You can think of solving a problem in any programming test as a two-stage process:
1) Design Phase: In the design phase, you try to design an algorithm that can solve the given problem.
2) Implementation Phase: In this phase, you implement the algorithm designed in stage 1.
Now among all the given problems, some might have a more involved design phase and a simple implementation phase while others might have a simple design phase and an involved implementation phase.
Try to find out the phase you are strong at, and then in the test, first approach the problems that you are more comfortable with.
There are very high chances that you encounter problems whose solution involves Dynamic Programming approach in the programming tests.
Solving Dynamic Programming problems often involves coming up with a recurrence relation to solve the given problem.Once you come up with the recurrence relation, generally, implementation is straightforward.
So I suggest you study the basics of Dynamic Programming.For this purpose, you might want to refer Chapter 6, on Dynamic Programming from the book - Algorithm Design by Kleinberg and Tardos.Cover at least sections 6.1 and 6.2 then you can switch to CLRS for studying LCS.
Study and implement LCS(along with Dynamic Programming, it will also give you some experience of working with strings).
Pick up some basic Dynamic Programming problems from any competitive programming website and try to design and implement solutions for them.
For working on your implementation skills try to implement some of the pseudo-codes given in CLRS e.g. comparison based sorts, binary search etc
A couple of questions from last year's programming test at IIT Kanpur:
1) Calculate (ab modulo p) without explicitly calculating ab.
2) A problem based on simple Dynamic Programming.
