Coefficient of constant term in the expansion of

${\left(x^3+5(3{)}^{-\log \sqrt{3}}\sqrt{x^3}\right)}^4$ is 

Let $y=3^{-{\log }_{\sqrt{3}}}\left(x^{3/2}\right)$

$\Rightarrow {\log }_3 y=-\frac{{\log }_3 \left(x^{3/2}\right)}{{\log }_3 \sqrt{3}}=-2{\log }_3 \left(x^{3/2}\right)$

$\Rightarrow y=x^{-3}$

$(r + 1)$th term in the expansion of 

$\begin{array}{l}{\left(x^3+5x^{-3}\right)}^4\text{ is }\\ T_{r+1}{=}^4{C}_r{\left(x^3\right)}^{4-r}{\left(5x^{-3}\right)}^r\\ {=}^4{C}_r{5}^r{x}^{12-3r-3r}\end{array}$

For $(r + 1)$th term to be independent of $x,$ set $12 – 6r$

$=0\text{ or }r=2$

$\therefore$ required constant term

${=}^4{C}_2{5}^2=\left(6\right)\left(25\right)=150$