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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 \[{{\left( 2x-\frac{1}{2{{x}^{2}}} \right)}^{12}}\]is  [RPET 1985]

    A) - 7930

    B) - 495

    C) 495

    D) 7920

    Correct Answer: D

    Solution :

    We have  \[{{(x)}^{12-r}}{{\left( \frac{1}{{{x}^{2}}} \right)}^{r}}={{x}^{0}}\,\,\Rightarrow {{x}^{12-3r}}={{x}^{0}}\Rightarrow r=4\] Hence the required term is \[^{12}{{C}_{4}}{{2}^{8}}{{\left( -\frac{1}{2} \right)}^{4}}=7920\].


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