JEE Main & Advanced Sample Paper JEE Main Sample Paper-7

  • question_answer
    If \[\{x,\,y\}\] is a subset of \[S=\left\{ 1,\,2,\,3,.........100 \right\}\] then probability that \[xy\] is a multiple of 3 is

    A)  \[\frac{43}{100}\]                                           

    B)  \[\frac{87}{200}\]

    C)  \[\frac{61}{150}\]                                           

    D)  \[\frac{83}{150}\]

    Correct Answer: D

    Solution :

    Let \[S=A\cup A',\] Where A contains the multiples of 3 and A? is its compliment. Then both \[x\] and \[y\in A\] or one \[\in A\] and other\[\in A'\]. \[\therefore \] Required probability \[=\frac{\left( ^{33}{{C}_{2}} \right)+\left( ^{33}{{C}_{1}} \right)\left( ^{67}{{C}_{1}} \right)}{^{100}{{C}_{2}}}=\frac{83}{150}\]


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