The principle involved here is `Torricelli`s Law`, which states that the speed of efflux from a hole at the bottom of a fluid-filled vessel is proportional to the square root of the height of the fluid above the hole. In this question, it is stated that the three vessels, A, B, and C are filled up to equal height with water, mercury and kerosene respectively. As the height of the fluid is the same for the three vessels, what differentiates them is the density of the fluid - mercury is denser than water and water is denser than kerosene. As the speed of efflux is inversely proportional to the fluid`s density, the vessel with the least dense fluid i.e., kerosene, will empty first. So, the correct answer is "4- Vessel C". Hence, options 1, 2 and 3 are incorrect as they suggest that vessel B, all vessels simultaneously, and vessel A empty first respectively.