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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  \[{{\left( {{x}^{2}}-\frac{3\sqrt{3}}{{{x}^{3}}} \right)}^{10}}\] is [RPET 1999]

    A) 153090

    B) 150000

    C) 150090

    D) 153180

    Correct Answer: A

    Solution :

    \[{{T}_{r+1}}={}^{10}{{C}_{r}}{{({{x}^{2}})}^{10-r}}{{\left( \frac{-3\sqrt{3}}{{{x}^{3}}} \right)}^{r}}\] For term independent of x, \[20-2r-3r=0\Rightarrow r=4\] \ \[{{T}_{4+1}}={}^{10}{{C}_{4}}{{(-3)}^{4}}{{(\sqrt{3})}^{4}}=153090.\]


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