The carbonyl group consists of a carbon atom double-bonded to an oxygen atom (C=O).
Oxygen is more electronegative than carbon. This leads to a polarization of the C=O double bond:
\begin{itemize}
\item The oxygen atom carries a partial negative charge ($\delta-$).
\item The carbon atom carries a partial positive charge ($\delta+$).
\end{itemize}
C$^{\delta+}$=O$^{\delta-}$
Let's analyze the statements based on this polarity:
a) Carbonyl Carbon is electrophilic
An electrophile ("electron-loving") is an atom, ion, or molecule that is electron-deficient and seeks electrons.
The carbonyl carbon has a partial positive charge ($\delta+$) due to the electronegative oxygen pulling electron density away from it. This makes the carbonyl carbon electron-deficient and thus electrophilic. It is susceptible to attack by nucleophiles.
This statement is correct.
b) Carbonyl Carbon is nucleophilic
A nucleophile ("nucleus-loving") is an atom, ion, or molecule that is electron-rich and donates an electron pair to form a bond with an electrophile.
The carbonyl carbon is electron-deficient ($\delta+$), not electron-rich. Therefore, it is not nucleophilic.
This statement is incorrect.
c) Carbonyl Oxygen is electrophilic
The carbonyl oxygen has a partial negative charge ($\delta-$) due to its higher electronegativity. It is electron-rich, not electron-deficient. Therefore, it is not electrophilic.
This statement is incorrect.
d) Carbonyl Oxygen is nucleophilic
The carbonyl oxygen is electron-rich ($\delta-$) and typically has lone pairs of electrons (two lone pairs in a standard C=O group). These lone pairs can be donated to an electrophile (e.g., a proton H$^+$ in acid catalysis, or a Lewis acid). Thus, the carbonyl oxygen can act as a nucleophile or a Lewis base.
This statement is correct.
So, the correct statements are (a) and (d).
This corresponds to option (a).
\[ \boxed{\text{a, d}} \]