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 General term, Coefficient of any power of x, Independent term, Middle term and Greatest term and Greatest coefficient

  • question_answer
    In the expansion of \[{{\left( {{x}^{2}}-2x \right)}^{10}}\], the coefficient of \[{{x}^{16}}\] is [MP PET 1985]

    A) -1680

    B) 1680

    C) 3360

    D) 6720

    Correct Answer: C

    Solution :

    The coefficient of \[{{x}^{16}}\]in the expansion of \[{{({{x}^{2}}-2x)}^{10}}\] = The coefficient of \[{{x}^{16}}\]in \[{{x}^{10}}{{(x-2)}^{10}}\] = The coefficient of \[{{x}^{6}}\]in \[{{(x-2)}^{10}}\] = \[^{10}{{C}_{4}}{{.2}^{4}},\,\,\,\,\left( \because \,\,{{T}_{r+1}}={{\,}^{n}}{{C}_{r}}{{x}^{n-r}}{{a}^{r}} \right)\] \[=210\times 16=3360\].


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