Which reserve mobilization authority provides the President a means to activate, without a declaration of national emergency, not more than 200,000 reservists for not more than 365 days to meet the support requirements of any operational mission

The mobilization only reports to your Army Reserve Home Station, which is usually your Army Reserve Center. Here, your unit prepares you to activate.
The President has the right to increase the active force by summoning up to 200,000 members of the reserve selected for up to 270 days to meet mission requirements in the United States or abroad. The President must inform Congress within 24 hours and state the reason for his action.
Public law, which provides a way to activate the president without declaring a national emergency, does not have more than 200,000 members and personal reserves in the selected reserve.
Member called under this provision may not be used for disaster relief or to suppress warranties. This authority has a special purpose when national or international codes of partial or complete mobilization are used in undesirable circumstances.
The forces available under this authority can provide a continuous, limited-range, preventive, or operational response, or be used as a precursor to any subsequent mobilization and it also known as PRC.