Step 1: Understanding the Concept: The plasmid pBR322 is a widely used cloning vector that contains specific antibiotic resistance genes with designated restriction sites.
Step 2: Key Formula or Approach: Recall the map of pBR322 and apply the concept of insertional inactivation to determine the survival of recombinant bacteria.
Step 3: Detailed Explanation: Statement I states that BamHI has its recognition site in the tetracycline resistance (tet$^{R}$) region of pBR322.
This is factually true; both BamHI and SalI are located within the tet$^{R}$ gene.
Statement II claims that E.coli having pBR322 with a desired DNA inserted at the BamHI site can still grow in a medium containing tetracycline.
This is false due to "insertional inactivation."
When foreign DNA is inserted at the BamHI site, the tet$^{R}$ gene gets disrupted and loses its function.
Consequently, the recombinant E.coli will lose resistance to tetracycline and will not be able to grow in a tetracycline-containing medium.
Step 4: Final Answer: Statement I is true, and Statement II is false.