Step 1: Use the truth tables:
A NAND gate gives $0$ only when both inputs are $1$. A NOR gate gives $1$ only when both inputs are $0$. An XOR gate gives $1$ only when the inputs differ.
Step 2: Apply:
(A) has both inputs $1$, so $0$. (B) has inputs $1, 0$, so $1$. (C) has one input $1$, so $0$. (D) has equal inputs, so $0$.
Final Answer:
Only gate (B) has output $1$, option (B).
\[ \boxed{\text{Gate (B)}} \]