Amongst the following, the total number of compounds soluble in concentrated `NH_(3)` solution is:
(A)`Ag_(2)CrO_(4)` , (B)`Cu(OH)_(2).CuSO_(4)` , ( C)`PbSO_(3)` , (D)`Al(OH)_(3)` , (E)`Ni(OH)_(2)`
(F)`Zn_(3)(PO_(4))_(2)` , (G)`BaSO_(4)` , (H)`Bi(OH)_(2)NO_(3)` , (I)`Mn(OH)_(2)`

Explanation

To determine the total number of compounds that are soluble in concentrated NH₃ (ammonia) from the given options, we will analyze each compound based on their ability to form complexes with ammonia.

### Step-by-Step Solution:

1. **Identify the Compounds:**
- (A) Ag₂CrO₄
- (B) Cu(OH)₂·CuSO₄
- (C) PbSO₃
- (D) Al(OH)₃
- (E) Ni(OH)₂
- (F) Zn₃(PO₄)₂
- (G) BaSO₄
- (H) Bi(OH)₂NO₃
- (I) Mn(OH)₂

2. **Analyze Each Compound:**
- **(A) Ag₂CrO₄:**
- When Ag₂CrO₄ reacts with NH₃, it forms a complex (Ag(NH₃)₂)⁺ and is soluble in concentrated NH₃.
- **Soluble.**

- **(B) Cu(OH)₂·CuSO₄:**
- This compound can form a complex with NH₃, resulting in the formation of [Cu(NH₃)₄]²⁺, thus it is soluble.
- **Soluble.**

- **(C) PbSO₃:**
- PbSO₃ does not form a complex with NH₃ and is not soluble in concentrated NH₃.
- **Not soluble.**

- **(D) Al(OH)₃:**
- Al(OH)₃ does not dissolve in concentrated NH₃; it is soluble in sodium hydroxide instead.
- **Not soluble.**

- **(E) Ni(OH)₂:**
- Ni(OH)₂ can form a complex with NH₃, resulting in [Ni(NH₃)₆]²⁺, hence it is soluble.
- **Soluble.**

- **(F) Zn₃(PO₄)₂:**
- Zn₃(PO₄)₂ can form a complex with NH₃, leading to the formation of [Zn(NH₃)₄]²⁺, thus it is soluble.
- **Soluble.**

- **(G) BaSO₄:**
- BaSO₄ does not dissolve in concentrated NH₃; it is soluble in concentrated H₂SO₄ instead.
- **Not soluble.**

- **(H) Bi(OH)₂NO₃:**
- Bi(OH)₂NO₃ does not form a complex with NH₃ and is not soluble.
- **Not soluble.**

- **(I) Mn(OH)₂:**
- Mn(OH)₂ is also not directly soluble in concentrated NH₃; it is soluble in ammonium salts that release ammonia.
- **Not soluble.**

3. **Count the Soluble Compounds:**
- The compounds that are soluble in concentrated NH₃ are:
- (A) Ag₂CrO₄
- (B) Cu(OH)₂·CuSO₄
- (E) Ni(OH)₂
- (F) Zn₃(PO₄)₂

Therefore, the total number of compounds soluble in concentrated NH₃ is **4**.

### Final Answer:
The total number of compounds soluble in concentrated NH₃ solution is **4**.