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+1 vote

The given NFA is itself DFA. So, Just apply DFA minimization algorithm on the given DFA.

Various DFA minimization algorithms could be used But let me use the most convenient one that I feel :

**DFA Minimization using Equivalence Theorem :**

0-equivalent : $\left \{ q_\lambda,q_0,q_1,q_{00},q_{01},q_{10} \right \} \left \{ q_{11} \right \}$

1- equivalent : $\left \{ q_\lambda,q_0,q_{00},q_{10} \right \} \left \{ q_1,q_{01} \right \} \left \{ q_{11} \right \}$

2-equivalent : $\left \{ q_\lambda,q_0,q_{00},q_{10} \right \} \left \{ q_1,q_{01} \right \} \left \{ q_{11} \right \}$

Hence, We get Three distingushable states in the given DFA.

So, Answer = $3$

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