JEE Main & Advanced JEE Main Online Paper (Held On 08 April 2018)

  • question_answer
    Two sets A and B are as under: \[A=\{(a,\,\,b)\in R\times R:|a-5|<1\] and \[|b-5|<1\};\] \[\text{B= }\!\!\{\!\!\text{ (a,}\,\,\text{b)}\in \,\,\text{R}\times \text{R : 4(a-6}{{\text{)}}^{2}}+9{{(b-5)}^{2}}\le 36\}\].Then                  [JEE Main Online 08-04-2018]

    A)  \[A\cap B=\phi \] (an empty set)

    B)  neither \[A\subset B\] nor \[B\subset A\]

    C)  \[B\subset A\]

    D)  \[A\subset B\]

    Correct Answer: D

    Solution :

      \[-1<a-5<1\]                       \[\Rightarrow a\in (4,6),b\in (4,6)\] \[\frac{{{(a-6)}^{2}}}{9}+\frac{{{(b-5)}^{2}}}{4}\le 1\] \[-3\le a-6\le 3\Rightarrow a\in (3,9)\] \[-2\le b-5\le 2\Rightarrow b\in (3,7)\]


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