Consider the following covalent compounds in their solid state and find the value of expression `(X+Y+Z)`.
`N_(2)O_(5),Cl_(2)O_(6),PC l_(),I_(2)Cl_(6),XeF_(6),PB r_(5)`
Where X=total number of compounds in which central atom of cationic or anionic part is `sp^(3)` hybridized.
Y=Total number of compounds having `90^(@)` bond angle either in cationic or anionic part.
Z=Total number of compounds having `109^(@)28'` bond angle either in cationic or anionic part.

Explanation

To solve the problem, we need to analyze the given covalent compounds and determine the values of X, Y, and Z based on the hybridization and bond angles of the central atoms in their cationic and anionic parts.

### Step-by-Step Solution:

1. **Identify the Cationic and Anionic Parts:**
- **N₂O₅**:
- Cation: NO₂⁺ (Nitronium ion)
- Anion: NO₃⁻ (Nitrate ion)
- **Cl₂O₆**:
- Cation: ClO₂⁺ (Chlorite ion)
- Anion: ClO₄⁻ (Perchlorate ion)
- **PCl₅**:
- Cation: PCl₄⁺ (Tetrachlorophosphonium ion)
- Anion: PCl₆⁻ (Hexachlorophosphate ion)
- **I₂Cl₆**:
- Cation: ICl₂⁺ (Dichloroiodine ion)
- Anion: ICl₄⁻ (Tetrachloroiodide ion)
- **XeF₆**:
- Cation: XeF₅⁺ (Pentafluoroxenon ion)
- Anion: F⁻ (Fluoride ion)
- **PBr₅**:
- Cation: PBr₄⁺ (Tetrachlorophosphonium ion)
- Anion: PBr₆⁻ (Hexabromophosphate ion)

2. **Determine Hybridization and Bond Angles:**
- **N₂O₅**:
- NO₂⁺: sp hybridized (180°)
- NO₃⁻: sp² hybridized (120°)
- **Cl₂O₆**:
- ClO₂⁺: sp² hybridized (less than 120°)
- ClO₄⁻: sp³ hybridized (109.5°)
- **PCl₅**:
- PCl₄⁺: sp³ hybridized (109.5°)
- PCl₆⁻: sp³d² hybridized (90°)
- **I₂Cl₆**:
- ICl₂⁺: sp³ hybridized (less than 109.5°)
- ICl₄⁻: sp³d² hybridized (90°)
- **XeF₆**:
- XeF₅⁺: sp³d² hybridized (90°)
- F⁻: sp³ hybridized (109.5°)
- **PBr₅**:
- PBr₄⁺: sp³ hybridized (109.5°)
- PBr₆⁻: sp³d² hybridized (90°)

3. **Count the Values of X, Y, and Z:**
- **X (sp³ hybridized)**:
- Compounds: ClO₄⁻, PCl₄⁺, ICl₂⁺, PBr₄⁺, F⁻ (5 compounds)
- **Y (90° bond angle)**:
- Compounds: PCl₆⁻, ICl₄⁻, XeF₅⁺, PBr₆⁻ (4 compounds)
- **Z (109° 28' bond angle)**:
- Compounds: ClO₄⁻, PCl₄⁺, PBr₄⁺ (3 compounds)

4. **Calculate the Expression (X + Y + Z)**:
- X = 5
- Y = 4
- Z = 3
- Therefore, X + Y + Z = 5 + 4 + 3 = 12

### Final Answer:
The value of the expression (X + Y + Z) is **12**.