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11th Grade > Mathematics

SETS MCQs

Total Questions : 30 | Page 2 of 3 pages
Question 11.


If A = [ x:x is a multiple of 3] and B = [x:x is a multiple of 5] , then A - B is (¯A means complement of A)


  1.     ¯A
  2.     A  ¯B
  3.     ¯A  ¯B
  4.     AB
 Discuss Question
Answer: Option B. -> A  ¯B
:
B

Try taking some values of A and B
We'll see that  A - B  = A  ¯B


Question 12.


Sets A and B have 3 and 6 elements respectively. What can be the minimum number of elements in (A U B )


  1.     3
  2.     6
  3.     9
  4.     18
 Discuss Question
Answer: Option B. -> 6
:
B

n(A B) = n(A) + n(B) - n(A B) = 3 + 6 - 1 (AB)


Since maximum number of elements in A B = 3


Minimum number of elements in A B = 9 - 3 = 6 .


Question 13.


In a group of 70 people, 37 like coffee, 52 like tea and each person like at least one of the two drinks. The number of persons liking both coffee and tea is:


  1.     16
  2.     13
  3.     19
  4.     20
 Discuss Question
Answer: Option C. -> 19
:
C

n(AB) = n(A)+n(B)n(AB)


We have, 70 = 37 + 52 - n(AB)
n(AB) = 19.


Question 14.


Let F1 be the set of all parallelograms, F2 the set of rectangles, F3 the set of rhombuses, F4 the set of squares and F5 the set of trapeziums in a plane, then F1 is equal to 


  1.     F2F3
  2.     F2F3F4
  3.     F3F4
  4.     F2F1
 Discuss Question
Answer: Option B. -> F2F3F4
:
B

Since every rectangle, rhombus and square is parallelogram so


F1=F2F3F4


Question 15.


A={x:xR, x2=16 and 2x=6} can be represented in the roster form as _________ .


  1.     A = {}
  2.     A = { 14, 3, 4 }
  3.     A = { 3 }
  4.     A = { 4 }
 Discuss Question
Answer: Option A. -> A = {}
:
A

x2=16x=±4
2x=6x=3


There is no value of x which satisfies both the given equations. The set A is an empty set or a null set.


Thus, A = {}.


Question 16.


In a town of 10,000 families it was found that 40% family buy newspaper A, 20% buy newspaper B and 10% families buy newspaper C, 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspapers, then number of families which buy A only is


  1.     3100
  2.     3300
  3.     2900
  4.     1400
 Discuss Question
Answer: Option B. -> 3300
:
B

n(A) = 40% of 10,000 = 4,000


n(B) = 20% of 10,000 = 2,000


n(C) = 10% of 10,000 = 1,000


n(A ∩ B) = 5% of 10,000 = 500


n(B ∩ C) = 3% of 10,000 = 300


n(C ∩ A) = 4% of 10,000 = 400


n(A ∩ B ∩ C) = 2% of 10,000 = 200


We want to find the number of families which buy only A = n(A) - [n(A ∩ B) + n(A ∩ C) - n(A ∩ B ∩ C)]


=4000 - [500 + 400 - 200] = 4000 - 700 = 3300


Question 17.


The group of intelligent students in a class is __________.


  1.     a null set
  2.     a finite set
  3.     a well defined collection
  4.     not a well defined collection
 Discuss Question
Answer: Option D. -> not a well defined collection
:
D

Intelligence cannot be defined for students in a class. Hence, the group of intelligent students is not a well defined collection.


Question 18.


If a set A has n  elements, then the total number of subsets of A is  


  1.     n
  2.     n2
  3.     2n
  4.     2n
 Discuss Question
Answer: Option C. -> 2n
:
C

Number of subsets of A = nC0nC1  + .............+ nCn2n


Question 19.


If a set A has n  elements, then the total number of subsets of A is  


  1.     n
  2.     n2
  3.     2n
  4.     2n
 Discuss Question
Answer: Option C. -> 2n
:
C

Number of subsets of A = nC0nC1  + .............+ nCn2n


Question 20.


A={x:xR, x2=16 and 2x=6} can be represented in the roster form as _________ .


  1.     A = {}
  2.     A = { 14, 3, 4 }
  3.     A = { 3 }
  4.     A = { 4 }
 Discuss Question
Answer: Option A. -> A = {}
:
A

x2=16x=±4
2x=6x=3


There is no value of x which satisfies both the given equations. The set A is an empty set or a null set.


Thus, A = {}.


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