!! LONG ANSWER !!
The answer is (3), that particular mixture of ammonium sulfate and sodium hydroxide will show buffer action.
Here's how the problem looks like
For a solution to exhibit buffer action, it must be able to resist significant pH changes when small quantities of a strong acid or of a strong base are added to it.
At first, neither of the proposed solutions look like they could act as a buffer, but one of them can indeed do so.
Take a look at the reaction between ammonium sulfate and sodium hydroxide
The net ionic equation will be
Notice that this reaction produces ammonia, which is a weak base. depending on how many moles of each reactant were added together, the solution can now contain ammonia, a weak base, and ammonium ion, its conjugate acid.
Use the molarities of the two solutions to determine how many moles you add together. For option (3) you'd get
Since 1 mole of ammonium sulfate produces 2 moles of ammonium ions in solution, you'll get
Look at the net ionic equation. You have a
At the same time, the reaction will produce 0.01 moles of ammonia, so you'll now have both a weak base and its conjugate acid in solution
If you look at option (4), you'll notice that you add twice as many moles of sodium hydroxide, which implies that
Both the reactants will be consumed in the reaction, so the resulting solution will only contain ammonia, a weak base, and not its conjugate acid.
Options (1) and (2) cannot exhibit buffer action because they lack one of the two components needed (a weak base for option 1 and a weak acid for option 2).