Question

tea cools faster in plate then in cup

Answer 1

I am not sure about my answer. I think that the cup of tea cools down by the following modes:

Radiation between the surface of the tea and the air molecules.
Conduction between the tea and the cup itself and between the cup and the table or whatever the surface is.

Answer 2

In plate the tea gets cool air from all sides but in cups we are getting cool air from upside only.