11th Grade > Mathematics
SETS MCQs
:
B
Try taking some values of A and B
We'll see that A - B = A ∩ ¯B .
:
B
n(A ∪ B) = n(A) + n(B) - n(A ∩B) = 3 + 6 - 1 (A∩B)
Since maximum number of elements in A ∩ B = 3
∴ Minimum number of elements in A ∪ B = 9 - 3 = 6 .
:
C
n(A∪B) = n(A)+n(B)−n(A∩B)
We have, 70 = 37 + 52 - n(A∩B)
n(A∩B) = 19.
:
B
Since every rectangle, rhombus and square is parallelogram so
F1=F2∪F3∪F4
:
A
x2=16⇒x=±4
2x=6⇒x=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 = {}.
:
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
:
D
Intelligence cannot be defined for students in a class. Hence, the group of intelligent students is not a well defined collection.
:
C
Number of subsets of A = nC0 + nC1 + .............+ nCn = 2n
:
C
Number of subsets of A = nC0 + nC1 + .............+ nCn = 2n
:
A
x2=16⇒x=±4
2x=6⇒x=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 = {}.