JEE Main 2025 (Online) 23rd January Evening ShiftQuestion 1
Let $A=\{(x,y)\in\mathbf{R}\times\mathbf{R}:|x+y|\ge 3\}$ and $B=\{(x,y)\in\mathbf{R}\times\mathbf{R}:|x|+|y|\le 3\}$.
If $C=\{(x,y)\in A\cap B: x=0\text{ or }y=0\}$, then $\sum_{(x,y)\in C}|x+y|$ is :
Sets, Relations and Function
Solution
On the axes, $|x|+|y|\le3$ and $|x+y|\ge3$ force $|x|=3$ or $|y|=3$: points $(\pm3,0),(0,\pm3)$. Each gives $|x+y|=3$, so the sum is $12$.