The given substances react with water in the following manner Na+H2ONaOH+H2(g) 2Na2O2+2H2O4NaOH+O2(g)+H2(g) Ca+H2OCaO+H2 CaH2+2H2OCa(OH)2+2H2CaO+H2OCa(OH)2 CaC2+2H2OCa(OH)2+C2H2 Ba+2H2OBa(OH)2+H2 BaO2+H2OBa2++O2+H2O2
Hence, Ca and CaH2 is the pair that gives same gaseous product on reaction with water.