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JEE Main & Advanced Sample Paper JEE Main Sample Paper-15

  • question_answer
    Let \[x={{4}^{{{\log }_{2}}\sqrt{{{9}^{k-1}}+7}}}\] and \[y=\frac{1}{{{32}^{\log 2\,\sqrt[5]{{{3}^{k-1}}+1}}}}\] and \[xy=4\], then the sum of the cubes of the real value(s) of k is

    A)  1                                            

    B)  5

    C)  8                                            

    D)  9

    Correct Answer: D

    Solution :

    \[xy=4\Rightarrow {{9}^{k-1}}+7=4,\,{{3}^{k-1}}+4\] \[{{3}^{2(k-1)}}-{{4.3}^{k-1}}+3=0\Rightarrow k=1\] or 2 Hence, \[({{1}^{3}}+{{2}^{3}})=9\] Ans.


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