# ace quetion bank

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the minimal finite automata accepting the set of all strings over { 0, 1} starting with 1 that interpreted as the binary representation of an integer are congruent to 0 modulo 5 has  ______ states.
0
7states.
0
It must be 7 states.

A minimal DFA which accepts strings divisible by 5 contains 5 states.

In the first production you have to add a dead state for transition on 0 and the first state would have transition 1 going to the next state and the rest is as usual for 0mod5.

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Find the no. of DFA’s that can be constructed over the alphabet Σ with 5 symbols, and with 10 states. (a) $2^5$^0$×$50^5$(b)$2^1$^0$ × $10^5$^0$(c)$2^5$×$10^5$^0$ (d) $2^5$^0$×$50^5\$