c
Key ldea \({S_{{N^1}}}\) reaction involves the formation of carbonation intermediate. More the stability of carbonation, more is the reactivity of alkyl/aryl halides towards \({S_{{N^1}}}\) reaction. The intermediate carbonations formed by given halldes are as:

\(C_{6} H_{5} C H\left(C_{6} H_{5}\right) B r \rightarrow\)\(\left(C_{6} H_{5}\right)_{2} \stackrel{+}{C} H+B r^{-} C_{6} H_{5} C H\left(C H_{3}\right) B r \rightarrow\)\( C_{6} H_{5} \stackrel{+}{C} H\left(C H_{3}\right)+B r^{-}\)

\(C_{6} H_{5} C\left(C H_{3}\right)\left(C_{6} H_{5}\right) B r \rightarrow\)\(\left(C_{6} H_{5}\right)_{2}\stackrel{+}{C}\left(C H_{3}\right)+B r^{-} C_{6} H_{5} C H_{2} B r \rightarrow\)\( C_{6} H_{5}\stackrel{+}{C} H_{2}+B r^{-}\)

The order of stability of these carbocations is as

\(\left(C_{6} H_{5}\right)_{2} \stackrel{+}{C}\left(C H_{3}\right)>\left(C_{6} H_{5}\right)_{2} \stackrel{+}{C} H\) \(>C_{6} H_{5} \stackrel{+}{C} H\left(C H_{3}\right)>C_{6} H_{5} \stackrel{+}{C} H_{2}\)

Thus, \(C_{6} H_{5} C\left(C H_{3}\right)\left(C_{6} H_{5}\right) B r\) is most reactive towards \({S_{{N^1}}}\) reaction.