Step 1: Understand the statements.
Statement (I): On nitration of m-xylene with \( \text{HNO}_3 \) and \( \text{H}_2\text{SO}_4 \), followed by oxidation, 4-nitrobenzene-1,3-dicarboxylic acid is obtained as the major product.
Statement (II): The –CH₃ group is an ortho/para-directing group, while the –NO₂ group is a meta-directing group.
Step 2: Analyze Statement (I).
m-Xylene is 1,3-dimethylbenzene. When it undergoes nitration using concentrated \( \text{HNO}_3 \) and \( \text{H}_2\text{SO}_4 \), the nitro group (\( \text{NO}_2 \)) enters the position that is ortho or para to one of the –CH₃ groups, taking into account the directing influence of both methyl substituents.
For m-xylene, the position 4 relative to one of the –CH₃ groups is the most favorable site for substitution, giving **4-nitro-m-xylene** as the major nitration product.
On oxidation (for example, using \( \text{KMnO}_4 \)), each –CH₃ group is converted into a –COOH group. Hence, the product obtained is **4-nitrobenzene-1,3-dicarboxylic acid**.
Therefore, Statement (I) is true.
Step 3: Analyze Statement (II).
The –CH₃ group is an electron-donating group that activates the benzene ring and directs incoming electrophiles to the **ortho and para positions**.
The –NO₂ group, on the other hand, is an electron-withdrawing group due to its –M (mesomeric) and –I (inductive) effects, and it directs incoming electrophiles to the **meta position**.
Hence, Statement (II) is also true.
Step 4: Conclusion.
Both statements are scientifically correct. Statement (I) describes the correct product formed in the reaction, and Statement (II) correctly explains the directive influence of the –CH₃ and –NO₂ groups.
Final Answer:
Both Statement I and Statement II are true.
\[
\boxed{\text{Both Statement I and Statement II are true.}}
\]