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
    The coefficient of \[{{x}^{5}}\] in the expansion of \[{{({{x}^{2}}-x-2)}^{5}}\] is  [EAMCET 2003]

    A) - 83

    B) - 82

    C) - 81

    D) 0

    Correct Answer: C

    Solution :

    \[{{({{x}^{2}}-x-2)}^{5}}={{(x-2)}^{5}}{{(1+x)}^{5}}\] = \[[\,{}^{5}{{C}_{0}}{{x}^{5}}-{}^{5}{{C}_{1}}{{x}^{4}}\times 2+...\,]\] \[[\,{}^{5}{{C}_{0}}+{}^{5}{{C}_{1}}x+...\,]\] Collecting the coefficient of x5: \[1-5.5.2+10.10.4-10.10.8+5.5.16-32\] = \[1-50+400-800+400-32=-81\].


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