The set of correct statements is:
(i) Manganese exhibits `+7` oxidation state in its oxide.
(ii) Ruthenium and Osmium exhibit `+8` oxidation in their oxides.
(iii) Sc shows `+4` oxidation state which is oxidizizing in nature.
(iv) Cr shows oxidising nature in `+6` oxidation state.

Options

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

Answer

To determine the set of correct statements regarding the oxidation states of manganese, ruthenium, osmium, scandium, and chromium, we will analyze each statement one by one.

### Step-by-Step Solution:

1. **Statement (i): Manganese exhibits +7 oxidation state in its oxide.**
- Manganese oxide can be represented as Mn2O7.
- To find the oxidation state of manganese (Mn), we set up the equation:
\[ 2X + 7(-2) = 0 \]
where \(X\) is the oxidation state of manganese.
- Solving this gives:
\[ 2X - 14 = 0 \implies 2X = 14 \implies X = +7 \]
- Therefore, this statement is **correct**.

2. **Statement (ii): Ruthenium and Osmium exhibit +8 oxidation in their oxides.**
- For ruthenium, the oxide is RuO4. Setting up the equation:
\[ X + 4(-2) = 0 \]
Solving gives:
\[ X - 8 = 0 \implies X = +8 \]
- For osmium, the oxide is OsO4. Similarly:
\[ Y + 4(-2) = 0 \]
Solving gives:
\[ Y - 8 = 0 \implies Y = +8 \]
- Thus, both ruthenium and osmium exhibit +8 oxidation state. This statement is **correct**.

3. **Statement (iii): Scandium shows +4 oxidation state which is oxidizing in nature.**
- Scandium typically exhibits a +3 oxidation state (as it has the electron configuration of [Ar] 3d¹ 4s²).
- It does not commonly exhibit a +4 oxidation state. Therefore, this statement is **incorrect**.

4. **Statement (iv): Chromium shows oxidizing nature in +6 oxidation state.**
- Chromium in the +6 oxidation state (as in CrO3) has lost all its valence electrons and has a noble gas configuration.
- In this state, chromium can accept electrons, which indicates oxidizing behavior. Thus, this statement is **correct**.

### Summary of Statements:
- Statement (i): Correct
- Statement (ii): Correct
- Statement (iii): Incorrect
- Statement (iv): Correct

### Conclusion:
The correct statements are (i), (ii), and (iv). Therefore, the answer is:
**Option 4: Statements (i), (ii), and (iv) are correct.**