Question

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

• A. 20 c
• B. 10 c
• C. 10 $c^3$
• D. 20 $c^3$

Answer 1

The correct option is C 10 $c^3$

$T_{r+1}{=}^5{C}_r\left(x^2{)}^{5-r}\right(c/x{)}^r{=}^5{C}_r{c}^r{x}^{10-2r-r}$
If $10-3r=1$, then $3r=9\Rightarrow r=3$
Coefficient of x is ${}^5{C}_3{c}^3=10c^3$