The least count of clinical thermometer is X and of laboratory thermometer is Y. X and Y are:
0.2 degree C, 1 degree C
A clinical thermometer is designed to measure the narrow range of human body temperature, normally between about 35 degree C and 42 degree C, and therefore needs very fine graduations to read small changes accurately.
A laboratory thermometer, on the other hand, is designed to measure a much wider range of temperatures, typically from about minus 10 degree C to 110 degree C, so its scale is marked in coarser, whole-degree divisions.
Because of this difference in purpose, the smallest division, or least count, of a clinical thermometer is a small fraction of a degree, while the least count of a laboratory thermometer is a full degree Celsius.
Going by the option marked correct in the official answer key for this question, X is 0.2 degree C and Y is 1 degree C.
Note: several standard science references instead state the least count of a clinical thermometer as 0.1 degree C rather than 0.2 degree C; this discrepancy has been flagged for verification against the original paper.
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