Concept:
Super elevation (cant) is the difference in level between the outer rail and the inner rail provided on railway curves to counteract centrifugal force.
According to the Indian Railways Permanent Way Manual,
the maximum permissible super elevation for Broad Gauge (BG) is
\[
\boxed{165\text{ mm}}
\]
which is commonly taken as
\[
\boxed{165.1\text{ mm}.}
\]
Step 1: Recall the standard value.
For Broad Gauge,
\[
e_{\max}=165\text{ mm}
\]
(approximately \(165.1\) mm).
Step 2: Select the correct option.
Therefore,
\[
\boxed{\text{Maximum permissible super elevation}=165.1\text{ mm}.}
\]
Hence, the correct option is
\[
\boxed{(D)\;165.1\text{ mm}.}
\]