Let's analyze each part of the sentence carefully:
Part A: The Indian Institute of Science
- This part is correct and acts as the subject of the sentence. Part B: offers research programme
- This part has an error. The word "programme" should be in the plural form "programmes" because it refers to more than one research program. - The corrected phrase should be: offers research programmes.
Part C: in Physics
- This part is correct as it specifies the field of research.
Summary: - Subject: The Indian Institute of Science (singular)
- Verb: offers (correct singular verb)
- Object: research programme (should be plural "programmes")
Therefore, the incorrect part is option (B).