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Q.
If the term independent of $x$ in the expansion of $\left(e^x+e^{-x}+\ln e^{x+2}\right)^{20}{ }^2{ }^n C_m$, then the least value of $\left(\frac{ n + m }{10}\right)$ is
Binomial Theorem
Solution:
$ E =\left[\left( e ^{ x / 2}+ e ^{- x / 2}\right)^2+ x \right]^{20} $
$\text { term independent of } x ={ }^{20} C _0{ }^{40} C _{20} $
$={ }^{40} C _{20}$
$n =40, m =20$ .