Explain why:

(b) a brass tumbler feels much colder than a wooden tray on a chilly day

Brass is a good conductor of heat. When one touches a brass tumbler, heat is conducted from the body to the brass tumbler easily. Hence, the temperature of the body reduces to a lower value and one feels cooler.
Wood is a poor conductor of heat. When one touches a wooden tray, very little heat is conducted from the body to the wooden tray. Hence, there is only a negligible drop in the temperature of the body and one does not feel cool. 
Thus, a brass tumbler feels colder than a wooden tray on a chilly day.