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
    \[{{6}^{th}}\]term in expansion of \[{{\left( 2{{x}^{2}}-\frac{1}{3{{x}^{2}}} \right)}^{10}}\] is 

    A) \[\frac{4580}{17}\]

    B) \[-\frac{896}{27}\]

    C) \[\frac{5580}{17}\]

    D)   None of these

    Correct Answer: B

    Solution :

    Applying \[{{T}_{r+1}}={{\,}^{n}}{{C}_{r}}{{x}^{n-r}}{{a}^{r}}\]for \[{{(x+a)}^{n}}\] Hence \[{{T}_{6}}={{\,}^{10}}{{C}_{5}}{{(2{{x}^{2}})}^{5}}{{\left( -\frac{1}{3{{x}^{2}}} \right)}^{5}}\] \[=-\frac{10\,!}{5\,!\,5\,!}32\times \frac{1}{243}=-\frac{896}{27}\]


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