A) \[4:1\]
B) \[25:9\]
C) \[16:9\]
D) \[5:3\]
Correct Answer: B
Solution :
| \[\frac{{{\text{I}}_{\text{max}}}}{{{\text{I}}_{\text{min}}}}\,=\,16\]\[\Rightarrow \] \[\frac{{{\text{A}}_{\text{max}}}}{{{\text{A}}_{\text{min}}}}\,\text{=}\,\text{4}\] |
| \[\Rightarrow \] \[\frac{{{\text{A}}_{1}}+{{\text{A}}_{2}}}{{{\text{A}}_{1}}-{{\text{A}}_{2}}}=\,\frac{4}{1}\] |
| Using componendo and dividendo |
| \[\frac{{{\text{A}}_{1}}}{{{\text{A}}_{2}}}\,=\,\frac{5}{3}\] |
| \[\Rightarrow \] \[\frac{{{\text{I}}_{\text{1}}}}{{{\text{I}}_{\text{2}}}}\,\text{=}\,{{\left( \frac{\text{5}}{\text{3}} \right)}^{\text{2}}}\text{=}\frac{\text{25}}{\text{9}}\text{.}\] |
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