in Theory of Computation
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is this correct DFA ?

in Theory of Computation
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Correct, just make $Q0Q2$ and $Q0Q1Q2$ final.
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Answer is correct but while conversion of NFA to DFA remember the set of final states.

Final states in DFA are states which has final state of NFA (While converting NFA to DFA).

means in your NFA Q2 is final state and after converting you have state Q0Q2 and Q0Q1Q2 are states which has Q2 so just make it final otherwise answer is correct.