JEE Main & Advanced JEE Main Paper (Held On 9 April 2017)

  • question_answer
    The function \[f:N\to N\] defined by \[f(x)=x-5\,\left[ \frac{x}{5} \right],\] where N is the set of natural numbers and \[[x]\] denotes the greatest integer less than or equal to x, is: [JEE Online 09-04-2017]

    A)  one-one but not onto

    B)  one-one and onto

    C)  neither one-one nor onto

    D)  onto but not one-one

    Correct Answer: C

    Solution :

                      \[\left. \begin{align}   & f(1)=1-5\,(1/5)=1 \\  & f(6)=6-6[6/5]=1 \\ \end{align} \right\}\to \] Many one \[f(10)\,=10-5(2)=0\] which is not in coduman many one + into


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