Relations and Functions

CBSE Class 12 · Mathematics · 13 past questions

8 of 13 · show all

1. Q2 2026

   Show that $f : R \to R$ defined as $f(x) = \dfrac{x}{\sqrt{1 + x^2}}$ is one-one but not onto.

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2. Q4 2025

   A class-room teacher is keen to assess the learning of her students the concept of "relations" taught to…

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3. Q5 2025

   For real x, let $f(x) = x^3 + 5x + 1$. Then…

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4. Q6 2025

   If $f:\mathbb{N}\to\mathbb{W}$ is defined as…

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5. Q9 2024

   A relation R on set $A = \{-4, -3, -2, -1, 0, 1, 2, 3, 4\}$ be defined as…

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6. Q10 2024

   Let $f : R_+ \to [-5, \infty)$ be defined as $f(x) = 9x^2 + 6x - 5$, where $R_+$ is the set of all…

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7. Q12 2023

   A relation R is defined on a set of real numbers $\mathbb{R}$ as…

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8. Q13 2023

   A function $f: [-4, 4] \to [0, 4]$ is given by $f(x) = \sqrt{16 - x^2}$. Show that f is an onto function but…

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