The correct palindromic sequence of the restriction enzyme, Hind III, is:

The correct option is A

$$\begin{gathered} AAGCTT \\ TTCGAA \end{gathered}$$

The correct option is option A.

Explanation of the correct option:

1. It is the restriction site of the enzyme Hind III.
2. It is palindromic in nature.
3. It cleaves the sequence AAGCTT between the AA in presence of Mg⁺² to give 5^' overhangs, also called sticky ends.
4. This enzyme is present in Haemophilus influenza hence the name Hind III.

Explanation of the incorrect options:

Option B:

1. It is the restriction site of the enzyme EcoRI.
2. This enzyme is present in the bacteria Escherichia coli strain RY.

Option C:

1. It is the restriction site of the enzyme EcoRV.
2. It is present in certain strains of the bacteria Escherichia coli.

Option D:

1. It is the restriction site of the enzyme BamHI.
2. It is present in the bacteria Bacillus amyloliquefaciens.

Final answer: The correct palindromic sequence of the restriction enzyme, Hind III, is $$\begin{gathered} AAGCTT \\ TTCGAA \end{gathered}$$.