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KVPY Sample Paper KVPY Stream-SX Model Paper-3

  • question_answer
    If the fractional part of the number \[\frac{{{2}^{403}}}{15}\]  is \[\frac{k}{15},\]then k is equal to:

    A) 14                                

    B) 6

    C) 4                                 

    D) 8

    Correct Answer: D

    Solution :

    \[\frac{{{2}^{403}}}{15}\,=\,\frac{8(16)}{15}\,=\,\frac{8{{(1+15)}^{100}}}{15}\]\[=\,\frac{8}{15}[1+15\alpha ]\] For some\[\alpha \in N\]\[=\,\left( \alpha +\frac{8}{15} \right)\] \[\therefore \] Fractional part \[=\,\frac{8}{15}\,=\,\frac{k}{15}\] \[\Rightarrow \]      \[k=8.\]


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