Question

If the third term in the expansion of ${(\frac{1}{x}+x^{log}{10}^x)}^5$ is 1000, then x =

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$3^{rd}term=1000\Rightarrow {}^5{C}_2{\left(\frac{1}{x}\right)}^{5-2}(x^{log}{10}^x{)}^2=1000\Rightarrow \frac{(x^{log}{10}^x{)}^2}{x^3}=100\Rightarrow x=100$