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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 greatest coefficient in the expansion of \[{{(1+x)}^{2n+2}}\]  is [BIT Ranchi 1992]

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

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

    C) \[\frac{(2n+2)!}{n!(n+1)!}\]

    D) \[\frac{(2n)!}{n!(n+1)!}\]

    Correct Answer: B

    Solution :

     Greatest coefficient of \[{{(1+x)}^{2n+2}}\] is \[={{\,}^{(2n+2)}}{{C}_{n+1}}=\frac{(2n+2)!}{{{\{(n+1)!\}}^{2}}}\]


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