$\text{ The sum of the co-efficients in the binomial expansion of }{\left(\frac{1}{x}+2x\right)}^n\text{ is equal to }6561\text{ . }$Then constant term in the expansion is

The sum of all the co-efficients  in an expansion is obtained by putting $x=1$ in the expression.

$\therefore {\left(\frac{1}{1}+2.1\right)}^n=6561$

$\Rightarrow 3^n=3^8\Rightarrow n=8$

$\text{In }{\left(\frac{1}{x}+2x\right)}^8, T_{r+1}{=}^8{C}_r{\left(\frac{1}{x}\right)}^{8-r}{\left(2x\right)}^r={}^8{C}_r{x}^{r-8+r}{2}^r$

$\text{ This is constant if }2r-8=0\Rightarrow r=4$

$\therefore \text{ constant term }=2^{4 8}{\mathrm{C}}_4$