1
GATE CSE 2013
MCQ (Single Correct Answer)
+1
-0.3
A Binary operation $$ \oplus $$ on a set of integers is defined as $$x$$ $$ \oplus $$ $$y$$ $$ = {x^2} + {y^2}$$. Which one of the following statements is TRUE about $$ \oplus $$ ?
A
Commutative but not associative
B
Both commutative and associative
C
Associative but not Commutative
D
Neither commutative nor associative
2
GATE CSE 2010
MCQ (Single Correct Answer)
+1
-0.3
What is the possible number of reflexive relations on a set $$5$$ elements?
A
210
B
215
C
220
D
225
3
GATE CSE 2010
MCQ (Single Correct Answer)
+1
-0.3
Consider the set $$S = \left\{ {1,\,\omega ,\,{\omega ^2}} \right\},$$ where $$\omega $$ and $${{\omega ^2}}$$, are cube roots of unity. If $$ * $$ denotes the multiplication operation, the structure $$\left\{ {S,\, * } \right\}$$ forms
A
a group
B
a ring
C
an integral domain
D
a field
4
GATE CSE 2009
MCQ (Single Correct Answer)
+1
-0.3
Which one of the following in NOT necessarily a property of Group?
A
Commutativity
B
Associativity
C
Existence of inverse for every element
D
Existence of identity
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