The correct answer is option 3, which states that the duration of the Lok Sabha can be extended for a period of one year at a time during a proclamation of emergency.
During a period of emergency, the normal functioning of the government and its institutions may be disrupted. In such situations, the duration of the Lok Sabha, which is the lower house of the Parliament of India, can be extended for a specified period.
Option 1 states that the extension cannot exceed three months. This is incorrect as the duration can be extended for a longer period.
Option 2 states that the extension cannot exceed nine months. This is also incorrect as the duration can be extended for a longer period.
Option 4 states that the extension can be for a period of two years at a time. This is incorrect as the duration can only be extended for a period of one year at a time.
Therefore, the correct answer is option 3, as it accurately states that the duration of the Lok Sabha can be extended for a period of one year at a time during an emergency.