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

  • question_answer
    If \[{{(a+bx)}^{-2}}=\frac{1}{4}-3x+......\], then \[(a,b)\]=  [UPSEAT 2002]

    A) (2, 12)

    B) \[(-2,12)\]

    C) \[(2,\,\,-12)\]

    D) None of these

    Correct Answer: A

    Solution :

    \[{{(a+bx)}^{-2}}=\frac{1}{{{a}^{2}}}{{\left( 1+\frac{b}{a}x \right)}^{-2}}=\frac{1}{{{a}^{2}}}\left[ a+\frac{(-2)}{1!}\left( \frac{b}{a} \right)x+.... \right]\] Equating it to \[\frac{1}{4}-3x+....,\]we get\[a=2,b=12\].


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