JEE Main & Advanced Mathematics Binomial Theorem and Mathematical Induction Question Bank Critical Thinking

  • question_answer
    The value of x in the expression \[{{[x+{{x}^{{{\log }_{10}}}}^{(x)}]}^{5}}\], if the third term in the expansion is 10,00,000 [Roorkee 1992]

    A) 10

    B) 11

    C) 12

    D) None of these

    Correct Answer: A

    Solution :

    \[{{T}_{3}}={{\,}^{5}}{{C}_{2}}.{{x}^{2}}{{({{x}^{{{\log }_{10}}x}})}^{3}}={{10}^{6}}\] Put\[^{5}{{C}_{2}}=10\,\,\,\,\,[\because {{\log }_{10}}10=1]\].   If\[x=10\],then\[{{10}^{3}}{{.10}^{2.1}}={{10}^{5}}\]is satisfied. Hence x =10.


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