SETS-QUIZ-5

MATHEMATICS SETS QUIZ-5

Dear Readers,

As per analysis for previous years, it has been observed that students preparing for JEE MAINS find Mathematics out of all the sections to be complex to handle and the majority of them are not able to comprehend the reason behind it. This problem arises especially because these aspirants appearing for the examination are more inclined to have a keen interest in Mathematics due to their ENGINEERING background. 

Furthermore, sections such as Mathematics are dominantly based on theories, laws, numerical in comparison to a section of Engineering which is more of fact-based, Physics, and includes substantial explanations. By using the table given below, you easily and directly access to the topics and respective links of MCQs. Moreover, to make learning smooth and efficient, all the questions come with their supportive solutions to make utilization of time even more productive. Students will be covered for all their studies as the topics are available from basics to even the most advanced. 

Q1. Let A and B have 3 and 6 elements respectively. What can be the minimum number of elements in A∪B?

•  3
•  6
•  9
•  18

Solution
A∪B will contain minimum number of elements if A⊂B and in that case, we have n(A∪B)=n(B)=6

Q2.

•  A∩B=ϕ
•  A∩B is a singleton set
•  A∩B contains two elements only
•  A∩B contains three elements only

Solution
Clearly, y²=x and y=|x| intersect at (0,0),(1,1) and (-1,-1). Hence, option (d) is correct

Q3.  If A and B are two given sets, then A∩(A∩B)^c is equal to

•  A
•  B
•  Φ
•  A∩B^c

Solution

Q4. 

•  3
•  4
•  5
•  6

Solution

Q5.In an office, every employee likes at least one of tea, coffee and milk. The number of
    employees who like only tea, only coffee, only milk and all the three are all equal.
    The number of employees who like only tea and coffee, only coffee and milk and only tea
    and milk are equal and each is equal to the number of employees who like all the three.
    Then a possible value of the number of employees in the office is

•  65
•  90
•  77
•  85

Solution

Q6. A and B are any two non-empty sets and A is proper subset of B. If n(A)=5, then find the minimum possible value of n(A∆B)

•  is 1
•  is 5
•  Can't be determined
•  None of these

Solution
It is given that A is a proper subset of B ∴A-B=ϕ⇒n(A-B)=0 We have, n(A)=5. So, minimum number of elements in B is 6 Hence, the minimum possible value of n(A Δ B) is n(B)-n(A)=6-5=1

Q7.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
We have, A∩B=ϕ and A⊂C ⇒A∩B=ϕ and A∪C=C ∴n(A∪B∪C)=n(A∪C∪B)=n(C∪B)=n(B∪C)

Q8.If A={(x,y) ∶y=4/x,x≠0} and
    B={(x,y):x^2+y^2=8,x,y∈R}, then

•  A∩B=ϕ
•  A∩B contains one point only
•  A∩B contains two points only
•  A∩B contains 4 points only

Solution
 

Q9.Let A be the non-void set of the children in a family. The relation 'x is a brother of y' on A is

•  Reflexive
•  Symmetric
•  Transitive
•  None of these

Solution
No Solution available

Q10. 

•  {3,5,7,11,13,17,19}
•  {2,3,5}
•  {2,3,5,7,11,13,17}
•  {3,5,7}

Solution