Final answer:
Eukaryotic cells lacking telomerase would have progressively shorter chromosomes because telomerase extends the telomeres, which without it, leads to chromosome end shortening with each round of cell division. The correct answer is option E.
Step-by-step explanation:
In the absence of telomerase, a eukaryotic cell would experience a reduction in chromosome length over time. This is due to the fact that telomerase is responsible for extending the ends of linear chromosomes through the addition of nucleotide sequences, thus preventing the shortening that normally occurs during DNA replication. Without telomerase, the very end of the chromosome, called the telomere, cannot be replicated properly, which leads to progressive shortening with each cell division.
The reduction in chromosome length in eukaryotic cells lacking telomerase addresses option E) from the question. On the other hand, the inability to form RNA primers (option A) relates to a different function that is not associated with telomerase. Similarly, the production of Okazaki fragments (option B) and the repair of mismatched DNA base pairs (option C) occur during replication but are not directly affected by the absence of telomerase. As for RNA-DNA hybrids (option D), these do occur naturally during certain stages of replication and are not immediately linked to the activity of telomerase.