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This mock test of Test: The Language of DFA for Computer Science Engineering (CSE) helps you for every Computer Science Engineering (CSE) entrance exam.
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QUESTION: 1

How many languages are over the alphabet R?

Solution:

A language over an alphabet R is a set of strings over A which is uncountable and infinite.

QUESTION: 2

According to the 5-tuple representation i.e. FA= {Q, ∑, δ, q, F}Statement 1: q ϵ Q’; Statement 2: FϵQ

Solution:

Q is the Finite set of states, whose elements i.e. the states constitute the finite automata.

QUESTION: 3

δˆ tells us the best:

Solution:

δ or the Transition function describes the best, how a DFA behaves on a string where to transit next, which direction to take.

QUESTION: 4

Which of the following option is correct?A= {{abc, aaba}. {ε, a, bb}}

Solution:

As the question has dot operation, ε will not be a part of the concatenated set. Had it been a union operation, ε would be a part of the operated set.

QUESTION: 5

For a DFA accepting binary numbers whose decimal equivalent is divisible by 4, what are all the possible remainders?

Solution:

All the decimal numbers on division would lead to only 4 remainders i.e. 0,1,2,3 (Property of Decimal division).

QUESTION: 6

Which of the following x is accepted by the given DFA (x is a binary string ∑= {0,1})?

Solution:

**Correct Answer :- d**

**Explanation : **The given DFA accepts all the binary strings such that they are divisible by 3 and 2.Thus, it can be said that it also accepts all the strings which is divisible by 6.

QUESTION: 7

Given:

L1= {xϵ ∑*|x contains even no’s of 0’s}

L2= {xϵ ∑*|x contains odd no’s of 1’s}

No of final states in Language L1 U L2?

Solution:

QUESTION: 8

The maximum number of transition which can be performed over a state in a DFA?∑= {a, b, c}

Solution:

The maximum number of transitions which a DFA allows for a language is the number of elements the transitions constitute.

QUESTION: 9

The maximum sum of in degree and out degree over a state in a DFA can be determined as:

∑= {a, b, c, d}

Solution:

The out degree for a DFA I fixed while the in degree depends on the number of states in the DFA and that cannot be determined without the dependence over the Language.

QUESTION: 10

The sum of minimum and maximum number of final states for a DFA n states is equal to:

Solution:

The maximum number of final states for a DFA can be total number of states itself and minimum would always be 1, as no DFA exits without a final state. Therefore, the solution is n+1.

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