QJEEM23Mae192: JEE Main 2023 Mathematics - Class 11 JEEM23Mae192 Solution: The coefficient of in the expansion of is :

Question

Verified Solution • 2025–26 Session moderate

The coefficient of $x^{5}$ in the expansion of $\left(2 x^{3}-\frac{1}{3 x^{2}}\right)^{5}$ is :

Accepted Answer

Given,

\left(2 x^{3}-\frac{1}{3 x^{2}}\right)^{5}

General term,

\begin{aligned}&amp; T_{r+1}={ }^5 C_r\left(2 x^3\right)^{5-r}\left(\frac{-1}{3 x^2}\right)^r={ }^5 C_r \frac{(2)^{5-r}}{(-3)^r}(x)^{15-5 r} \\\\&amp; \therefore 15-5 \mathrm{r}=5 \\\\&amp; \therefore \mathrm{r}=2 \\\\&amp; T_3=10\left(\frac{8}{9}\right) x^5\end{aligned}

So, coefficient is

\frac{80}{9}

.

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