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J & K CET Engineering J and K - CET Engineering Solved Paper-2013

  • question_answer
    The cartesian product \[A\times A\] has 9 elements among which are found \[(-1,0)\] and \[(0,1),\] then set A is equal to

    A)  \[\{1,\,\,0\}\]             

    B)  \[\{1,\,\,-1,\,\,\,0\}\]

    C)  \[\{\,0,\,\,-1\}\]           

    D)  \[\{1,\,\,-1\}\]

    Correct Answer: B

    Solution :

    Given,  \[n(A\times A)=9\,\,\,\,\,\,\,\Rightarrow \,\,\,\,\,n(A)\times n(A)=9\] which is possible when, \[n(A)=3.\] i.e., set A contain only three elements i.e.,  \[A=\{1,-1,0\}\] So, \[A\times A\] contain \[(-1,0)\] and \[(0,\,1)\]


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