All the questions were very basic, not the ones your would expected for a PhD position. 1. Number 1-10, of which 3 numbers are chosen without replacement. what is the probability that the sum of these numbers is divisible by 3. 2. Three identical metal balls, when tossed in air come back in time T. After first ball, the second is released when the first ball is at its peak and then third ball is released when the first and second collide. After how much time the first ball is back ? All collisions are assumed elastic. (ans: 3/4T+T) 3. How to you estimate a derivative from discrete nodal values on a 1D nodal mesh starting from 0, h, 2h,...etc where h is the interval between the nodes and the derivative needs to be second order accurate at all nodal points. (Ans: Easy except for initial node '0', for node '0' use taylor series expansion)