pls help with this because i always do the same logic mistakes in this type of questions.

(correct answer : D)

the problem i'm having is with the given data of μ<0 . i understand it's given to prevent solutions C,D to explode, but the coefficient of friction could normally be very well above >1. and in such cases the derivation obviously fails and solutions C,D cannot be true. how could i solve this for every μ ?

edit: additional clarification