You can just put the value and verify the answer. I think the answer should be option B because for the question is asking for the largest input we can give so that the problem could be solved in $1sec$. Therefore, for algorithm A if we give the input of size $2^{10^{6}}$, then it is taking $log(2^{10^{6}})=10^{6}\mu s=1sec$. Similarly, for algorithm B, if we give the input of size $10^{^{12}}$, then it is taking $\sqrt{10^{12}}=10^{6}\mu s=1sec$.
