The set of correct statements is: (i) Manganese exhibits + 7...

(i) The oxidation state of $Mn$ in oxide (${Mn}_{2}{O}_{7}$) is:

Let us consider $Mn$ as $x$.

$⇒ 2x + 7 ( - 2 ) = 0$

$⇒ 2x + ( - 14 ) = 0$

$⇒ 2x - 14 = 0$

$⇒ 2x = 14$

$⇒ x = 7$

(ii) The oxidation state of Ruthenium in oxide (${RuO}_{4}$) is:

Consider $Ru$ as $x$.

$⇒ x + 4 ( - 2 ) = 0$

$⇒ x - 8 = 0$

$⇒ x = 8$

The oxidation state of Osmium in oxide (${OsO}_{4}$) is:

Consider $Os$ as $x$.

$⇒ x + 4 ( - 2 ) = 0$

$⇒ x - 8 = 0$

$⇒ x = 8$

Hence, Ruthenium and Osmium has +7 oxidation state in its oxide.

(iii) $Sc$ has ${ns}^{2} ( n - 1 ) {d}^{1}$ electronic configuration.

It utilizes two electrons from its $ns$ sub-shell then its oxidation state = +2. When it utilizes both the electrons then its oxidation state = +3.

(iv) In the modern periodic table, chromium metal is present in group 6. It is a transition metal and belongs to the first transition series. The atomic number of chromium is 24. Its electronic configuration is $[ Ar ] 3{d}^{5}4{s}^{1}$.

It has five electrons in the 3d sub-shell and one electron in the 4s sub-shell. Thus, chromium metal has six valence electrons. Chromium can lose some or all of its valence electrons to form ions with different oxidation states. Thus, chromium shows the oxidation states of +1, +2, +3, +4, +5, and +6 respectively.
The most common oxidation states of chromium are +2, +3, and +6.

So, the statement (i), (ii) and (iv) are correct.