My elder brother used to be a student of XLRI and he had to come across some tricky, if not weird questions. 

• They asked him the difference between a lion and a tiger, the difference between a penguin and a bird. They asked him to differentiate between an alligator and a crocodile, between a turtle and a tortoise, and also between a donkey and a mule.
• He had to refer to the group discussion where the professor asked my brother to rate the group and how he contributed. 
• The professor asked him about the error of commission and the error of omission. 
• He could not say if the professor was satisfied with his answer and all he got in response from the latter was a straight face.
• Other questions the professors have asked their interviewees were the difference between the tragedies of Sophocles and Shakespeare. It is a good question to test our knowledge of dramatic narratives. 
• Another question was how Shakespeare can be related to human resources.

Interviews in B-schools can sometimes be non-standardized and are often reactive of the experiences of the interviewee(s). My brother cannot say if the testing is deliberately non-standardized, whether responses are calibrated or normalized, or if the professors test the reliability. A lot of people who made it past the personal interview ended up joining the IIMs and vice-versa.