Let [t] denote the greatest integer <t. If the constant term in the expansion of ${(3{\mathrm{x}}^2-\frac{1}{2{\mathrm{x}}^5})}^7\mathrm{is}\mathrm{\alpha },\mathrm{then}\left[\mathrm{\alpha }\right]$  is equal to …… 

$\text{ General term }\left(T_{r+1}\right){=}^7{C}_r{\left(3x^2\right)}^{7-r}{\left(-\frac{1}{2x^5}\right)}^r$
$T_{r+1}={(-1{)}^r}^7{C}_r{3}^{7-r}\cdot 2^{-r}{x}^{14-7r}$
$14-7r=0\Rightarrow \mathrm{r}=2$
$\text{ Constant term }=a=(-1{)}^2{\cdot }^7{C}_2\cdot 3^5\cdot 2^{-2}=\frac{5103}{4}$
$\begin{array}{r}a=1275.75\\ \Rightarrow \left[a\right]=1275\end{array}$