1
GATE CSE 1996
MCQ (Single Correct Answer)
+2
-0.6
Which one of the following is false?
A
The set of all bijective functions on a finite set forms a group under function composition.
B
The set {1, 2, ..., p - 1} forms a group under multiplication mod p where p is a prime number.
C
The set of all strings over a finite alphabet $$\sum $$ forms a group under concatenation.
D
A subset $$s\, \ne \,\phi $$ of G is a subgroup of the group if and only if for any pair of elements $$a,\,\,b\,\, \in \,\,s,\,\,a\,\,*\,\,{b^{ - 1}}\,\, \in \,s$$.
2
GATE CSE 1996
MCQ (Single Correct Answer)
+2
-0.6
Let R be a non-emply relation on a collection of sets defined by $${A^R}\,B $$ if and only if $$A\, \cap \,B\, = \,\phi $$. Then, (pick the true statement)
A
R is reflexive and transitive
B
R is symmetric and not transitive
C
R is an equivalence relation
D
R is not reflexive and not symmetric
3
GATE CSE 1995
MCQ (Single Correct Answer)
+2
-0.6
Let A be the set of all nonsingular matrices over real numbers and let * be the matrix multiplication operator. Then
A
A is closed under * but $$ < A,\,* > $$ is not a semigroup.
B
$$ < A,\,* > $$ is a semigroup but not a monoid.
C
$$ < A,\,* > $$ is a monoid but not a group.
D
$$ < A,\,* > $$ is a group but not an abelian group
4
GATE CSE 1994
MCQ (Single Correct Answer)
+2
-0.6
Some group (G, o) is known to be abelian. Then, which one of the following is true for G?
A
$$g = {g^{ - 1}}\,$$ for every $$g\, \in \,G$$.
B
$$g = {g^{ 2}}\,$$ for every $$g\, \in \,G$$.
C
$${(goh)^2} = \,{g^2}\,o\,\,{h^2}$$ for every g, $$h\, \in \,G$$.
D
G is of finite order.
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Software Engineering
Web Technologies
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