Under what circumstances can a train operator enter an under-river tunnel during a smoke condition?

The correct choice is that a train operator should not enter an under-river tunnel when smoke is present under any circumstances. This rule is in place primarily for the safety of both the train operator and any passengers on board. Smoke indicates a potential fire, which can be dangerous and may lead to hazardous conditions, such as reduced visibility, toxic air, or even the risk of a fire spreading.

The fundamental principle here is to prioritize safety above all else during smoke conditions. Entering a tunnel filled with smoke can complicate evacuation efforts and increase the risk of exposure to harmful substances.

Considering the other options, while they might suggest scenarios where a train operator could enter a tunnel under certain conditions, each option introduces significant risk factors that compromise safety. For instance, relying on the Control Center's instructions does not eliminate the inherent dangers of smoke. Similarly, minimal smoke or functional ventilation systems do not guarantee safety, as the situation can rapidly deteriorate, and those features might not be sufficient to ensure a safe passage. Thus, it is critical to adhere strictly to the guideline of avoiding entry into tunnels under smoke conditions to ensure the safety of everyone involved.