The middle term of expansion of (10/x+x/10 )^10

Correct answer: (D) ^10^10 C_5. Given expression, (10/x+x/10 )^10 here n=10 . So, middle term is 6 th term Therefore, T_6=^10 C_5 (10/(χ) )^5 ((χ)/10 )^5=^10 C_5

Q67 / 180 · KCET 2015 · Mathematics

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

A
\( {}^{7} C_{5} \)
B
\( { }_{0}^{8} C_{5} \)
C
\( { }_{0}^{9} C_{5} \)
Correct answer
D
\( { }^{10}{ }^{10} C_{5} \)

Solution

Given expression, \( \left(\frac{10}{x}+\frac{x}{10}\right)^{10} \)
here \( n=10 \). So, middle term is \( 6 \) th term
Therefore, \( T_{6}={ }^{10} C_{5}\left(\frac{10}{\chi}\right)^{5}\left(\frac{\chi}{10}\right)^{5}={ }^{10} C_{5} \)

Hence, the correct answer is option: 'D'.

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