A Successful attempt at CeNSE IISc

Hi all,
Firstly I would like to congratulate you presuming that you got your call letter for interview from IISc, if not I hope you'll get it very soon. I think its important to tell you guys what the chairperson of CeNSE(Center for Nano-science and Engg.) briefed us about the interviews just before the interview. He told us that the interviews here, are to accommodate you unlike other competitive examinations to eliminate you. He elaborated further that we will not test your knowledge about the subject you have studied rather we will check if you have a good learning ability and the abilities to explore the problem you have been given, he gave an example of plotting a function and the importance of critical points and other points which are important while plotting a function. He further explained to us that how the life of a researcher is different from others. Long story short he was motivating and at the same time explaining what it needs to be a researcher. Now why did I mentioned all that ? I did so, so that you can understand that interviews at IISc focus on your abilities not your disabilities.
Now lets come to the interview procedure:
1. When I visited the department I had to present my call letter and sign at a prescribed place along with providing my academic background i.e. from which department I have completed my graduation/PG.
2. Unlike what is mentioned in the call letter "you have to bring a xerox of your mark-sheets etc. failing which you may not be interviewed" they were not serious while mentioning. Even they didn't asked if guys have it or not. Story is same for all departments.
3. We had to wait in a room for our turn to come.
Now its time for The interview:
At this point I should mention that I am from Mechanical Engg. There were 4 profs in my panel :

1 Prof Rudra Pratap 
2 Prof Ambarish Ghosh
3 Prof Shankar Kumar Selvaraja 

I can't remember the other prof who was there. It is so because I was asked questions only by Prof  RP and Prof Ghosh.
Here is the transcript of interview
Me: (After opening the door) May I come in?
Prof RP: Come in. Sudhanshu Tiwari ?
Me: Yes Sir.
Prof RP: Have a seat.
Me: Thank you Sir.
Prof Rp: So Sudhanshu how do you know about IISc.
Me: Sir one of my teachers told me once that IIsc is the best institute in India for research. Also I was there at IIT Kanpur for an workshop on mechanics and mathematics and there I met with Dr. Pankaj Wahi who did his Phd here, and I was fascinated by him.
Prof RP: So are you going to IITK for an interview?
Me: No sir?
Prof RP: Do you  know about research work we are offering before coming to interview?
Me: Yes sir I did.
Prof RP: So If you got selected, in which area you would like to work.
Me: Sir I think it would be MEMS and NEMS.
Prof RP: But you don't know about MEMS and NEMS, do you?
Me: No sir I don't know. (Remember its good accepting that you don't know at all about something)
Prof RP: Okay sudhanshu what should we ask?
Me: Thermodynamics, and I visited the website and there it was mentioned that I should be good in differential equations so I think differential equation.
Prof RP: (Adressing Prof Ghosh) He wants some differential equations.
Prof Ghosh; So sudhanshu lets get on the board( A white board :))
Then he gave me simple differential equation but with a tweaked initial condition.
Initial Condition was at x=0 y=0
I struggled a while and said " Sir its not possible to have a y=0 in the entire domain of solutions.
Then .
Prof RP: what sir meant is  at x=0 y=Y0
then I solved the equation but I left it as
                ln (Y)=F(s)
then they told me that solutions to differential equationn is Y= something not that you have written.
Then I solved the equation completely.
Prof Ghosh: Okay sudhanshu now lets get something so that we can plot it.
But he suddenly realized something ( I think the equation he though he gave to me was not the same he has in his mind) So he told me get rid of that equation.
Prof RP: Sudhanshu, I will ask you questions from basic mechanics, is it okay?
Me:  Its okay sir.
Prof RP: Can you explain how to express 2D state of strain?
Me: Yes sir I can.
Then I drew the matrix representation of 2D stress and explained the elements of matrix to them.
Prof: RP: Can you explain what is  Principal stress?
Me: Sir its the axial stress on a plane where shear stress is zero.
Prof RP: Can you tell me how to calculate it ?
Me: I have a problem remembering formulas, but I can try. (Believe me guys I used the phrase "I have a problem remembering"  4-5 times during the whole interview)
I wrote a formula for principal stress but I am not sure its was correct.
Prof RP: Its okay. Now tell me how the stress and strain are related.
I explained the hook's law with the phrase "Under the elastic limits"
Prof RP: Write the expression for that
I wrote the expression   
Prof RP: That's more like a generalized equation write an specific equation.
I altered the equation specifying the stress as linear stress and strain as linear strain.
Prof RP: Is the expression valid for shear stress and shear strain.
Me: Yes
Prof RP: No its not.
Me:(After looking again at the board) sir its valid but we have to change the constant.
Prof RP: Whats that constant.
Me:(In a hurry) Bulk modulus.
Prof: Its not Bulk modulus.(Me and Prof spoke simultaneously)
Me: Its modulus of rigidity.
Prof RP: Sudhanshu can you write the expression for 2-D stress and strain.
Me: I don't remember the exact expression but I can tell you that for 2-D we have take care of lateral strain also.
Prof RP: And how do we take care of that?
Me: We use Poisson ratio and this time I remember the name correctly (Smiling)
Prof RP: Good Sudhanshu. Now get rid of all that.
I erased all from the board..
Prof RP: Now consider a ball heated and then dropped in the cold water what will be the temperature profile?
Me: Sir, is the internal thermal gradient of the ball is negligible.
Prof RP: I din't get your question.
Me: Do we have the temp profile varying with space also or only with time?
Prof RP: What if the info is not given?
Me: Then if its varying with space we have two charts for temp profile.
and if not then it will be exponential with time.
I drew a graph but forgot to mention the parameters
Prof RP: Whats there on Hz and Vertical axes?
I wrote Temp on vertical Axis and time Hz axis.
Prof RP: Can you derive a expression for that?
Me: I'am not sure if I can do it.
Prof RP: Try.
I tried but failed
Prof RP: Can you write the differential equation for the derivation.( He tried to help me)
Me: Sir actually I am struggling to get that differential equation only, if can find I'll derive the expression.
I struggled more. After a while
Prof RP: Sudhanshu don't you think there should be a time parameter in the differential equation. (He helped me again)
Me: Thank you sir.
Then I wrote the differential equation after writing the differential equation Prof. told me stop.
Prof RP: its okay. Get rid of that. Now tell me what is First Law of Thermodynamics ?
I explained the F.L.O.T.
Prof RP: can you write the expression for me?
Me: Yes I can.
I wrote the integral form of FLOT.
Prof RP: Write the differential one for me.
I wrote dQ-dW= ΔE
Prof RP: Sudhanshu you should be consistent while using symbols.
Me: Sir the difference in symbols is to differentiate the path functions with point function. DeltaE can be written as E2-E1 but dQ and dW can't be written like that.
Prof RP: Can you explain more about Path and point functions.
I explained them well.
That concluded the technical questions.
Now Prof asked me if I have a rank in my class and I denied. Prof Ghosh asked me why do I want to do a Phd.
Believe me guys you should have a sound explanation of the question that why do want to do a Phd.

At the end I also asked a question related to differential equation which was bothering me.

I don't think I need to mention that questions started from basics of your background. So its good a good grasp of basics of your area of study and also you should have a good understanding of basic mathematics.