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Option 1: Nizam Sagar - This is not the correct answer. Nizam Sagar is a reservoir in the state of Telangana and does not have a hydroelectric power plant.
Option 2: Shivasamudram - This is the correct answer. The first hydroelectric power plant in India was set up at Shivasamudram in the state of Karnataka. It was established in the year 1902 and is located on the River Kaveri. The power plant played a significant role in the industrial development of the region.
Option 3: Ramagundam - This is not the correct answer. Ramagundam is a town in the state of Telangana and does not have the first hydroelectric power plant in India.
Option 4: Mettur - This is not the correct answer. Mettur is a reservoir in the state of Tamil Nadu and does not have the first hydroelectric power plant in India.
In conclusion, the correct answer is option 2, Shivasamudram.