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KVPY Sample Paper KVPY Stream-SX Model Paper-31

  • question_answer
    If mean and variance of 7 variates are 8 and 16 respectively and five of them are 2, 4, 10, 12, 14 then find the product of remaining two variates:

    A) 49

    B) 48

    C) 45

    D) 40

    Correct Answer: B

    Solution :

    Let remaining two variates are a and b then
    \[\frac{a+b+2+4+10+12+14}{7}=8\] And \[\frac{{{a}^{2}}+{{b}^{2}}+4+16+100+144+196}{7}-{{(8)}^{2}}=16\]
    \[\Rightarrow \]   \[a+b=4\] and \[{{a}^{2}}+{{b}^{2}}=100\] \[\Rightarrow \]\[ab=\frac{{{(a+b)}^{2}}-({{a}^{2}}+{{b}^{2}})}{2}=\frac{196-100}{2}=48.\]


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