Indigo cultivation in India declined by the beginning of the 20th century because of

The correct option is "its unprofitability in the world market because of new inventions".

Detailed Explanation:

Indigo cultivation in India had been highly lucrative for British planters throughout the 18th and 19th centuries due to the high demand for natural blue dye in Europe. However, by the late 19th and early 20th centuries, this demand experienced a severe decline.

The primary reason for this decline was the invention of synthetic indigo (artificial chemical dyes) in Germany. German chemists successfully synthesized indigo, which was much cheaper to produce, easier to standardize, and more durable than the natural dye extracted from indigo plants in India.
As a result, natural indigo could no longer compete with the cheaper and more efficient synthetic alternative in the global market. This made indigo cultivation in India highly unprofitable, leading to a rapid decline of the industry by the beginning of the 20th century.