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Railways Quantitative Aptitude Power, Surds And Indices Sample Paper Surds Indices Sample Test Paper-4

  • question_answer
    If \[{{27}^{k}}=\frac{9}{{{3}^{k}}},\] then value of \[\frac{1}{{{k}^{2}}}\] is

    A)  \[\frac{1}{4}\]             

    B)  4        

    C)  \[\frac{1}{2}\] 

    D)  2

    Correct Answer: B

    Solution :

    [b] If \[{{27}^{k}}=\frac{9}{{{3}^{k}}}\] \[\Rightarrow {{3}^{3k}}=\frac{9}{{{3}^{k}}}\Rightarrow {{3}^{4k}}=9\]                  \[[{{a}^{m}}\times {{a}^{n}}={{a}^{m+n}}]\] \[\Rightarrow {{9}^{2k}}=9\Rightarrow k=\frac{1}{2}\]    \[\left[ {{a}^{m}}={{a}^{n}}\,\,then\,\,m=n \right]\] \[\Rightarrow \frac{1}{{{k}^{2}}}=4\]


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