Relations and Functions 4 marks Questions, CBSE Class 12 PYQs 2026

1 different 4 marks questions on Relations and Functions from CBSE Class 12 Maths board exams 2026, newest first.

Q364 marksCase StudyRelations and Functions CBSE 2026 · 65/5/1

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 :
(i) How many relations are possible from Set A $\to$ Set B ? (1)
(ii) Let R be a relation from A $\to$ B such that R = ${(G_{1}, B_{1}), (G_{2}, B_{2}), (G_{3}, B_{2}), (G_{4}, B_{3}), (G_{1}, B_{2})}$ . Is R an injective function ? Justify your answer. (1)
(iii) (a) Let the relation R from A $\to$ A be such that R = {(x, y), x, y $\in$ A, x and y are students from the same colony in the city} Verify if R is an equivalence relation. (2)
OR (iii) (b) Verify if any function f : B $\to$ A is bijective. Give reason to support your answer. (2)

Show answer & solution

Answer: (i)

2^{12} = 4096

(ii) No, R is not a function (

G_{1}

has two images), so it is not an injective function. (iii) (a) Yes, R is an equivalence relation. OR (iii) (b) No; since n(B) = 3 < n(A) = 4, no function from B to A can be onto, so none is bijective.

(i) $n (A \times B) = 4 \times 3 = 12$ , so the number of relations is $2^{12} = 4096$ .
(ii) $G_{1}$ is related to both $B_{1}$ and $B_{2}$ , so R is not a function and hence not an injective function.
(iii) (a) Reflexive: every student is from the same colony as himself/herself. Symmetric: if x and y are from the same colony, so are y and x. Transitive: if x, y and y, z are from the same colony, then x, z are too. So R is an equivalence relation.
(iii) (b) B has 3 elements and A has 4, so a function f : B → A has at most 3 images and cannot be onto; hence no such f is bijective.

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Relations and Functions: 4 marks Questions (CBSE Class 12)