Can you provide me previous year question paper for preparation of PhD Admissions Test as offered by Department of Computer Science and Engineering in IIT Bombay?

The previous year question paper for preparation of PhD Admissions Test as offered by Department of Computer Science and Engineering in IIT Bombay is as follows:

1.
n people each know a different piece of gossip. They can telephone each other and exchange all the information they know, so that after the call they both know everything that either of them knew before the call. Our interest is in coming up with a scheme such that the smallest number of calls are made so that everyone knows everything. Find the best scheme you can as a function of n.

2.
Two points are picked independently and uniformly at random from the circumference of a circle of radius R. Determine the function f such that the “the probability that the distance between the two points is at least f(R) is 0.5”.

3.
Consider a cell phone network. Assume that the geographical area covered by the network has been divided into a 2-dimensional array of square cells. When there is an incoming call for a given mobile, the network has to find the cell in which the mobile is currently located.

This is done by having each mobile inform a central control of its current location, every once in a while. The network queries for the mobile in a group of cells near the mobile's last known location.

One strategy is for the mobile to inform the central control after every k cell changes, for a given integer k. What is the number of cells the system must query if k=3?

4.
Exactly 7 persons - P, Q, R, S, T, U and V - participate in and finish all of a series of races. There are no ties for any position at the finish of the races. The following statements about the races are always true:
V finishes somewhere ahead of P
P finishes somewhere ahead of Q
Either R finishes first and T finishes last, or S finishes first and U or Q finishes last
If in a race S finishes sixth and Q finishes fifth, which of the following can be true?
A. V finishes first or fourth
B. R finishes second or third
C. P finishes second or fifth
D. U finishes third or fourth
E. T finishes fourth or fifth

Attached Files

IIT Bombay Ph D Question Paper.pdf (57.0 KB, 75 views)