Step 1: Aromatization of alkane.
The given alkane undergoes aromatization in the presence of
\[
Cr_2O_3,\ 773K,\ 10-20\ atm
\]
This gives an alkyl benzene compound.
Here, the product \(X\) is toluene:
\[
C_6H_5CH_3
\]
Step 2: Oxidation of toluene.
Toluene is oxidized using
\[
KMnO_4,\ OH^-
\]
followed by
\[
H_3O^+
\]
The methyl group of toluene is oxidized to carboxylic acid group:
\[
C_6H_5CH_3 \rightarrow C_6H_5COOH
\]
Thus, product \(Y\) is benzoic acid.
So, one substituent is
\[
P=-COOH
\]
Step 3: Nitration of benzoic acid.
Benzoic acid undergoes nitration with
\[
Conc.\ HNO_3+H_2SO_4
\]
The \(-COOH\) group is a meta-directing group.
Therefore, nitration gives mainly meta-nitrobenzoic acid.
So, the second substituent is
\[
Q=-NO_2
\]
Step 4: Final conclusion.
Hence, the substituents \(P\) and \(Q\) are
\[
\boxed{-COOH,\ -NO_2}
\]
Therefore, the correct option is
\[
\boxed{(4)}
\]