What are the questions asked in an interview for an integrated PhD (maths) at IISc Bangalore?

One of my friends appeared for the integrated Ph.D. Math at IISc Bangalore and shared her experience of the same. A total of 72 students had been shortlisted for the interview and her interview took place on the last day. As she entered the room, they asked for her introduction and her interest to which she told them it was analysis. She was asked the following questions

• Construct a differential function satisfying the following conditions, f(1)=f(-1)=o; f(0)=1, and f(x) is zero everywhere except (-1, 1)
• Group theory question wherein they gave her an order of the group and asked to check the elements of some order

The entire interview was based on the above questions which my friend was not able to answer most of the time and thus did not get selected. However, she learned a lot from that interview and summed the entire experience in these points

• She learned a new problem-solving approach that requires breaking the problem into small cases.
• The panelists here are very friendly and you can even postpone your interview till the last day if you are not comfortable.
• The questions asked to a candidate are never repeated for other candidates. 

So, overall the experience was very knowledgeable and I hope it's so for you too.