Sets-Quiz-4

Sets Quiz-4

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. For real numbers x and y, we write x Ry⇔x-y+√2 is an irrational number. Then, the relation R is

•  Reflexive
•  Symmetric
•  Transitive
•  None of these

Solution

Q2.A survey shows that 63% of the Americans like cheese whereas 76% like apples. If x% of the Americans like both cheese and apples, then

•  x=39
•  x=63
•  39≤x≤63
•  None of these

Solution

Q3.  If R={(a,b):|a+b|=a+b} is a relation defined on a set {-1,0,1}, then R is

•  Reflexive
•  Symmetric
•  Anti symmetric
•  Transitive

Solution

Q4. From 50 students taking examinations in Mathematics, Physics and Chemistry, 37 passed Mathematics, 24 Physics and 43 Chemistry. At most 19 passed Mathematics and Physics, at most 29 passed Mathematics and Chemistry and at most 20 passed Physics and Chemistry. The largest possible number that could have passed all three examinations is

•  11
•  12
•  13
•  14

Solution

Q5.If A={1,3,5,7,9,11,13,15,17},B={2,4…,18} and N is the universal set, then A'∪((A∪B)∩B') is

•  A
•  N
•  B
•  None of these

Solution

Q6. Let A and B be two sets, then (A∪B)^'∪(A^'∩B)is equal to

•  A'
•  A
• B'
•  None of these

Solution

Q7.If S is the set of squares and R is the set of rectangles, then (S∪R)-(S∩S) is

•  S
•  R
•  Set of squares but not rectangles
•  Set of rectangles but not squares

Solution

Q8.If A={ϕ,{ϕ}}, then the power set of A is

•  A
•  {ϕ,{ϕ},A}
•  {ϕ,{ϕ},{{ϕ}},A}
•  None of these

Solution
c) Power set of A contains 2ⁿ which come out to be 4. Power set will be {ϕ,{ϕ},{{ϕ}},A}

Q9.If A is a finite set having n elements, then P(A) has

•  2n elements
•  2ⁿ elements
•  n elements
•  None of these

Solution
b) Number of elements in power set is 2ⁿ

Q10. Let A be a set of compartments in a train. Then the relation R defined on A as aRb iff "a and b have the link between them”, then which of the following is true for R?

•  Reflexive
•  Symmetric
•  Transitive
• Equivalence

Solution
b) Relation R will be symmetric

Written by: AUTHORNAME

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