Which of the following carbocations is the most stable?

The benzyl cation carries charge at the ortho and para ring carbons. A para $\mathrm{OCH}{}_3$ group donates its lone pair (+M) directly to the cationic centre, giving an extra oxonium-type structure. Nitro groups withdraw electrons and destabilise the cation, so 4-methoxybenzyl is the most stable.