The relationship between British India and the feudatory states was formalized through:

Treaties and agreements
Royal decrees
Military conquest
Democratic elections

The correct answer is: a) Treaties and agreements.

The British East India Company established trading posts in India in the early 17th century. Over time, the company gained control of more and more territory, and by the 18th century it was effectively ruling most of India. The company’s rule was based on a system of treaties and agreements with local rulers. These treaties gave the company control over certain areas in exchange for protection and other benefits.

The relationship between British India and the feudatory states was complex and ever-changing. The company often intervened in the affairs of the states, and there were frequent disputes between the two sides. However, the treaties and agreements provided a framework for the relationship, and they helped to maintain stability in India for many years.

Option b) is incorrect because royal decrees were not the primary means of formalizing the relationship between British India and the feudatory states. Option c) is incorrect because military conquest was not the primary means of formalizing the relationship between British India and the feudatory states. Option d) is incorrect because democratic elections were not held in British India during the period in question.