The correct option is C but
The sentence in question, "I wrote a letter to you last week ____[1]_____ without any response from your side." has two contrasting ideas 'I wrote a letter' 'you didn't respond back'. So, the conjunction must be an adversative one, i.e. a contrasting one.
Options A and C: 'Yet' and 'but' are both adversative. They refer to contrasting ideas and are often interchangeable, depending on the context of the sentence.
But, they cannot be used interchangeably over here.
(Compare: Yet, they cannot be used interchangeably here.)
'Yet' means 'in spite of the fact that', whereas 'but' refers to 'something that is different from what you said before'. The latter meaning is more suitable here.
So, in this sentence, 'but' is more suitable than 'yet'.
Hence option C is correct and A is incorrect.
Option B: 'Also' refers to an addition; it connects two ideas that are merely added, they do not affect each other.
Option D: 'Till' relates to time: 'till she comes home'
It does not relate to the sentence, hence B and D are incorrect.