The middle term of expansion ( 10 x + x 10 ) 10 is

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Solution

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

1 ${}^{8}C_{5}$

2 ${}^{10}C_{5}$

3 ${}^{7}C_{5}$

4 ${}^{9}C_{5}$

Ans.
(2)

$Given expansion is {(\frac{10}{x} + \frac{x}{10})}^{10}$

Since, $n = 10$ is even

$∴$ $Middle term = t_{\frac{n}{2} + 1} = t_{6}$

$∴$ $t_{6} = {}^{10}C_{5} {(\frac{10}{x})}^{5} {(\frac{x}{10})}^{5} = {}^{10}C_{5}$

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