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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 coefficient of \[{{(2r+3)}^{th}}\] and \[{{(r-1)}^{th}}\] terms in the expansion of \[{{(1+x)}^{15}}\] are equal, then value of r is [RPET 1995, 2003; UPSEAT 2001]

    A) 5

    B) 6

    C) 4

    D) 3

    Correct Answer: A

    Solution :

    \[^{15}{{C}_{2r+2}}{{=}^{15}}{{C}_{r-2}}\] But \[^{15}{{C}_{2r+2}}={{\,}^{15}}{{C}_{15-(2r+2)}}={{\,}^{15}}{{C}_{13-2r}}\] Þ \[^{15}{{C}_{13-2r}}=\,{{\,}^{15}}{{C}_{r-2}}\Rightarrow r=5\].


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