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Q.
The middle term in the expansion of $\left(\frac{10}{x}+\frac{x}{10}\right)^{10}$ is
Binomial Theorem
Solution:
General term $= T _{r+1}={ }^{10} C _{r}\left(\frac{10}{x}\right)^{10-r}\left(\frac{x}{10}\right)^{r}$
Here $n=10$, which is an even number.
Now, $\left[\frac{10}{2}+1\right]^{\text {th }}$ term i.e. $6^{\text {th }}$ term is the middle term.
Hence, middle term $= T _{6}$
$T _{5+1}={ }^{10} C _{5}\left(\frac{10}{x}\right)^{10-5}\left(\frac{x}{10}\right)^{5}={ }^{10} C _{5}\left(\frac{10}{x}\right)^{5}\left(\frac{x}{10}\right)^{5}={ }^{10} C _{5}$