JEE Mains · Maths · STD 11 - 1. set theory
Let \(A=\{(\alpha, \beta) \in \mathbf{R} \times \mathbf{R}:|\alpha-1| \leq 4 \text { and }|\beta-5| \leq 6\}\) and \(B=\{(\alpha, \beta) \in \mathbf{R} \times\) \(\mathbf{R}: 16(\alpha-2)^2+9(\beta-6)^2 \leq 144\}\)
- A \(\mathrm{B} \subset \mathrm{A}\)
- B \(\mathrm{A} \cup \mathrm{B}=\{(\mathrm{x}, \mathrm{y}):-4 \leq \mathrm{x} \leq 4,-1 \leq \mathrm{y} \leq 11\}\)
- C neither \(\mathrm{A} \subset \mathrm{B}\) nor \(\mathrm{B} \subset \mathrm{A}\)
- D \(A \subset B\)
Answer & Solution
Correct Answer
(A) \(\mathrm{B} \subset \mathrm{A}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { A : }|x-1| \leq 4 \text { and }|y-5| \leq 6 \\ & \Rightarrow-4 \leq x-1 \leq 4 \Rightarrow-6 \leq y-5 \leq 6 \\ & \Rightarrow-3 \leq x \leq 5 \quad \Rightarrow-1 \leq y \leq 11 \\ & \text { B : } 16(x-2)^2+9(y-6)^2 \leq 144 \\ & \text { B : }…
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