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SSC Sample Paper SSC CGL - Sample Paper-2

  • question_answer
    The value of \[\frac{{{(243)}^{{{5}^{n}}}}\cdot {{3}^{2n+1}}}{{{9}^{n}}\cdot {{3}^{n-1}}}\] is

    A)  1                                

    B)  9

    C)  3                                

    D)  \[{{3}^{n}}\]

    Correct Answer: B

    Solution :

    \[\frac{{{(243)}^{\frac{n}{5}}}\cdot {{3}^{2n+1}}}{{{9}^{n}}\cdot {{3}^{n-1}}}=\frac{{{({{3}^{5}})}^{\frac{n}{5}}}\cdot {{3}^{2n+1}}}{{{3}^{2n}}\cdot {{3}^{n-1}}}\] \[=\frac{{{3}^{n}}\cdot {{3}^{2n+1}}}{{{3}^{2n}}\cdot {{3}^{n-1}}}=\frac{{{3}^{3n+1}}}{{{3}^{3n-1}}}=\frac{{{3}^{2}}\cdot {{3}^{3n-1}}}{{{3}^{3n-1}}}\] \[={{3}^{2}}=9\]


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