Which of the following compounds belong to the same homologous series?
(I) `C_2H_6O_2` (II)`C_3H_8O` (III) `C_2H_6` (IV)`CH_4O`

Options

A. I and II
B. II and III
C. III and IV
D. II and IV

Explanation

To determine which of the given compounds belong to the same homologous series, we need to analyze the molecular formulas of each compound and see if they fit a common general formula.

### Step-by-Step Solution:

1. **Identify the Compounds:**
- (I) `C2H6O2`
- (II) `C3H8O`
- (III) `C2H6`
- (IV) `CH4O`

2. **Determine the General Formula for Each Compound:**
- For (I) `C2H6O2`:
- This compound can be represented as CnH2nO2. Here, n = 2, so the formula is C2H6O2.
- For (II) `C3H8O`:
- This compound can be represented as CnH2nO. Here, n = 3, so the formula is C3H8O.
- For (III) `C2H6`:
- This compound can be represented as CnH2n+2. Here, n = 2, so the formula is C2H6.
- For (IV) `CH4O`:
- This compound can also be represented as CnH2n+2O. Here, n = 1, so the formula is CH4O.

3. **Compare the General Formulas:**
- For (I) `C2H6O2`: General formula is CnH2nO2.
- For (II) `C3H8O`: General formula is CnH2nO.
- For (III) `C2H6`: General formula is CnH2n+2.
- For (IV) `CH4O`: General formula is CnH2n+2O.

4. **Identify Similarities:**
- The compounds (II) `C3H8O` and (IV) `CH4O` both fit the general formula CnH2nO.
- The compounds (III) `C2H6` and (IV) `CH4O` both fit the general formula CnH2n+2.

5. **Conclusion:**
- The compounds that belong to the same homologous series are (II) `C3H8O` and (IV) `CH4O`.

### Final Answer:
The compounds that belong to the same homologous series are (II) `C3H8O` and (IV) `CH4O`.

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