Explanation: To understand the context of the statements provided, it is essential to delve into the historical and geographical aspects of the Delhi Metro and the Delhi Sultanate.
**Delhi Metro and Agra:**
The Delhi Metro is a rapid transit system that serves the National Capital Region of India, primarily focusing on the city of Delhi and its immediate suburbs. While Agra is a significant city in Uttar Pradesh, it is not connected directly by the Delhi Metro. The Delhi Metro's network is designed to cater to the urban transportation needs of Delhi and its surrounding areas, and it does not extend to Agra, which is approximately 200 kilometers away. Therefore, the first statement is incorrect.
**Administrators, Poets, Courtiers, and Secretaries:**
During the period of the Delhi Sultanate, the administrative structure was centralized, with key officials such as administrators, poets, courtiers, and secretaries residing in urban centers. These individuals were crucial for the functioning of the Sultanate's administration and were typically based in the capital city of Delhi or other major urban centers. The idea that they lived in villages is a misconception, as the administrative and cultural activities were concentrated in urban areas. Thus, the second statement is incorrect.
**Territorial Decline of the Delhi Sultanate:**
By the early 16th century, the Delhi Sultanate had indeed experienced a significant reduction in its territorial control. The Sultanate, which had once stretched over large parts of the Indian subcontinent, faced internal conflicts and external threats, particularly from the Mughals. The Mughal invasions, led by Babur, marked the beginning of the end for the Delhi Sultanate. By the early 16th century, the Sultanate's influence had diminished, and it was no longer the dominant power in the region. Therefore, the third statement is correct.
In summary, the correct answer is (C) Only 3, as it accurately reflects the historical context of the territorial decline of the Delhi Sultanate by the early 16th century. The other statements are incorrect due to misconceptions about the Delhi Metro's reach and the living arrangements of key officials during the Sultanate period.