If the sum of the numerical coefficients in the binomial

expansion of  ${\left(\frac{1}{x}+2x\right)}^n$ is equal to 6561., then the term

independent of $x,$ is

It is given that the sum of the numerical

coefficients in the binomial expansion of${\left(\frac{1}{x}+2x\right)}^n$ is 6561.

$\therefore (1+2{)}^n=6561$                          [Putting $x=1$]

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

The general term in the expansion of ${\left(\frac{1}{x}+2x\right)}^n$ is given by

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

This will be independent of $x$ if $r=4.$

Hence, the constant term ${=}^8{C}_4{2}^4.$