$(1-Y/n^\alpha)^n$ tends to $1-Y$, $e^{-Y}$ or $1$ according as $\alpha<1$, $=1$, $>1$

Let Y be a Bernoulli random variable with $P(Y=0)=P(Y=1)=\tfrac12$. Let $X_n=(1-Y/n^\alpha)^n$, $\alpha\ge0$, then, which of the following statements are correct? (i) $X_n\overset{d}{\longrightarrow} Y$ when $0\le\alpha<1$; (ii) $X_n\overset{d}{\longrightarrow} e^{-Y}$ when $\alpha=1$; (iii) $X_n\overset{d}{\longrightarrow} Y$ when $\alpha>1$.