IIT Madras Mechanical Engineering PhD elimination test question pattern 2016

I recently attended the written elimination test for IIT Madras PhD candidates in the Design stream of Mechanical engineering department. I am listing out the questions I remember from the test so that somebody in future might get an idea of the kind of questions you can expect.

Test is for 3 streams, Design, Manufacturing and Thermal. You are supposed to attempt any one according to your preference. The exam is on a computer, 15 questions with 30 minutes of time. You are provided with a rough sheet and calculators are allowed if you have one. Mobile phones are not.

My Bachelors is not from mechanical engineering. Those questions that I did not understand , I am only recollecting vaguely. 

1. One problem on IC engine swept volume calculation from crank radius and piston diameter .
2. One on calculation of Von Mises equivalent yield stress for a given stress matrix
3.  One problem on finding the radius of Mohr's circle of stress .
4.  One problem on finding natural frequency of a spring mass system. Some springs were in series, some in parallel. Typical interview question.
5.  One problem on finding deflection of cantilever beam subject to moment loading. It was solvable with double integration. Advanced techniques not required.
6. One sum on properties of Eigen values of a 3x3 matrix. 
7. One sum on simultaneous linear equations, with a 3x3 A matrix.  We were asked to find if it is consistent / unique / infinite?
8. Number of unique elastic constants required to describe composites, some types of Cu crystals ?
9. Material selection for a lathe bed construction? cast iron/. wrought iron/ steel?
10. Which property cannot be directly measured? strain/ stress/ displacement?
11. Which of the following is a first order tensor? one of the options was velocity. I did not see other options. :)

 Some questions I did not understand:

1. Decreasing yield point of a material : Options were about manipulating crystal structure.  
2. Rate of release of strain energy in a structure depends on what? Material/ loading pattern / Geometry of structure / crystal structure?
3. Austentite Martensite crystal structure , options were about FCC BCC types.

Concepts I do not understand clearly, but where in options of some questions:

1. Precipitation hardening of alloys using some secondary medium
2. Irwins theory : It has something to do with fracture mechanics.
3. Goodmans theory : It has something to do with fatigue loading of ductile materials

Good luck |^|