"Left" is the past participle of "leave". With "left", the item receivesreceives the action, so you use passive voice:
How many classes are left today?
How many eggs are left in the refrigerator?
With "remain", the item performsperforms the action, so you should say:
How many classes remain today?
How many eggs remain in the refrigerator?
How many classes are remaining today?
How many eggs are remaining in the refrigerator?
Here "are remaining" is present progressive rather than passive voice. Also, since "classes" and "eggs" are plural, you should use "remain".