The correct answer to the given question is (1),(3) and (4). I understood how 3 and 4 are correct but I could not understand how (1) is also a correct answer.
I know that here $\sum_i X_i$ is a sufficient statistic and any one-one function of this statistic is also a sufficient statistic but according to my calculations $X_1 + 2X_2$ is not a one-one function of $X_1 + X_2$.
My argument being that when $X_1 = 1$ and $X_2= 0$ or $X_1 =0$ and $X_2=1$ then $X_1 + X_2 =1$ but in case of $X_1 + 2X_2$, it takes value 1 or 2 respectively. 1 is matched with two values 1 and 2. Therefore, it is not a one-one function.