Step 1: Analyze \( Cr_2O_7^{2-} \).
Dichromate ion \( Cr_2O_7^{2-} \) is interconvertible with chromate ion \( CrO_4^{2-} \) depending on the pH of the medium.
In acidic medium, dichromate ion is favoured.
In basic medium, chromate ion is favoured.
\[
Cr_2O_7^{2-} + H_2O \rightleftharpoons 2CrO_4^{2-} + 2H^+
\]
So:
\[
A = S
\]
Step 2: Analyze \( FeCr_2O_4 \).
\( FeCr_2O_4 \) is chromite ore.
When chromite ore is fused with \( Na_2CO_3 \) in air, it forms yellow sodium chromate.
\[
4FeCr_2O_4 + 8Na_2CO_3 + 7O_2 \rightarrow 8Na_2CrO_4 + 2Fe_2O_3 + 8CO_2
\]
So:
\[
B = R
\]
Step 3: Analyze \( CrO_3 \).
\( CrO_3 \) is chromium trioxide.
It is an acidic oxide because chromium is present in a high oxidation state \( +6 \).
Acidic character generally increases with increase in oxidation state of the metal.
So:
\[
C = Q
\]
Step 4: Analyze \( CrO \).
In \( CrO \), chromium is present in \( +2 \) oxidation state.
Metal oxides in lower oxidation states are generally basic in nature.
Therefore, \( CrO \) is predominantly basic.
So:
\[
D = P
\]
Step 5: Write the complete matching.
From the above analysis:
\[
A = S,\quad B = R,\quad C = Q,\quad D = P
\]
Step 6: Match with the given options.
The matching \( A = S,\; B = R,\; C = Q,\; D = P \) corresponds to option (D).
Step 7: Conclusion.
Thus, the correct matches are:
\[
\boxed{A = S,\; B = R,\; C = Q,\; D = P}
\]