A) 2
B) 3
C) 4
D) 9
Correct Answer: D
Solution :
\[\frac{a}{b}=\frac{c}{d}=\frac{e}{f}=3\] \[\Rightarrow \]\[a=3b:c=3d:e=3f\] \[\therefore \] \[\frac{2{{a}^{2}}+3{{c}^{2}}+4{{e}^{2}}}{2{{b}^{2}}+3{{d}^{2}}+4{{f}^{2}}}\] \[=\frac{2\times 9{{b}^{2}}+3\times 9{{d}^{2}}+4\times 9{{f}^{2}}}{2{{b}^{2}}+3{{d}^{2}}+4{{f}^{2}}}\] \[=\frac{9\left( 2{{b}^{2}}+3{{d}^{2}}+4{{f}^{2}} \right)}{2{{b}^{2}}+3{{d}^{2}}+4{{f}^{2}}}=9\]
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