Key Idea $S_{\mathrm{N}} 1$ reaction involves the formation of carbocation intermediate. More the stability of carbocation, more is the reactivity of alkyl/aryl halides towards $\mathrm{S}_{\mathrm{N}} 1$ reaction.
The intermediate carbocations formed by given halides are as :
(a) $\mathrm{C}_6 \mathrm{H}_5 \mathrm{CH}\left(\mathrm{C}_6 \mathrm{H}_5\right) \mathrm{Br} \longrightarrow\left(\mathrm{C}_6 \mathrm{H}_5\right)_2 \stackrel{+}{\mathrm{C}} \mathrm{H}+\mathrm{Br}^{-}$
(b) $\mathrm{C}_6 \mathrm{H}_5 \mathrm{CH}\left(\mathrm{CH}_3\right) \mathrm{Br} \longrightarrow \mathrm{C}_6 \mathrm{H}_5 \stackrel{+}{\mathrm{C}} \mathrm{H}\left(\mathrm{CH}_3\right)+\mathrm{Br}^{-}$
(c) $\mathrm{C}_6 \mathrm{H}_5 \mathrm{C}\left(\mathrm{CH}_3\right)\left(\mathrm{C}_6 \mathrm{H}_5\right) \mathrm{Br} \longrightarrow$
$$
\left(\mathrm{C}_6 \mathrm{H}_5\right)_2 \stackrel{+}{\mathrm{C}}\left(\mathrm{CH}_3\right)+\mathrm{Br}^{-}
$$
(d) $\mathrm{C}_6 \mathrm{H}_5 \mathrm{CH}_2 \mathrm{Br} \longrightarrow \mathrm{C}_6 \mathrm{H}_5 \stackrel{+}{\mathrm{C}} \mathrm{H}_2+\mathrm{Br}^{-}$
The order of stability of these carbocations is as
$$
\begin{aligned}
\left(\mathrm{C}_6 \mathrm{H}_5\right)_2 \stackrel{+}{\mathrm{C}}\left(\mathrm{CH}_3\right) & >\left(\mathrm{C}_6 \mathrm{H}_5\right)_2 \stackrel{+}{\mathrm{C}} \mathrm{H} \\
& >\mathrm{C}_6 \mathrm{H}_5 \stackrel{+}{\mathrm{C}} \mathrm{H}\left(\mathrm{CH}_3\right)>\mathrm{C}_6 \mathrm{H}_5 \stackrel{+}{\mathrm{C}} \mathrm{H}_2
\end{aligned}
$$
Thus, $\mathrm{C}_6 \mathrm{H}_5 \mathrm{C}\left(\mathrm{CH}_3\right)\left(\mathrm{C}_6 \mathrm{H}_5\right) \mathrm{Br}$ is most reactive towards $\mathrm{S}_{\mathrm{N}} 1$ reaction.