The correct order of the rate of the reaction for the following reaction with respect to nucleophiles is:
$$CH_{3}Br + Nu^{\ominus} \rightarrow CH_{3}Nu+Br^{\ominus}$$

The reaction $$CH_3Br + Nu^- \to CH_3Nu + Br^-$$ is an SN2 reaction. The rate depends on the nucleophilicity of $$Nu^-$$.

Nucleophilicity order:

$$^-OH$$ is a strong nucleophile (small, high charge density).

$$PhO^-$$ (phenoxide) is a moderate nucleophile (resonance-stabilized, less nucleophilic than OH⁻).

$$CH_3COO^-$$ (acetate) is a weak nucleophile (resonance-stabilized carboxylate).

$$ClO_4^-$$ (perchlorate) is an extremely weak nucleophile (highly stabilized by resonance).

Order of nucleophilicity: $$^-OH > PhO^- > CH_3COO^- > ClO_4^-$$

The answer is Option 2: $$^-OH > PhO^- > CH_3COO^- > ClO_4^-$$.