1
GATE CSE 2013
+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 2013
+1
-0.3
Which one of the following functions is continuous at $$x = 3$$?
A
$$f\left( x \right) = \left\{ {\matrix{ {2,} & {if} & {x = 3} \cr {x - 1} & {if} & {x > 3} \cr {{{x + 3} \over 3},} & {if} & {x < 3} \cr } } \right.$$
B
$$f\left( x \right) = \left\{ {\matrix{ {4,} & {if} & {x = 3} \cr {8 - x} & {if} & {x \ne 3} \cr } } \right.$$
C
$$f\left( x \right) = \left\{ {\matrix{ {x + 3,} & {if} & {x \le 3} \cr {x - 4} & {if} & {x > 3} \cr } } \right.$$
D
$$f\left( x \right) = \matrix{ {{1 \over {{x^3} - 27}},} & {if} & {x \ne 3} \cr }$$
3
GATE CSE 2010
+1
-0.3
What is the possible number of reflexive relations on a set $$5$$ elements?
A
210
B
215
C
220
D
225
4
GATE CSE 2010
+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
GATE CSE Subjects
Discrete Mathematics
Programming Languages
Theory of Computation
Operating Systems
Digital Logic
Computer Organization
Database Management System
Data Structures
Computer Networks
Algorithms
Compiler Design
Software Engineering
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