Question

In the expansion of ${(x+\frac{1}{x})}^{10}$ the coefficient of middle term is

• A. ${}^{10}{C}_4$
• B. ${}^{-10}{C}_4$
• C. ${}^{10}{C}_5$
• D. ${}^{10}{C}_6$

Answer 1

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

Since the total number of term is 11, which is odd, hence there will be only one middle term.

Thus the middle term will be $\frac{n}{2}+1$ th term

$=6th$ term

$T_6$

$=T_{5+1}$

$={}^{10}{C}_5{x}^{10-5}.x^{-5}$
$={}^{10}{C}_5$

Hence the coefficient of the middle term is ${}^{10}{C}_5$