If the term independent of x in the expansion of ${\left(\sqrt{\mathrm{x}}-\frac{\mathrm{k}}{{\mathrm{x}}^2}\right)}^{10}$ is 405 , then k=

$(\mathrm{r}+1{)}^{\text{th }}\text{ term of }{\left(\sqrt{\mathrm{x}}-\frac{\mathrm{k}}{{\mathrm{x}}^2}\right)}^{10}{\text{ is }}^{10}{\mathrm{C}}_{\mathrm{r}}(\sqrt{\mathrm{x}}{)}^{10-\mathrm{r}}{\left(-\frac{\mathrm{k}}{{\mathrm{x}}^2}\right)}^{\mathrm{r}}$

${\mathrm{T}}_{\mathrm{r}+1}{=}^{10}{\mathrm{C}}_{\mathrm{r}}(\sqrt{\mathrm{x}}{)}^{10-\mathrm{r}}{\left(-\frac{\mathrm{k}}{{\mathrm{x}}^2}\right)}^{\mathrm{r}}$

The term independent of x

$\frac{10-r}{2}-2r=0$

r=2

Hence,

${ }^{10}{\mathrm{C}}_2(-\mathrm{k}{)}^2=405$
k=$\pm 3$