To solve this problem, we need to understand the implications of inserting a gene into the plasmid pBR322 using the PstI restriction enzyme site.$\newline$Let's analyze the situation:$\newline \bullet$Plasmid pBR322 contains an ampicillin resistance gene, denoted as $amp^R. \newline \bullet$The PstI restriction enzyme cuts within the $amp^R$ gene.$\newline \bullet$Inserting a gene for $\beta$-galactosidase production at the PstI site will disrupt the $amp^R$ gene.$\newline \bullet$As a result, the recombinant plasmid will no longer confer ampicillin resistance to the host cell.$\newline$Now, let's evaluate the options:$\newline \bullet$Option 1: It will not be able to confer ampicillin resistance to the host cell.$\newline$ - This is correct because the insertion disrupts the $amp^R$ gene.$\newline \bullet$Option 2: The transformed cells will have the ability to resist ampicillin as well as produce $\beta$-galactosidase.$\newline$ - This is incorrect because the $amp^R$ gene is disrupted, so ampicillin resistance is lost.$\newline \bullet$Option 3: It will lead to lysis of host cell.$\newline$ - This is incorrect as there is no indication that the insertion causes cell lysis.$\newline \bullet$Option 4: It will be able to produce a novel protein with dual ability.$\newline$ - This is incorrect because the insertion does not create a novel protein with dual functions.$\newline$Therefore, the correct option is Option 1: It will not be able to confer ampicillin resistance to the host cell.