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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 term independent of x in the expansion of \[{{\left( 2x-\frac{3}{x} \right)}^{6}}\] is [Pb. CET 1999]

    A) 4320

    B) 216

    C) - 216

    D) - 4320

    Correct Answer: D

    Solution :

    \[{{T}_{r+1}}=\,{}^{6}{{C}_{r}}{{(2x)}^{6-r}}{{\left( -\frac{3}{x} \right)}^{r}}\] = \[{}^{6}{{C}_{r}}{{(2)}^{6-r}}{{(-3)}^{r}}{{(x)}^{6-2r}}\] For term independent of x, 6 - 2r = 0 i.e. r = 3 \ \[{{T}_{4}}={{\,}^{6}}{{C}_{3}}\,{{2}^{6-3}}{{(-3)}^{3}}\] = - 4320.


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