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JCECE Engineering JCECE Engineering Solved Paper-2011

  • question_answer
    The coefficient of \[y\] in expansion of\[{{\left( {{y}^{2}}+\frac{c}{y} \right)}^{2}}\] is

    A) \[29c\]                                 

    B) \[10c\]

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

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

    Correct Answer: C

    Solution :

    We have,                 \[{{T}_{r+1}}{{=}^{5}}{{C}_{r}}{{({{y}^{2}})}^{5-r}}{{\left( \frac{c}{y} \right)}^{r}}{{=}^{4}}{{C}_{r}}{{y}^{10-3r}}{{c}^{r}}\] Now,\[10-3r=1\Rightarrow r=3\] So, coefficient of\[y{{=}^{5}}{{C}_{3}}\,\,{{c}^{3}}=10{{c}^{3}}\]


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