1
GATE CSE 2004
+2
-0.6
The following finite state machine accepts all those binary strings in which the number of $$1's$$ and $$0's$$ are respectively
A
Divisible by $$3$$ and $$2$$
B
Odd and even
C
Even and odd
D
Divisible by $$2$$ and $$3$$
2
GATE CSE 2003
+2
-0.6
Consider the $$NFA$$ $$M$$ shown below.

Let the language accepted by $$M$$ be $$L.$$ Let $${L_1}$$ be the language accepted by the $$NFA$$, $${M_1}$$ obtained by changing the accepting state of $$M$$ to a non accepting state and by changing the non accepting state of $$M$$ to accepting states. Which of the following statements is true?

A
$${L_1} = \left\{ {0,\,1} \right\}{}^ * - L$$
B
$${L_1} = \left\{ {0,\,1} \right\}{}^ *$$
C
$${L_1} \subseteq \,L$$
D
$${L_1} = \,L$$
3
GATE CSE 2003
+2
-0.6
Consider the following deterministic finite state automation $$M.$$

Let $$S$$ denote the set of seven bit binary strings in which the first, the fourth, and the last bits are $$1$$. The number of strings in $$S$$ that are accepted by $$M$$ is

A
$$1$$
B
$$5$$
C
$$7$$
D
$$8$$
4
GATE CSE 2002
+2
-0.6
The smallest finite automaton which accepts the language
$$L = \left. {\left\{ x \right.} \right|$$ length of $$x$$ is divisible by $$\left. 3 \right\}$$ has
A
$$2$$ states
B
$$3$$ states
C
$$4$$ states
D
$$5$$ states
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