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 Self Evaluation Test - Binomial Theorem

  • question_answer
    What is the coefficient of \[{{x}^{3}}\] in \[\frac{(3-2x)}{{{(1+3x)}^{3}}}?\]

    A) - 272

    B) - 540

    C) - 870

    D) -918

    Correct Answer: D

    Solution :

    [d] \[\frac{(3-2x)}{{{(1+3x)}^{3}}}=(3-2x){{(1+3x)}^{-3}}\] \[=(3-2x)[1-9x+\frac{(-3)(-4)}{2!}\,\,.\,9{{x}^{2}}\]             \[+\frac{(-3)(-4)(-5)}{3!}.27{{x}^{3}}+....]\] [Expanding \[{{(1+3x)}^{-3}}\]] \[=(3-2x)(1-9x+54{{x}^{2}}-270{{x}^{3}}+.....)\] \[\therefore \] Coefficient of \[{{x}^{3}}=-270\times 3-2\times 54=-918\]


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