The atomic numbers of elements A,B,C and D are Z - 1, Z, Z + 1 and Z + 2 respectively. If B is a noble gas, choose the correct statement among the following statements :
I. A has higher electron affinity.
II. C exists in +2 oxidation state.
III. D is an alkaline earth metal.

Options

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

Answer

To solve the problem, we need to analyze the information provided about the elements A, B, C, and D based on their atomic numbers and the fact that B is a noble gas.

### Step-by-step Solution:

1. **Identify the Elements Based on Atomic Numbers:**
- The atomic numbers of the elements are given as:
- A: Z - 1
- B: Z
- C: Z + 1
- D: Z + 2

2. **Determine the Nature of Element B:**
- Since B is a noble gas, it has a complete outer shell configuration, typically represented as \( ns^2 np^6 \). This means that B is likely to be in Group 18 of the periodic table.

3. **Identify Element A:**
- Element A has an atomic number of \( Z - 1 \). If B is a noble gas, then A is likely to be a halogen (Group 17), which has a high electron affinity because it needs one more electron to complete its octet.

4. **Evaluate Statement I:**
- **Statement I:** "A has higher electron affinity."
- This statement is correct because halogens (like A) have higher electron affinities compared to noble gases and other groups.

5. **Identify Element C:**
- Element C has an atomic number of \( Z + 1 \). Since B is a noble gas, C is likely to be in Group 1 (alkali metals), which typically have one valence electron.

6. **Evaluate Statement II:**
- **Statement II:** "C exists in +2 oxidation state."
- This statement is incorrect. Alkali metals (Group 1) typically exhibit a +1 oxidation state, not +2.

7. **Identify Element D:**
- Element D has an atomic number of \( Z + 2 \). Since C is in Group 1, D must be in Group 2 (alkaline earth metals).

8. **Evaluate Statement III:**
- **Statement III:** "D is an alkaline earth metal."
- This statement is correct because elements in Group 2 are indeed alkaline earth metals.

### Conclusion:
- From the analysis:
- Statement I is correct.
- Statement II is incorrect.
- Statement III is correct.

Thus, the correct statements are I and III.

### Final Answer:
The correct statements are I and III.