Which variance claim fails for two unbiased estimators

For $n\ge 2$, let $\epsilon_1,\epsilon_2,…,\epsilon_n$ be i.i.d. random variables having the $N(0,1)$ distribution. Consider $n$ independent random variables $Y_1,Y_2,…,Y_n$ defined by $Y_i=\beta i+\epsilon_i$, $i=1,2,…,n$, where $\beta\in\mathbb{R}$. Define $\bar Y=\frac1n\sum_{i=1}^n Y_i$, $T_1=\frac{2\bar Y}{n+1}$, and $T_2=\frac1n\sum_{i=1}^n\frac{Y_i}{i}$. Then which of the following statements is NOT correct?