Sets-Quiz-1

Sets Quiz-1

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}, B={a,b}, then A×B mapped A to B is

•  {(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

Q2.If A={n:(^n3+5n2+2⁄_n is an integer and itself is an integer}, then the number of elements in the set A, is

•  1
•  2
•  3
•  4

Solution

Q3.  Out of 800 boys in a school 224 played cricket, 240 played hockey and 336 played basketball. Of the total, 64 played both basketball and hockey; 80 played cricket and basketball and 40 played cricket and hockey; 24 played all the three games. The number of boys who did not play any game is

•  160
•  240
•  216
•  128

Solution

Q4. If A={θ∶cos⁡θ>-1/2,0≤θ≤π} and B={θ∶sin⁡ θ>1/2,π/3≤θ≤π}, then

•  A∩B={θ∶π/3≤θ≤2π/3}
•  A∩B={θ∶-π/3≤θ≤2π/3}
•  A∪B={θ:-5π/6≤θ≤5π/6}
•  A∪B={θ∶0≤θ≤π/6}

Solution

Q5.The void relation on a set A is

•  Reflexive
•  Symmetric and transitive
•  Reflexive and symmetric
•  Reflexive and transitive

Solution

Q6. Two points P and Q in a plane are related if OP=OQ, where O is a fixed point. This relation is

•  Partial order relation
•  Equivalence relation
• Reflexive but not symmetric
•  Reflexive but not transitive

Solution
b) equivalence relation is a binary relation that is reflexive, symmetric and transitive

Q7.{n(n+1)(2n+1):n∈Z}⊂

•  {6k∶k∈Z}
•  {12k∶k∈Z}
•  {18k∶k∈Z}
•  {24k∶k∈Z}

Solution

Q8.Let A={1,2,3,4}, and let R={(2,2),(3,3),(4,4),(1,2)} be a relation on A. Then, R is

•  Reflexive
•  Symmetric
•  Transitive
•  None of these

Solution

Q9.If A and B are two sets, then A∩(A∪B) equals

•  A
•  B
•  ϕ
•  None of these

Solution

Q10. Let U be the universal set for sets A and B such that n(A)=200,n(B)=300 and n(A∩B)=100. Then, n(A'∩B') is equal to 300, provided that n(U) is equal to

•  600
•  700
•  800
• 900

Solution