Hello Traian,
You are very correct that the default active time is 3 minutes. However, all recent IOSes support a feature called SIA-Query that allows a router to ask its neighbor whether it is still processing its Query, and extend the active time if a corresponding SIA-Reply has been received.
A router supporting the SIA-Query mechanism would wait one half of the active timer, that is, 90 seconds, and send a SIA-Query to the unresponsive neighbor after that. If a SIA-Reply is received, the router will wait another 90 seconds, then send another SIA-Query. At most three SIA-Queries can be sent during the Active state, which amounts in total to 6 minutes (initial 90 seconds plus each responded SIA-Query providing next extra 90 seconds, in total 4x90 = 360 seconds). So a router can wait in the Active state for up to 6 minutes in default setting.
Ranji, you are asking about how long a router can stay in "stuck-inactive". This is in fact not a correct question - the name of the event is Stuck-In-Active, and it is not a state but rather a name of a particular action taken to resolve a situation when a Reply cannot be obtained in a reasonable time (6 minutes as explained before). If no Reply has been received after this time, the unresponsive neighbor is considered Stuck-In-Active and the adjacency toward that neighbor is torn down. This is all there is to Stuck-In-Active. The Stuck-In-Active does not have any duration - it is only an action taken to recover from an unresponsive neighbor.
Best regards,
Peter
