Sets-Quiz-10

Sets Quiz-10

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. If A={1,2,3,4}, then the number of subsets of A that contain the element 2 but not 3, is

•  16
•  4
•  8
•  24

Solution

Q2.Let R be a relation defined on S, the set of squares on a chess board such that xRy iff x and y share a common side. Then, which of the following is false for R?

•  Reflexive
•  Symmetric
•  Transitive
•  All the above

Solution

Q3.  Let R_1 be a relation defined by R₁={(a,b)│a≥b,a,b∈R}. Then, R₁ is

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

Solution

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

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

Solution

Q5.The finite sets A and B have m and n elements respectively. if the total number of subsets of A is 112 more than the total number of subsets of B, then the volume of m is

•  7
•  9
•  10
•  12

Solution

Q6.In a battle 70% of the combatants lost one eye, 80% an ear, 75% an arm, 85% a leg, x% lost all the four limbs. The minimum value of x is

•  10
•  12
• 15
•  None of these

Solution
a) 10

Q7.Let A be a set represented by the squares of natural number and x,y are any two elements of A. Then,

•  x-y∈A
•  xy∈A
•  x+y∈A
•  x/y∈A

Solution

Q8.If n(A) denotes the number of elements in the set A and if n(A)=4,n(B)=5 and n(A∩B)=3, then n[(A×B)∩(B×A)] is equal to

•  8
•  9
•  10
•  11

Solution

Q9.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

Q10. Let A={x:x is a multiple of 3} and B={x:x is a multiple of 5}. Then, A∩Bis given by

•  {3, 6, 9, ...…}
•  {5, 10, 15, 20, .......}
•  {15, 30, 45, ......}
• None of these

Solution