11. Observe the array: $(1),(3,5),(7,9,11),(13,15,17$,
19), $\cdots \cdots$. Then 2003 is in the group.
11.45 .
Using the trial method.
Assume 2003 is in the 50th group, then the first 50 groups have
$$
1+2+3+\cdots+50=51 \times 25=1275
$$

numbers, the last number in this group is 2549, and the first number is 2451, so 2003 is not in the 50th group;
Assume 2003 is in the 40th group, then the first 40 groups have
$$
1+2+3+\cdots+40=41 \times 20=820
$$

numbers, the last number is 1639, so 2003 is not in the 40th group.
Therefore, 2003 is between the 40th and 50th groups.
Assume 2003 is in the 45th group, then the first 45 groups have
$$
1+2+3+\cdots+45=46 \times 22+23=1035
$$

numbers, the last number in this group is 2069, and the first number is 1981, so 2003 is in the 45th group.