The sum of coefficients of integral powers of x in the binomial expansion of ${(1-2\sqrt{x})}^{50} is$ is

${\left(1-2\sqrt{\mathrm{x}}\right)}^{50}=1-{}^{50}{\mathrm{C}}_1 \left(2\sqrt{\mathrm{x}}\right)+{}^{50}{\mathrm{C}}_2 {\left(2\sqrt{\mathrm{x}}\right)}^2-{}^{50}{\mathrm{C}}_3 {\left(2\sqrt{\mathrm{x}}\right)}^3$

                            $+{}^{50}{\mathrm{C}}_4 {\left(2\sqrt{\mathrm{x}}\right)}^4-......{}^{50}{\mathrm{C}}_{50} {\left(2\sqrt{\mathrm{x}}\right)}^{50}$

Sum of the Coeff of Integral Powers of x

$$\begin{gathered} =1+{}^{50}{\mathrm{C}}_2 2^2+{}^{50}{\mathrm{C}}_4 2^4+{}^{50}{\mathrm{C}}_6 2^6+.....+{}^{50}{\mathrm{C}}_{50} 2^{50} \\ =\frac{\mathrm{f}\left(1\right)+\mathrm{f}(-1)}{2} \mathrm{is} {(1+2\mathrm{x})}^{50} \\ =\frac{3^{50}+1}{2} \end{gathered}$$