Question

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

• A. ${}^7{C}_5$
• B. ${}^8{C}_5$
• C. ${}^9{C}_5$
• D. ${}^{10}{C}_5$

Answer 1

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

Given

Fact: middle in the expansion of $(x+y{)}^n$ will be $(\frac{n}{2}+1)$th term if $n$ is even

Hence $n=10=$ even

So middle term will be $6$th term

Which is given by, ${}^{10}{C}_5{\left(\frac{10}{x}\right)}^5{\left(\frac{x}{10}\right)}^5{=}^{10}{C}_5$