IISc Bangalore CSA M.Tech (by research) Interview and Written Test Experience

(AIR 422 GATE 2019 CSE)

I appeared for M.Tech (by research) admission interview at IISc Bangalore on 24th May 2019. 

There were 10 slots for the exam, a morning session and an afternoon session, everyday, from 20th May 2019 to 24th May 2019. 
There were three streams to choose from, for the written test and the interview, namely, Theory, Systems and Intelligent Systems. 

I find Intelligent systems interesting, so I chose that. It would mainly require the knowledge of linear algebra and probability.


First we had to clear a 30 minutes written test, consisting of 10 questions. It was very very simple, and here I am adding the questions which I can remember: -

1. X1 to Xn are Bernoulli random variables, Y is a variable = summation(Xi), what is the expected value of Y.
2. Finding the characteristic equation of a given matrix.
3. Finding the output of a given C program.
4. Ordering given algorithms in ascending order of time complexities.
5. A game is being played between two players. They keep playing until a winner is found. Winner is declared when one of them wins 4 games in total. What is the probability that the match will be concluded after 6 games.
6. Finding the rank of a matrix.
7. Number of vertices in the maximum complete graph in a bipartite graph.

(There were three more questions which I don't remember :p )

They shortlisted some of us based on the written test, for the interview. It went as follows: -

(The professors were very polite, and if they see that we don't know a question, but are trying hard, taking various approaches, examples, diagrams etc., they even give hints and help us reach the final answer.)

prof1: Checked all my semester marks, asked me the aggregate. Then he asked me about my final year project. The discussion on all possible aspects of the project went on for a while.

Then he asked me to take the marker and go to the board.

prof1: Do you know what is pdf?

me: I described what a pdf does.

prof1: What is the standard definition? What is the range and the domain of a pdf.

me: I was struggling with this one but then he told me to draw graphs of few pdfs, and then I answered.

prof1: I am giving you a uniform random variable, say X, such that it is uniformly distributed between 0 and 1, find and draw it's pdf. 

me: Did that at once.

prof1: Now suppose Y is another random variable, = 2(X) + 5, then, find it's pdf.

me:  By intuition I directly concluded that if X is uniform, Y should also be uniform, and hence it should be uniformly distributed between 5 and 7, and hence found the pdf at once.

prof1: (Bursts into laughter) But you cannot do that directly. Okay can you tell me what is cdf?

me: Told the standard definition, then he told me to find that for Y. 
He kept giving me hints here and there, and I managed to reach the final answer, which proved that Y is also uniform. So my initial and direct answer was correct, but obviously proof is needed.

I am just skipping the discussion in the middle, and providing a link to a solution to a similar problem, which I found on stackexchange.(Look at the first solution in the page).
https://math.stackexchange.com/questions/1359237/if-xu0-1-and-y-2x-4-what-is-the-density-function-of-y

prof2: Can I ask you questions from linear algebra?

me: Yeah! 

prof2: Prove that AtA (t=transpose) and AAt have the same eigen values.

me: I had seen this question before, somewhere during my interview preparations. All I had to do was write 
AtA X = bX (X is the eigen vetor and b is the eigen value for AtA).
Then multiply both sides with A.
AAt AX = AX b. Now for AAt, AX is the eigen vector, and b is the eigen value, hence the same.


prof2: (Impressed)Can you tell me the exception to this? When this won't hold true.

me: When A is a zero matrix.

With this the interview was concluded. It went on for around 20-25 minutes.

On 5th June I received a mail saying that I got selected! 

Thanks for your patience!