Which doctrine allows a mobile conveyance search without a warrant under certain conditions?

The Carrol Doctrine is the correct answer because it establishes the legal precedent that allows law enforcement officers to search a vehicle without a warrant when they have probable cause to believe that the vehicle contains evidence of a crime. This doctrine is rooted in the inherent mobility of vehicles and the practical considerations that prevent officers from obtaining a warrant in situations where urgent action is necessary.

Under this doctrine, if an officer has reasonable grounds to suspect that a vehicle contains contraband or evidence of criminal activity, they can legally conduct a search. This was established in the landmark case, Carroll v. United States, which recognized the necessity for quick action given that vehicles can easily be moved out of jurisdiction, potentially destroying evidence or making it impossible to later secure a warrant.

In comparison, the other concepts mentioned do not pertain to warrantless searches of vehicles. The Terry Doctrine allows for "stop and frisk" procedures based on reasonable suspicion, but it is not specifically about vehicle searches. The Exclusionary Rule pertains to the legal principle that evidence obtained unlawfully cannot be used in court, and the Search Warrant Rule requires law enforcement to obtain a warrant to conduct searches in most situations, which contrasts with the allowances provided by the Carrol Doctrine concerning vehicles.