If you are talking about the same paper then you can’t take the supplementary examination as well as improvement examination in the same semester at Calicut University. Let’s say you fail in paper A in the first semester and scored a B grade in paper B. During the third semester, you can write any paper of the first semester, if you pay the required fees. For paper B you will need to take an improvement examination and for paper A you need to take a supplementary examination. 

At Calicut University, the improvement examination is for those students who have passed the examination but want to improve their scores. While supplementary examination is for those who failed the subject and want to try again. 

Now as per the university rules, you can write supplementary examinations for four subjects. But if you have failed a subject in a semester and want to write the supplementary examination, you can’t improve another subject in the same semester.