For the SN2 reaction CH₃Br + Nu⁻, nucleophilicity in aprotic solvents is determined by basicity and polarizability.
⁻OH (hydroxide) is the strongest nucleophile and base, making it highly reactive.
PhO⁻ (phenoxide) is a good nucleophile with reasonable basicity.
CH₃COO⁻ (acetate) is weakened by resonance stabilization of its negative charge across the C-O bonds, reducing its nucleophilicity.
ClO₄⁻ (perchlorate) is a very weak nucleophile, being the conjugate base of a strong acid (HClO₄).
The correct order of nucleophilicity is: ⁻OH > PhO⁻ > CH₃COO⁻ > ClO₄⁻, which matches option (3).