i. There is so much love..................the two of them.
ii. I have not seen Aditi..................Friday.
iii. I started my exam preparation...............January.
iv. The three sisters did not look for new friend as they were quite happy playing......... themselves.
v. I have not seen Mohan....................six months.

We use 'between' to refer to two things which are clearly separated. We use 'among' to talk about things which are not clearly separated because they are part of a group or crowd or mass of objects
Thus, in i Between should be used and Among should be used in iv.
In ii the tense is 'present perfect' and the starting point of time of the action is mentioned thus, the correct word use in ii will be ‘since’.
In iii the tense is simple past and the starting point of time is mentioned—January and thus, we should use ‘from’.If in iii instead present perfect tense was used like in ii then we would have to use 'since'.
In v 'six months', a period of time, warrants the use of 'for'.
The only option in which all of this is correctly used is option D.
Hence, option D is the correct answer.