The number of distinct prime factors of the largest 4-digit number is

1. 2

2. 3

3. 5

4. none of these

The largest 4-digit number is 9999.

By prime factorisation:

9999 = 3 × 3 × 11 × 101.

The distinct prime factors are 3, 11 and 101 — that is 3 distinct prime factors.

Hence, option 2 is the correct option.