Final answer:
In the event of a two-way radio communications failure under IFR conditions, a pilot should follow the last ATC clearance received, the route ATC advised to expect, or, if none, the route filed in the flight plan.
Step-by-step explanation:
When a pilot is operating under IFR conditions and experiences a two-way radio communications failure, there is a specific protocol to follow regarding the route to be flown. The correct procedure is outlined in aviation regulations, such as FAA's FAR Part 91. According to these regulations, the pilot should continue the flight by the route assigned in the last ATC clearance received. If being vectored, the pilot should fly the direct route from the point of radio failure to the fix, route, or airway specified in the vector clearance. In the absence of an assigned route, the pilot should revert to the route that ATC has advised to expect in a further clearance. As a last resort, if no such route has been advised, the pilot would follow the route filed in the flight plan.