If A = 1 + 2^P and B = 1 + 2^-P, then what is the value of B?

A. $$\frac{{A + 1}}{{A - 1}}$$

B. $$\frac{{A + 2}}{{A + 1}}$$

C. $$\frac{A}{{A - 1}}$$

D. $$\frac{{A - 2}}{{A + 1}}$$

Answer: Option C

Solution(By Examveda Team)

$$\eqalign{ & A = 1 + {2^P} \cr & B = 1 + {2^{ - P}} \cr & {\text{Put }}P = 1 \cr & A = 3,\,B = \frac{3}{2} \cr & {\text{Option C is correct}} \cr & \cr & {\bf{Alternate:}} \cr & A = 1 + {2^P}\,......\,\left( {\text{i}} \right) \cr & B = 1 + {2^{ - P}} \cr & = 1 + \frac{1}{{{2^P}}} \cr & = \frac{{{2^P} + 1}}{{{2^P}}} \cr & = \frac{A}{{A - 1}}\,\,\,\,\,\left( {{\text{from equation }}\left( {\text{i}} \right)} \right) \cr} $$