This is the rough work I did during the interview, the question were added in a separate post (https://gateoverflow.in/blog/10800/iisc-csa-research-interview-questions) as I did not want to reveal hints in the original post (perhaps open the questions side by side to make sense of the following rough work)
CSA prof 1 (not everything is correct in my solution):
CSA prof 2 (not everything is complete in my rough work):
Feel free to ask in the comments, I am sure, some of the answers are not complete as the prof. just asked to explain some bits instead of writing everything down.