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
I have been asked this question in a national level competition.
This question is from The Universal Language-Undecidability in division Undecidability of Automata Theory