Option 1 states that the Prime Minister of India is the ex-officio Chairman of the Planning Commission, while Option 2 states that the Union Finance Minister is the ex-officio Chairman of the Finance Commission.

To understand the given statements, we need to know the meanings of the terms "ex-officio Chairman" and the roles of the Planning Commission and the Finance Commission.

An ex-officio Chairman is someone who holds a position by virtue of their other office or position. This means that the person becomes Chairman of a particular commission automatically because of their role in another office.

The Planning Commission is responsible for formulating five-year plans for economic development in India and suggesting policies to achieve them. The Finance Commission, on the other hand, is responsible for making recommendations on how the financial resources of the country should be distributed between the Union government and the State governments.

Given this information, we can conclude that Statement 1 is correct because the Prime Minister does hold the position of the ex-officio Chairman of the Planning Commission. However, Statement 2 is incorrect as the Union Finance Minister does not hold the position of the ex-officio Chairman of the Finance Commission.

Therefore, the correct answer is Option 1, which states that only Statement 1 is correct.