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Mathematics · 2025 · 4 marks
CBSE 2025 · Region 5 · Set 1 · Q37
Let A be the set of 30 students of class XII in a school. Let f: A → N, N is a set of natural numbers such that function f ( x )= Roll Number of…
Let $\displaystyle A$ be the set of $\displaystyle 30$ students of class XII in a school. Let $\displaystyle \mathrm{f}: A \rightarrow N, N$ is a set of natural numbers such that function $\displaystyle \mathrm{f}(\mathrm{x})=$ Roll Number of student x . On the basis of the given information, answer the following :
(i)
Is f a bijective function?
(ii)
Give reasons to support your answer to (i).
(iii)
Let $\displaystyle \mathrm{R}$ be a relation defined by the teacher to plan the seating arrangement of students in pairs, where $\displaystyle \mathrm{R}=\{(\mathrm{x}, \mathrm{y}): \mathrm{x}, \mathrm{y}$ are Roll Numbers of students such that $\displaystyle \mathrm{y}=3 \mathrm{x}\}$. List the elements of $\displaystyle \mathrm{R}$. Is the relation $\displaystyle \mathrm{R}$ reflexive, symmetric and transitive ? Justify your answer.
Let R be a relation defined by $\displaystyle \mathrm{R}=\left\{(\mathrm{x}, \mathrm{y}): \mathrm{x}, \mathrm{y}\right.$ are Roll Numbers of students such that $\displaystyle \left.\mathrm{y}=\mathrm{x}^{3}\right\}$. List the elements of $\displaystyle \mathrm{R}$. Is $\displaystyle \mathrm{R}$ a function? Justify your answer. Case Study - $\displaystyle 3$
Marking-scheme solution
(i)
No, f is not bijective function
(ii)
Range $\displaystyle =\{1,2,3,4, \ldots \ldots \ldots \ldots \ldots, 30\}$ and codomain $\displaystyle =N$
Since, Range $\displaystyle \neq$ codomain $\displaystyle \Rightarrow \mathbf{f}$ is not onto and hence $\displaystyle \mathbf{f}$ is not bijective.
(iii)
$\displaystyle \mathrm{R}=\{(1,3),(2,6),(3,9),(4,12),(5,15),(6,18),(7,21),(8,24),(9,27),(10,30)\}$
Since $\displaystyle (1,1) \notin \mathrm{R} \Rightarrow \mathbf{R}$ is not reflexive.
$\displaystyle (1,3) \in \mathrm{R}$ but $\displaystyle (3,1) \notin \mathrm{R} \Longrightarrow \mathrm{R}$ is not symmetric $\displaystyle (1,3) \in \mathrm{R},(3,9) \in \mathrm{R}$ but $\displaystyle (1,9) \notin \mathrm{R} \Rightarrow \mathrm{R}$ is not transitive.
$\displaystyle \mathrm{R}=\{(1,1),(2,8),(3,27)\}$
∵ elements $\displaystyle 4$, $\displaystyle 5$, $\displaystyle 6 \ldots 30$ do not have an image. Hence the above relation is not a function.
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CBSE Class 12 Mathematics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.