When a capacitor is subjected to a D.C. source it takes small time internal to get fully charged up. During this small time interval there is no passage of charge through dielectric, yet we use a term - displacement current. This term is used because:

There is a continues change of electric field between plates and hence electric flux

The correct answer is Option (2) → There is a continues change of electric field between plates and hence electric flux

When a capacitor is connected on a DC source, it starts charging and due to it a displacement current is produced.

and, displacement current is used because there is continuous change in electric field and flux between the capacitor plates.