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JEE Main & Advanced Mathematics Binomial Theorem and Mathematical Induction Question Bank Expansion of binomial theorem

  • question_answer
    The formulae\[{{(a+b)}^{m}}={{a}^{m}}+m{{a}^{m-1}}b\]\[+\frac{m(m-1)}{1.2}{{a}^{m-2}}{{b}^{2}}+....\] holds when

    A) \[b<a\]

    B) \[a<b\]

    C) \[|a|\,<\,|b|\]

    D) \[|b|\,<\,|a|\]

    Correct Answer: D

    Solution :

    The expression can be written as \[{{a}^{m}}\left\{ {{\left( 1+\frac{b}{a} \right)}^{m}} \right\}\] Hence it is valid only when\[\left| \frac{b}{a} \right|<1\Rightarrow |b|\,<\,|a|\].


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