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.

11. Consider the following relation on subsets of the set S of integers between 1 and 2014. For two distinct subsets U and V of S we say U < V if the minimum element in the symmetric difference of the two sets is in U. Consider the following two statements:

S1: There is a subset of S that is larger than every other subset.
S2: There is a subset of S that is smaller than every other subset.

Which one of the following is CORRECT?
a. Both S1 and S2 are true
b. S1 is true and S2 is false
c. S2 is true and S1 is false
d. Neither S1 nor S2 is true
View Answer Report Discuss Too Difficult! Search Google
Answer: (a).Both S1 and S2 are true

12. Let G be a group with 15 elements. Let L be a subgroup of G. It is known that L != G and that the size of L is at least 4. The size of L is __________.
a. 3
b. 5
c. 7
d. 9
View Answer Report Discuss Too Difficult! Search Google
Answer: (b).5

13. If V1 and V2 are 4-dimensional subspaces of a 6-dimensional vector space V, then the smallest possible dimension of V1 ∩ V2 is ______.
a. 1
b. 2
c. 3
d. 4
View Answer Report Discuss Too Difficult! Search Google
Answer: (b).2

14. There are two elements x, y in a group (G,∗) such that every element in the group can be written as a product of some number of x's and y's in some order. It is known that

x ∗ x = y ∗ y = x ∗ y ∗ x ∗ y = y ∗ x ∗ y ∗ x = e

where e is the identity element. The maximum number of elements in such a group is __________.
a. 2
b. 3
c. 4
d. 5
View Answer Report Discuss Too Difficult! Search Google
Answer: (c).4

15. Consider the set of all functions f: {0,1, … ,2014} → {0,1, … ,2014} such that f(f(i)) = i, for all 0 ≤ i ≤ 2014. Consider the following statements:

P. For each such function it must be the case that
for every i, f(i) = i.
Q. For each such function it must be the case that
for some i, f(i) = i.
R. Each such function must be onto.

Which one of the following is CORRECT?
a. P, Q and R are true
b. Only Q and R are true
c. Only P and Q are true
d. Only R is true
View Answer Report Discuss Too Difficult! Search Google
Answer: (b).Only Q and R are true

16. Let E, F and G be finite sets. Let X = (E ∩ F) - (F ∩ G) and Y = (E - (E ∩ G)) - (E - F). Which one of the following is true?
a. X ⊂ Y
b. X ⊃ Y
c. X = Y
d. X - Y ≠ φ and Y - X ≠ φ
View Answer Report Discuss Too Difficult! Search Google
Answer: (c).X = Y

17. Given a set of elements N = {1, 2, ..., n} and two arbitrary subsets A⊆N and B⊆N, how many of the n! permutations π from N to N satisfy min(π(A)) = min(π(B)), where min(S) is the smallest integer in the set of integers S, and π(S) is the set of integers obtained by applying permutation π to each element of S?
a. (n - |A ∪ B|) |A| |B|
b. (|A|^2+|B|^2)n^2
c. n! |A∩B| / |A∪B|
d. |A∩B|^2nC|A∪B|
View Answer Report Discuss Too Difficult! Search Google
Answer: (c).n! |A∩B| / |A∪B|

18. Let A, B and C be non-empty sets and let X = (A - B) - C and Y = (A - C) - (B - C). Which one of the following is TRUE?
a. X = Y
b. X ⊂ Y
c. Y ⊂ X
d. none of these
View Answer Report Discuss Too Difficult! Search Google
Answer: (a).X = Y

19. The set {1, 2, 4, 7, 8, 11, 13, 14} is a group under multiplication modulo 15. The inverses of 4 and 7 are respectively
a. 3 and 13
b. 2 and 11
c. 4 and 13
d. 8 and 14
View Answer Report Discuss Too Difficult! Search Google
Answer: (c).4 and 13

20. Let R and S be any two equivalence relations on a non-empty set A. Which one of the following statements is TRUE?
a. R ∪ S, R ∩ S are both equivalence relations
b. R ∪ S is an equivalence relation
c. R ∩ S is an equivalence relation
d. Neither R ∪ S nor R ∩ S is an equivalence relation
View Answer Report Discuss Too Difficult! Search Google
Answer: (c).R ∩ S is an equivalence relation

Page 2 of 23