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_(3)` (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 given compounds and determine the H-C-H bond angles for each of them. We will categorize them into two groups: those with bond angles equal to 109°28' (X) and those with bond angles greater than 109°28' and less than 120° (Y). Finally, we will calculate the value of Y + X.

### Step-by-Step Solution:

1. **Identify the Compounds:**
We have the following compounds:
- (1) H₃CF
- (2) H₂CF₂
- (3) CH₄
- (4) H₃C-CF₃
- (5) CH₃CH₃
- (6) C₂H₄

2. **Determine the H-C-H Bond Angles:**
- **(1) H₃CF:**
- Carbon is bonded to 3 hydrogens and 1 fluorine.
- Steric number = 4 (3 H + 1 F).
- Hybridization = sp³.
- Bond angle = 109°28'.

- **(2) H₂CF₂:**
- Carbon is bonded to 2 hydrogens and 2 fluorines.
- Steric number = 4 (2 H + 2 F).
- Hybridization = sp³.
- Bond angle = 109°28'.

- **(3) CH₄:**
- Carbon is bonded to 4 hydrogens.
- Steric number = 4 (4 H).
- Hybridization = sp³.
- Bond angle = 109°28'.

- **(4) H₃C-CF₃:**
- One carbon is bonded to 3 hydrogens and the other to 3 fluorines.
- The H-C-H bond angle is still 109°28' (due to sp³ hybridization).

- **(5) CH₃CH₃:**
- Each carbon is bonded to 3 hydrogens.
- Steric number = 4 (4 H).
- Hybridization = sp³.
- Bond angle = 109°28'.

- **(6) C₂H₄:**
- Each carbon is bonded to 2 hydrogens and 1 carbon (double bond).
- Steric number = 3 (2 H + 1 C).
- Hybridization = sp².
- Bond angle = 120°.

3. **Count the Compounds:**
- **Compounds with H-C-H bond angles equal to 109°28' (X):**
- (1) H₃CF
- (2) H₂CF₂
- (3) CH₄
- (4) H₃C-CF₃
- (5) CH₃CH₃
- Total = 5 compounds (X = 5).

- **Compounds with H-C-H bond angles greater than 109°28' and less than 120° (Y):**
- (6) C₂H₄ has a bond angle of 120°.
- No compounds fall into this category (Y = 0).

4. **Calculate Y + X:**
- Y + X = 0 + 5 = 5.

### Final Answer:
The value of Y + X is **5**.