CBSE Maths › Class 12 PYQs › Relations and Functions

Relations and Functions: 3 marks Questions (CBSE Class 12)

2 different 3 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)

Q263 marksShort AnswerRelations and Functions CBSE 2026 · 65/4/1

Let $A = R - {3}$ and $B = R - {1}$ . A function $f : A \to B$ is defined by $f (x) = (\frac{x - 2}{x - 3})$ . Find whether f is one-one and onto.

Show answer & solution

Answer: f is one-one and onto.

One-one: $\frac{x _{1} - 2}{x _{1} - 3} = \frac{x _{2} - 2}{x _{2} - 3} \Rightarrow (x_{1} - 2) (x_{2} - 3) = (x_{2} - 2) (x_{1} - 3)$ .
$\Rightarrow - 3 x_{1} - 2 x_{2} = - 3 x_{2} - 2 x_{1} \Rightarrow x_{1} = x_{2}$ . So f is one-one.
Onto: for $y \in B$ , solve $y = \frac{x - 2}{x - 3}$ : $x = \frac{3 y - 2}{y - 1}$ , defined since $y \neq = 1$ .
$x \neq = 3$ (else $3 y - 2 = 3 y - 3$ , impossible), so $x \in A$ and $f (x) = y$ .
Hence f is onto; f is one-one and onto.

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

Q26 (OR) (OR)3 marksShort AnswerRelations and Functions CBSE 2026 · 65/4/1

Let n be a fixed positive integer. A relation R is defined in set Z such that $R = {(x, y) : (x - y)$ is divisible by $n, x, y \in Z}$ . Determine if R is an equivalence relation.

Show answer & solution

Answer: Yes, R is an equivalence relation.

Reflexive: $x - x = 0 = 0 \cdot n$ , so $(x, x) \in R$ for all $x \in Z$ .
Symmetric: if $x - y = k n$ then $y - x = (- k) n$ , so $(y, x) \in R$ .
Transitive: if $x - y = k n$ and $y - z = mn$ then $x - z = (k + m) n$ , so $(x, z) \in R$ .
Hence R is an equivalence relation.

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

Inverse Trigonometric Functions →

Practise smarter: chapter-wise revision, formula sheets and step-by-step NCERT solutions on MonoMath CBSE →