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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2007

  • question_answer
    Let Z denote the set of all integers and\[A=\{(a,b):{{a}^{2}}+3{{b}^{2}}=28,a,b\in z\}\]and\[B=\{(a,b):a>b,a,b\in z\}\]. Then the number of elements in\[A\cap B\]is

    A)  2           

    B)         3

    C)  4           

    D)         5

    E)  6

    Correct Answer: E

    Solution :

    \[\because \] \[A=\{(a,b):{{a}^{2}}+{{b}^{2}}=28,a,b\in Z\}\] \[=\{(5,1),(-5,-1)(5,-1),(-5,1)(1,3),\] \[(-1,-3),(-1,3)(1,-3),(4,2)(-4,-2)\] \[(4,-2),(-4,2)\}\] and\[B=\{(a,\text{ }b):a>b,\text{ }a,b\in Z\}\] \[\therefore \] \[A\cap B=\{(-1,-5),(1,-5),(-1,-3),\] \[(1,-3),(4,2),(4,-2)\}\] \[\therefore \]Number of elements in\[A\cap B\]is 6.


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