You need to give JEE exam to get admission in NIT Calicut, IIT Palakkad or IIITMK.

There are many private universities as well who take admission on the basis of JEE.

You can appear for Amrita exam as well it comes in one of the top private universities.

You can check the list of colleges from te given below link

Top Engineering colleges in Kerala

For preparation you can follow below strategies

PHYSICS:
Note down the formulae and results, it will help during revision.
Practice as many questions as you can, keeping in mind the availability of time.
Avoid lengthy and complicated problems at the last minute, if time is limited.
Focus on your strong areas.
Suggested Reference Books : H.C. Verma & Resnick Halliday

CHEMISTRY:
Chemistry is amongst the tough subjects as it involves cramming of formulae and reactions.
Understand the conceptual base of the topics.
Periodic table is the most scoring part.
Suggested Reference Books:  Morrison & Boyd and O.P. Tandon
MATHEMATICS :
Conceptual understanding should be preferred.

Practice a lot.

In Mathematics JEE (Main)-2013, 32% questions were easy, 58% Medium level and 10% difficult.
Suggested Reference Books:  R.D. Sharma, Arihant, Hall Knight & S. L. Loonely

Good Luck!!