Which of the following statements are correct?
(I) A pair of positional isomers differs in the position of the same functional group.
(II) A pair of structural isomers have the same relative molar mass.
(III) A pair of functional group isomers belongs to different homologous series.

Options

A. `II` and `III`
B. `I` and `III`
C. `I` and `II`
D. `I,II` and `III`

Explanation

To determine which of the statements are correct, let's analyze each statement one by one.

### Step 1: Analyze Statement I
**Statement I:** A pair of positional isomers differs in the position of the same functional group.

- **Explanation:** Positional isomers are compounds that have the same molecular formula and the same functional group but differ in the position of that functional group within the molecule. For example, consider butanol:
- 1-butanol (C₄H₁₀O) has the hydroxyl (-OH) group on the first carbon.
- 2-butanol (C₄H₁₀O) has the hydroxyl (-OH) group on the second carbon.

Thus, this statement is **correct**.

### Step 2: Analyze Statement II
**Statement II:** A pair of structural isomers have the same relative molar mass.

- **Explanation:** Structural isomers have the same molecular formula but differ in the connectivity of their atoms. Since they have the same number and types of atoms, their molar masses will be the same. For example, both butanol and isobutanol (C₄H₁₀O) have the same molar mass despite differing structures.

Thus, this statement is **correct**.

### Step 3: Analyze Statement III
**Statement III:** A pair of functional group isomers belongs to different homologous series.

- **Explanation:** Functional group isomers are compounds that have the same molecular formula but different functional groups. For example, ethanol (C₂H₆O) and dimethyl ether (C₂H₆O) are functional group isomers. They belong to different functional groups but can belong to the same homologous series if they have similar structural features. Therefore, this statement is **incorrect**.

### Conclusion
Based on the analysis:
- Statement I is correct.
- Statement II is correct.
- Statement III is incorrect.

Thus, the correct statements are **I and II**.

### Final Answer
The correct option is **C (I and II)**.

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