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The correct answer is option 2: 1 and 3 only.
Option 1 states that Coal India Limited (CIL) has its headquarters in Kolkata. This statement is true. CIL, the largest coal-producing company in the world, has its headquarters located in Kolkata, West Bengal, India.
Option 2 states that CIL operates through 82 mining areas spread over twenty provincial States of India. This statement is not mentioned in the question, so we do not have enough information to determine its accuracy. Without further evidence, it is not possible to determine if this statement is true or false.
Option 3 states that CIL is the single largest coal-producing company in the world. This statement is true. CIL is indeed the largest coal-producing company globally, accounting for around 80% of India`s coal production.
To summarize, option 1 is true, and option 2 is unverifiable based on the information provided. However, option 3 is true. Therefore, the correct answer is option 2: 1 and 3 only.