Answer:Among the options given on the question the correct answer is option A and D.
A.Political movement worked to overthrow the government to create utopia.
D. Nomadic invaders sacked and destroyed property in the empire.
Explanation: The Roman empire was based of Rome and it was on of the powerful empires during that time. The Roman empire lasted for almost 503 years but technically it was lasted for 1000 years under the Byzantine empire.However the reason for falling of the Roman empire was attack of German Nomadic invaders and the the corrupted officials of the empire who did not obey their duty.
On the other hand the Han dynasty was the second dynasty of the China.It lasted for four centuries and succeeded by three kingdom periods. The Han dynasty became week by the attack after attack from the nomadic Xiongu later formed as Hun . They weakened the empire and later the empire came to an end. Moreover the assassination mentality grew up into the officials for higher posts.
The Gupta empire was one of the oldest empire of India and it lasted from 3rd century to CE 543. The empire is known as the golden period of Indian empire. But the attack from the tribal white Huna caused a lot of damage to the empire. Moreover many revolt from inside of the empire weakened the empire and made faster the fall of the empire.
So, it is seen that these three empires have some common reason for fall.