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KVPY Sample Paper KVPY Stream-SX Model Paper-21

  • question_answer
    If x, \[y\in R\] and \[x-y=2\] then minimum value of  \[x+y+xy\] is

    A) 2

    B) \[-\,2\]

    C) 0

    D) 1

    Correct Answer: B

    Solution :

    \[x-y=2\]
    \[x+y+xy\] is to be minimized.
    Putting  \[y=x-2.\]
    we get, \[f\,(x)=2x-2+x\,(x-2)\]
    \[f'\,(x)=2+2x-2=0\]       at \[x=0.\]
    \[f''\,(x)=2\]\[\Rightarrow \]\[x=0\] is a
    point of minima
    Thus minimum value is at \[x=0\] & \[y=-\,2.\]
    Hence [B] is correct.


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