To determine the correctness of the given statements, we examine each one in turn:
Statement I: RNA mutates at a faster rate.
RNA is known to mutate at a faster rate compared to DNA. This is because RNA-dependent RNA polymerases, which replicate RNA genomes, typically lack the proofreading mechanisms that DNA polymerases have. As a result, errors introduced during replication are more likely to persist in RNA, leading to a higher mutation rate. Therefore, Statement I is true.
Statement II: Viruses having RNA genome and shorter life span mutate and evolve faster.
RNA viruses tend to have shorter life cycles, resulting in more replication cycles over a given time period. Coupled with a high mutation rate, as explained in Statement I, RNA viruses are capable of rapidly acquiring genetic variations and adapting quickly to environmental changes, thus evolving faster. Therefore, Statement II is also true.
Thus, the correct answer is that both Statement I and Statement II are true.