JEE Main & Advanced Mathematics Binomial Theorem and Mathematical Induction Question Bank Critical Thinking

  • question_answer
    Middle term in the expansion of \[{{(1+3x+3{{x}^{2}}+{{x}^{3}})}^{6}}\]is [MP PET 1997]

    A) \[{{4}^{th}}\]

    B) \[{{3}^{rd}}\]

    C) \[{{10}^{th}}\]

    D) None of these

    Correct Answer: C

    Solution :

    \[{{(1+3x+3{{x}^{2}}+{{x}^{3}})}^{6}}={{\{{{(1+x)}^{3}}\}}^{6}}={{(1+x)}^{18}}\] Hence the middle term is\[{{10}^{th}}\].


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