The correct option is A The E1 mechanism does not require a base.
E1 reaction is a two step process.
In step 1, leaving group leaves and form a carbocation.
In step 2, the base will attack the proton and proton abstraction takes place. Thus, base is required in E1 reaction and hence option (a) is wrong.
In E2 reaction, two groups/atoms depart simultaneously from adjacent carbons with a proton being abstracted by a base thus it occur in highly basic condition.
In E1cB, the reaction proceeds through the conjugate base of the starting material, thus, they called as unimolecular elimination via conjugate base.