Which of the following letter-clusters will replace the question mark (?) in the given series?
EIMC, DKOD, CMQE, ?, AQUG

Write the five given clusters one below the other and study each column of letters separately:

$$\begin{array}{ccccc} \text{E} & \text{I} & \text{M} & \text{C} \\ \text{D} & \text{K} & \text{O} & \text{D} \\ \text{C} & \text{M} & \text{Q} & \text{E} \\ \;? & \;? & \;? & \;? \\ \text{A} & \text{Q} & \text{U} & \text{G} \end{array}$$

Case 1: First-column letters
E(5) → D(4) → C(3) → ? → A(1)
Each step is $$-1$$, so the missing letter is $$5-3=2$$, i.e. $$\mathbf{B}$$.

Case 2: Second-column letters
I(9) → K(11) → M(13) → ? → Q(17)
Here the pattern is $$+2$$. The number between 13 and 17 is $$15$$, corresponding to $$\mathbf{O}$$.

Case 3: Third-column letters
M(13) → O(15) → Q(17) → ? → U(21)
Again the difference is $$+2$$, so $$17+2=19$$, i.e. $$\mathbf{S}$$.

Case 4: Fourth-column letters
C(3) → D(4) → E(5) → ? → G(7)
This time the sequence increases by $$+1$$. Hence the missing letter is $$5+1=6$$, i.e. $$\mathbf{F}$$.

Combining the four missing letters we get the cluster $$\mathbf{BOSF}$$.

Option D which is: BOSF