The correct option is D Both I and III
SN1 reactions are favored at low temperature whereas at high temperature E1 reaction is favored.
The nucleophile is not involved in the RDS in SN1 reaction, thus it does not affect the rate of SN1 reaction.
However, a stronger nucleophile may lead to side reactions. So, weak & moderate nucleophiles are preferred.
Rate of the reaction ∝[R−X]1[Nu]0
Polar protic solvent solvates the halide ion formed due to C-X bond breaking. Therefore, polar protic solvent favours the SN1 reaction.
Hence correct option is d.