Step 1: Analyze Statement I.
In Statement I, the carbocation is stabilized by the +R effect of the \( \text{-OCH}_3 \) group. The \( \text{-OCH}_3 \) group is an electron-donating group through resonance (+R effect), which helps stabilize the positive charge on the carbocation. Thus, Statement I is correct.
Step 2: Analyze Statement II.
In Statement II, the carbocation is stabilized by the +R effect of the \( \text{-NO}_2 \) group. The \( \text{-NO}_2 \) group, however, is an electron-withdrawing group through resonance (-M effect), not a donating group. This destabilizes the carbocation, making Statement II incorrect.
Step 3: Conclusion.
Thus, Statement I is correct, and Statement II is incorrect.
Final Answer: (A) Both statement 1 and statement 2 are correct