JEE Main 2025 (Online) 7th April Evening ShiftQuestion 1
Let $A=\{(\alpha,\beta)\in\mathbb{R}\times\mathbb{R}:|\alpha-1|\le4\text{ and }|\beta-5|\le6\}$ and $B=\{(\alpha,\beta)\in\mathbb{R}\times\mathbb{R}:16(\alpha-2)^{2}+9(\beta-6)^{2}\le144\}$. Then
Sets, Relations and Function
Solution
$A$: $\alpha\in[-3,5]$, $\beta\in[-1,11]$. $B$: ellipse centred $(2,6)$ with semi-axes $3$ (in $\alpha$) and $4$ (in $\beta$): $\alpha\in[-1,5]$, $\beta\in[2,10]$, which lies inside $A$'s ranges. So $B\subset A$; $A\not\subset B$ (e.g. $(-3,5)\in A$ not in $B$). Option B.