question_answer

The minimum distance between a point on the curve \[y={{e}^{x}}\]and a point on the curve \[y={{\log }_{e}}x\] is

A) \[\frac{1}{\sqrt{2}}\]

B) \[\sqrt{2}\]

C) \[\sqrt{3}\]        

D) \[2\sqrt{2}\]     

Correct Answer: B

Solution :

\[y={{e}^{x}}\]and \[y={{\log }_{e}}x\]are inverse of each other Minimum distance of the curve at (0, 1) and \[(1,0).\] \[\sqrt{1+1}=\sqrt{2}\]