Question

The coefficient of $\frac{1}{y^2}$ in ${(y-\frac{c^3}{y^2})}^{10}$ in is

• A. $187c^{12}$
• B. $\frac{210}{c^{12}}$
• C. $\frac{c^{12}}{210}$
• D. $210c^{12}$

Answer 1

Answer: (D)

$210c^{12}$

$T_{r+1}={}^{10}{C}_r{y}^{10-r}{\left(\frac{-C^3}{y^2}\right)}^{10-r}$

$={}^{10}{C}_r{y}^{10-r}(-1{)}^x{C}^{3r}{y}^{-2r}$

$={}^{10}{C}_r{y}^{10-3r}(-1{)}^r{C}^{3r}$

For coefficient of $y^{-2}$

$10-3r=-2$

$12=3r$

$r=4$

$\Rightarrow {}^{10}{C}_4{C}^{12}$

$\Rightarrow \frac{10\times 9\times 8\times 7}{4\times 3\times 2}\times C^{12}=210C^{12}$.