2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Binomial Theorem and Mathematical Induction

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

  • question_answer
    The coefficient of \[{{x}^{n}}\] in the expansion of \[{{(1-2x+3{{x}^{2}}-4{{x}^{3}}+.....)}^{-n}}\]is

    A) \[\frac{(2n)!}{n!}\]

    B) \[\frac{(2n)!}{{{(n!)}^{2}}}\]

    C) \[\frac{1}{2}\frac{(2n)!}{{{(n!)}^{2}}}\]

    D) None of these

    Correct Answer: B

    Solution :

    \[{{(1-2x+3{{x}^{2}}-4{{x}^{3}}+...)}^{-n}}={{[{{(1+x)}^{-2}}]}^{-n}}={{(1+x)}^{2n}}\] \ Coefficient of \[{{x}^{n}}\]in \[{{(1-2x+3{{x}^{2}}-4{{x}^{3}}+...)}^{-n}}\] = Coefficient of \[{{x}^{n}}\]in \[{{(1+x)}^{2n}}={{\,}^{2n}}{{C}_{n}}=\frac{(2n)!}{{{(n!)}^{2}}}\]


You need to login to perform this action.
You will be redirected in 3 sec spinner