Which of the following statements are correct ?
(a) All the three N___O bond lengths in `HNO_(3)` are equal.
(b) All P___Cl bond lengths in `PCl_(5)` molecule in gaseous state are equal
(c ) `P_(4)` molecule in white phosphrus have angular strain therefore white phosphorus is very reactive
(d) `PCl_(5)` is ionic in solid state in which cation is tetrahedral and anion is octahedral . And anion is octahedral.

Explanation

To determine which statements are correct regarding the given compounds, let's analyze each statement step by step.

### Step 1: Analyze Statement (a)
**Statement (a):** All the three N___O bond lengths in HNO₃ are equal.

**Analysis:**
- The structure of HNO₃ (Nitric acid) can be represented as:
```
O
||
H - N - O⁻
|
O
```
- In this structure, there is one N=O double bond and two N-O single bonds.
- Double bonds are shorter than single bonds, so the bond lengths cannot be equal.

**Conclusion:** Statement (a) is **incorrect**.

### Step 2: Analyze Statement (b)
**Statement (b):** All P___Cl bond lengths in PCl₅ molecule in gaseous state are equal.

**Analysis:**
- PCl₅ has a triangular bipyramidal structure with:
- 3 equatorial P-Cl bonds
- 2 axial P-Cl bonds
- The equatorial bonds are shorter than the axial bonds due to the geometry of the molecule.

**Conclusion:** Statement (b) is **incorrect**.

### Step 3: Analyze Statement (c)
**Statement (c):** P₄ molecule in white phosphorus has angular strain; therefore, white phosphorus is very reactive.

**Analysis:**
- The P₄ molecule has a tetrahedral structure, which creates angular strain due to the bond angles being less than the ideal tetrahedral angle (109.5°).
- This strain makes the molecule unstable and highly reactive.

**Conclusion:** Statement (c) is **correct**.

### Step 4: Analyze Statement (d)
**Statement (d):** PCl₅ is ionic in solid state in which cation is tetrahedral and anion is octahedral.

**Analysis:**
- In the solid state, PCl₅ dissociates into PCl₄⁺ (tetrahedral) and PCl₆⁻ (octahedral).
- The tetrahedral cation and octahedral anion confirm the ionic nature of PCl₅ in solid state.

**Conclusion:** Statement (d) is **correct**.

### Final Summary
- **Correct Statements:** (c) and (d)
- **Incorrect Statements:** (a) and (b)