Understanding the Concept:
The mesomeric effect ($M$) refers to the redistribution of $\pi$-electron density through a conjugated system via resonance.
Positive Mesomeric ($+M$) Effect: Occurs when a substituent group contains a lone pair of electrons available to donate into the conjugated benzene ring system, increasing the ring's overall electron density.
Negative Mesomeric ($-M$) Effect: Occurs when an electronegative substituent group pulls $\pi$-electron density out of the benzene ring toward itself, deactivating the ring.
Step 1: Analyze the electron donation properties of the substituent choices.
Groups like $-\text{OCH}_3$, $-\text{O}^-$, and $-\text{NH}_2$ contain heteroatoms (oxygen and nitrogen) carrying non-bonding lone pairs right next to the aromatic system. These groups push electron density into the ring through resonance, acting as $+M$ activators.
The nitro group ($-\text{NO}_2$) contains a highly electrophilic central nitrogen bonded to highly electronegative oxygen atoms. Due to the conjugate $\pi$-system layout ($\text{C}=\text{C}-\text{N}=\text{O}$), it pulls electrons away from the aromatic ring, making it a powerful $-M$ deactivating substituent group.