The correct answer is option 3: one year at a time.

During a proclamation of Emergency, the duration of the Lok Sabha, which is the lower house of the Parliament of India, can be extended. The Constitution of India allows for this extension but places a limit on the duration. According to Article 83(2) of the Constitution, the maximum duration of the Lok Sabha can be extended by one year at a time, as long as the proclamation of Emergency is in operation.

This means that during an Emergency, the Lok Sabha`s term, which is normally five years, can be extended for additional periods of one year each. The extension can continue for as long as the Emergency situation persists. Once the Emergency is lifted, the normal rules for the duration of the Lok Sabha come into play again.

It is important to note that options 1, 2, and 4 are incorrect. Option 1 states that the Lok Sabha`s duration can be extended by three months, which is not the case. Option 2 states nine months, which is also incorrect. Option 4 states two years at a time, which is not in line with the provision in the Constitution.