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  • Coefficient of x in the expansion of <img alt="\left(x^2+\frac{a}{x}\right)^5" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cleft%28x%5E2&plus;%5Cfrac%7Ba%7D%7Bx%7D%5Cright%29%5E

Coefficient of x in the expansion of \left(x^2+\frac{a}{x}\right)^5 is 

Option: 1

9 a^2


Option: 2

10 a^3


Option: 3

10 a^2


Option: 4

10 a


Answers (1)

best_answer

In the expansion of \left(x^2+\frac{a}{x}\right)^5 the general term is 

T_{r+1}={ }^5 C_r\left(x^2\right)^{5-r}\left(\frac{a}{x}\right)^r={ }^5 C_r a^r x^{10-3 r}

Here, exponent of x is 10-3 r=1 \Rightarrow r=3

\therefore \quad T_{2+1}={ }^5 C_3 a^3 x=10 a^3 \cdot x

Hence coefficient of x is 10a^3

Posted by

jitender.kumar

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