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$\text{IISc CSA MTech (Research) Interview Experience}$

$\text{Gate Score-}$ 759   $\text{Gate Rank}$- 410
$\text{Category-}$ General – EWS

$\text{Research Area –}$ Intelligent Systems
$\text{Background Subjects- }$
1. Linear Algebra
2. Probability

Interviews were conducted over a period of 5 days (20th  to 24th   May). Each day there were 2 slots morning (9 am) and afternoon (2 pm). Mine was morning slot on 22nd May.

$\text{Written test –}$ 9 to 9:30 AM
There were 10 questions of easy to moderate level. I attempted all the question out of which 7-8 were correct to my knowledge. For the rest 2 questions, I just wrote my approach.

$\text{My advice on written test-}$
1. Write your solutions clearly. Coming to the final answer is not that much important. They are more interested in your approach.
2. Try to attempt all the questions.

After half an hour (at 10 AM), results were out and I was the 1st one from the intelligent system pool to get interviewed in that slot.
I was called in at 10:05 am.
The panel consisted of 3 professors.

$I_1$ –  Soumya, You have graduated from Indore Institute of Science and Technology and you have a CGPA of 7.60
$Me-$ Yes sir.

$I_1$ – Your graduation year is 2017. So what have you done in the past 2 years?
$Me-$ Sir, I had taken the decision of appearing for GATE after my B.E. Last year I got some lower rank so I again took the full-time drop for GATE.

$I_1$- Ok Soumya, So your GATE 2019 SCORE is 759 and rank is 410.
$Me-$ Yes Sir.

$I_1$- You have applied in 3 departments. CSA is your 1st  preference, CDS is 2nd   and Electrical is 3rd .
$Me-$ Yes Sir.

Then he asked me about my other interviews and other offers that were in my hand.
$I_1$ Ok Soumya, You mentioned background subjects as linear algebra and probability. Should we start with linear algebra?
Me – Yes Sir.

$I_1$ Which topics have you prepared in Linear Algebra?
$Me-$ System of linear equations, vector spaces, Eigen values and Eigen vectors.

$I_1$  We should start with eigenvalues and eigenvectors.
$Me-$ Sure sir

Till now 5 minutes have passed. Then they sent me to the whiteboard.

$I_1$- What are eigen vectors?
$Me-$ I wrote $Ax = \lambda x$ on the board. Sir, x will be an eigen vector of A- if I give vector x as input here and if the output vector  $\lambda x$ comes out to be in the same direction as x.

$I_1$- Why eigen vectors are non zero?
$Me-$ Sir, they are defined as non-zero (I could have explained it properly but at that time this is what came out of my mind).

$I_1$- What are eigen values?
$Me-$ Explained it properly.

$I_1$- Can you explain how you came to this equation $(A – \lambda I)x=0$?
$Me-$ Explained.

$I_1$-Why determinant of this matrix  $(A – \lambda I)$ is zero?
$Me-$ Sir, As null space of this matrix, contains non zero vectors, columns of $(A – \lambda I)$ are linearly dependent. So this matrix is non-invertible hence its determinant is 0.

$I_1$- If matrix A is $nXn$ then how many eigenvalues will it have?
$Me-$ Sir, the degree of the characteristic polynomial of A is $n$. A polynomial equation of degree $n$ has $n$ roots and as roots of the characteristic polynomial are the eigenvalues of A so A will have n eigenvalues.

$I_1$- Can matrix A be rectangular?
$Me-$ No sir. We need to equate the determinant of $(A – \lambda I)$ to zero and determinant is defined for square matrices only.
(At this point, I was disappointed with my answer 😑).

$I_1$- Suppose matrix A is $3 X 3$
Write on the board – $A^3 = 0$ . Find the determinant of the matrix $A-3I$
Is this information is sufficient to find the determinant?

Initially, I was able to find one eigenvalue of A i.e 0 but with the help of a small hint, I got all 3 eigenvalues of A. Still, I struggled to find the determinant.
Then somehow I reached to the trace of (A- 3I).

$I_1$- How the trace of this matrix (A – 3I) is $-9?$
$Me-$ Explained.

$I_1$ - Ok. we should proceed further.

After this, I was handed over to the 2nd  professor.

$I_2$- What is your GATE year?
$Me-$ 2019

$I_2$- Oh, you gave the GATE recently so subjects must be fresh in your mind. 🙂
$Me-$ Yes sir 😊

$I_2$- Let's start.
I have given you a six-faced dice. You have to roll it until you get the 1st   even number. For Ex- you rolled it for the 1st   time and got a 3 so you rolled it again. You got 1 now. You rolled again. You got 6 this time. Now you stopped. So what is the average number of times you have to roll the dice to get an even number for the 1st  time?
Do you understand the ques? Repeat it once, what you have to find?
$Me-$ Yes sir. Basically, I have to roll the dice until I get the 1st   even no. I have to find the expected number of trials until I get the 1st  success.

$I_2$-– Exactly. So find it.
$Me-$ Sir I can model this situation using a geometric random variable

He stopped me in the middle.

$I_2$-, Correct. So as you said Random Variable. First, explain it.
$Me-$ Explained.

$I_2$- What is a geometric random variable?
Explain it on the board.
I explained it properly.

$I_2$- Now model the given scenario and find the expectation.
I found the required probabilities and derived the expectation of a geometric random variable using its memorylessness property.

When I was busy in deriving the expectation, I heard some voice from the background. When I turned they told me that I am going excellent. It boosted my confidence.🤩

$I_3$ (who remained silent all this while)- From where have you studied probability?
$Me-$ Sir- MIT OCW lectures. (I forgot the name of the professor- John Tsitsiklis 😔)

$I_3$- You have studied probability solely for GATE or this course was there in your B.E?
$Me-$ No sir. I studied it only for GATE.

$I_3$-- Ok. Complete your proof.
I completed it in the next 3 minutes

$I_2$ asked me to explain the memorylessness property mathematically and how I used it in one of the equation.
After a few hints, I was able to explain everything.

$I_1$- Ok Soumya, We are done with the interview.

$I_3$ – As you mentioned ML and DL as your sub areas, are you open to other areas as well?
$Me-$ Yes sir.

The interview lasted exactly for 30 minutes. I came out exactly at 10:35 AM.
It was an amazing experience.

25th May 2019 -the list of shortlisted candidates declared and my application number was there on the list.
5th  June  4:07 PM – Received a mail – $\text{IISc Admissions 2019- MTech (Res) Programme Offer Letter.}$ 😍

posted Jun 15, 2019
edited Jun 16, 2019 | 1,807 views
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Congo :) U deserve it :)
Congratulations 👍 Very nice experience 😊
Very Nice. Congratulations ))👍

Thank you @Arjun sir :)
Thanks, Srestha :)
Thanks, Shubham :)

Congratulations

​​🙂😇

a heartiest congratulations mam :)

@Soumya29-Heartiest Congratulations. :)

What were the Eigen values of A apart from 0? I know the Eigen values of A - kI will be given by - (Eigen values of A) - k.

Using this information about the Eigen values of (A - 3I), we can find det(A - 3I).

Besides, congrats.

Thanks 😇
Thank you @shaik sir and @ayush :)

@debargha all the eigen values will be 0.
$Ax = \lambda x$
$A^3x = \lambda^3 x$
$\lambda^3 x= 0$
$\lambda^3 = 0$   (as x is non zero)
$\Rightarrow \lambda = 0$
Now replace this lambda with $\theta \ and \ \delta$

Thanks. Regarding the probability question, was the answer $2$?
@Debargh, Yes. 👍

Congratulations @Soumya29

U really deserve it :)

Congrats @Soumya29 . You deserved it.