Let A=\ (α, β) in mathbb R × mathbb R : α-1 leq 4 and β-5 leq 6\ and B= \ (α, β) in mathbb R × mathbb R : 16(α-2) 2 +9(β-6) 2 leq 144 \ . Then

A cup B=\ (x, y):-4 leq x leq 4,-1 leq y leq 11\

Neither A subset B nor B subset A

Mathematics · Sets and Relations

JEE Main 2025 — 7 April, Evening Shift — Question 33

Let $A=\{(\alpha, \beta) \in \mathbb{R} \times \mathbb{R}:|\alpha-1| \leq 4$ and $|\beta-5| \leq 6\}$ and

$B=\left\{(\alpha, \beta) \in \mathbb{R} \times \mathbb{R}: 16(\alpha-2)^{2}+9(\beta-6)^{2} \leq 144\right\}$ . Then

Set A : For $\alpha$

\begin{aligned} & -4 \leq \alpha-1 \leq 4 \\& \Rightarrow-3 \leq \alpha \leq 5 \end{aligned}

For $\beta$ $-6 \leq \beta-5 \leq 6$

$\Rightarrow-1 \leq \beta \leq 11$

Set B : $\frac{(\alpha-2)^{2}}{9}+\frac{(\beta-6)^{2}}{16} \leq 1$

Clearly $B \subset A$

Answer key and solution verified before publishing.

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