Step 1: Alternate reasoning: terrain and population size:
Arunachal Pradesh has the largest area among the four (about 83,743 sq. km) combined with one of India's smallest state populations, which mathematically forces the lowest density of the group.
Step 2: Cross-check:
This matches its well-known status as India's most sparsely populated large state.
Step 3: Final Answer:
\[ \boxed{\text{Arunachal Pradesh}} \]