Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

$r=\frac{10\times \frac{1}{2}}{\frac{1}{2}+2}=\frac{10}{5}=2$

$\therefore$ Term independent of x is ${}^{10}{C}_2(-k{)}^2=45k^2.\therefore 45k^2=405\Rightarrow k^2=9\Rightarrow k=\pm 3$