The coefficient of y in the expansion of $(y^{2} + \frac{c}{y})^{5}$ is

20c

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10c

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c^{3}

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c^{2}

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Solution

The correct option is C 10 $c^{3}$
$(y^{2} + \frac{c}{y})^{5}$
$^{5} C_{r} \cdot (y^{2})^{r} \cdot (\frac{c}{y})^{5 - r}$
$=^{5} C_{r} \cdot y^{2 r} \cdot \frac{c^{5 - r}}{y^{5 - r}}$
$y^{2 r - 5 + r} = y^{1}$
$\Rightarrow 3 r - 5 = 1$
$\Rightarrow 3 r = 6$
$\Rightarrow r = 2$
Co-efficient will be $^{5} C_{2} \cdot c^{5 - 2} =^{5} C_{2} \cdot c^{3} =^{10} c^{3}$

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