Practice Questions on Set Theory and Relation with Answers

**Questions on Set Theory and Relation with Answers**

Q1. Let D be the set of tuples (w_{1},..,w_{10}) where wi ∈{1,2,3} , 1 ≤ i ≤ 10 and w_{i} + w_{i+1} is an even number for each i with 1 ≤ i ≤ 9 . Then the number of elements in D is

(a) 2^{11} + 1.

(b) 2^{10} + 1.

(c) 3^{10} + 1.

(d) 3^{11} + 1

Q2. The number of subjective maps from a set of 4 elements to a set of 3 elements is

(a) 36

(b) 64

(c) 69

(d) 81

Q3. If n is a positive integer such that the sum of all positive integers a satisfying 1 ≤ a ≤ n and GCD(a, n) = 1 is equal to 240n, then the number of summands, namely, φ(n) , is

(a) 120

(b) 124

(c) 240

(d) 480

Q4. An ice cream shop sells ice creams in five possible flavors: Vanilla, Chocolate, Strawberry, Mango, and Pineapple. How many combinations of three scoop cones are

possible? [Note: The repetition of flavors is allowed but the order in which the flavors are chosen does not matter.]

(a) 10

(b) 20

(c) 35

(d) 243

Q5. We are given a class consisting of 4 boys and 4 girls. A committee that consists of a President, a Vice-President and a Secretary is to be chosen among the 8 students of the class. Let a denote the number of ways of choosing the committee in such a way that the committee has at least one boy and at least one girl. Let b denote the number of ways of choosing the committee in such a way that the number of girls is greater than or equal to that of the boys. Then

(a) a = 288

(b) b = 168

(c) a = 144

(d) b = 192

Q6. In a group of 265 people, 200 like singing, 110 like dancing, and 55 like painting. If 60 people like both singing and dancing, 30 like both singing and painting, and 10 like all three activities, then the number of persons who like only dancing and painting are

(a) 10

(b) 20

(c) 30

(d) 40

Q7. The last two digits of 781 are

(a) 07

(b) 17

(c) 37

(d) 47

Q8. The number of positive divisors of 50,000 is

(a) 20

(b) 30

(c) 40

(d) 50

Q9. The last digit of (38)^{2011} is

(a) 6

(b) 2

(c) 4

(d) 8

Q10. The number of multiples of 10^{44} that divide 10^{55}

(a) 11

(b) 12

(c) 121

(d) 144

Q11. Let A = {1, 2, 3, 4} and let R = {(2, 2), (3, 3), (4, 4), (1, 2)} be a relation in A. Then R is

(a) Reflexive

(b) Symmetric

(c) Transitive

(d) None of these

Q12. Let A = {1, 2, 3, 4} and R be a relation in A given by R={(1, 1), (2, 2), (3, 3), (4, 4), (1,2), (2, 1), (3, 1), (1,3)}. Then R is

(a) Reflexive

(b) Symmetric

(c) Transitive

(d) An equivalence relation

Q13. A survey shows that 63 % of Americans like cheese whereas 76 % like apples. If x % of Americans like both cheese and apples, then

(a) x = 39

(b) x = 63

(c) 39 ≤ x ≤ 63

(d) None of these

Q14. A set contains 2^{n+1} elements. The number of subsets of this set containing more than n elements is equal to

(a) 2^{n-1}

(b) 2^{n}

(c) 2^{n+1}

(d) 2^{2n}

Q15. If two sets A and B are having 99 elements in common, then the number of elements common to each of the sets A × B and B × A are

(a) 299

(b) 992

(c) 100

(d) 18

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*Answer Key*

*Answer Key*

01. | (b) | 06. | (a) | 11. | (c) |

02. | (a) | 07. | (a) | 12. | (a), (b) |

03. | (d) | 08. | (b) | 13. | (c) |

04. | (c) | 09. | (b) | 14. | (d) |

05. | (a), (b) | 10. | (d) | 15. | (b) |