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