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

  • question_answer
    The expansion of \[\frac{1}{{{(4-3x)}^{1/2}}}\]binomial theorem will be valid, if

    A) \[x<1\]

    B) \[|x|\,<1\]

    C) \[-\frac{2}{\sqrt{3}}<x<\frac{2}{\sqrt{3}}\]

    D) None of these

    Correct Answer: D

    Solution :

    The given expression can be written as \[{{4}^{-1/2}}{{\left( 1-\frac{3}{4}x \right)}^{-1/2}}\] and it is valid only when \[\left| \frac{3}{4}x \right|\,<1\Rightarrow -\frac{4}{3}<x<\frac{4}{3}\].


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