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 term independent of x in the expansion of \[{{\left( 2x+\frac{1}{3x} \right)}^{6}}\]is  [MNR 1995]

    A) \[\frac{160}{9}\]

    B)   \[\frac{80}{9}\]

    C) \[\frac{160}{27}\]

    D)   \[\frac{80}{3}\]

    Correct Answer: C

    Solution :

    \[1(6-r)+(-1)r=0\Rightarrow r=3,\] therefore fourth term will be independent of x i.e. \[^{6}{{C}_{3}}{{(2x)}^{3}}{{\left( \frac{1}{3x} \right)}^{3}}=20\times 8\times \frac{1}{27}=\frac{160}{27}\]


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