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The problems which have no algorithm, regardless of whether or not they are accepted by a turing machine that fails to halts on some input are referred as:

(a) Decidable

(b) Undecidable

(c) Computable

(d) None of the mentioned

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Correct answer is (b) Undecidable

For explanation: The problems that can be solved by a turing machine can divided into two classes:

a) Those that have an algorithm

b) Intractable problems: Those that are only solved by a turing machine that may run forever on inputs they do not accept.

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