JEE Main & Advanced Sample Paper JEE Main Sample Paper-46

  • question_answer
    Range of the function f defined by \[f(x)\,=\left[ \frac{1}{\sin \,\{x\}} \right],\], (where, [.] and {.} respectively, denotes the greatest integer and the fractional part function) is

    A)  \[l,\]the set of integers                     

    B)  N, the set of natural numbers

    C)  W, the set of whole numbers             

    D)  Q, the set of rational numbers

    Correct Answer: B

    Solution :

     \[\because \]    \[0<\{x\}<1\] \[0<\sin \,\{x\}<\sin \,1\] Also,    \[\frac{1}{\sin \,\{x\}}>0\] Then,   \[\left[ \frac{1}{\sin \,\{x\}} \right]=1,\,2,\,3,...\] \[\therefore \]    \[{{R}_{f}}=N\]


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