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JEE Main & Advanced Mathematics Binomial Theorem and Mathematical Induction Question Bank Binomial theorem for any index

  • question_answer
    \[\frac{1}{{{\left( {{x}^{2}}+\frac{1}{x} \right)}^{\frac{4}{3}}}}\] can be expanded by binomial theorem, if

    A) \[x<1\]

    B) \[|x|<1\]

    C) \[x>1\]

    D) \[|x|>1\]

    Correct Answer: D

    Solution :

    The expression is \[{{x}^{-8/3}}{{\left( 1+\frac{1}{{{x}^{3}}} \right)}^{-4/3}}\] Hence \[\left| \frac{1}{{{x}^{3}}} \right|\,<1\Rightarrow |x|\,>1\]


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