A) \[\text{ }\!\!\beta\!\!\text{ }\,\text{=}\,\frac{a}{1+a}\]
B) \[\text{ }\!\!\beta\!\!\text{ }\,\text{=}\,\frac{a+1}{a}\]
C) \[a\,\text{=}\,\frac{\text{ }\!\!\beta\!\!\text{ }}{a+\text{ }\!\!\beta\!\!\text{ }}\]
D) \[\,\text{ }\!\!\beta\!\!\text{ =}\,\frac{\text{ }\!\!\beta\!\!\text{ +1}}{\text{ }\!\!\beta\!\!\text{ }}\]
Correct Answer: C
Solution :
Relation between \[\alpha \] and \[\beta \] is given by \[\beta =\frac{\alpha }{1-\alpha }\] \[\Rightarrow \] \[\beta (1-\alpha )=\alpha \] \[\beta -\beta \alpha =\alpha \] \[\beta =\alpha (1+\beta )\] or \[\alpha =\left( \frac{\beta }{1+\beta } \right)\]
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