Sets-Quiz-6

Sets Quiz-6

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 R and S be two relations on a set A. Then, which one of the following is not true?

•  R and S are transitive, then R∪S is also transitive
•  R and S are transitive, then R∩S is also transitive
•  R and S are reflexive, then R∩S is also reflexive
•  R and 𝑆 are symmetric, then 𝑅∪𝑆 is also symmetric

Solution
a) R and S are transitive, then R∪S is also transitive

Q2.In a city 20% of the population travels by car, 50% travels by bus and 10% travels by both car and bus. Then, persons travelling by car or bus is

•  80%
•  40%
•  60%
•  70%

Solution

Q3.  Consider the following statements: (i) Every reflexive relation is antisymmetric (ii) Every symmetric relation is antisymmetric Which one among (i) and (ii) is true?

•  (i) alone is true
•  (ii) alone is true
•  Both (i) and (ii) true
•  Neither (i) and (ii) is true

Solution
d) Neither (i) and (ii) is true

Q4. If a N={a x∶x∈N} and b N ∩c N=d N, where b,c∈N are relatively prime, then

•  d=bc
•  c=bd
•  b=cd
•  None of these

Solution

Q5.Let A={1,2,3,4},B={2,4,6}. Then, the number of sets C such that A∩B⊆C⊆A ∪B is

•  6
•  9
•  8
•  10

Solution

Q6. 

•  R-{0}
•  R-{0,1,3}
• R-{0,-1,-3}
•  R-{0,-1,-3,+1/2}

Solution

Q7.In a class of 175 students the following data shows the number of students opting one or more subjects. Mathematics 100; Physics 70; Chemistry 40; Mathematics and Physics 30; Mathematics and Chemistry 28; Physics and Chemistry 23; Mathematics, Physics and Chemistry 18. How many students have offered Mathematics alone?

•  35
•  48
•  60
•  72

Solution

Q8.If X and Y are two sets, then X∩(Y∪X)' equals

•  X
•  Y
•  ϕ
•  None of these

Solution

Q9.In a class of 30 pupils 12 take needls work, 16 take physics and 18 take history. If all the 30 students take at least one subject and no one takes all three, then the number of pupils taking 2 subjects is

•  16
•  6
•  8
•  20

Solution

Q10. Let A and B be two non-empty subsets of a set X such that A is not a subset of B. Then,

•  A is a subset of complement of B
•  B is a subset of A
•  A and B are disjoint
• A and the complement of B are non-disjoint

Solution
d) A and the complement of B are non-disjoint