The correct code for stability, of oxidation states for given cations is:
(i) `Pb^(2+) gt Pb^(4+) ,Tl^(+) lt Tl^(3+)`
(ii) `Bi^(3+) lt Sb^(3+) , Sn^(3+) lt Sn^(4+)`
(iii) `Pb^(3+) gt Pb^(4+),Bi^(3+) gt Bi^(3+)`
(iv) `Tl^(3+) lt ln^(3+), Sn^(2+) gt Sn^(4+)`
(v) `Sn^(2+) lt Pb^(2+) , Sn^(4+) gt Pb^(4+)`
(vi) `Sn^(2+) lt Pb^(2+), Sn^(4+) lt Pb^(4+)`

Options

A. (v) and (vi)
B. (i), (iii) and (vi)
C. (iii) and (v)
D. (ii) and (iv)

Explanation

To solve the question regarding the stability of oxidation states for the given cations, we will analyze each statement based on the inert pair effect and the general trends in the periodic table.

### Step-by-Step Solution:

1. **Understanding the Inert Pair Effect**:
- The inert pair effect refers to the tendency of the s-electrons in the outermost shell to remain non-bonding or inert due to the increased effective nuclear charge as we move down a group in the periodic table. This leads to a preference for lower oxidation states.

2. **Analyzing Each Statement**:
- **Statement (i)**: `Pb^(2+) > Pb^(4+) , Tl^(+) < Tl^(3+)`
- For lead (Pb), the +2 oxidation state is more stable than +4 due to the inert pair effect. For thallium (Tl), the +3 state is more stable than +1. **This statement is correct.**

- **Statement (ii)**: `Bi^(3+) < Sb^(3+) , Sn^(3+) < Sn^(4+)`
- Bismuth (Bi) prefers +3 over +5, but Sb^(3+) is more stable than Bi^(3+). For tin (Sn), +4 is more stable than +3. **This statement is incorrect.**

- **Statement (iii)**: `Pb^(3+) > Pb^(4+), Bi^(3+) > Bi^(3+)`
- The comparison of Pb^(3+) and Pb^(4+) is incorrect; +2 is more stable than both. Bi^(3+) cannot be compared to itself. **This statement is incorrect.**

- **Statement (iv)**: `Tl^(3+) < In^(3+) , Sn^(2+) > Sn^(4+)`
- Thallium (Tl) +3 is less stable than indium (In) +3 due to the inert pair effect. For tin, +2 is less stable than +4. **This statement is incorrect.**

- **Statement (v)**: `Sn^(2+) < Pb^(2+) , Sn^(4+) > Pb^(4+)`
- Tin +2 is less stable than lead +2, but tin +4 is more stable than lead +4. **This statement is incorrect.**

- **Statement (vi)**: `Sn^(2+) < Pb^(2+) , Sn^(4+) < Pb^(4+)`
- Tin +2 is less stable than lead +2, but tin +4 is more stable than lead +4. **This statement is incorrect.**

3. **Final Conclusion**:
- The correct statements are: **(i)** and **(v)**. Therefore, the correct code for stability of oxidation states for the given cations is **(i) and (v)**.