From above table, we look at next state part
Whenever we reach state $00$ we get output $1$ [at row $1$,row $6$, row $8$], so we have state 00 with output 1
When we reach at state $01$, we get output $0$ [at row $3$, row $5$] and output $1$ [row $7$], so we have two state 01 with output 0, 01 with output 1.
When we reach at state $10$, we get output we get output $0$ [at row $2$, row $4$], so we have state 10 with output 0.
We don't reach at state $11$ [$11$ is not there in next state part], but we have state 11 with don't know (N) output.
If we draw the Moore Machine for above FSM [ from the table: present state x input symbol -> next state ]
It is clear from FSM from state $00$ to reach state $01$ with output $1$ i.e, $01/1$ with need minimum length input 101
Minimum length of input $=$ length of $101$. That is 3.
Correct Answer: $A$