J_2, J_3\}$ . Each speaker can be assigned one judge. Let R be a relation from set S to J defined as $R = \{(x, y) : \text{speaker } x \text{ is judged by judge } y,\ x \in S,\ y \in J\}$ . Based on the above, answer the following :
#23Types of Relations
A class-room teacher is keen to assess the learning of her students the concept of "relations" taught to them. She writes the following five relations each defined on the set A = {1, 2, 3} : $R_1 = \{(2, 3), (3, 2)\}$ $R_2 = \{(1, 2), (1, 3), (3, 2)\}$ $R_3 = \{(1, 2), (2, 1), (1, 1)\}$ $R_4 = \{(1, 1), (1, 2), (3, 3), (2, 2)\}$ $R_5 = \{(1, 1), (1, 2), (3, 3), (2, 2), (2, 1), (2, 3), (3, 2)\}$ The students are asked to answer the following questions about the above relations :
#24Types of Relations
A class-room teacher is keen to assess the learning of her students the concept of "relations" taught to them. She writes the following five relations each defined on the set A = {1, 2, 3} : $R_1 = \{(2, 3), (3, 2)\}$ $R_2 = \{(1, 2), (1, 3), (3, 2)\}$ $R_3 = \{(1, 2), (2, 1), (1, 1)\}$ $R_4 = \{(1, 1), (1, 2), (3, 3), (2, 2)\}$ $R_5 = \{(1, 1), (1, 2), (3, 3), (2, 2), (2, 1), (2, 3), (3, 2)\}$ The students are asked to answer the following questions about the above relations :
#25Types of Relations
A class-room teacher is keen to assess the learning of her students the concept of "relations" taught to them. She writes the following five relations each defined on the set A = {1, 2, 3} : $R_1 = \{(2, 3), (3, 2)\}$ $R_2 = \{(1, 2), (1, 3), (3, 2)\}$ $R_3 = \{(1, 2), (2, 1), (1, 1)\}$ $R_4 = \{(1, 1), (1, 2), (3, 3), (2, 2)\}$ $R_5 = \{(1, 1), (1, 2), (3, 3), (2, 2), (2, 1), (2, 3), (3, 2)\}$ The students are asked to answer the following questions about the above relations :
#26Types of Relations
#27Types of Relations
Let A be the set of 30 students of class XII in a school. Let $f : A \to N$ , N is a set of natural numbers such that function $f(x) =$ Roll Number of student x. On the basis of the given information, answer the following :
#28Types of Relations
Let A be the set of 30 students of class XII in a school. Let $f : A \to N$ , N is a set of natural numbers such that function $f(x) =$ Roll Number of student x. On the basis of the given information, answer the following :
#29Equivalence Relations and Classes
Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.
#30Equivalence Relations and Classes
A school wants the students of class XII to do a project on ‘Sustainability’ keeping the world environment in mind. They select the student participants on the basis of an essay writing competition. 7 students out of 80 are selected for the project and are categorized into two sets such that : Girl students belong to Set $A = \{G_1,\ G_2,\ G_3,\ G_4\}$ , Boy students belong to Set $B = \{B_1,\ B_2,\ B_3\}$ . Based on the above information, answer the following questions :
#31Equivalence Relations and Classes
#32Equivalence Relations and Classes
#33Equivalence Relations and Classes
#34Equivalence Relations and Classes
#35Equivalence Relations and Classes
#36Equivalence Relations and Classes
#37Equivalence Relations and Classes
Students of a school are taken to a railway museum to learn about railways heritage and its history. An exhibit in the museum depicted many rail lines on the track near the railway station. Let L be the set of all rail lines on the railway track and R be the relation on L defined by R = $\{(l_1, l_2) : l_1$ is parallel to $l_2\}$ On the basis of the above information, answer the following questions :
#38Equivalence Relations and Classes
#39Equivalence Relations and Classes
#40Equivalence Relations and Classes
An organization conducted bike race under two different categories – Boys and Girls. There were 28 participants in all. Among all of them, finally three from category 1 and two from category 2 were selected for the final race. Ravi forms two sets B and G with these participants for his college project. Let B = $\{b_1, b_2, b_3\}$ and G = $\{g_1, g_2\}$ , where B represents the set of Boys selected and G the set of Girls selected for the final race. Based on the above information, answer the following questions :
#41Equivalence Relations and Classes
#42Equivalence Relations and Classes
A class-room teacher is keen to assess the learning of her students the concept of "relations" taught to them. She writes the following five relations each defined on the set A = {1, 2, 3} : $R_1 = \{(2, 3), (3, 2)\}$ $R_2 = \{(1, 2), (1, 3), (3, 2)\}$ $R_3 = \{(1, 2), (2, 1), (1, 1)\}$ $R_4 = \{(1, 1), (1, 2), (3, 3), (2, 2)\}$ $R_5 = \{(1, 1), (1, 2), (3, 3), (2, 2), (2, 1), (2, 3), (3, 2)\}$ The students are asked to answer the following questions about the above relations :
#43Equivalence Relations and Classes
#44One-One and Onto Functions
#45One-One and Onto Functions
#46One-One and Onto Functions
A school wants the students of class XII to do a project on ‘Sustainability’ keeping the world environment in mind. They select the student participants on the basis of an essay writing competition. 7 students out of 80 are selected for the project and are categorized into two sets such that : Girl students belong to Set $A = \{G_1,\ G_2,\ G_3,\ G_4\}$ , Boy students belong to Set $B = \{B_1,\ B_2,\ B_3\}$ . Based on the above information, answer the following questions :
#47One-One and Onto Functions
A school wants the students of class XII to do a project on ‘Sustainability’ keeping the world environment in mind. They select the student participants on the basis of an essay writing competition. 7 students out of 80 are selected for the project and are categorized into two sets such that : Girl students belong to Set $A = \{G_1,\ G_2,\ G_3,\ G_4\}$ , Boy students belong to Set $B = \{B_1,\ B_2,\ B_3\}$ . Based on the above information, answer the following questions :
#48One-One and Onto Functions
Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.
#49One-One and Onto Functions
#50One-One and Onto Functions

Showing the first 50 of 87.

See all 87 questions

Send them this chapter's questions. It's free for them too.

Relations and Functions

Studying this with friends?

More chapters in this subject