Metaphosphoric acid exists in polymeric form and may have :

Options

A. a linear structure
B. a cyclic structure
C. both linear as well as cyclic structure
D. none

Explanation

To solve the question regarding the polymeric forms of metaphosphoric acid, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Metaphosphoric Acid**:
- Metaphosphoric acid is a type of phosphoric acid that can exist in different structural forms. The basic unit or monomeric form of metaphosphoric acid can be represented as HPO₃, which can also be depicted as P(=O)(=O)(-OH).

2. **Identifying the Polymerization**:
- Metaphosphoric acid can polymerize, meaning that multiple monomer units can link together to form larger structures. This polymerization can occur in two main ways: linear and cyclic.

3. **Linear Structure**:
- In the linear polymeric form, the monomer units are connected in a straight chain. The structure can be represented as:
- HPO₃ - HPO₃ - HPO₃ - ...
- This indicates that the phosphorus atoms are connected through oxygen atoms, forming a chain.

4. **Cyclic Structure**:
- In the cyclic polymeric form, the monomer units are arranged in a loop. This can be represented as:
- (HPO₃)ₙ (where n indicates the number of repeating units)
- The cyclic structure allows the ends of the chain to connect back to form a ring.

5. **Conclusion**:
- Since metaphosphoric acid can exist in both linear and cyclic forms, the correct answer to the question is that it may have both structures.

### Final Answer:
Metaphosphoric acid exists in polymeric form and may have both linear and cyclic structures. Therefore, the correct option is **C (both linear and cyclic structures)**.