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I have looked through articles and closest I feel is in this question there will be a nucleophilic aromatic substitution. Now, a lot of questions are available where there is a halogen and OMe group substitutes the halogen.

My take on this is maybe due to SIR effect (steric inhibition of resonance) The NO2 group present in between the two methyl groups would be substituted by OMe? Will this be the approach?

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You are correct that the nitro group can be displaced by methoxide, this has been reported examples here.

My instinct is that the less hindered nitro group is the one that will be displaced.

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