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KVPY Sample Paper KVPY Stream-SX Model Paper-4

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

    A) 2                                 

    B) \[-\,2\]   

    C) 0                                 

    D) 1

    Correct Answer: B

    Solution :

    [B]
    \[x-y=2\]
    \[x+y+xy\] 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 \[x=0\]&\[y=-2.\]


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