Select the combination of letters that when sequentially placed in the gaps of the given letter series will complete the series.

U_D_UP_M_PDMU_DM

By Trial and Error method,

Option A 

UUDM | UPDM | UPDM | UDDM

The above letters do not form a series. Hence option A is incorrect.

Option B

UMDP | UPUM | PPDM | UUDM

The above letters do not form a series. Hence option B is incorrect.

Option C

UPDM | UPUM | PPDM | UDDM

The above letters do not form a series. Hence option C is incorrect.

Option D

UPDM | UPDM | UPDM | UPDM

The above letters form a series.

Hence, the correct answer is Option D