SETS-QUIZ-4

MATHEMATICS SETS QUIZ-4

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. If A={1,2,3},B={a,b}, then A×B mapped A to Bis

•  {(1,a),(2,b),(3,b)}
•  {(1,b),(2,a)}
•  {(1,a),(1,b),(2,a),(2,b),(3,a),(3,b)}
•  {(1,a),(2,a),(2,b),(3,b)}

Solution
Given, A={1,2,3},B={a,b} ∴ A×B={(1,a),(1,b),(2,a),(2,b),(3,a),(3,b)}

Q2.If P is the set of all parallelograms, and T is the set of all trapeziums, then P∩T is

•  P
•  T
•  ϕ
•  None of these

Solution
Clearly, P⊂T ∴P∩T=P

Q3.  If A={4,6,10,12} and R is a relation defined on A as “two elements are related iff they have exactly one common factor other than 1”. Then the relation R is

•  Antisymmetric
•  Only transitive
•  Only symmetric
•  Equivalence

Solution
Clearly, R={(4,6),(4,10),(6,4),(10,4)(6,10),(10,6),(10,12),(12,10)} Clearly, R is symmetric (6,10)∈R and (10,12)∈R but (6,12)∉R So, R is not transitive Also, R is not reflexive

Q4. 

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

Solution

Q5.If A is a non-empty set, then which of the following is false?
      p∶ There is at least one reflexive relation on A
      q∶ There is at least one symmetric relation on A

•  p alone
•  q alone
•  Both p and q
•  Neither p nor q

Solution
The identity relation on a set A is reflexive and symmetric both. So, there is always a reflexive and symmetric relation on a set

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

•  4000
•  3300
•  4200
•  5000

Solution

Q7.

•  1
•  2
•  3
•  4

Solution

Q8.Consider the set A of all determinants of order 3 with entries 0 or 1 only. Let B be the subset
       of A consisting of all determinants with value 1. Let C be the subset of the set of all
       determinants with value -1. Then

• C is empty
•  B has as many elements as C
•  A=B∪C
•  B has twice as many elements as C

Solution
Since the value of a determinant charges by minus sign by interchanging any two rows or columns. Therefore, corresponding to every element ∆ of B there is an element ∆' in C obtained by interchanging two adjacent rows (or columns) in ∆. It follows from this that n(B)≤n(C) Similarly, we have n(C)≤n(B) Hence, n(B)=n(C) ⇒B=C

Q9.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
Since R is reflexive relation on A ∴(a,a)∈R for all a∈A ⇒ The minimum number of ordered pairs in R is n Hence, m≥n

Q10. For any two sets A and B, A-(A-B) equals

•  A
•  A-B
•  A∩B
•  A^C∩B^C

Solution