Which amongst the following is the most stable carbocation?

The most stable carbocation is $t$-alkyl carbocation because the order of stability of alkyl carbocation is $t$-alkyl $\gt s$-alkyl $\gt$ p-alkyl $\gt \mathrm{CH}_3^{+}$ carbocation. This stability order is described with the help of hyperconjugation and inductive effect. On the basis of hyper conjugation, $\left(\mathrm{CH}_3\right)_2 \stackrel{+}{\mathrm{C}} \mathrm{H}$ shows six resonating structures due to presence of six $\alpha \mathrm{C}-\mathrm{H}$ bonds,

due to presence of nine $\alpha \mathrm{C}-\mathrm{H}$ bonds $\stackrel{+}{\mathrm{C}} \mathrm{H}_3$ does not show the property of resonance while $\mathrm{CH}_3-\stackrel{+}{\mathrm{C}} \mathrm{H}_2$ shows three resonating structures due to presence of three $\alpha \mathrm{C}-\mathrm{H}$ bonds. Hence, larger number of resonating structures are possible in (2), so it is most stable. The above order of stability is also explained with the help of (+) I-effect of $-\mathrm{CH}_3$ group. More the number of $-\mathrm{CH}_3$ group. more will be tendency to displace the electrons towards positive charged carbon of carbocation. Thus (+) charge is decreased or compensated i.e, positive charge is decreased and stability of carbocation is increased.