1
GATE CSE 2013
MCQ (Single Correct Answer)
+1
-0.3
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
A
$$1$$ and $$4$$ only
B
$$1$$ and $$3$$ only
C
$$2$$ only
D
$$3$$ only
2
GATE CSE 2008
MCQ (Single Correct Answer)
+1
-0.3
Which of the following is true for the language $$\left\{ {{a^p}} \right.\left| P \right.$$ prime $$\left. \, \right\}$$?
A
It is not accepted by a Turing machine
B
It is regular but not context-free
C
It is context-free but not regular
D
It is neither regular nor context-free, but accepted by a Turing machine
3
GATE CSE 2003
MCQ (Single Correct Answer)
+1
-0.3
Nobody knows yet if $$P=NP$$. Consider the language $$L$$ defined as follows
$$L = \left\{ {\matrix{ {{{\left( {0 + 1} \right)}^ * }\,\,\,if\,\,P = NP} \cr {\,\,\,\,\,\,\,\phi \,\,\,\,Otherwise} \cr } } \right.$$

Which of the following statement is true?

A
$$L$$ is recursive
B
$$L$$ is recursively enumerable but not recursive
C
$$L$$ is not recursively enumerable
D
Whether $$L$$ is recursive or not will be known after we find out if $$P=NP.$$
4
GATE CSE 2003
MCQ (Single Correct Answer)
+1
-0.3
If the strings of a language $$L$$ can be effectively enumerated in lexicographic (i.e., alphabetic$$(c)$$ order, which of the following statements is true?
A
$$L$$ is necessarily finite
B
$$L$$ is regular but not necessarily finite
C
$$L$$ is context free but not necessarily regular
D
$$L$$ is recursive but not necessarily context free
GATE CSE Subjects
Software Engineering
Web Technologies
EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12