Which set of letters when sequentially placed at the gaps in the given letter series shall complete it?
A _ B C _ B B C _ B B _

The given series consists of 12 letter positions:
A
 
​
BC
 
​
BBC
 
​
BB
 
​

Let us divide the series into groups of 3 letters each:

A
 
​
B∣C
 
​
B∣BC
 
​
∣BB
 
​

Let's test Option C (B, A, B, A):

1
st
blank =B→A B B

2
nd
blank =A→C A B

3
rd
blank =B→B C B

4
th
blank =A→B B A
This pattern does not show clear repetition.

Let's test Option B (B, B, B, C):

1
st
blank =B→A B B

2
nd
blank =B→C B B

3
rd
blank =B→B C B

4
th
blank =C→B B C
This gives us: ABB∣CBB∣BCB∣BBC. No clean repeating pattern.

Let's group it by 4 letters instead:

A
 
​
BC∣
 
​
BBC∣
 
​
BB
 
​

Let's test Option A (B, A, A, C):

1
st
blank =B→A B B C

2
nd
blank =A→A B B C

3
rd
blank =A→A B B

4
th
blank =C→C
This forms the repeating pattern A B B C:

A B B C∣A B B C∣A B B C
The letters filled in the blanks are B, A, A, C.