In recombinant DNA technology, cloning vectors like pBR322 are used to carry foreign DNA into host cells. pBR322 contains two specific antibiotic resistance genes that serve as selectable markers: the ampicillin resistance gene (ampR) and the tetracycline resistance gene (tetR).

Step 1: Locate the BamHI restriction site
The restriction endonuclease BamHI has its specific recognition sequence located precisely within the coding region of the tetracycline resistance gene (tetR) on the pBR322 plasmid.

Step 2: Analyze the mechanism of Insertional Inactivation
When foreign DNA is ligated into the vector at the BamHI site, the physical insertion of this new DNA disrupts the continuous sequence of the tetR gene.

Step 3: Determine the consequence of the disruption
Because the tet^R gene is interrupted, it can no longer produce functional proteins to confer resistance against tetracycline. This phenomenon is called insertional inactivation.

Step 4: Evaluate the status of the other marker
Since the insertion occurred only at the BamHI site (within tetR), the ampicillin resistance gene (ampR) remains completely intact and fully functional.

Step 5: Conclude the Correct Option
Therefore, the recombinant plasmid will lose resistance towards tetracycline but retain resistance to ampicillin. Option (2) is the correct answer.