Step 1: Understanding palindromic sequence.
A palindromic DNA sequence reads the same in the 5$' \rightarrow$ 3$'$ direction on both strands. Such sequences are important as recognition sites for restriction enzymes.
Step 2: Checking option (B).
In option (B), when the complementary strand is read in the 5$' \rightarrow$ 3$'$ direction, it matches the original strand sequence, satisfying the condition of a palindrome.
Step 3: Analysis of remaining options.
Options (A), (C), and (D) do not read the same in opposite directions and hence are not palindromic.
Step 4: Conclusion.
The palindromic DNA sequence is given in option (B).