Explanation:

During British Rule, the industrial development in India was largely shaped to serve British economic interests. The **Cotton Textile** industry (i) saw significant growth, particularly with the establishment of mills in Bombay and Ahmedabad from the mid-19th century. This was driven by indigenous entrepreneurship and the availability of raw cotton, though it faced stiff competition from British imports. **Coal Mines** (iii) also flourished, primarily to meet the demands of the expanding railway network in India and to supply fuel for British industries. The British actively developed coal mining to facilitate their infrastructure and industrial needs. However, **Heavy engineering machines** (ii) did *not* flourish in India under British rule. The British deliberately discouraged the development of heavy industries in India to prevent competition with their own manufacturing sector and to ensure India remained a market for British finished goods and a supplier of raw materials. Therefore, only (i) and (iii) flourished. Option C is correct.