Step 1: Note the chemical nature of the gases.
Argon is a noble gas and is chemically inert, while nitrogen gas is very unreactive because of its strong $N\equiv N$ triple bond. Together they make an inert atmosphere.
Step 2: Ask what an inert filling is good for.
An inert gas filling is useful wherever a hot or reactive part must be protected from oxidation or burning.
Step 3: Recall the incandescent bulb problem.
A tungsten filament glows white hot. If oxygen or moisture touched it, the filament would oxidise and snap almost at once.
Step 4: See how Ar and N$_2$ help.
Filling the bulb with the inert Ar-N$_2$ mixture removes oxygen, preventing the filament from burning out.
Step 5: Add the second benefit.
The gas pressure also slows the evaporation of tungsten atoms from the hot filament, so the bulb lasts much longer.
Step 6: Eliminate the other uses.
MRI uses liquid helium, lasers use specific gases like He-Ne, and very low temperatures use liquid helium - none match Ar-N$_2$. So the use is to fill electric bulbs, option (3).
\[ \boxed{\text{Ar + N}_2 \text{ is used to fill electric bulbs (option 3)}} \]