Final answer:
A pilot flying under IFR using V32 should make a position report upon crossing the Battle Mountain VOR if radar contact is lost, including details such as position, time, altitude, ETA, and the next reporting point.
Step-by-step explanation:
If you are flying along V32 from Lovelock (LLC) VOR to Elko Regional Airport (KEKO) and experience oxygen equipment failure which forces you to maintain the Minimum Enroute Altitude (MEA) of 11,000 feet, and you are at the FESKO intersection eastbound with Center having lost radar contact with you, there is a specific action required upon crossing the Battle Mountain VOR (BAM). Given the options provided, the correct action to take is to: Make a position report giving position, time, altitude, ETA to the next reporting point, and the name of the reporting point beyond that.
This is in accordance with FAA regulations which require pilots to make periodic position reports over specified reporting points while on IFR flights in non-radar environments. Landing at Battle Mountain airport to repair the oxygen tanks, requesting a lower MEA, or doing nothing are not the required actions specified by the question scenario. Therefore, the correct answer is to make a position report upon crossing Battle Mountain VOR (BAM).