I took the JEST-2010 (Joint Entrance Screening Test) today.
Institutes such as the Institute of Mathematical Sciences Chennai, and now apparently even the Chennai Mathematical Institute shortlist candidates for their MSc and PhD programs based on scores of this test. I wrote the Theoretical Computer Science paper.
I thought that the paper was very easy. The paper consisted of 25 objective questions and 6 “prove this” type subjective questions worth 40 marks.
I managed to answer 24 of the 25 objective questions. I couldn’t answer the one which was based on Graph coloring, a subject which I had skipped during my preparation.
Of the 6 subjective questions, I answered 5 worth 31 marks. I did not solve the 9 mark problem which was again based on Graph-coloring. I thought I would come back to it after finishing the other 5, but never got around to do it.
I have forgotten most of the objective questions. I do remember the subjective ones though. So, listing subjective questions just for the record.
- A five pointed star can be formed by joining the Vertices (1,3), (3,5), (5,2), (2, 4), (4,1) of a regular pentagon. Show that the sum of the angles formed at the vertices of the 5-pointed star is 180 degrees. [4 marks]
- An array contains N elements. Write an efficient algorithm to check if there are two numbers whose sum is zero. [5 marks]
- Show that the Tower of hanoi problem can be solved in (2^n) – 1 steps if there are n-rings. For extra credit prove that this is optimal solution. [6 marks]
- A triolimo is an L shaped object formed by connecting three square tiles of a chess board. Given a (2^k)*(2^k) chessboard, if one of the squares, any arbitrary one, is marked red, prove that the rest of the chess board can be filled up with triolimos. [6 marks]
- A Partition() Algorithm almost similar to the one presented in CLRS in the quicksort section was given. We were asked to answer
- What are the assumptions made in the code.
- What does the algorithm return.
- What happens when a certain loop is rewritten without certain conditions.
- What is the loop invariant. Prove it’s invariance. [10 marks]
- Something on d-colorable, degenerate graphs, and their vertex cover. Don’t remember the problem since I didn’t get time to solve this one. [9 marks]
Like I said earlier, the paper was easier than I had expected. But in the case of competitive exams, and I have experienced this in the past, there are good chances that you don’t make it to the next round if the paper was easy. An easy paper implies that most people would have solved as many questions as you would have. Since its on a relative scale, even a minor mistake in an easy paper would be severely penalised. More so in the case of JEST, since the subjective questions will be evaluated only if you have cleared the cut-offs set for the objective questions. Which means that no scope for any mistakes in the objective questions.
So, I hope that I haven’t screwed up anywhere in the objective questions, since they were way too easy.
The other thing about JEST subjective questions is that you have to answer within the space provided in the question paper. Which means that if you are proving a theorem, you need to be very judicious about which steps you are going to skip in case there is a space constraint.
Now, I not used to solving theorems in a space-constrained environment like this one. I don’t usually skip steps but on the contrary try to include as many of them for the sake of completeness. This is probably a bad-habit that I have acquired over the years due to my 100/100-in-mathematics obsession. Basically in those days, you wouldn’t want to lose out on a perfect score in mathematics just because the evaluator could not follow how you derived one step from the previous one. IOW, you didn’t want to give any opportunity to the evaluator to deprive you from scoring full marks. And in my home-town, a 100 in mathematics used to earn you a lot of respect.
But in the case of JEST, I guess the strategy has got to be different. One should make use of the space provided for rough work and copy only the relevant portions into the space provided for answers.
According to the IMSc website, the results should be out by end of March. So not much to do till then.
Finally, I must admit that I enjoyed the whole process of preparation very much[*]. I am revisiting CLRS after a span of 4 years, and it has been a very enjoyable experience. I think, after four years of working in the kernel and having dealt with a lot of similar algorithms, I am able to appreciate the design of some of the algorithms better than I would have while I was at college. Now that I have started studying the book, I want to continue the study habit. Of course, I won’t be spending as many hours per day as I have spent in these last couple of months.
Anyway, this is the first technical paper that I wrote after 4 years. I am glad that I it went well.
[*] I must also admit that the last couple of days weren’t exactly fun. That was the time when it struck me that I am not supposed to be reading for pleasure, but am supposed to be “preparing for an exam”. That was when I started having doubts if my preparation was sufficient. For that matter, I still wonder if any amount of preparation is sufficient for any exam ?! Especially for an exam like JEST which is relatively unknown unlike GATE. Thus without any problem sets to practice and with just one sample paper, I wasn’t sure if all that I had enjoyed studying in the last couple of months would be helpful on the day of the test.