$S=S_{1}\bigcup S_{2}\bigcup S_{1}\bigcup S_{3}\bigcup S_{4}\bigcup..........\bigcup S_{n}$
And in question given that S is infinite set
in option A is wrong because it say atleast one of the set $S_{i}$ is a finite set means if all are finite then S is finite
in option D not more than one of the sets$S_{i}$ can be infinite means all are finite same as option A . if all are finite then S is finite
in option B not more than one of the sets $S_{i}$ can be finite means all $S_{i}$ are infinite,if all $S_{i}$ are infinite so S is infinte so option B is true.
in option C at least one of the sets $S_{i}$ is an infinite set means if one set is infinite hole S is infinite so option C Is also true
but option C is more correct than option B because atleast one $S_{i}$ is infinite cover all $S_{i}$ are infinite
all $S_{i}$ are infinite $\subset$ atleast one $S_{i}$ is infinite
so ans is option C :- S be an infinite set if at least one of the sets $S_{I}$ is an infinite set