If Emperor Trajan had conquered India and the Romans had held it for several centuries, the country might be different in several significant ways.

First, the administrative structure would have been transformed. The Romans organized all territories into provinces subject to taxation. India would likely have been divided into provinces with a systematic taxation system, creating a more centralized administrative framework.

Second, urbanisation would have been a major feature of Indian society. The context states that urbanisation was the key to how the Roman Empire managed its vast and diverse territories. India might have developed numerous Roman-style cities with distinct urban planning and infrastructure.

Third, the legal position of women might have been stronger. The textbook notes that Roman women had a stronger legal position than they do in many countries today. This could have led to more progressive laws regarding women's rights and property.

Fourth, the economy would have been heavily dependent on slave labour. Much of the Roman economy was run on slave labour, denying freedom to substantial numbers of persons. This institution might have become deeply entrenched in Indian society.

Finally, despite Roman rule, local cultures and languages would likely have survived. The Roman Empire embraced a wealth of local cultures and languages across its territories, suggesting that India's diverse traditions would have been preserved alongside Roman influences.