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JEE Main & Advanced Mathematics Functions Question Bank Self Evaluation Test - Relations and Functions-I

  • question_answer
    Let \[R=\{x|x\in N,x\] is a multiple of 3 and \[x\le 100\}\] \[S=\{x|x\in N,\,\,x\] is a multiple of 5 and \[x\le 100\}\] What is the number of elements in \[(R\times S)\cap (S\times R)\]

    A) 36

    B)        33

    C) 20

    D)        6

    Correct Answer: A

    Solution :

    [a] Let R = \[\{x:x\in N,x\] is a multiple of 3 and \[x\le 100\}\] and S =  \[\{x:x\in N,x\] is a multiple of 5 and \[x\le 100\}\] \[\therefore R=\{3,6,9,12,15...99\}\] And \[S=\{5,10,15,...,95,100\}\] Now, \[(R\times S)\cap (S\times R)=(R\cap S)\times (S\cap R)\] \[=(15,30,45,60,75,90)\times (15,30,45,60,75,90)\] \[\therefore \]Number of elements in \[(R\times S)\cap (S\times R)\] \[=6\times 6=36\]


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