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