Explanation: To understand the context of the statements provided, it is essential to delve into the historical and demographic aspects of Tamil Nadu and Sri Lanka.
**Agricultural History of Tamil Nadu:**
Tamil Nadu has a rich agricultural history that dates back to ancient times. The region is known for its diverse agricultural practices, which have been documented in ancient Tamil literature such as the Sangam literature. The Sangam period, which is believed to have spanned from the 3rd century BCE to the 3rd century CE, provides evidence of advanced agricultural techniques and a well-developed agrarian society. Therefore, the claim that large-scale cultivation in Tamil Nadu began only after the 4th century CE is not accurate. Tamil Nadu's agricultural practices have a much longer and more complex history that predates this period.
**Demographics of Tamils in Sri Lanka:**
The Tamils in Sri Lanka are divided into two main groups: Sri Lankan Tamils and Indian Tamils. Sri Lankan Tamils are the descendants of the ancient inhabitants of Sri Lanka and have lived in the country for centuries. They are primarily concentrated in the northern and eastern provinces of Sri Lanka. Indian Tamils, on the other hand, are the descendants of Tamil-speaking laborers who were brought to Sri Lanka by the British during the colonial period to work on tea plantations. They are mainly found in the central and southern parts of the country. This classification is based on historical origins and migration patterns, and it is an important aspect of the demographic makeup of Sri Lanka.
**Capital of Tamil Nadu:**
The capital of Tamil Nadu is Chennai, formerly known as Madras. It is a major metropolitan city and the largest urban agglomeration in the state. Amaravati is not the capital of Tamil Nadu; it is a city in Andhra Pradesh, India, and is the proposed new capital of Andhra Pradesh.
In conclusion, the correct statement among the given options is statement 3, which correctly identifies the classification of Tamils in Sri Lanka. The other statements are not accurate, making option C the correct choice. Understanding the historical and demographic contexts is crucial for comprehending the complexities of Tamil Nadu's agricultural history and the demographic landscape of Sri Lanka.