Which of the following letter-clusters will replace the question mark (?) in the given series?
AM, DK, GI, JG, ?

The correct option is ME.

To find the next term in the series, let us analyze the pattern followed by the first and second letters of each cluster separately.

First Letter Series: A, D, G, J, ...
Let us look at their numerical positions in the English alphabet:
A = 1
D = 4
G = 7
J = 10
The difference between the consecutive first letters is constant:

$4\; -\; 1\; =\; 3$

$7\; -\; 4\; =\; 3$

$10\; -\; 7\; =\; 3$

Following this pattern, the position of the next first letter should be:

$10\; +\; 3\; =\; 13$

The 13th letter of the alphabet is M.

Second Letter Series: M, K, I, G, ...
Let us look at their numerical positions in the English alphabet:
M = 13
K = 11
I = 9
G = 7
The difference between the consecutive second letters is constant:

$11\; -\; 13\; =\; -2$

$9\; -\; 11\; =\; -2$

$7\; -\; 9\; =\; -2$

Following this pattern, the position of the next second letter should be:

$7\; -\; 2\; =\; 5$

The 5th letter of the alphabet is E.

Combining the two letters, we get the next cluster in the series as ME.