Section 376 of the CrPC lists specific petty sentences for which the ordinary right of appeal does not apply, and one month's imprisonment imposed by a Magistrate of the Second Class is one of the situations it names. Reading the options against this specific bar, rather than against the general rules for appeals, gives the answer quickly.
Testing the facts directly against Section 376's specific exclusion shows that no appeal can be brought in this instance.
The clearest way through this question is to compare the general rule that convictions can usually be appealed against the specific, narrower carve-out that Section 376 creates for very minor sentences, since the two options most likely to be picked, an appeal to the Sessions Court and no appeal at all, sit at opposite ends of that comparison.
Comparing the general appeal right against the specific statutory exception shows that the facts here, a one-month sentence from a Second Class Magistrate, sit inside the exception, so the general right of appeal is displaced and no appeal is maintainable.
Therefore, the correct answer is no appeal is maintainable in this specific instance.