JEE Main On 08 April 2018 Question 11
Question: Two sets A and B are as under: A={$(a,b)\in R\times R:|a-5|<1 $ and $ |b-5|<1$}; $ \text{B= }{\text{ (a,}\text{b)}\in R\times \text{R : 4(a-6}{{)}^{2}}+9{{(b-5)}^{2}}\le 36} $ .Then [JEE Main Online 08-04-2018]
Options:
A) $ A\cap B=\phi $ (an empty set)
B) neither $ A\subset B $ nor $ B\subset A $
C) $ B\subset A $
D) $ A\subset B $
Show Answer
Answer:
Correct Answer: D
Solution:
$ -1<a-5<1 $
$ \Rightarrow a\in (4,6),b\in (4,6) $
$ \frac{{{(a-6)}^{2}}}{9}+\frac{{{(b-5)}^{2}}}{4}\le 1 $
$ -3\le a-6\le 3\Rightarrow a\in (3,9) $
$ -2\le b-5\le 2\Rightarrow b\in (3,7) $
