JEE Main 2024 (Online) 9th April Evening ShiftQuestion 1
Let $A=\{(x,y):2x+3y=23,\ x,y\in\mathbb{N}\}$ and $B=\{x:(x,y)\in A\}$. Then the number of one-one functions from $A$ to $B$ is equal to $\_\_\_\_\_\_$ .
Sets, Relations and Function
Answer$24$
Solution
$2x+3y=23$ with $x,y\in\mathbf N$: $y=1,3,5,7\Rightarrow x=10,7,4,1$. $|A|=4$, $B=\{10,7,4,1\}$, $|B|=4$. One-one functions $A\to B$: $4!=24$.