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This paper finds a limiting region for the number of subjects required and hence number of failed in screening test in multi-centric clinical trials. This situation follows a properly normalized independent vector sequences comprising of moving maxima (Yk (n)) for m (>1) multi centric set up in clinical trials, where 1≤k (n)≤n. Results are given for bi-centric and multi-centric situations, under certain conditions on k (n).