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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 coefficients of \[{{(2r+1)}^{th}}\] term and \[{{(r+2)}^{th}}\] term are equal in the expansion of \[{{(1+x)}^{43}},\] then the value of  r  will be   [UPSEAT 1999]

    A) 14

    B) 15

    C) 13

    D) 16

    Correct Answer: A

    Solution :

    Coefficient of \[{{(2r+1)}^{th}}\] term in expansion of\[{{(1+x)}^{43}}{{=}^{43}}{{C}_{2r}}\]and coefficient of \[{{(r+2)}^{th}}\] term = coefficient of \[{{\{(r+1)+1\}}^{th}}\] term = \[{}^{43}{{C}_{r+1}}\] According to question \[{}^{43}{{C}_{2r}}={}^{43}{{C}_{r+1}}\] \[={}^{43}{{C}_{43-(r+1)}}\] then \[2r=43-(r+1)\]or \[3r=42\] or \[r=14\].


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