Which of the following is (are) most likely to be produced under conditions resembling perfect competition - automobiles, beer, corn, diamonds, and...

The best answer for this would be corn.  Eggs are just about as good, but corn is probably a little bit better.  The relevant aspects of perfect competition for the purposes of this answer are that the good needs to be homogeneous and there need to be many small firms competing to provide it.

Because the good have to be homogeneous, beer and cars are clearly out.   People will prefer one beer to another or one car to another.  They will not think these things are all the same.  Diamonds are not all the same either.  In addition, neither cars nor diamonds can be produced by many small firms.

This leaves us with corn and eggs.  I will go with corn because it is more homogeneous than eggs.  Eggs come in different grades whereas corn is simply corn.  It is also easier to have a small farm growing some corn than to have a small egg-producing company.  Thus, there are likely to be more small firms participating in the market for growing corn than for producing eggs.

For these reasons, I would pick corn, but eggs would be a defensible answer as well.