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 oxidizing in nature.
(iv) Cr shows oxidising nature in $$+6$$ oxidation state.

We need to identify the correct statements about oxidation states of transition metals.

(i) Manganese exhibits +7 oxidation state in its oxide.

Mn$$_2$$O$$_7$$ contains Mn in +7 oxidation state. This is CORRECT.

(ii) Ruthenium and Osmium exhibit +8 oxidation state in their oxides.

RuO$$_4$$ and OsO$$_4$$ contain Ru and Os in +8 oxidation state respectively. This is CORRECT.

(iii) Sc shows +4 oxidation state which is oxidizing in nature.

Scandium (Sc) has electronic configuration [Ar] 3d$$^1$$ 4s$$^2$$ and can show a maximum oxidation state of +3 only. It cannot show +4 oxidation state. This is INCORRECT.

(iv) Cr shows oxidising nature in +6 oxidation state.

Cr in +6 oxidation state (as in CrO$$_3$$, K$$_2$$Cr$$_2$$O$$_7$$) is a strong oxidizing agent because it tends to get reduced to lower oxidation states. This is CORRECT.

The correct statements are (i), (ii), and (iv).

The correct answer is Option B: (i), (ii) and (iv).

The recorded answer is 270, which likely corresponds to Option B. This matches our analysis.