The coefficient of $x^7$ in the expansion of $( x^2 + \frac {1}{x})^{11}$ is 

$\textbf{Step 1: Find value of general term for expansion}$

$\text{Given equation is}$

$\bigg ( x^2 +\dfrac {1}{x}\bigg)^{11}$

$\text{General term of expansion $ (p+q)^n$ is given by-}$

$T_n= T_{r +1 }=^nC_r p^{ (n-r)}.q^r$

$\text{Comparing given equation with standard form, p=x$^2$ and q=1/x and n=11}$

$\Rightarrow T_n=T_{r+1} = ^{11}C_r. (x^2)^{(11-r)} .\bigg( \dfrac {1}{x}\bigg)^r$

$= ^{11}C_r. (x)^{(22-2r)} .\bigg( \dfrac {1}{x}\bigg)^r$

$= ^{11}C_r. (x)^{(22-2r-r)}$

$= ^{11}C_r. (x)^{(22-3r)}$

$\textbf{Step 2: Find value of coefficient of x$^7$}$

$\text{To obtain coefficient of x}^7 :$

$\Rightarrow 22-3r=7$

$\Rightarrow$ $3r=15$

$\therefore$ $r=5$

$\text{For r=5,6th term is given by-}$

$T_6=T_{5+1} = ^{11}C_5 x^{(22 -15)} = ^{11}C_5 x^7 .$

$\therefore$ $\text{Coefficient of} x^7$$=^{11}C_5$

$= \dfrac { 11 \times 10 \times 9 \times 8 \times 7}{5 \times 4 \times 3 \times 2 \times 1}$

$= 462$

$\textbf{Therefore,value of coefficient of x$^7$ is 462}$