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The main objectives of the Farakka barrage are to protect and save Calcutta harbour from silting and to improve navigability of the Hoogly.
Option 1 is incorrect. The Farakka barrage is not primarily intended for obtaining hydroelectric power and additional water for irrigation for common use by India and Bangladesh.
Option 2 is incorrect. While the Farakka barrage does help in reducing the impact of periodic floods in the Ganga, it is not the main objective of the project.
Option 3 is correct. Protecting and saving Calcutta harbour from silting is one of the main objectives of the Farakka barrage.
Option 4 is incorrect. Although options 3 and 4 are both objectives of the Farakka barrage, option 1 is not a main objective of the project.
In conclusion, the correct option is option 3 - 3 and 4 are the main objectives of the Farakka barrage.