Which statement is/are correct?
(a) Ionic compounds like sulphate and phosphates of Ba and Sr `[e.g BaSO_(4),SrSO_(4),Ba_(3)(PO_(4))_(2)` and `Sr_(3)(PO_(4))_(2)]` are insoluble in water
(b) The above compounds are soluble in water
(c ) Magnitude of lattice energy `(Delta_(U)H^(Θ))` of the above compounds is greater than their hydration energy `(Delta_(hyd)H^(Θ))` High `Delta_(U)H^(Θ)` of these compounds is due to polyvalent nature of both the cations and the anions
(d) In these cases,hydration of ions fails to liberate sufficient energy to offset the lattice energy .

Explanation

To solve the question, we need to analyze each statement regarding the solubility of barium and strontium sulfates and phosphates in water, as well as the concepts of lattice energy and hydration energy.

### Step-by-Step Solution:

1. **Analyzing Statement (a)**:
- **Statement**: Ionic compounds like sulfates and phosphates of Ba and Sr (e.g., BaSO₄, SrSO₄, Ba₃(PO₄)₂, and Sr₃(PO₄)₂) are insoluble in water.
- **Analysis**: As we move down the alkaline earth metals group, the solubility of their sulfates and phosphates decreases. Barium and strontium sulfates and phosphates are known to be insoluble in water.
- **Conclusion**: This statement is **correct**.

2. **Analyzing Statement (b)**:
- **Statement**: The above compounds are soluble in water.
- **Analysis**: Since we established that BaSO₄ and SrSO₄ are insoluble in water, this statement contradicts our previous conclusion.
- **Conclusion**: This statement is **false**.

3. **Analyzing Statement (c)**:
- **Statement**: The magnitude of lattice energy (ΔU_H°) of the above compounds is greater than their hydration energy (Δ_hydH°). High ΔU_H° of these compounds is due to the polyvalent nature of both the cations and the anions.
- **Analysis**: Lattice energy is indeed high for these compounds due to the charges of the ions involved (Ba²⁺, Sr²⁺, SO₄²⁻, PO₄³⁻). The higher the charge, the greater the lattice energy. Since the lattice energy is greater than hydration energy, this statement is correct.
- **Conclusion**: This statement is **correct**.

4. **Analyzing Statement (d)**:
- **Statement**: In these cases, hydration of ions fails to liberate sufficient energy to offset the lattice energy.
- **Analysis**: This statement aligns with our understanding that if the hydration energy is less than the lattice energy, the compound will not dissolve in water. Since we established that the lattice energy is greater, this statement is also correct.
- **Conclusion**: This statement is **correct**.

### Final Answer:
The correct statements are (a), (c), and (d). Therefore, the answer is **A, C, and D**.