Consider the following compounds
(1)`H_(3)CF` (2)`H_(2)CF_(2)` (3)` CH_(4)` (4)`H_(3)C CF_(3)` (5)`CH_(3)CH_(2)+` (6)`C_(2)H_(4)`
and calculate value of Y+X, (where X is the total number of compounds which have `H-C-H` bond angles equal to `109^(@)28'` and Y is the total number of compounds which have `H-C-H` bond angles greater than `109^(@)28'` and less than `120^(@)`

Explanation

To solve the problem, we need to analyze the bond angles in the given compounds and categorize them based on the specified criteria.

### Step-by-Step Solution:

1. **Identify the Compounds**: We have the following compounds:
- (1) H₃CF
- (2) H₂CF₂
- (3) CH₄
- (4) H₃C CF₃
- (5) CH₃CH₂⁺
- (6) C₂H₄

2. **Determine the Hybridization and Bond Angles**:
- **(1) H₃CF**:
- Carbon is sp³ hybridized.
- Normal bond angle = 109° 28'.
- Due to the electronegative fluorine atom, the H-C-H bond angle will be slightly greater than 109° 28'.
- **Conclusion**: Y (greater than 109° 28').

- **(2) H₂CF₂**:
- Carbon is sp³ hybridized.
- Normal bond angle = 109° 28'.
- The presence of two fluorine atoms increases the H-C-H bond angle, making it greater than 109° 28'.
- **Conclusion**: Y (greater than 109° 28').

- **(3) CH₄**:
- Carbon is sp³ hybridized.
- Bond angle = 109° 28'.
- **Conclusion**: X (equal to 109° 28').

- **(4) H₃C CF₃**:
- Carbon is sp³ hybridized.
- The presence of three fluorine atoms increases the H-C-H bond angle, making it greater than 109° 28'.
- **Conclusion**: Y (greater than 109° 28').

- **(5) CH₃CH₂⁺**:
- The positive charge on carbon affects the bond angles.
- The bond angle will be slightly less than 109° 28' due to the positive charge but greater than 120°.
- **Conclusion**: Y (greater than 109° 28' but less than 120°).

- **(6) C₂H₄**:
- Carbon is sp² hybridized.
- Bond angle = 120°.
- Due to steric effects, the bond angle will be less than 120°.
- **Conclusion**: Y (greater than 109° 28' but less than 120°).

3. **Count X and Y**:
- **X (H-C-H bond angles equal to 109° 28')**:
- Only CH₄ contributes to X.
- **X = 1**.

- **Y (H-C-H bond angles greater than 109° 28' and less than 120°)**:
- H₃CF, H₂CF₂, H₃C CF₃, CH₃CH₂⁺, and C₂H₄ contribute to Y.
- **Y = 5**.

4. **Calculate Y + X**:
- Y + X = 5 + 1 = 6.

### Final Answer:
Y + X = 6.