Statement 1:set can be {1,2,3...} or {1}. in either case frequency is 1 but no of elements are different. Hence insufficient

Statement 2: implies St. Dvi is 0 because standard deviation cannot be negative, it is either positive or 0. Note standard deviation is the square root of variance, hence cannot be negative. so in Set A all elements are equal i.e {1,1,1,1....} or {1}. In either case no of elements are different. hence Insufficient

Combining 1 & 2,it is clear that the set A has only One element. Hence Sufficient

Option C