Gate Exam

Which of the following statements is/are FALSE?
(1) For every non-deterministic Turing machine, there exists an equivalent
deterministic Turing machine.
(2) Turing recognizable languages are closed under union and complementation.
(3) Turing decidable languages are closed under intersection and
complementation
(4) Turing recognizable languages are closed under union and intersection.

Option
(A) 1 and 4 only
(B) 1 and 3 only
(C) 2 only
(D) 3 only

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Gate Other Question

Which of the following statements are TRUE?
(1) The problem of determining whether there exists a cycle in an undirected
graph is in P.
(2) The problem of determining whether there exists a cycle in an undirected
graph is in NP.
(3) If a problem A is NP-Complete, there exists a non-deterministic polynomial time algorithm to solve A.

Option
(A) 1,2 and 3
(B) 1 and 2 only
(C) 2 and 3 only
(D) 1 and 3 only An index is clustered, if
(A) it is on a set of fields that form a candidate key.
(B) it is on a set of fields that include the primary key.
(C) the data records of the file are organized in the same order as the data
entries of the index.
(D) the data records of the file are organized not in the same order as the data
entries of the index.