The correct option is C Nucleophile is involved in the RDS
Polar protic solvent solvates the halide ion formed due to C-X bond breaking. Also it enables the leaving group to leave. Therefore, polar protic solvent favours the SN1 reaction.
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
Hence, correct option are (a), (b) and (c).