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JEE Main & Advanced Mathematics Sets Question Bank Self Evaluation Test - Sets

  • question_answer
    The number of elements in the set \[\{(a,b):2{{a}^{2}}+3{{b}^{2}}=35,a,b\in Z\}\], where Z is the set of all integers, is

    A) 2

    B)                                4

    C) 8

    D)                                12

    Correct Answer: C

    Solution :

    [c]Given set is \[\{(a,b):2{{a}^{2}}+3{{b}^{2}}=35,a,b\in Z\}\] We can see that, \[2{{(\pm 2)}^{2}}+3{{(\pm 3)}^{2}}=35\] And \[2{{(\pm 4)}^{2}}+3{{(\pm 1)}^{2}}=35\] \[\therefore (2,3),(2,-3),(-2,-3),(-2,3),(4,1),(4,-1),\] \[(-4,-1),(-4,1)\] are 8 elements of the set. \[\therefore n=8.\]


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