The power of princely states declined with the rise of:

British colonialism
Mughal influence
Maratha Confederacy
Vijayanagara Empire

The correct answer is: a) British colonialism.

The British East India Company began to establish trading posts in India in the early 17th century. Over time, the Company’s influence in India grew, and it began to exert control over the country’s political and economic affairs. The British government took over direct control of India from the Company in 1858, and the British Raj (rule) lasted until India’s independence in 1947.

During the British Raj, the power of the princely states declined. The British government treated the princely states as independent entities, but they were ultimately under British control. The British government could interfere in the affairs of the princely states, and it could also depose their rulers.

The decline of the princely states was a result of a number of factors, including the British government’s policy of centralization, the rise of nationalism in India, and the economic and social changes that took place during the British Raj.

The British government’s policy of centralization was aimed at bringing all of India under its direct control. This policy led to the decline of the princely states, as they were increasingly subject to British control.

The rise of nationalism in India was another factor that contributed to the decline of the princely states. Indian nationalists opposed British rule, and they saw the princely states as a relic of the past. They argued that the princely states should be abolished and that India should be a united country.

The economic and social changes that took place during the British Raj also contributed to the decline of the princely states. The British introduced new technologies and industries to India, which led to the growth of a new middle class. This new middle class was educated and had a strong sense of national identity. They opposed the princely states, which they saw as outdated and corrupt.

The decline of the princely states was a complex process that was caused by a number of factors. The British government’s policy of centralization, the rise of nationalism in India, and the economic and social changes that took place during the British Raj all contributed to the decline of the princely states.