QJEEM23Ma8649: JEE Main 2023 Mathematics - Class 11 JEEM23Ma8649 Solution: The coefficient of , in the expansion of , is

Question

Verified Solution • 2025–26 Session moderate

The coefficient of

x^{-6}

, in the

expansion of

\left(\frac{4 x}{5}+\frac{5}{2 x^{2}}\right)^{9}

, is

Accepted Answer

Coeff of

x^{-6}

in

\left(\frac{4 x}{5}+\frac{5}{2 x^{2}}\right)^{9}

\begin{aligned} T_{r + 1} & =^{9} C_{r} {(\frac{4 x}{5})}^{9 - r} {(\frac{5}{2 x^{2}})}^{r} \\ 9 - 3 r & = - 6 \\ r & = 5 \end{aligned}

Coeff of

x^{-6}={ }^{9} C_{5}\left(\frac{4}{5}\right)^{4}\left(\frac{5}{2}\right)^{5}

= 5040

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