A directory of Objective Type Questions covering all the Computer Science subjects. Here you can access and discuss Multiple choice questions and answers for various compitative exams and interviews.

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 non-isomorphic 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

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