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 :
\[|u|+|v|\,=x\] \[m=-\frac{v}{u}\] \[|v|\,=mu\] 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 \[\frac{1+m}{mx}-\left[ -\left( \frac{1+m}{x} \right) \right]=\frac{1}{f}\] \[\Rightarrow \] \[f=\frac{mx}{{{(1+m)}^{2}}}\]You need to login to perform this action.
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