In lieu of my article about my lucky tryst at cracking IISc CSA M.Sc(Engg) interview in 2014 being helpful to a few folks preparing for admissions, I requested a good friend of mine who took up GATE in 2015 to share her experiences about the written tests and interviews during admisssions post GATE.
My friend had greater success than me in GATE (CS Stream, Score: 765, Rank: 323) but however applied to all eligible courses in 2 institutions - IISc, Bangalore and IIT Madras.
IISc, Bangalore: SERC - MTech, M.Sc(Engg) & CSA - M.Sc(Engg)
IIT Madras: CSE - MTech, M.Sc(Engg)

The following is her annotation of the interviews and written tests for post graduate admission at IISc Bangalore and IIT Madras.

IISc, SERC - MTech

The cut off for written round was GATE Score 750 for the CS Stream. The admission process consists of a written test and on being shortlisted, an interview.
The written round was held on 20th April and about 250-300 students attended the test. The call letter, sent about 20 days in advance, gave details about the nature of test. The test has questions on Basic Mathematics and Programming. Basic Maths includes topics from undergraduate and high school mathematics such as algebra, geometry, trigonometry, coordinate geometry, linear algebra, calculus, probability and statistics, and elementary discrete mathematics. The programming part includes topics such as basic data structures, simple concepts on algorithms, and a working knowledge of programming languages
What I found from the written test is that the tricky parts are clearing the high school math questions. It consisted of 30 MCQ questions to be answered in 60 minutes. The results were announced later that evening and 75 candidates were shortlisted. I recall about half of the questions from the test.
Here are some of the questions :

1.  Given 3 sides of triangle find the radius of the circumcircle
2.  Given a sphere and the triangle is drawn inside the sphere with its internal angles all right angles. Find radius of sphere
3.  A dice is tossed 5 times what is the probability that u have one odd number 
4.  Given a matrix which of the following is true?
        (a) AAt = AtA    (b) A-At /2 is skew symmetric  (c) A inverse exists     
5.  Given that multiplication and addition are the only operations how many operations are performed in a matrix multiplication 
6.  Given two sets with cardinality m and n. How many functions can be possible from m to n
7.  Consider 1/(1/(1/(1+....))) What does it evaluate to?
8.  4x3 -7x2 -4x -11. What is the min value of the function 
9.  output of a simple c program in a loop
10.  Given that a person speed is two times while walking as compared to swimming. There is a circular pool. 
       Person A wants to move from point a to point b on the diameter. 
       Which is faster swimming across or walking on perimeter or swimming half and then walking rest or 
       walking half and swimming rest
11.  Given a system or equations how many solutions exist
12.  Integral sinx /x - infinity to infinity. The integral exists only if 0 is excluded
13.  Integral x^n e-x dx. Where n>0. The integral has a finite value only 
         (a) for n <= 1    (b) for n<= 2   (c) for n<=3   (d) None
14.  There is a triangular park XYZ. Given XY = XZ = 100. There is pole in the center of YZ. 
      The angle made by X,Y and Z are 45,60 and 60 respectively. What is the height of the pole. 
15.  Given a 3*3 square matrix. One of the entries is x. If the rank of the matrix should be 3 then what is the value of x.
16.  Two sinusoidal waves are graphed. The image forms an 8. Which waves are mapped?
         (a) Sin t ,cos t  (b) Cos t , sin t   (c) Sin 2t , cos t   (d) Cos 2t ,sin t

IIT Madras, CSE Department - MSc(Engg)

The Computer Science and Engineering department at IIT Madras held admissions for M.Sc(Engg) on 5th May 2015. One month advance notice was given after shortlist for preparation for interview.
Some statistics from the CSE Dept shows:
Total Number of Applications - 790
Number of candidates called for written test - 373
The shorlist criteria was UG percent >= 70 AND Gate Score >= 600.

On the day of the admission there were 2 papers:
First paper consisted of 30 MCQs of 1.5 hours duration. Some of the questions from the first paper are as below:

1.  Types of functions - injective, surjective and bijective -> questions based on that
2.  Aptitude question based on the dependency
3.  Question on statements and connectives which two are equivalent
4.  Code snippets and their output
5.  Question on pointers (++, & and * operator precedence)
6.  Lots of combinatoric and Probability questions

Second paper consisted of 15 paragraph answer questions. Any 10 questions had to be attempted. Some of the questions from the second paper were as below:

1.  Algorithm question- k array, n elements each need to merge them into a single array with a complexity of n log k
2.  2 Questions to write DFA for a given language and prove that is the minimal DFA
3.  Question to construct Annotated Parse tree for an expression in Compiler Design
4.  Digital Design - Construct a Mod-7 counter (with a different order) using T- flip flop
5.  Given the bytes required for each level in a network. calculate the latency on the channel
6.  Computer network - find if a collision occurred or not given mode of transmission & speed of transmission
7.  Question on set associative cache mapping
8.  Given a code, find the recursive function and solve the function to find complexity

Indian Institute of Science (IISc), Bangalore - MSc(Engg)
I was shortlisted for 3 MSc(Engg) interviews - Computer Systems(CS) at SERC, Computational Science(CP) at SERC and also CSA Department. The interviews were held in batches through the week of 1st June to 5th June 2015. There were morning, noon and post-noon sessions every day. I had one interview each on consecutive days starting on Monday, 1st June. Each interview gave me more confidence and I got progressively better at facing the professors. The profs were friendly and the interviews seemed like a discussion (specially the one at CSA).

IISc, SERC Department - Computer Systems(CS) - MSc(Engg)
The admission for Computer Systems stream in IISc Supercomputer Education and Research Department was held on 1st June, Monday. My written round started at a few minutes past 9:00AM. It consisted of 5 simple questions as below:

1.  Question on conditional probability
2.  Question on String matching code output
3.  Number of Boolean functions possible given n variable
4.  Number of strictly increasing six digit numbers possible
5.  Fill in the blank type question to complete the loop bounds and the content of a program to traverse a tree

They evaluated the paper within 10-15 minutes and selected about 60-70% of the candidates for interview. I had selected high performance computing (HPC) lab for specialization and accordingly the questions were around computer architecture - cache design, set associative caches, cache coherence. Questions from data structures like pre-order tree traversal and heaps. There were a few questions on compilers about basic blocks and control flow graphs. The panel consisted of 6 professors whom I recognize as Prof R. Govindarajan, Prof Satish Vadhiyar, Vijay Natrajan, Partha Talukdar, Yogesh Simmham and Lakshmi J. I must admit I was intimidated by the large panel but only 1 prof was asking questions at a time and some were inactive throughout the interview. My interview lasted only about 15 minutes and didn't go as well as I would have liked.

IISc, SERC Department - Computational Science(CP) - MSc(Engg)
My admission interview for Computational Science at SERC was held on 2nd June, Tuesday again in the morning session at 9:00AM. The initial written test was for 20 minutes and consisted of the following questions.

1.  Solve d²y/dx² + 2dy/dx +y(x) =0. Plot the solution. Given some initial condition for y(0) and y'(0).
2.  Given a 4×4 square matrix. Find the eigen values.
3.  One integration question with initial values to find the constant after integration
4.  Question on probability and Bayes theorem.
5.  Write a program to multiply a diagonal and a non diagonal matrix in the least complexity possible

Again they evaluated the paper within 15-20 minutes and selected almost 60-70% of the candidates. The panel for this interview was much smaller and I felt more comfortable and relaxed answering questions. The previous days systems interview had hardened my resolve to do better at interviews. The panel consisted of 3 professors - Soumyendu Raha, Debnath Pal, and Sekar K. I had selected Scientific computing lab and accordingly the questions were on linear algebra. They were also interested in my work at my company and college GPA / courses. We had a conversation about my plans for future and why I was planning to pursue masters. I was asked the following technical questions and was allowed to use the white board to explain my answers.

1.  Given a combination of vectors find another vector
2.  Write a program to find transpose of a matrix without using temp variable
3.  Given a triangle with co ordinates of vertices. Write the determinant for its area.
4.  A few more questions on eigen values and Eigen vectors.

My CP interview at SERC went on much better than the previous day and lasted for about 20 minutes.

IISc, CSA Department - MSc(Engg)
The admission was held on 3rd June, Wednesday. There were in all about 30 students who wrote the written test. These were from all the 3 streams. The majority of candidates had chosen Intelligent systems which also had 2 interview rooms. I had chosen Compilers within Computer Systems stream for specialization. The written round started at 9:00AM and consisted of 10 questions of 1 mark each which were to be answered in 40 minutes. The questions were as follows:

1.  Given a circle with Diameter 'D'. We inscribe a rectangle in it with all its vertices on the circumference of the circle. 
      Find the maximum value of the perimeter of the rectangle.
2.  Use a 2:1 MUX to realize an XOR gate. Given (A,A',B,B')
3.  Which layer of TCP/IP protocol is responsible for end to end semantics
4.  2 questions on output of a 'C' program. Swap function
5.  Conditional probability question
6.  Given a set of functions arrange them in the increasing order of their complexity.
      root2^(logn), (log n)!, n^2, e^n, 2^(root log n). Find the second and the 4th element
7.  Matrix question. 

They selected the majority of the people in the Systems stream and theory stream. There were a few people who were dropped after written test in the Intelligent Systems stream. The interview panel consisted of Aditya Kanade, K.V. Raghavan, Murali Krishna Ramanathan (was on the Video Conference on Skype), Uday Kumar Reddy and R.C. Hansdah. This was by far my best interview of the 3 of which I appeared and went on for about 1.5 hours (Trust me, it didn't at all feel that long in the room). The interview felt like a discussion with the professors guiding me to arrive at the correct answer. They were also interested in knowing about my work, college projects / courses and my future plans. Again white board was provided to explain my answers. The questions asked were as follows:

1.  Write a program to traverse a binary tree inorder without using recursion.
2.  Questions on structures and pointers. 
3.  Questions on recursive function call an the state of the machine or the steps that take place when the function is called. 
4.  Explain call by value , the memory structure when this happens
5.  Whats is a function
6.  Number of functions possible from a Set A with m elements to Set B with n elements
7.  Number of onto functions for the above two sets
8.  Explain automata, regular language, cardinality of a language
9.  Given two languages L(A) and L(B), how to prove that one is a subset of another (they waived off this one in the end)

As per my discussion about my plans with the panel at the end of the interview Prof. Raghavan gave me a choice for upgrade to a Direct PhD as the number of seats for M.Sc(Engg) were limited and my chances would be better if I opted for Direct PhD program. They also assured me that I would also get the M.Sc(Engg) degree if I completed the Direct PhD Program. They were very friendly and allowed me to speak to my parents about this. As I was unable to reach my parents over the phone when I returned to the Profs in the break Prof. Raghavan gave me his card and asked me to mail him by end of the day regarding my decision.

On 11th June the results for Research Interviews in CSA Department were announced and I'm proud to say that my friend secured an admission in the M.Sc(Engg) course here!