Ans: (A)
Hint : \((101)^{100}-1=(1+100)^{100}-1\)
$$
\begin{aligned}
&=\left[1+{ }^{100} \mathrm{C}_{1} 100+{ }^{100} \mathrm{C}_{2} 100^{2}+\ldots \ldots .+{ }^{100} \mathrm{C}_{100}(100)^{100}\right]-1=10^{4}\left(1+{ }^{100} \mathrm{C}_{2}+{ }^{100} \mathrm{C}_{3} 10^{2}+\ldots .+{ }^{100} \mathrm{C}_{100}(100)^{98}\right) \\
&=10^{4}(1+\text { an integer multiple of } 10)
\end{aligned}
$$