Question

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

• A. 2, -2
• B. 3, -3
• C. 4, -4
• D. 1, -1

Answer 1

Answer: (B)

3, -3

For the above binomial equation,
$T_{r+1}={}^{10}{C}_r{k}^r{x}^{5-\frac{5r}{2}}$ ...(i)
For the term independent of x
$5=\frac{5r}{2}$
$r=2$
Substituting in i, we get
$T_3={}^{10}{C}_2{k}^3$
$=405$
$45k^2=405$
$k^2=9$
$k=\pm 3$