Generally water is considered as ionic solvent thus the ionic salts are dissolved in water.
Now among these salts K2SO4 and BaSO4 are ionic in nature since K and Ba are ionic in character as they belong to s-block elements.
Cu , Ag Co and Pb belong to d-block and all are transition metals and covalent in nature.
So, K2SO4 and BaSO4 are soluble in water and remaining salts are water insoluble at room tempeture.
Water soluble- K2SO4 , BaSO4
Water insoluble - CuCO3 , AgI, CoCl2 ,Pb(NO3)2
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