A) \[0.24\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
B) \[0.27\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
C) \[0.32\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
D) \[0.48\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
Correct Answer: B
Solution :
\[\frac{1}{{{\lambda }_{\alpha }}}={{(z-b)}^{2}}R\left[ \frac{1}{{{1}^{2}}}-\frac{1}{{{1}^{2}}} \right]\] \[\frac{1}{{{\lambda }_{\beta }}}={{(z-b)}^{2}}R\left[ \frac{1}{{{1}^{2}}}-\frac{1}{{{3}^{2}}} \right]\] \[\therefore \]\[\frac{{{\lambda }_{\beta }}}{{{\lambda }_{\alpha }}}=\frac{1-\frac{1}{4}}{1-\frac{1}{9}}=\frac{27}{32}\]\[\therefore \]\[{{\lambda }_{B}}=\frac{27}{32}{{\lambda }_{\alpha }}=\frac{27}{32}\times 0.32\,\overset{\text{o}}{\mathop{\text{A}}}\,\] \[=0.27\,\overset{\text{o}}{\mathop{\text{A}}}\,.\] Hence, the correction option is (b).
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