GATE CSE 2001


Question 1
Consider the following statements:

S1: The sum of two singular nxn matrices may be non-singular
S2: The sum of two nxn non-singular matrices may be singular.


Which of the following statements is correct?
A
S1 and S2 are both true
B
S1 is true, S2 is false
C
S1 is false, S2 is true
D
S1 and S2 are both false
Engineering Mathematics   Linear Algebra
Question 2
Consider the following relations: 
  
R1(a,b) iff (a+b) is even over the set of integers
R2(a,b) iff (a+b) is odd over the set of integers
R3(a,b) iff a.b > 0 over the set of non-zero rational numbers
R4(a,b) iff |a - b| <= 2 over the set of natural numbers
Which of the following statements is correct?
A
R1 and R2 are equivalence relations, R3 and R4 are not
B
R1 and R3 are equivalence relations, R2 and R4 are not
C
R1 and R4 are equivalence relations, R2 and R3 are not
D
R1, R2, R3 and R4 are all equivalence relations
Discrete Mathematics   Relation


Question 3
Consider two well-formed formulas in prepositional logic.
F1: \; P\Rightarrow \neg P
F2: \;( P\Rightarrow \neg P)\vee ( \neg P\Rightarrow P)
Which of the following statements is correct?
A
F1 is satisfiable, F2 is valid
B
F1 unsatisfiable, F2 is satisfiable
C
F1 is unsatisfiable, F2 is valid
D
F1 and F2 are both satisfiable
Discrete Mathematics   Propositional Logic
Question 4
Consider the following two statements :
S1: {0^{2n}|n\geq 1|} is a regular language
S2 : {0^{m}1^{n}0^{m+n}|m\geq 1 and n\geq 1|} is a regular language
Which of the following statements is correct?
A
Only S1 is correct
B
Only S2 is correct
C
Both S1 and S2 are correct
D
None of S1 and S2 is correct
Theory of Computation   Regular Language
Question 5
Which of the following statements true ?
A
If a language is context free it can be always be accepted by a deterministic push-down automaton.
B
The union of two context free language is context free.
C
The intersection of two context free language is context free
D
The complement of a context free language is context free
Theory of Computation   Context Free Language


There are 5 questions to complete.

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