The answer is Ba(NO3)2 and K2CO3.
The explanation in each choice will be explained:
1. is not true because BaCO3 is insoluble in water.
2. CaCO3 is insoluble but not much CO3^2- in solution.
3. BaSO4 is insoluble, not much Ba2+ in solution.
4. Ba(NO3)2 and K2CO3 are both soluble in water.