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My argument is that the +I effect of CH3 group increases the electron density at oxygen atom, making it a better nucleophile

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When the donor atom is same, a general rule applies: nucleophilicity parallels basicity. Thus, comparing the basic strength of methoxide and hydroxide, it is observed that methoxide is a stronger base than hydroxide (as it the conjugate base of a weaker acid i.e. methanol when compared to water). Thus, methoxide is a stronger nucleophile than hydroxide.

However, at the same time NMR data predicts that methanol is a stronger acid than water (despite the I+ effect of $\ce{-CH3}$ group). So, in this case, there exists a controversy.

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