Deadlock is a situation in which two or more processes are unable to proceed because each is waiting for the other to release a resource. Deadlocks can occur in a system when certain conditions are met. One of these conditions is the presence of a circular wait, where each process is waiting for a resource held by another process in a circular chain.

In the given scenario, we have a single resource and the question asks us when a deadlock occurs. Let's analyze the options one by one.

a) If there are more than two processes competing for that resource:
In this case, there may be a chance of deadlock if the processes are waiting for each other's resources in a circular manner. However, deadlock can still be avoided if proper resource allocation and scheduling techniques are used. Therefore, a deadlock is not guaranteed to occur in this situation.

b) If there are only two processes competing for that resource:
If there are only two processes competing for the single resource, a deadlock cannot occur. This is because there is no possibility of a circular wait with only two processes. Each process can acquire the resource it needs and release it when it is done, allowing the other process to acquire it. Therefore, deadlock cannot occur in this scenario.

c) If there is a single process competing for that resource:
If there is only one process competing for the resource, deadlock is not possible. Deadlock occurs when multiple processes are waiting for each other's resources, which cannot happen when there is only one process.

d) None of these:
The correct answer is option 'd' because deadlock cannot occur in any of the given scenarios. Deadlock requires multiple processes to be waiting for each other's resources in a circular manner, which is not possible with a single resource or a single process.

In conclusion, deadlock cannot occur with a single resource, regardless of the number of processes competing for it. Deadlock requires specific conditions to be met, including circular wait, which is not possible in the given scenario.