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
    If the expansion of \[{{\left( {{y}^{2}}+\frac{c}{y} \right)}^{5}}\], the coefficient of y will be [MNR 1983]

    A) \[20c\]

    B) \[10c\]

    C) \[10{{c}^{3}}\]

    D) \[20{{c}^{2}}\]

    Correct Answer: C

    Solution :

     2(5 - r) + (-1) r = 1 \[\Rightarrow \] 10 - 2r - r = 1 \[\Rightarrow \,r=3\] Thus coefficient of y is\[^{5}{{C}_{3}}{{c}^{3}}=\frac{5\times 4}{2\times 1}{{c}^{3}}=10{{c}^{3}}\].


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