If a term independent of x in the expansion of ${\left(\mathrm{x}+\frac{1}{{\mathrm{x}}^2}\right)}^{\mathrm{n}}$ exists, then one of the possible value of n is

$\begin{array}{rcl} & & {\left(\mathrm{x}+\frac{1}{{\mathrm{x}}^2}\right)}^{\mathrm{n}}\\ \mathrm{G}.\mathrm{T}& =& {}^{\mathrm{n}}{\mathrm{C}}_{\mathrm{r}} {\left(\mathrm{x}\right)}^{\mathrm{n}-\mathrm{r}} {\left(\frac{1}{{\mathrm{x}}^2}\right)}^{\mathrm{r}}\\ & =& {}^{\mathrm{n}}{\mathrm{C}}_{\mathrm{r}} {\mathrm{x}}^{\mathrm{n}-3\mathrm{r}}\end{array}$

For Independent term  $\mathrm{n}-3\mathrm{r}=0$

                                                 $\mathrm{n}=3\mathrm{r}$

    $\therefore$ n must be a multiple of 3

    $\therefore \mathrm{n}=2010$