mode of heat transfer in

1) A paper cup full of hot soup lying on the table

2) cooking vegetables in a pan

1)

Soup being a fluid the heat from it will spread to the surrounding via convection. Air near the soup will get heated and move away allowing cooler air to come to its contact and this process of convection repeats until the soup cools down.

2)

Heat from the cooking pan will be transferred to vegetables via conduction, since, cooking pan is made up of metal.