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

  • question_answer
    The term independent of y in the expansion of \[{{({{y}^{-1/6}}-{{y}^{1/3}})}^{9}}\] is [BIT Ranchi 1980]

    A) 84

    B) 8.4

    C) 0.84

    D) - 84

    Correct Answer: D

    Solution :

    \[(9-r)\left( -\frac{1}{6} \right)+r\left( \frac{1}{3} \right)=0\Rightarrow r=3\] So the term independent of y = \[^{9}{{C}_{3}}{{({{y}^{-1/6}})}^{6}}{{(-{{y}^{1/3}})}^{3}}=-84\].


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