A) \[\frac{mx}{{{(m+1)}^{2}}}\]
B) \[\frac{mx}{{{(m-1)}^{2}}}\]
C) \[\frac{{{(m+1)}^{2}}}{mx}\]
D) \[\frac{{{(m-1)}^{2}}}{mx}\]
Correct Answer: A
Solution :
[a]| \[|u|+|v|\,=x\] |
| \[m=-\frac{v}{u}\] |
| \[|v|\,=mu\] |
| Using (i) and (ii), we get \[|u|+m|u|\,=x\] |
| \[\Rightarrow \] \[|u|\,=\frac{x}{1+m}\] and \[|v|=\frac{mx}{1+m}\] |
| Putting values of \[v\] and \[u\] in, \[\frac{1}{v}-\frac{1}{u}=\frac{1}{f},\] |
| we get \[\frac{1+m}{mx}-\left[ -\left( \frac{1+m}{x} \right) \right]=\frac{1}{f}\] \[\Rightarrow \] \[f=\frac{mx}{{{(1+m)}^{2}}}\] |
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