Question

The coefficient of $x^{30}$ in $(3x^2+\frac{2}{3x^2}{)}^{15}$ is

• A. ${}^{15}{C}_2{.3}^8{.2}^7$
• B. ${}^{15}{C}_1{.3}^7{.2}^8$
• C. $3^{15}$
• D. $3^{14}{.2}^2$

Answer 1

The correct option is C $3^{15}$

The general term is
$t_{r+1}{=}^{15}{C}_r.(3x^2{)}^{15-r}.(\frac{2}{3x^2}{)}^r$
If the power of $x$ in above general term should be $30$, we have,
$2(15-r)-2r=30$ which gives $r=0$.
Putting this value of $r$ in the general term expression, we get the coefficient of $x^{30}$ as $3^{15}$