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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
    In the expansion of \[{{\left( x-\frac{3}{{{x}^{2}}} \right)}^{9}},\] the term independent of x is   [Karnataka CET  2001]

    A) Non existent

    B) \[^{9}{{C}_{2}}\]

    C) 2268

    D) - 2268

    Correct Answer: D

    Solution :

    \[{{T}_{r+1}}={{\,}^{9}}{{C}_{r}}{{(x)}^{9-r}}{{\left( -\frac{3}{{{x}^{2}}} \right)}^{r}}\] = \[^{9}{{C}_{r}}{{(-3)}^{r}}{{(x)}^{9-3r}}\] For term independent of x, \[9-3r=0\Rightarrow r=3\] \[{{T}_{4}}={{\,}^{9}}{{C}_{3}}\,{{(-3)}^{3}}=-2268\].


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