Step 1: Identify Arun.
Condition: All specialisations except intensive care work with Arun, the anaesthetist.
\(⇒\) Arun = Anaesthesia.
Step 2: Group Jaya, Arun, Sushama.
Jaya, Arun, Sushama always work together.
So, Jaya and Sushama must belong to specialisations that require anaesthesia.
Step 3: Neurosurgeon and Orthopaedician relation.
Neurosurgeons always need orthopaedics in theatre.
\(⇒\) Neurosurgery + Orthopaedics + Anaesthesia always linked.
So, Jaya, Arun, Sushama = (Neurosurgery, Orthopaedics, Anaesthesia).
Step 4: Sudhir and Dilip.
They work together but have never met Sushama.
So they belong to Gynaecology and Paediatrics (since they must work together, as gynaecologists need paediatricians).
Step 5: Leftover.
We’ve assigned:
- Arun = Anaesthesia,
- Jaya/Sushama = Orthopaedics + Neurosurgery,
- Sudhir/Dilip = Gynaecology + Paediatrics,
- Remaining = Intensive Care + ?
Step 6: Who is Rama?
By elimination, Rama is the third person in Jaya–Sushama–Arun set. Arun is anaesthesia, so Jaya and Sushama = Neuro + Ortho. Rama = the one left = Neurosurgery.
Final Answer:
\[
\boxed{\text{A – Neurosurgery}}
\]