Relations and Functions

CBSE Class 12 · Mathematics · 13 past questions

1. Q1 2026

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

   Try it →
2. Q2 2026

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

   Try it →
3. Q3 2025

   Direction : Question numbers 19 and 20 are Assertion (A) and Reason (R) based questions carrying 1 mark each.…

   Try it →
4. Q4 2025

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

   Try it →
5. Q5 2025

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

   Try it →
6. Q6 2025

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

   Try it →
7. Q7 2024

   A function f : R_+ → R (where R_+ is the set of all non-negative real numbers) defined by f(x) = 4x + 3 is…

   Try it →
8. Q8 2024

   Let $R_+$ denote the set of all non-negative real numbers. Then the function $f : R_+ \to R_+$ defined as…

   Try it →
9. Q9 2024

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

   Try it →
10. Q10 2024

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

    Try it →
11. Q11 2023

    A function $f : A \to B$ defined as $f(x) = 2x$ is both one-one and onto. If $A = \{1, 2, 3, 4\}$, then find…

    Try it →
12. Q12 2023

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

    Try it →
13. 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…

    Try it →