The correct answer is option 3, "can be extended by one year at a time during the proclamation of emergency". This option refers to the provision in the Indian constitution that allows the term of the Lok Sabha to be extended during a state of emergency, but only for a period of one year at a time.

Option 1, "cannot be extended under any circumstances", is incorrect as the Indian constitution does allow for extension of the Lok Sabha`s term under special circumstances, such as an emergency.

Option 2, "can be extended by six months at a time", is also incorrect because the extension period during an emergency is one year, not six months.

Option 4, "can be extended for two years at a time during the proclamation of emergency", is incorrect for similar reasons. The constitution only allows for the one-year extension in the event of an emergency. Any extension beyond that must be re-proclaimed after the initial one year.