An infinitely long hollow conducting cylinder with radius R carries...

According to Ampere's law,

$∮ \overset{\to}{B} \cdot d \overset{\to}{l} = {\mu}_{0}i$

Inside the hollow cylinder, current will be zero. Therefore, magnetic field will also be zero.

Outside the cylinder,

$B2\pir = {\mu}_{0}i ⇒ B = \dfrac{{\mu}_{0}i}{2\pir} ⇒ B ∝ \dfrac{1}{r}$

Hence, the correct answer is D.