A) \[{{10}^{2}}\]
B) 10
C) 0.1
D) 0.01
Correct Answer: B
Solution :
\[\sqrt{\frac{{{(0.1)}^{2}}+{{(0.01)}^{2}}+{{(0.009)}^{2}}}{{{(0.01)}^{2}}+{{(0.001)}^{2}}+{{(0.0009)}^{2}}}}\] \[=\sqrt{\frac{{{\left( \frac{1}{10} \right)}^{2}}+{{\left( \frac{1}{100} \right)}^{2}}+{{\left( \frac{9}{1000} \right)}^{2}}}{{{\left( \frac{1}{100} \right)}^{2}}+{{\left( \frac{1}{1000} \right)}^{2}}+{{\left( \frac{9}{10000} \right)}^{2}}}}\] \[=\sqrt{\frac{{{\left( \frac{1}{10} \right)}^{2}}+{{\left( \frac{1}{100} \right)}^{2}}+{{\left( \frac{9}{1000} \right)}^{2}}}{{{\left( \frac{1}{10} \right)}^{2}}\left[ {{\left( \frac{1}{10} \right)}^{2}}+{{\left( \frac{1}{100} \right)}^{2}}+{{\left( \frac{9}{1000} \right)}^{2}} \right]}}\] \[=10\]
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