Question

Find the coefficient of $\frac{1}{y^2}$ in ${(y+\frac{c}{y^2})}^{10}$.

• A. $210c^4$
• B. $210c^5$
• C. $120c^3$
• D. $120c^4$

Answer 1

The correct option is A $210c^4$

$(y+\frac{c}{y^2}{)}^{10}$
$T_{r+1}={}^{10}{C}_r{y}^{10-3r}{c}^r$
Hence for $y^{-2}$
$10-3r=-2$
$12=3r$
$r=4$
Coefficient will be
${}^{10}{C}_4{c}^4$
$=210c^4$