Introduction:
The given events are related to the industrial development in India during the colonial period. The chronological order of these events is as follows:

1. Establishment of the first modern cotton mill in India:
- This event took place in the early 19th century.
- The first modern cotton mill was established in Bombay (now Mumbai) in 1854 by a Parsi entrepreneur, Jamsetjee Nusserwanjee Tata.
- This marked the beginning of the textile industry in India, which played a significant role in the country's industrialization.

2. Introduction of railways in India:
- The introduction of railways in India was a major development in the mid-19th century.
- The first railway line was opened for public use in 1853, which connected Bombay with Thane.
- The railway network expanded rapidly, connecting different parts of the country and transforming transportation, trade, and communication.

3. The establishment of the first jute mill at Rishra, West Bengal:
- The establishment of the first jute mill in India took place in the late 19th century.
- The mill was set up in Rishra, near Kolkata, in 1855 by George Acland and John C. McAdam.
- Jute, a natural fiber, became a major cash crop in Bengal, and the jute industry played a significant role in the industrialization of the region.

Chronological Order:
Based on the information provided, the correct chronological order of these events is:
2-1-3

Explanation:
The introduction of railways in India (event 2) took place before the establishment of the first modern cotton mill (event 1) and the first jute mill (event 3). The railways played a crucial role in facilitating the transportation of raw materials, finished goods, and people, which contributed to the growth of industries like cotton and jute mills. Therefore, event 2 predates events 1 and 3.

The establishment of the first modern cotton mill (event 1) occurred after the introduction of railways. The availability of the railway network enabled the transportation of raw cotton from various regions to the mills and facilitated the distribution of finished cotton goods across the country. Thus, event 1 follows event 2.

The establishment of the first jute mill (event 3) happened after the establishment of the first cotton mill. The success of the cotton industry inspired entrepreneurs to explore other industries, leading to the establishment of jute mills. The jute industry developed in Bengal due to the availability of jute fiber in the region. Hence, event 3 follows events 1 and 2.

Therefore, the correct chronological order is 2-1-3 (events 2, 1, and 3).