How many of the following statement/s is/are correct?
(1). For isothermal process `DeltaE` and `DeltaH` are 0.
(2). On increasing temperature `pK_(w)` of water decreases.
(3). For adiabatic process `DeltaS` is always 0.
(4). Indicator methyl orange can be used for titration between strong acid and weak base.
(5). At triple point liquid. vapour and solid state are in simultaneous equilibrium with one another.
(6). `DeltaH_(f)^(@)` of `D_(2)` (gas) is zero.
(7). Molal elevation constant `(K_(b))` depends upon nature of solute.
(8). Be does not give flame test.
(9). Solubility of `AgCN` increases in KCN solution.

Answer

To determine how many of the statements provided are correct, we will analyze each statement one by one.

### Step-by-Step Solution:

1. **Statement 1**: For isothermal processes, ΔE and ΔH are 0.
- **Analysis**: In an isothermal process, the temperature remains constant (ΔT = 0). Therefore, the change in internal energy (ΔE) and the change in enthalpy (ΔH) are both zero.
- **Conclusion**: **Correct**.

2. **Statement 2**: On increasing temperature, pK_w of water decreases.
- **Analysis**: The ionization product of water (K_w) increases with temperature. Since pK_w = -log(K_w), an increase in K_w leads to a decrease in pK_w.
- **Conclusion**: **Correct**.

3. **Statement 3**: For adiabatic processes, ΔS is always 0.
- **Analysis**: In an adiabatic process, no heat is exchanged (ΔQ = 0). However, this does not imply that the entropy change (ΔS) is always zero. ΔS can be non-zero if there is a change in the state of the system.
- **Conclusion**: **Incorrect**.

4. **Statement 4**: Indicator methyl orange can be used for titration between strong acid and weak base.
- **Analysis**: Methyl orange is suitable for titrations involving strong acids and weak bases because it changes color in the pH range of 3 to 5, which is appropriate for such titrations.
- **Conclusion**: **Correct**.

5. **Statement 5**: At the triple point, liquid, vapor, and solid states are in simultaneous equilibrium with one another.
- **Analysis**: By definition, at the triple point, all three phases (solid, liquid, and gas) coexist in equilibrium.
- **Conclusion**: **Correct**.

6. **Statement 6**: ΔH_f^(@) of D_2 (gas) is zero.
- **Analysis**: The standard enthalpy of formation of a pure element in its standard state is defined as zero. Since D_2 is a diatomic molecule of deuterium, it is in its standard state.
- **Conclusion**: **Correct**.

7. **Statement 7**: Molal elevation constant (K_b) depends upon the nature of the solute.
- **Analysis**: The molal elevation constant (K_b) is a property of the solvent, not the solute. It does not depend on the nature of the solute.
- **Conclusion**: **Incorrect**.

8. **Statement 8**: Be does not give a flame test.
- **Analysis**: Beryllium does not produce a characteristic color in a flame test, unlike other alkaline earth metals.
- **Conclusion**: **Correct**.

9. **Statement 9**: Solubility of AgCN increases in KCN solution.
- **Analysis**: The presence of KCN leads to the formation of a soluble complex (Ag(CN)_2^-), which increases the solubility of AgCN.
- **Conclusion**: **Correct**.

### Summary of Conclusions:
- Correct Statements: 1, 2, 4, 5, 6, 8, 9 (Total: 7)
- Incorrect Statements: 3, 7 (Total: 2)

### Final Answer:
**Total Correct Statements: 7 out of 9.**