SETS-QUIZ-1

MATHEMATICS SETS QUIZ-1

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. 

•  1
•  2
•  3
•  4

Solution

Q2.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

•  18
•  25
•  7
•  32

Solution
 

Q3.  Let R₁ be a relation defined by R₁={(a,b)│a≥b,a,b∈R}. Then, R₁ is

•  Reflexive, transitive but not symmetric
•  An equivalence relation on R
•  Symmetric, transitive but not reflexive
•  Neither transitive not reflexive but symmetric

Solution
For any a∈R, we have a≥a Therefore, the relation R is reflexive. R is not symmetric as (2,1)∈R but (1,2)∉R. The relation R is transitive also, because (a,b)∈R,(b,c)∈R imply that a≥b and b≥c which in turn imply that a≥c

Q4. 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

•  2⁹⁹
•  99²
•  100
•  18

Solution
∵ Number of elements common to each set is 99×99=99²

Q5.If X={4ⁿ-3n-1∶n∈N} and Y={9(n-1):n∈N}, then X∪Y is equal to

•  X
•  None of these
•  N
•  Y

Solution

Q6. If A and B are two sets such that n(A)=7,n(B)=6 and (A∩B)≠ϕ. Then the greatest possible value of         n(A Δ B), is

•  12
•  11
•  13
•  10

Solution

Q7.An investigator interviewed 100 students to determine the performance of three drinks milk,
    coffee and tea. The investigator reported that 10 students take all three drinks milk, coffee
    and tea; 20 students take milk and coffee, 30 students take coffee and tea, 25 students take
    mile and tea, 12 students take milk only, 5 students take coffee only and 8 students take tea only.
    Then, the number of students who did not take any of the three drinks, is

• 10
•  25
•  20
•  30

Solution

Q8.If R={(a,b):|a+b|=a+b} is a relation defined on a set{-1,0,1}, then R is

•   Reflexive
•   Anti symmetric
•   Symmetric
•  Transitive

Solution

Q9.If sets A and B are defined as A={(x,y):y=1/x,0≠x∈R}, B={(x,y):y=-x,x∈R}, then

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

Solution
The set A is the set of all points on the hyperbola xy=1 having its two branches in the first
and third quadrants, while the set B is the set of all points on y=-x which
lies in second and four quadrants. These two curves do not intersect. Hence, A∩B=ϕ.

Q10. If R is a relation from a set A to a set B and S is a relation from B to a setC, then the relation SoR

•  Is from A to C
•  Is from C to A
•  Does not exist
•  None of these

Solution
No solution available