Let's examine each of the pairs provided with reference to the history of India to determine which ones are correctly matched.

Understanding Historical Terms: Aurang, Banian, and Mirasidar

The question asks about the correct matching of historical terms with their descriptions in the context of Indian history. We need to understand the meaning and role of each term:

1. Aurang - In-charge of treasury of the State

The term 'Aurang' (also spelled 'Areng') in historical contexts, particularly during the Mughal and early British periods, referred to a warehouse or factory where goods were collected, produced, or stored, especially textiles or saltpetre. European trading companies, like the English and Dutch, often had their own aurangs where they managed their production and procurement activities.

The official in charge of the state treasury during the Mughal period was typically the 'Diwan' (especially Diwan-i-kul at the central level) or officers under the 'Diwan-i-arz' (Military Department) or 'Mir Bakhshi', depending on the specific aspect of finance or expenditure. An 'Aurang' was not the in-charge of the treasury of the state. Therefore, this pair is incorrectly matched.

2. Banian - Indian agent of the East India Company

The term 'Banian' (or 'Banyan') referred to Indian merchants or agents, particularly in Bengal and other parts of India, who served as brokers, financial agents, or business intermediaries for European trading companies, including the East India Company. They played a crucial role in facilitating trade, providing local knowledge, and managing financial transactions on behalf of the Europeans. This description accurately reflects the role of a Banian in relation to the East India Company.

Therefore, this pair is correctly matched.

3. Mirasidar - Designated revenue payer to the State

The term 'Mirasidar' is associated with the 'Mirasi' system, which was prevalent in parts of South India, particularly in Tamil Nadu, during pre-colonial and colonial times. A Mirasidar was a person or a group who held hereditary rights (mirasi) over land or a share of the village produce or revenue. They were considered proprietors or hereditary shareholders in the village and were responsible for paying land revenue to the state. They were indeed designated revenue payers to the state by virtue of their hereditary rights and position within the rural structure.

Therefore, this pair is correctly matched.

Evaluating the Pairs

Based on the historical context of each term, we can evaluate the given pairs:

1. Aurang - In-charge of treasury of the State: Incorrect match. Aurang was a warehouse.
2. Banian - Indian agent of the East India Company: Correct match. Banians were intermediaries for European companies.
3. Mirasidar - Designated revenue payer to the State: Correct match. Mirasidars held hereditary rights and paid revenue.

The pairs that are correctly matched are 2 and 3.

Revision Table: Key Historical Terms

Additional Information on Mughal Administration and Land Systems

Understanding these terms requires a broader context of historical administration and economic systems in India.

• Mughal Administration: The Mughal Empire had a complex administrative structure. Key officials included the 'Diwan' (finance and revenue), 'Mir Bakhshi' (military administration), 'Mir Saman' (household and stores), and 'Sadr-us-Sadr' (religious affairs and charities). The treasury was under the Diwan's purview, not an 'Aurang'.
• European Trade: European companies like the East India Company relied heavily on Indian intermediaries like Banians (in Bengal) and Compradors (in South China) for procurement, sales, and financial management due to language barriers, lack of local knowledge, and established trade networks.
• Land Tenure Systems: Various land tenure and revenue systems existed across India. The 'Mirasi' system in the South, the 'Zamindari' system in Bengal, and the 'Ryotwari' system were prominent examples introduced or formalized during different periods, particularly under British rule. Mirasidars represent a specific type of hereditary landholder and revenue payer within one such system.

These terms highlight different facets of the economic and administrative landscape of India during the transition from the Mughal era to the British colonial period.