JEE Main 2022 (Online) 25th July Morning ShiftQuestion 1
The total number of functions, $f:\{1,2,3,4\}\to\{1,2,3,4,5,6\}$ such that $f(1)+f(2)=f(3)$, is equal to :
Sets, Relations and Function
Solution
$f(1)+f(2)=f(3)\le6$ with $f(1),f(2)\ge1$: number of $(a,b)$ with $a+b\le6$ is $5+4+3+2+1=15$. $f(4)$ is free: $6$ choices. Total $15\cdot6=90$. Option B.