Option 1 (trusted) -> Grammatically incorrect; "trusted with" is not the proper construction in this context.
Option 2 (mistrusted) -> Does not form a valid collocation with "with the care of."
Option 3 (entrusted) -> Forms the correct phrase "entrusted with," meaning to assign responsibility or trust to someone for a task.
Option 4 (encouraged) -> Grammatically incorrect; "encouraged with" doesn't work in this context.
Hence, Option 3: entrusted -> "Entrusted with" is the proper collocation that means the senior officer was given the responsibility and trust to care for the new recruits -> correct