The correct answer is option 2: Singareni Collieries Company Limited. Singareni Collieries Company Limited is the oldest and the first government-owned coal mining company in India. It was established in the year 1920 by the Hyderabad (Deccan) Company, under the British colonial rule, to exploit the coal reserves in the region of Singareni in Telangana. Singareni Collieries Company Limited is a public sector undertaking owned jointly by the Telangana government and the central government. It operates several coal mines in the state of Telangana and contributes significantly to the energy sector in India.

Option 1: Neyveli Lignite Corporation is a government-owned lignite mining and power generating company, but it does not deal with coal mining.

Option 3: Coal India Limited is the largest coal-producing company in the world. However, it is not the first and oldest government-owned coal mining company in India.

Option 4: Mahanadi Coalfields Limited is a subsidiary of Coal India Limited and is a major coal producer in Odisha. However, it is not the first and oldest government-owned coal mining company in India.

Therefore, the correct answer is option 2.