Sets-Quiz-12

Sets Quiz-12

Dear Readers,

Mathematics is an important subject in JEE ADVANCED and other engineering exams. In any engineering enterance exam, Mathematics carries weightage of 33% of questions. In mathematics a set is a collection of distinct elements. The elements that make up a set can be letters, numbers, points in space, lines, other geometrical shapes, variables, or even other sets. Two sets are equal if and only if they have precisely the same elements. With focused practice good marks can be fetched from this section. These questions are very important in achieving your success in JEE and Other Engineering Exams.

Q1. Let A be the set of all students in a school. A relation R is defined on A as follows: "aRb iff a and b have the same teacher”

•  Reflexive
•  Symmetric
•  Transitive
•  Equivalence

Solution

Q2.If A={x∶x is a multiple of 3} and, B={x∶x is a multiple of 5}, then A-B is

•  A̅∩B
•  A∩B̅
•  A̅∩B̅
•  (A∩B)'

Solution

Q3.  

•  3
•  4
•  5
•  6

Solution

Q4. Let A={1,2,3},B={3,4},C={4,5,6}. Then, A∪(B∩C) is

•  {3}
•  {1,2,3,4}
•  {1,2,5,6}
•  {1,2,3,4,5,6}

Solution
b) {1,2,3,4}

Q5.For any two sets A and B, if A∩X=B∩X=ϕ and A∪X=B∪X for some set X, then

•  A-B=A∩B
•  A=B
•  B-A=A∩B
•  None of these

Solution

Q6.Let R be a reflexive relation on a finite set A having n elements, and let there be m ordered pairs in R. Then,

•  m≥n
•  m≤n
• m=n
•  None of these

Solution

Q7.In a town of 10,000 families it was found that 40% families buy newspaper A,20% families buy newspaper B and 10% families buy newspaper C,5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspapers, then the number of families which buy A only is

•  3100
•  3300
•  2900
•  1400

Solution

Q8.Let R be a relation from a set A to a set B, then

•  R=A∪B
•  R=A∩B
•  R⊆A×B
•  R⊆B×A

Solution
c) R⊆A×B

Q9.If n(A∩B=10,n(B∩C)=20) and n(A∩C)=30, then the greatest possible value of n(A∩B∩C) is

•  15
•  20
•  10
•  4

Solution

Q10. For any three sets A₁,A₂,A₃, let B₁=A₁,B₂=A₂-A₁ and B₃=A₃-(A₂∪A₂ ), then which one of the following statement is always true

•  A₁∪A₂∪A₃⊃B₁∪B₂∪B₃
•  A₁∪A₂∪A₃=B₁∪B₂∪B₃
•  A₁∪A₂∪A₃⊂B₁∪B₂∪B₃
• None of these

Solution