Among the given options, the state that does not have any significant coal resources is Bihar (option 2).

Let`s dissect each option to understand why Bihar does not have significant coal resources:

1. Andhra Pradesh (option 1): Andhra Pradesh is known for its rich coal resources. The state has several major coal deposits, including the Singareni coalfields.

2. Bihar (option 2): Bihar does not have any significant coal resources. The state`s geographical location and geological formation do not favor the accumulation of coal deposits.

3. Chhattisgarh (option 3): Chhattisgarh is one of the richest states in terms of coal resources in India. The state has abundant coal deposits in the Korba, Raigarh, and Bilaspur regions.

4. Maharashtra (option 4): Maharashtra has some coal resources, particularly in the western part of the state. Though not as significant as states like Chhattisgarh, Maharashtra does have some coal-bearing areas.

In conclusion, among the given options, Bihar is the state that does not have any significant coal resources.