The question involves understanding the function of the plasmid $pBR322$ and the effect of inserting a gene at a specific restriction site. Let's analyze the provided scenario step-by-step.
Step 1: Understanding the Background
Plasmid $pBR322$ is a common cloning vector in genetic engineering. It contains several important features:
Step 2: Recombinant DNA Technique
When the PstI restriction enzyme is used to cut the plasmid, the am^{R} gene is disrupted. This disruption means that if a foreign gene, such as the one coding for β-galactoside production, is inserted at this site, the plasmid is now a recombinant plasmid.
Step 3: Consequences of Disruption
When inserted into an E. coli strain, the recombinant plasmid results in the following:
Conclusion:
The correct answer is: it will not be able to confer ampicillin resistance to the host cell. Inserting the gene for β-galactoside production disrupts the function of the relevant resistance gene, thus preventing the recombinant cells from surviving in the presence of ampicillin.
Frequency of recombination between gene pairs on same chromosome as a measure of the distance between genes to map their position on chromosome, was used for the first time by

Recombinant DNA technology is the process used for producing new genetic combinations by joining different genetic material (DNA) together and inserting them into host organisms from two different species or sources. These new combinations are of value to medicine, science, industry, and agriculture.
Step 1- Isolation of Genetic Material.
Step 2- Cutting the gene at the recognition sites.
Step 3- Amplifying the gene copies through Polymerase chain reaction ( PCR)
Step 4- Ligation of DNA Molecules.
Step 5- Insertion of Recombinant DNA into Host.