If a National Emergency is in place under Article 352, then the Parliament can extend the term of the Legislative Assemblies for _________ at a time.

The correct answer is upto one year. While a Proclamation of National Emergency is in operation, Parliament can by law extend the normal five-year term of a State Legislative Assembly (Article 172) and of the Lok Sabha (Article 83) by up to one year at a time. There is also an outer limit: the extension cannot continue beyond six months after the proclamation has ceased to operate. During the Emergency of 1975–77 the term of the Fifth Lok Sabha was extended in this way.

The other durations come from elsewhere in the chapter and are meant to confuse. Six months is the period for which an approved emergency lasts, and also the outer limit after an emergency ends. One month is the time within which Parliament must approve a National Emergency. Nine months has no basis. The logic of the rule is that elections may be impossible during a war or rebellion, so the Constitution lets the existing legislatures continue, but only one year at a time and never for long after the crisis has passed.