JEE Main & Advanced Mathematics Binomial Theorem and Mathematical Induction Question Bank Critical Thinking

  • question_answer
    The term independent of x in \[{{\left[ \frac{\sqrt{x}}{3}+\frac{\sqrt{3}}{{{x}^{2}}} \right]}^{10}}\] is  [EAMCET 1984; RPET 2000]

    A) \[\frac{2}{3}\]

    B) \[\frac{5}{3}\]

    C) \[\frac{4}{3}\]

    D) None of these

    Correct Answer: B

    Solution :

    Accordingly, \[{{(\sqrt{x})}^{10-r}}{{\left( \frac{1}{{{x}^{2}}} \right)}^{r}}={{x}^{0}}\Rightarrow r=2\] Hence the term is \[^{10}{{C}_{2}}{{\left( \frac{1}{\sqrt{3}} \right)}^{8}}.\,\,\,{{(\sqrt{3})}^{2}}=\frac{5}{3}\].


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