CBSE Maths › Class 12 PYQs › Relations and Functions

Relations and Functions: 1 mark Questions (CBSE Class 12)

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

1 mark (5)2 marks (3)3 marks (2)4 marks (1)5 marks (5)

Q11 markMCQRelations and Functions CBSE 2026 · 65/2/1

A relation R on set $A = {1, 2, 3}$ defined as $R = {(1, 1), (2, 2), (1, 2)}$ is

(A)Reflexive only
(B)Reflexive and Transitive
(C)Symmetric and Transitive
(D)Transitive only

Show answer & solution

Answer: (D) Transitive only

$(3, 3) \in / R$ , so R is not reflexive.
$(1, 2) \in R$ but $(2, 1) \in / R$ , so R is not symmetric.
The only pairs that chain are $(1, 1), (1, 2)$ giving $(1, 2) \in R$ and $(1, 2), (2, 2)$ giving $(1, 2) \in R$ , so R is transitive.
Hence R is transitive only.

Q121 markMCQRelations and Functions CBSE 2026 · 65/2/2

A relation R on set $A = {1, 2, 3}$ defined as $R = {(1, 2), (2, 1), (2, 2)}$ is

(A)Reflexive only
(B)Reflexive and Transitive
(C)Symmetric and Transitive
(D)Symmetric only

Show answer & solution

Answer: (D) Symmetric only

$(1, 1) \in / R$ , so R is not reflexive.
$(1, 2)$ and $(2, 1)$ both belong to R and $(2, 2)$ is its own reverse, so R is symmetric.
$(1, 2), (2, 1) \in R$ but $(1, 1) \in / R$ , so R is not transitive.
Hence R is symmetric only.

Q51 markMCQRelations and Functions CBSE 2026 · 65/2/3

A relation R on set $A = {1, 2, 3}$ is defined as $R = {(1, 3), (3, 3), (1, 1), (2, 2), (3, 1)}$ is

(A)only reflexive and symmetric
(B)reflexive only
(C)only reflexive and transitive
(D)reflexive, symmetric and transitive

Show answer & solution

Answer: (D) reflexive, symmetric and transitive

$(1, 1), (2, 2), (3, 3) \in R$ : reflexive.
$(1, 3) \in R$ and $(3, 1) \in R$ : symmetric.
$(1, 3), (3, 1) \Rightarrow (1, 1) \in R$ ; $(3, 1), (1, 3) \Rightarrow (3, 3) \in R$ ; all other chains involve a pair $(a, a)$ and give a pair already in R: transitive.
R is reflexive, symmetric and transitive.

Q201 markAssertion–ReasonRelations and Functions CBSE 2026 · 65/4/1

Assertion (A) : A function $f : N \to N$ given by $f (x) = x^{3} + 2, \forall x \in N$ is one-one but not onto.
Reason (R) : Since $\forall y \in N$ (Codomain), there does not exist $x = (y - 2)^{1/3}$ in N (Domain) such that $f (x) = x^{3} + 2 = y$ .

(A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
(B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
(C)Assertion (A) is true, but Reason (R) is false.
(D)Assertion (A) is false, but Reason (R) is true.

Show answer & solution

Answer: (C) Assertion (A) is true, but Reason (R) is false.

$x_{1}^{3} + 2 = x_{2}^{3} + 2 \Rightarrow x_{1} = x_{2}$ , so f is one-one.
$y = 1$ (or 2) has no pre-image in N, so f is not onto. A is true.
R says that for every $y \in N$ no such x exists, which is false: for $y = 3$ , $x = 1 \in N$ .
So A is true but R is false.

Also asked in: 2026 65/4/2, 2026 65/4/3

Q191 markAssertion–ReasonRelations and Functions CBSE 2026 · 65/5/1

Assertion (A): A relation R on the set {1, 2, 3} defined as R = {(1, 1), (1, 2), (2, 1), (2, 2), (3, 3)} is an equivalence relation.
Reason (R): A relation that is reflexive, symmetric and transitive is an equivalence relation.

(A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
(B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
(C)Assertion (A) is true, but Reason (R) is false.
(D)Assertion (A) is false, but Reason (R) is true.

Show answer & solution

Answer: (A) Both A and R are true and R is the correct explanation of A.

Reflexive: (1, 1), (2, 2), (3, 3) are in R.
Symmetric: (1, 2) and (2, 1) are both in R.
Transitive: (1, 2), (2, 1) give (1, 1) in R; (2, 1), (1, 2) give (2, 2) in R; all other cases are trivial.
So R is an equivalence relation; R is the definition of an equivalence relation and explains A.

Also asked in: 2026 65/5/2, 2026 65/5/3

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