Sets-Quiz-14

Sets Quiz-14

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. Which of the following is true?

•  A∩ϕ=A
•  A∩ϕ=ϕ
•  A∩ϕ=U
•  A∩ϕ=A'

Solution

Q2.In a rehabilitation programme, a group of 50 families were assured new houses and compensation by the government. Number of families who got both is equal to the number of families who got neither of the two. The number of families who got new houses is 6 greater than the number of families who got compensation. How many families got houses?

•  22
•  28
•  23
•  25

Solution

Q3.  In a class of 35 students, 17 have taken Mathematics, 10 have taken Mathematics but not Economics. If each student has taken either Mathematics or Economics or both, then the number of students who have taken Economics but not Mathematics is

•  7
•  25
•  18
•  32

Solution

Q4. If n(A×B)=45, then n(A) cannot be

•  15
•  17
•  5
•  9

Solution

Q5.If A,B and C are three non-empty sets such that A and B are disjoint and the number of elements contained in A is equal to those contained in the set of elements common to the sets A and C, then n(A∪B∪C) is necessarily equal to

•  n(B∪C)
•  n(A∪C)
•  Both (a) and (b)
•  None of these

Solution

Q6.In the above question, the number of families which buy none of A,B and C is

•  4000
•  3300
• 4200
•  5000

Solution

Q7.Universal set, U={x:x⁵-6x⁴+11x³-6x²=0} And A={x:x²-5x+6=0} B={x:x²-3x+2=0} Then, (A∩B)' is equal to

•  {1, 3}
•  {1, 2, 3}
•  {0, 1, 3}
•  {0, 1, 2, 3}

Solution

Q8.If A⊆B, then B∪A is equal to

•  B∩A
•  A
•  B
•  None of these

Solution

Q9.Let X and Y be the sets of all positive divisors of 400 and 1000 respectively (including 1 and the number). Then, n(X∩Y) is equal to

•  4
•  6
•  8
•  12

Solution

Q10. Let X be the set of all engineering colleges in a state of Indian Republic and R be a relation on X defined as two colleges are related iff they are affiliated to the same university, then R is

•  Only reflexive
•  Only symmetric
•  Only transitive
• Equivalence

Solution