Final answer:
The correct answer is Type II restriction enzymes, which are known for their precise cuts in specific palindromic DNA sequences used extensively in genetic engineering.
Step-by-step explanation:
The type of restriction enzymes that recognize palindromic sequences of DNA, cut within the recognition sequence, do not have methylating activity, and are frequently used in laboratories are Type II restriction enzymes. These enzymes are known for their precision in cutting DNA at specific sequences, which are typically palindromic and are used extensively in recombinant DNA technology for cloning and genetic engineering. An example of a Type II restriction enzyme is EcoRI, which recognizes the palindromic sequence 5'GAATTC3' and cuts within this sequence, resulting in 'sticky ends' that are useful for DNA recombination.