Two similar vessels contain water and mercury upto same level on a table. A hole is made on the side wall of vessels at equal depth from the free surface of liquid. In which case the liquid will seep (leak) out with greater velocity? In which case the stream of flow has greater horizontal range?

The velocity of efflux from an orifice is independent of density of liquid but depends on the height of free surface of liquid from orifice. Since the height of free surface of water and mercury is same from the holes made in the two vessels, so the velocity of efflux will be same. Also the height of orifices from the ground is same, therefore the horizontal range will also be same.