Which of the following signal indications require a train to reduce its speed to 30 mph in manual block?

The choice highlighting Caution and Approach as indications that require a train to reduce its speed to 30 mph in manual block is accurate because these signals are specifically designed to communicate safety-related information about the track ahead.

When a train receives a Caution signal, it warns the crew that they must be prepared to face a potential stop or a more restrictive signal further down the line, meaning they should slow down to ensure safety. The Approach signal indicates that a stop signal is ahead, again necessitating a reduction in speed to ensure the crew can react appropriately if the subsequent signal is indeed a stop signal.

In the context of the LIRR operational rules, understanding the function and implications of these signals is crucial. They ensure that the train crew has sufficient time to recognize, react to, and comply with upcoming track conditions. This significantly enhances safety on the network, particularly in areas where manual block operations are in place, imposing specific speed limits for the safety of the train and passengers.

The other options do not correctly identify the combination of signals that necessitate the 30 mph speed limit in manual block situations.