Step 1: Understanding the Question:
The problem asks to identify which functional group exhibits a negative resonance effect ($-\text{R}$ effect), meaning it actively withdraws electron density away from an attached conjugated $\pi$-system.
Step 2: Key Formula or Approach:
$+\text{R}$ (Positive Resonance) groups: Possess at least one lone pair of electrons on the atom directly linked to the conjugated system, allowing them to donate electron density into the ring/chain.
$-\text{R}$ (Negative Resonance) groups: Typically contain electronegative atoms connected by multiple bonds ($\pi$-bonds) capable of pulling electron pairs toward themselves via delocalization.
Step 3: Detailed Explanation:
Let's evaluate the electronic behaviors of each group:
$-\text{Br}$ (Bromine), $-\text{OR}$ (Alkoxy), and $-\text{NHR}$ (Amino) all possess unshared lone pairs on their connecting atoms (Br, O, and N respectively). Consequently, they can push these lone pairs into an adjacent $\pi$-system, exhibiting a $+\text{R}$ effect.
The carbonyl group, $-\text{CO}-$, contains a highly polarized carbon-oxygen double bond (C=O). Because oxygen is significantly more electronegative than carbon, it pulls the shared $\pi$-electrons toward itself:
$$-\text{C=O} \longleftrightarrow -\xrightarrow{+}{\text{C}}-\text{O}^-$$
When attached to a conjugated system (like a benzene ring), the carbonyl carbon draws electron density out of the system via resonance, which is defined as a $-\text{R}$ (electron-withdrawing resonance) effect.
Step 4: Final Answer:
The functional group exhibiting the $-\text{R}$ effect is $-\text{CO}-$, matching option (A).