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