As of the Census Report 2011, the population of urban agglomerations in India was recorded in ascending order based on population:

1. Chennai (B):
  - Chennai, the capital city of the Indian state of Tamil Nadu, is the first in the list in ascending order. Chennai is a major cultural, economic, and educational center in southern India. The population of the urban agglomeration includes not only the city itself but also the surrounding areas that form a continuous urban area.

2. Kolkata (C):
  - Kolkata, the capital city of the Indian state of West Bengal, is the second in the list in ascending order. Kolkata is a historic city with significant cultural and economic importance. Like other major cities, its urban agglomeration includes both the city and the neighbouring areas that are closely connected economically and socially.

3. Delhi (A):
  - Delhi, the capital territory of India, is the fourth and last in the list in ascending order based on population as per the Census Report 2011. Delhi is a major political, cultural, and economic hub. The population includes not only the central urban area but also the extended National Capital Region (NCR) that encompasses neighbouring cities and towns.

4. Greater Mumbai (D):
  - Greater Mumbai, also known as Mumbai Metropolitan Region (MMR), is a vast urban agglomeration that includes Mumbai, the financial capital of India, along with its surrounding areas. It is the third in the list in ascending order based on population. Greater Mumbai is a densely populated and economically vibrant region.

So, option (4) (B), (C), (A), (D) is correct.