A) \[{{a}^{3}}/{{b}^{3}}\]
B) \[{{a}^{4}}/{{b}^{4}}\]
C) \[{{b}^{3}}/{{a}^{3}}\]
D) \[{{b}^{4}}/{{a}^{4}}\]
Correct Answer: B
Solution :
| Since, a b, c, d and e are in continued proportion. |
| \[\therefore \] \[\frac{a}{b}=\frac{b}{c}=\frac{c}{d}=\frac{d}{e}\] |
| \[\Rightarrow \] \[\frac{e}{d}=\frac{d}{c}=\frac{c}{b}=\frac{b}{a}\] |
| \[\therefore \] \[c=\frac{{{b}^{2}}}{a}\] \[\left( \because \frac{c}{b}=\frac{b}{a} \right)\] |
| \[\therefore \]\[d=\frac{{{c}^{2}}}{b}=\frac{{{b}^{4}}}{{{a}^{2}}}\cdot \frac{1}{b}=\frac{{{b}^{3}}}{{{a}^{2}}}\] |
| \[\therefore \]\[e=\frac{{{d}^{2}}}{c}=\frac{{{b}^{6}}}{{{a}^{4}}}\cdot \frac{a}{{{b}^{2}}}=\frac{{{b}^{4}}}{{{a}^{3}}}\] |
| \[\therefore \]\[\frac{a}{e}=\frac{a}{({{b}^{4}}/{{a}^{3}})}=\frac{{{a}^{4}}}{{{b}^{4}}}\] |
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