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

  • question_answer
    The largest term in the expansion of \[{{(3+2x)}^{50}}\] where \[x=\frac{1}{5}\] is [IIT Screening 1993]

    A) 5th

    B) 51st

    C) 7th

    D) 6th

    Correct Answer: C

    Solution :

    \[{{3}^{50}}{{\left( 1+\frac{2x}{3} \right)}^{50}}\] \[\therefore \,\,\,\frac{{{T}_{r+1}}}{{{T}_{r}}}\ge 1\,\,\,\Rightarrow 102-2r\ge 15r\Rightarrow r\le 6\]


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