Patentability search is done to get:
a) all of the above
b) Report on FTO
c) Validity/invalidity search report
d) Patentibility search report
I am confused between a) all the above and d) Patentibility search report
My reason for for option d) is quite straight forward and for a):
Validity / Invalidity is done with respect to section 64 and 64 (1) e, f and g relate to novelty, industrial application and use (main components of patentability search) and section 64 (1) d relates to non patantable subject matter (another indespensible component of pentantibility search with respect to India) . FTO also is targeted towards finding a way to operate an invention in a particular jurisdiction without infringing any patent. Therefore, one of the stategy should be to invalidate potential overlapping patent or the respective claim of that patent.
A Patentability search is carried out to understand the patentability scope or chances of procuring IP in that space. However, as you rightly mentioned, searches are carried out towards FTO and Validity/Invalidity analysis too. But since the question was directed towards patentability, the right answer would be a patentability search report.