Relations And Functions XII — JEE Advanced PYQs

12 previous year questions on Relations And Functions XII (Mathematics), newest first. Open any question for its complete step-by-step solution.

Let $S = {1, 2, 3, \dots, 10}$ . Consider the set
$X = {R : R$ is an equivalence relation on the set S such that R has exactly 42 elements $}$ .
Then the number of elements in X is ____.
JEE Advanced 2026View solution →
Let $N$ denote the set of all positive integers. Consider the sets
$A = {1, 2, 3, 4, 5} and B = {1, 2, 3, 4, 5, 6, 7} .$

Let S be the set of all functions $f : A \to B$ such that $f (2) \neq = 2$ and $f (4) \neq = 4$ . Consider the s …
JEE Advanced 2026View solution →
Let $N$ denote the set of all natural numbers, and $Z$ denote the set of all integers. Consider the functions $f : N \to Z$ and $g : Z \to N$ defined by …
JEE Advanced 2025View solution →
Let $f : R \to R$ be a function such that $f (x + y) = f (x) + f (y)$ for all $x, y \in R$ , and $g : R \to (0, \infty)$ be a function such that $g (x + y) = g (x) g (y)$ for all $x, y \in R$ . If $f (\frac{- 3}{5}) = 12$ and …
JEE Advanced 2024View solution →
Let $S = (0, 1) \cup (1, 2) \cup (3, 4)$ and $T = {0, 1, 2, 3}$ . Then which of the following statements is(are) true ?
JEE Advanced 2023View solution →
Let the function $f : [0, 1] \to R$ be defined by $f (x) = \frac{4 ^{x}}{4 ^{x} + 2}$
Then the value of $f (\frac{1}{40}) + f (\frac{2}{40}) + f (\frac{3}{40}) + \dots + f (\frac{39}{40}) - f (\frac{1}{2})$ is ____
JEE Advanced 2020View solution →
Let $f (x) = sin (\frac{π}{6} sin (\frac{π}{2} sin x))$ for all $x \in R$ and $g (x) = \frac{π}{2} sin x$ for all $x \in R$ . Let $(f \circ g) (x)$ denote $f (g (x))$ and $(g \circ f) (x)$ denote $g (f (x))$ . Then which of the following is (ar …
JEE Advanced 2015View solution →
Let $f : (- \frac{π}{2}, \frac{π}{2}) \to R$ be given by
$f (x) = (lo g (sec x + tan x))^{3} .$

Then
JEE Advanced 2014View solution →
Let $f (x) = x^{2}$ and $g (x) = sin x$ for all $x \in R$ . Then the set of all $x$ satisfying $(f \circ g \circ g \circ f) (x) = (g \circ g \circ f) (x)$ , where $(f \circ g) (x) = f (g (x))$ , is
JEE Advanced 2011View solution →
Let $f$ be a real-valued function defined on the interval $(- 1, 1)$ such that $e^{- x} f (x) = 2 + \int_{0}^{x} t^{4} + 1 dt$ , for all $x \in (- 1, 1)$ , and let $f^{- 1}$ be the inverse function …
JEE Advanced 2010View solution →
If the function $f (x) = x^{3} + e^{\frac{x}{2}}$ and $g (x) = f^{- 1} (x)$ , then the value of $g^{'} (1)$ is
JEE Advanced 2009View solution →
Let $g (x) = lo g f (x)$ where $f (x)$ is a twice differentiable positive function on $(0, \infty)$ such that $f (x + 1) = x f (x)$ . Then, for $N = 1, 2, 3 \dots$ ,
$g^{''} (N + \frac{1}{2}) - g^{''} (\frac{1}{2}) =$
JEE Advanced 2008View solution →