1.  A binary operation on a set of integers is defined as x y = x^2 + y^2. Which one of the following statements is TRUE about ? 
a.  Commutative but not associative 
b.  Both commutative and associative 
c.  Associative but not commutative 
d.  Neither commutative nor associative 
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Answer: (a).Commutative but not associative

2.  Consider the set S = {1, ω, ω^2}, where ω and w^2 are cube roots of unity. If * denotes the multiplication operation, the structure (S, *) forms 
a.  A group 
b.  A ring 
c.  An integral domain 
d.  A field 
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Answer: (a).A group

3.  Which one of the following in NOT necessarily a property of a Group? 
a.  Commutativity 
b.  Associativity 
c.  Existence of inverse for every element 
d.  Existence of identity 
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Answer: (a).Commutativity

4.  Consider the binary relation R = {(x, y), (x, z), (z, x), (z, y)} on the set {x, y, z}. Which one of the following is TRUE? 
a.  R is symmetric but NOT antisymmetric 
b.  R is NOT symmetric but antisymmetric 
c.  R is both symmetric and antisymmetric 
d.  R is neither symmetric nor antisymmetric 
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Answer: (d).R is neither symmetric nor antisymmetric

5.  Let S be a set of n elements. The number of ordered pairs in the largest and the smallest equivalence relations on S are: 
a.  n and n 
b.  n^2 and n 
c.  n^2 and 0 
d.  n and 1 
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Answer: (b).n^2 and n

6.  How many different nonisomorphic Abelian groups of order 4 are there 
a.  2 
b.  3 
c.  4 
d.  5 
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Answer: (a).2

7.  Let X, Y, Z be sets of sizes x, y and z respectively. Let W = X x Y. Let E be the set of all subsets of W. The number of functions from Z to E is: 
a.  z^2^xy 
b.  z x 2^xy 
c.  z^2^(x + y) 
d.  2^xyz 
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Answer: (d).2^xyz

8.  The set {1, 2, 3, 5, 7, 8, 9} under multiplication modulo 10 is not a group. Given below are four plausible reasons. Which one of them is false? 
a.  It is not closed 
b.  2 does not have an inverse 
c.  3 does not have an inverse 
d.  8 does not have an inverse 
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Answer: (c).3 does not have an inverse

9.  A relation R is defined on ordered pairs of integers as follows: (x,y) R(u,v) if x < u and y > v. Then R is: Then R is: 
a.  Neither a Partial Order nor an Equivalence Relation 
b.  A Partial Order but not a Total Order 
c.  A Total Order 
d.  An Equivalence Relation 
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Answer: (a).Neither a Partial Order nor an Equivalence Relation

10.  Let S denote the set of all functions f: {0,1}^4 > {0,1}. Denote by N the number of functions from S to the set {0,1}. The value of Log2Log2N is ______. 
a.  12 
b.  13 
c.  15 
d.  16 
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Answer: (d).16

Questions from Previous year GATE question papers
UGC NET Previous year questions and practice sets
Attempt a small test to analyze your preparation level. This GATE exam includes questions from previous year GATE papers.
Practice test for UGC NET Computer Science Paper. The questions asked in this NET practice paper are from various previous year papers.