Hydrogen gas is not obtained when zinc reacts with:
Cold water
Conc. H2SO4
Zinc does not react with cold water to produce hydrogen and it produces hydrogen gas by reacting with steam.
When zinc reacts with concentrated sulphuric acid then,
Zn(s) + conc. 2H2SO4(l)→ZnSO4(aq) + SO2↑ +2H2O(l)
Instead of hydrogen, zinc reacts with concentrated sulphuric acid to produce zinc sulphate, sulphur dioxide gas and water. Moreover, sulphur dioxide gas has the property to convert lime water milky.