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JEE Main & Advanced Sample Paper JEE Main Sample Paper-28

  • question_answer
    If \[\left\{ x\left| x\in N\,and \right.{{x}^{2}}\le 6\frac{1}{4} \right\}\] and\[B=\left\{ x\left| x\in N\,and\,{{x}^{2}}\le 5 \right. \right\}\]. Then the number of subsets of set \[A\times (A\cap B)\] which contains 3 elements is

    A)  126                                       

    B)  220

    C)  280                                       

    D)  144

    Correct Answer: B

    Solution :

    \[A=\{1,\,\,2,\,\,3,\,\,4,\,\,5,\,\,6\}\Rightarrow n(A)=6\] \[B=\{1,\,\,2\}\Rightarrow n(B)=2\]        \[\therefore \]\[A\cap B=\{1,\,\,2\}\Rightarrow n(A\cap B)=2\]                 So, number of elements \[A\times (A\cap B)=12\] \[\therefore \]Number of subsets containing 3 elements \[{{=}^{12}}{{C}_{3}}=220\]


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