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JEE Main & Advanced Mathematics Binomial Theorem and Mathematical Induction Question Bank General term, Coefficient of any power of x, Independent term, Middle term and Greatest term and Greatest coefficient

  • question_answer
    If the middle term in the expansion of \[{{\left( {{x}^{2}}+\frac{1}{x} \right)}^{n}}\]is \[924{{x}^{6}}\], then \[n=\]

    A) 10

    B) 12

    C) 14

    D) None of these

    Correct Answer: B

    Solution :

    Since n is even therefore \[{{\left( \frac{n}{2}+1 \right)}^{th}}\] term is middle term, hence \[^{n}{{C}_{n/2}}{{({{x}^{2}})}^{n/2}}{{\left( \frac{1}{x} \right)}^{n/2}}=924{{x}^{6}}\] \[\Rightarrow \] \[{{x}^{n/2}}={{x}^{6}}\Rightarrow n=12\].


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