So use them. I'll be happy to check your answers. Here is a simplified set of rules.
http://www.files.chem.vt.edu/RVGS/ACT/notes/solubility_rules.html
barium sulfate
copper(II) carbonate
Ni(OH)2
Ca(NO3)2
FeCl2
silver nitrate
http://www.files.chem.vt.edu/RVGS/ACT/notes/solubility_rules.html
1. All compounds containing alkali metal cations (Group 1A) and ammonium cations (NH4+) are soluble.
2. All nitrates (NO3-) and acetates (CH3COO-) are soluble.
3. Most chlorides (Cl-), bromides (Br-), and iodides (I-) are soluble; however, those of silver (Ag+), mercury(I) (Hg2 2+), and lead (Pb2+) are exceptions and insoluble.
4. Most sulfates (SO4 2-) are soluble; however, those of barium (Ba2+), strontium (Sr2+), calcium (Ca2+), and lead (Pb2+) are exceptions and insoluble.
5. Most carbonates (CO3 2-), phosphates (PO4 3-), sulfides (S 2-), and hydroxides (OH-) are insoluble; however, those of alkali metal cations (Group 1A) and ammonium cations (NH4+) are exceptions and soluble.
Now let's apply these rules to the given compounds:
1. Barium sulfate (BaSO4): According to rule 4, sulfates of barium are insoluble. Therefore, barium sulfate is insoluble in water.
2. Copper(II) carbonate (CuCO3): According to rule 5, carbonates are insoluble except for those of alkali metals and ammonium. Therefore, copper(II) carbonate is insoluble in water.
3. Ni(OH)2: According to rule 5, hydroxides are insoluble except for those of alkali metals and ammonium. Therefore, Ni(OH)2 is insoluble in water.
4. Ca(NO3)2: According to rule 2, nitrates are soluble. Therefore, Ca(NO3)2 is soluble in water.
5. FeCl2: According to rule 3, most chlorides are soluble. Therefore, FeCl2 is soluble in water.
6. Silver nitrate (AgNO3): According to rule 3, silver salts are insoluble, but nitrates are soluble (rule 2). Therefore, silver nitrate is soluble in water.
So, the soluble compounds in water are Ca(NO3)2, FeCl2, and silver nitrate.