JEE Main & Advanced Mathematics Binomial Theorem and Mathematical Induction Question Bank Expansion of binomial theorem

  • question_answer
    The total number of terms in the expansion of \[{{(x+a)}^{100}}+{{(x-a)}^{100}}\] after simplification will be  [Pb. CET 1990]

    A) 202

    B) 51

    C) 50

    D) None of these

    Correct Answer: B

    Solution :

    We know  \[\frac{1}{2}\left\{ {{(1+a)}^{n}}+{{(1-a)}^{n}} \right\}={{\,}^{n}}{{C}_{0}}+{{\,}^{n}}{{C}_{2}}{{a}^{2}}+{{\,}^{n}}{{C}_{4}}{{a}^{4}}+.....\] Therefore, number of terms in expansion of  \[\{{{(x+a)}^{100}}+{{(x-a)}^{100}}\}\] is 51.


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