The correct option is C (iii), (iv) and (v)
Restriction enzymes are the endonucleases that cleave the phosphodiester bonds present between the nucleotides within or near to specific DNA sequences called recognition sites. When these enzymes cut the sugar phosphate backbone in the double stranded DNA at specific points slightly away from the centre, they leave single stranded free ends called sticky ends.
Each restriction enzyme has a specific recognition site. Therefore, the same kind of sticky ends are produced when a DNA is cut by the same restriction enzyme and different kinds of sticky ends would be produced if cut by different restriction enzymes. Hence, the statement (i) is incorrect.
Several fragments are produced by the vector when digested by a particular restriction enzyme if it has more than one recognition site for that enzyme. Generation of multiple fragments with same sticky ends (generated due to the action of the same restriction enzyme at multiple sites) will provide multiple possible sites for the gene of interest to get incorporated into. This might lead to the incorporation of the gene of interest at an undesired location or attachment of foreign DNA molecules at multiple sites. All these undesirable consequences complicate the gene cloning process. Therefore to avoid this, the vector should preferably have a single recognition site for the particular restriction enzyme used. Hence, the statement (v) is correct.
Hind II was the first restriction endonuclease to be isolated from a bacterium Haemophilus influenzae. Hence, the statement (iii) is correct.
Exonucleases cleave phosphodiester bonds between consecutive nucleotides of DNA at their terminal ends (either 5’ or 3’) one nucleotide at a time. Hence, the statement (ii) is also incorrect.
A bacteriophage is a virus that infects bacteria and has the ability to replicate within bacterial cells by integrating its DNA with the bacterial DNA. Hence, the statement (iv) is correct.
Thus, statements (iii), (iv) and (v) are correct.