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Q.
The term independent of $x$ in the expansion of $\left(x^3+\frac{2}{x^2}\right)^{15}$ is
Binomial Theorem
Solution:
$T _{ r +1}={ }^{15} C _{ r } \cdot\left( x ^3\right)^{15- r }\left(\frac{2}{ x ^2}\right)^{ r } $
$={ }^{15} C _{ r } x ^{45-3 r } \cdot 2^{ r } \cdot x ^{-2 r } $
$={ }^{15} C _{ r } x ^{45-5 r } \cdot 2^{ r }$
Term independent of ' $x$ ' $\Rightarrow 45-5 r =0 \Rightarrow r =9$
$\text { Term }= T _{9+1}= T _{10}$