The correct answer is option 'C': Hindu, Muslims, and British periods. Let's explore this answer in detail:

1. Hindu Period:
The Hindu period refers to the ancient and medieval periods of Indian history when Hinduism was the dominant religion and Hindu rulers governed various regions of India. This period extends from ancient times to the 12th century when Muslim invasions began.

2. Muslim Period:
The Muslim period refers to the period of Indian history when Muslim rulers and dynasties ruled over parts or the whole of India. It began with the arrival of Arab traders in the 7th century and continued with the establishment of the Delhi Sultanate in the 13th century. The Mughal Empire also played a significant role during this period, from the 16th to the 18th century.

3. British Period:
The British period refers to the period of Indian history when India was under British colonial rule. It began with the establishment of the East India Company's trading posts in the 17th century and continued until India gained independence in 1947. This period witnessed significant political, economic, and social changes as British administrators and policies had a profound impact on Indian society.

Explanation:
The division of Indian history into Hindu, Muslims, and British periods is based on the major political and cultural influences that shaped India during these times. This categorization helps in understanding the different phases of Indian history and the significant events that occurred during each period.

The Hindu period represents the indigenous rulers and the development of Hindu culture and civilization in India. The Muslim period highlights the impact of Islamic rulers and their contributions to Indian society, such as the establishment of new dynasties, architectural marvels like the Taj Mahal, and the synthesis of Hindu and Islamic traditions.

The British period marks a significant turning point in Indian history as it witnessed the decline of Muslim rulers and the establishment of British colonial rule. This period saw the introduction of British administration, education, legal systems, and the exploitation of Indian resources for British economic gains. The Indian independence movement also gained momentum during this period, leading to India's struggle for freedom.

In conclusion, dividing Indian history into Hindu, Muslims, and British periods helps in understanding the different phases and influences that have shaped the country over centuries.