Question

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

• A. 3
• B. 5
• C. 6
• D. 12

Answer 1

Answer: (C)

$E={\left[{\left(e^{x/2}+e^{-x/2}\right)}^2+x\right]}^{20}$
$\text{ term independent of }x={}^{20}{C}_0{}^{40}{C}_{20}$
$={}^{40}{C}_{20}$
$n=40,m=20$ .