Question

The middle term in the expansion of ${(\frac{10}{x}+\frac{x}{10})}^{10}$ is

• A. ${}^{10}{C}_5$
• B. ${}^{10}{C}_6$
• C. ${}^{10}{C}_5\frac{1}{x^{10}}$
• D. ${}^{10}{C}_5{x}^{10}$
• E. ${}^{10}{C}_5{10}^{10}$

Answer 1

The correct option is A ${}^{10}{C}_5$

MIddle term of the expansion of ${(\frac{10}{x}+\frac{x}{10})}^{10}$ is $T_6.$

$T_6={}^{10}{C}_5{\left(\frac{10}{x}\right)}^5{\left(\frac{x}{10}\right)}^5$

$T_6={}^{10}{C}_5$

Hence, A is the correct option.