All column 1 and Ammonium ion are soluble. That lets out A
Rule 1 says the nitrates are all soluble. That eliminates B
All column 1 compounds are soluble. That does C in. (C is Not the answer).
D is very nasty. You don't have any way to eliminate it. But two metals as reactive as K and Ba won't combine by ionization. In fact they shouldn't combine at all. D is incorrect.
E is the answer. All Sulfates react with any metal except a couple. Ba+2 is one of the exceptions.
Answer: E