Find the coefficient of 1 y^ 2 in (y+ c y^ 2 )^ 10 . - Vidyadip

MCQ

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

✓
$ 210 c^4 $
B
$ 210 c^5 $
C
$ 120 c^3 $
D
$ 120 c^4 $

✓

Answer

Correct option: A.

$ 210 c^4 $

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

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