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JEE Main & Advanced Mathematics Binomial Theorem and Mathematical Induction Question Bank Binomial theorem for any index

  • question_answer
    The coefficient of \[{{x}^{3}}\] in the expansion of \[\frac{{{(1+3x)}^{2}}}{1-2x}\] will be

    A) 8

    B) 32

    C) 50

    D) None of these

    Correct Answer: C

    Solution :

    \[={{(1+3x)}^{2}}{{(1-2x)}^{-1}}\] \[={{(1+3x)}^{2}}\left( 1+2x+\frac{1.2}{2.1}{{(-2x)}^{2}}+.... \right)\] \[=(1+6x+9{{x}^{2}})(1+2x+4{{x}^{2}}+8{{x}^{3}}+....)\] Therefore coefficient of \[{{x}^{3}}\] is\[(8+24+18)=50\].


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