CBSE Maths › Class 12 PYQs › Relations and Functions

Relations and Functions: 2 marks Questions (CBSE Class 12)

3 different 2 marks 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)

Q212 marksVery Short AnswerRelations and Functions CBSE 2026 · 65/2/1

Check whether $f : R - {3} \to R$ defined as $f (x) = \frac{x - 2}{x - 3}$ is onto or not.

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Answer: Not onto (1 has no pre-image).

Let $y = \frac{x - 2}{x - 3}$ . Then $x y - 3 y = x - 2 \Rightarrow x (y - 1) = 3 y - 2 \Rightarrow x = \frac{3 y - 2}{y - 1}$ .
This is not defined for $y = 1$ .
Indeed $\frac{x - 2}{x - 3} = 1$ would need $x - 2 = x - 3$ , which is impossible.
So $1 \in R$ has no pre-image; f is not onto.

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

Q21 (OR) (OR)2 marksVery Short AnswerRelations and Functions CBSE 2026 · 65/2/1

Check whether $f : Z \times Z \to Z \times Z$ (where Z is the set of integers) defined as $f (x, y) = (2 y, 3 x)$ is injective or not.

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Answer: Injective.

Let $f (x_{1}, y_{1}) = f (x_{2}, y_{2})$ .
Then $(2 y_{1}, 3 x_{1}) = (2 y_{2}, 3 x_{2})$ , so $2 y_{1} = 2 y_{2}$ and $3 x_{1} = 3 x_{2}$ .
Hence $y_{1} = y_{2}$ , $x_{1} = x_{2}$ , i.e. $(x_{1}, y_{1}) = (x_{2}, y_{2})$ .
f is injective (one-one).

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

Q23 (OR) (OR)2 marksVery Short AnswerRelations and Functions CBSE 2026 · 65/3/1

A relation R on $A = {1, 2, 3}$ is defined as $R = {(1, 1) (3, 3), (1, 2)}$ . Is R a symmetric relation ? Justify. Write the smallest relation set $R_{1}$ such that $R \cup R_{1}$ becomes an equivalence relation on the set ${1, 2, 3}$ .

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Answer: R is not symmetric;

R_{1} = {(2, 1), (2, 2)}

$(1, 2) \in R$ but $(2, 1) \in / R$ , so R is not symmetric.
For reflexivity we need $(2, 2)$ ; for symmetry we need $(2, 1)$ .
$R \cup {(2, 1), (2, 2)} = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)}$ is reflexive, symmetric and transitive.
So the smallest $R_{1} = {(2, 1), (2, 2)}$ .

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

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