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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
     The middle term in the expansion of \[{{(1+x)}^{2n}}\] is [DCE 2002]

    A) \[\frac{(2n)!}{n!}{{x}^{2}}\]

    B) \[\frac{(2n)!}{n!(n-1)!}{{x}^{n+1}}\]

    C) \[\frac{(2n)!}{{{(n!)}^{2}}}{{x}^{n}}\]

    D) \[\frac{(2n)!}{(n+1)!(n-1)!}\,{{x}^{n}}\]

    Correct Answer: C

    Solution :

    Middle term = \[{{T}_{\frac{2n+2}{2}}}={{T}_{n+1}}={}^{2n}{{C}_{n}}{{x}^{n}}\]= \[\frac{2n!}{{{(n!)}^{2}}}\,.\,{{x}^{n}}\].


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