TIFR Mumbai Experience
TIFR Mumbai took the written test on 11th March 2019. Luckily I do have the question paper of this test. You can go through the images below. As with ICTS, we were supposed to attempt any 4 questions.
I attempted the questions 1,2,3,5 and 6. I attempted an extra question since I was not getting the value of force as given in the 3rd question. I don’t know whether they evaluated the last question or not. After lunch, we were taken to various labs on the campus. This was the most beautiful experience in my life. The orientation process completed at around 6 p.m. When I came out of the campus, the list of candidates shortlisted for the interview was attached on the notice board. I was glad to know that my name was on the list. 43 students were shortlisted for the interviews.
Next day I arrived at the campus at 8:30 a.m. as informed. We were divided into 7 groups. Students from each group would be interviewed by a panel. I was the first one to be interviewed by my panel.
My panel consisted of Four faculty members, let’s call them F1, F2, F3, and F4. All of them were quite friendly. I was first asked about my final choices for the department. I gave DTP(Department of Theoretical Physics) my first choice. Then we talked about my final year project which is on Additive Manufacturing. It took about 5-10 minutes.
Then F-1 asked me this question:
There is a well, The surrounding temperature is at some temperature below the freezing point of water. Find out the expression relating the thickness of the ice layer as a function of time.
Initially, I made a mistake and wasted some time. Then I corrected the mistake and finally derived the equation.
Given a 2×2 matrix say ‘X’, how can you find X^500 without multiplying the matrix 500 times?
This is a standard diagonalization problem which I was able to solve. Then,
F 3 asked me about how to
Find the speed of molecules inside this room.
I wrote the formula of mean speed, root mean squared speed and most probable speed. Then he asked me this: If I heat a gas container containing say sodium vapor, it emits some characteristic lines. Is the width of this lines finite of zero, and why? I knew that the width is finite, but I didn’t know the reason. He gave me the hint that the gas is at some temperature. It rang a bell. Since the molecules of the gas are moving, there will be a Doppler shift. So, molecules moving away would emit light at lower frequencies compared to molecules moving towards us. This would cause the broadening of the line. He agreed with my answer.
Then F4 asked me this:
What would happen if I put a block of ice in a microwave oven?
I didn’t know the answer, but I explained the mechanism of heating in an oven, that the heating is due to absorption of light in the form of rotation of molecules. However, since the water molecules in ice at bonded to each other by H- bond, this bond must be broken for molecules to rotate. But I wasn’t sure whether this bond can be broken by MW rays. He told that I am on the right track. Then he gave the answer that since the molecules cannot rotate freely in the solid form, the ice block would be transparent to MW rays.
Then F3 asked me two more questions: First, he asked me about
The average sum of numbers appearing on the set of 100 thrown dice.
The answer was pretty easy(350) but I took some time(It happens during interviews, you know). Then he asked me to find the deviation from this mean value. Since we were out of time, he told me to just write the formula. which I wrote correctly. Then he asked me to
Find out the No. of solutions to the equation: 2^x=x^2.
I draw the graph of both curves and found the intersection of both curves. I got 3 solutions, but he told there are 5 solutions. Maybe two other solutions were complex. The interview completed here.
Update: I got selected for IPhD at TIFR in the department of Theoretical physics.
You can read my Interview experience at ICTS Banglore in case you have not read already
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