The deactivating as well as meta directing group(s) among the following is/are (a) \(-\mathrm{CH}_{2} \mathrm{Cl}\) (b) \(-\mathrm{CCl}_{3}\) (c) \(-\stackrel{\oplus}{\mathrm{NR}}_{3}\) (d) \(-\mathrm{C}_{6} \mathrm{H}_{5}\)

In the context of electrophilic aromatic substitution (EAS), a deactivating group is one that decreases the rate of the reaction when attached to an aromatic ring. These groups are electron-withdrawing, meaning they pull electron density away from the ring, making it less reactive towards electrophiles.

Electron-withdrawing can occur through two main effects: the inductive effect and the resonance effect. Groups like \texttt{\text{-CH\(_2\)Cl}} have a deactivating influence because the chlorine atom is electronegative and pulls electron density away through the sigma bonds (inductive effect). When you have groups such as \texttt{\text{-CCl\(_3\)}}, the electron-withdrawing power is amplified due to the presence of multiple electronegative atoms, leading to a stronger deactivating capability.

Therefore, in the provided exercise, the groups \texttt{\text{-CCl\(_3\)}}, \texttt{\text{-NR\(_3^+\)}}, and \texttt{\text{-C\(_6\)H\(_5\)}} act as deactivators of EAS due to their electron-withdrawing characteristics.

Meta directing groups are a specific type of deactivating groups that not only reduce the reactivity of the aromatic ring but also influence the position where the electrophilic substitution will occur. In benzene derivatives, these groups direct the incoming electrophile to the meta position relative to themselves. This is important in predicting the structure of the product in EAS reactions.

The meta position is the carbon two positions away from the substituent group. Not all deactivating groups are meta directing, but all meta directing groups are deactivating. In the exercise, the groups \texttt{\text{-CCl\(_3\)}}, \texttt{\text{-NR\(_3^+\)}}, and \texttt{\text{-C\(_6\)H\(_5\)}} are examples of meta directing groups. Their ability to direct the electrophile to the meta position can be attributed to either their inductive or resonance effects, which destabilize the ortho and para carbocations that form during the reaction.

The inductive effect refers to the transmission of electron density through sigma bonds in a molecule due to the electronegativity of atoms or the presence of a polar bond. Electronegative atoms pull electron density toward themselves, leading to a partial positive charge on the atom directly bonded to it.

In the context of EAS, substituents that wield a strong inductive effect, such as \texttt{\text{-CCl\(_3\)}}, withdraw electron density from the aromatic ring, making it less nucleophilic and consequently less reactive to attack by electrophiles. This withdrawal can decrease the rate of EAS reactions. With each additional electronegative atom, like chlorine in this example, the inductive effect is enhanced, exemplifying the cumulative nature of this effect.

The resonance effect involves the delocalization of electrons within a molecule and can either donate to or withdraw electron density from the aromatic ring based on the nature of the substituent group.

Electron-withdrawing groups (EWGs) that are capable of resonance will pull electron density out of the aromatic ring through pi bonds. This can be seen with substituents like \texttt{\text{-NR\(_3^+\)}} and \texttt{\text{-C\(_6\)H\(_5\)}} in the exercise, where the EWGs stabilize the ring's electron density through overlapping p-orbitals, which affects the location and rate of electrophilic attack. In contrast to the inductive effect, the resonance effect can either enhance or reduce the reactivity of the ring, depending on whether the substituent is electron-donating or electron-withdrawing.