The correct answer is option 1, INS Kesari. INS Kesari was deployed in `Mission Sagar` on 10 May 2020. `Mission Sagar` was an initiative taken by the Indian government to provide assistance to countries affected by the COVID-19 pandemic. INS Kesari was sent to different countries in the Indian Ocean, carrying food and COVID related items as part of this mission.

Option 2, INS Satpura, was not deployed in `Mission Sagar`. Option 3, INS Shivalik, and option 4, INS Gomati, were also not deployed in `Mission Sagar`. It is important to note that `Mission Sagar` was a significant initiative taken by the Indian Navy to provide timely aid and support to countries in need during the global health crisis.

In summary, INS Kesari was the ship deployed in `Mission Sagar`, which was sent to different countries carrying food and COVID related items on 10 May 2020.