Which of the following network media connectors can use a MAXIMUM of two copper wire pairs?

The F-connector is used with coaxial cable, which has a single center conductor and a shield - it does not use copper wire pairs at all.

RJ-11 connectors have a 6-position housing and can accommodate a maximum of two copper wire pairs (4 conductors), making them suitable for standard analog telephone lines and basic DSL connections. In most deployments only one pair is active, but the physical connector design caps out at two pairs. This distinguishes it from RJ-45, which supports up to four pairs for Ethernet use.

MTRJ (Mechanical Transfer Registered Jack) is a fiber optic connector that carries two optical fibers, not copper wire pairs.

RJ-45 supports up to four copper wire pairs (8 conductors), which exceeds the two-pair maximum asked about in the question.