DD attended a few last year in London and around. It's all jumbled up in my mind unfortunately and don't remember which school asked what, but roughly the folowing categories -
Common to all : general chit-chat about likes/dislikes, favourite books, hobbies, inspirations, which other schools applied to, sports/musical instruments etc.
Some expanded the discussion on books : Favourite book -> His Dark Materials -> Fav character -> Lyra -> What's Lyra's greatest weakness -> Why do you think so etc
Picture questions : Shown a photograph, describe the photograph
Expanded picture question : Become a character in the photograph, describe how you feel (specifically, a Knight saving a woman from a dragon, describe the woman's point of view, how does it make the woman feel being saved by the Knight)
Maths question : Don't have much details (DD was tightlipped), but a word problem with two unknowns and two equations. DD attempted algebraic approach, got nervous, and then gently nudged to use trial and error that worked.
Logic puzzles : Mostly knighs and knaves kind and variations around it.
Reading comprehension : Straight forwawrd, read a passage, then answer questions on that.
Philosophical questions (received with gratitude from a mum in the eleven plus forum, NW London school, 2021 batch) - DD was never asked these though -
Would you rather be a clever coward or a brave fool?
Do you think zoos are a good or a bad thing?
Do you think that animals should have rights? What would it mean for pets? Should they be set free?
Hope these help. Good luck to your DC!