Question

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

Answer 1

Answer: 3.00

$t_{r+1}={}^{10}{C}_r(\sqrt{x}{)}^{10-r}{\left(-\frac{k}{x^2}\right)}^r$
$={}^{10}{C}_r{x}^{5-\frac{5r}{2}}(-k{)}^r$
For the independent of $x,r$ must be $2$ so that
${}^{10}{C}_2{k}^2=405$
$\therefore k=3$