Test: Cartesian Product Of Sets - JEE MCQ

Test: Cartesian Product Of Sets - JEE MCQ

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20 Questions MCQ Test Chapter-wise Tests for JEE Main & Advanced - Test: Cartesian Product Of Sets

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Test: Cartesian Product Of Sets - Question 1

If A = Φ, n(B) = 4 then n(A × B) is

Detailed Solution for Test: Cartesian Product Of Sets - Question 1

n(A × B) = n(A) × n(B)

Test: Cartesian Product Of Sets - Question 2

If A = {-1, 1, 2}, then n(A × A × A) =

Detailed Solution for Test: Cartesian Product Of Sets - Question 2

n(A) = 3
n(A × A × A) = n(A) * n(A) * n(A)
n(A × A × A) = 3 * 3 * 3 = 27

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Test: Cartesian Product Of Sets - Question 3

The set O of odd positive integers less than 10 can be expressed by ______

Detailed Solution for Test: Cartesian Product Of Sets - Question 3

Test: Cartesian Product Of Sets - Question 4

Given A = {1, 2} and B = {5, 6, 7} then A × B =

Detailed Solution for Test: Cartesian Product Of Sets - Question 4

A = {1, 2} and B = {5, 6, 7}
A x B = {(1, 5), (1, 6), (1, 7), (2, 5), (2, 6), (2, 7)}

Test: Cartesian Product Of Sets - Question 5

If A = {3, 5},then A × A × A is

Detailed Solution for Test: Cartesian Product Of Sets - Question 5

A = {3, 5}
A × A = {(3, 3), (3, 5), (5, 3), (5, 5)}
A × (A × A) = {(3, 3, 3), (3, 3, 5), (3, 5, 3), (3, 5, 5), (5, 3, 3), (5, 3, 5), (5, 5, 3), (5, 5, 5)}

Test: Cartesian Product Of Sets - Question 6

If A = {3, 4} and B = {5, 6} then B × A is

Detailed Solution for Test: Cartesian Product Of Sets - Question 6

Cartesian product B x A of two sets A and B is given by

B x A = {(a, b): a ϵ B, b ϵ A}

Hence, B x A = {(5, 3), (5, 4), (6, 3), (6, 4)}

Test: Cartesian Product Of Sets - Question 7

If (x – 1, y + 1) = (5, 6), then the value of x and y is given by

Detailed Solution for Test: Cartesian Product Of Sets - Question 7

(x – 1, y + 1) = (5, 6)
x – 1 = 5
x = 6
y + 1 = 6
y = 5

Test: Cartesian Product Of Sets - Question 8

Given A = {X : X ∈ N. - 1 < X < 1} 1 and B = {0, 1, 2, 3, 4, 5, 6} then A × B is

Detailed Solution for Test: Cartesian Product Of Sets - Question 8

A = Φ
B = {0, 1, 2, 3, 4, 5, 6}
A × B = Φ (Cartesian product with an empty set is an empty set)

Test: Cartesian Product Of Sets - Question 9

If n(A) = 3, n(B) = 2 and if (x, 4), (y, 5), (z, 4) are three distinct elements of A × B, then

Detailed Solution for Test: Cartesian Product Of Sets - Question 9

n(A) = 3
n(B) = 2
(x, 4), (y, 5), (z, 4) are three distinct elements of A x B
So, x, y, z ϵ A
4, 5 ϵ B
A = {x, y, z}
B = {4, 5}

Test: Cartesian Product Of Sets - Question 10

If A × B = {(x, a), (x, b), (y,a), (y, b)} then A =

Detailed Solution for Test: Cartesian Product Of Sets - Question 10

A × B = {(x, a), (x, b), (y, a), (y, b)}
A = {x, y}

Test: Cartesian Product Of Sets - Question 11

If A = {2, 4} and B = {5, 6} then (A x B) ∪ Φ will be:

Detailed Solution for Test: Cartesian Product Of Sets - Question 11

A = {2, 4}
B = {5, 6}
A x B = {(2, 5), (2, 6), (4, 5), (4, 6)}
(A x B) U Φ = A x B = {(2, 5), (2, 6), (4, 5), (4, 6)}

Test: Cartesian Product Of Sets - Question 12

The cardinality of the power set of {0, 1, 2 . . ., 10} is ______.

Detailed Solution for Test: Cartesian Product Of Sets - Question 12

The power set has 2n elements. For n = 11, size of power set is 2048.

Test: Cartesian Product Of Sets - Question 13

If= {a, b}, B = {c, d}, C = {d, e}, then {(a, c),(a, d),(a, e),(b, c),(b, d),(b, e)} is equal to

Detailed Solution for Test: Cartesian Product Of Sets - Question 13

A+2B=7------(1)
3A+2B=9------(2)
Subtracting (2) from (1)
we get, 2A=2
A=1
Subsitute A=1 in (1)
1+2B=7
2B=6
B=3
therefore A = 1, B = 3

Test: Cartesian Product Of Sets - Question 14

If set A has 4 elements and B = {5, 6}, then the number of elements in A x B are

Detailed Solution for Test: Cartesian Product Of Sets - Question 14

n(A) = 4
B = {5, 6}
n(B) = 2
n(A x B) = n(A)*n(B) = 4*2 = 8

Test: Cartesian Product Of Sets - Question 15

If P, Q and R are subsets of a set A, then × (P' ∪ Q' )' =

Detailed Solution for Test: Cartesian Product Of Sets - Question 15

× ( P'Q' )'=× [( P' )' ∩ ( Q' )' ] =× (∩ Q) = (× P) ∩ (× Q)

Test: Cartesian Product Of Sets - Question 16

If a set contains 3 elements then the number of subsets is

Detailed Solution for Test: Cartesian Product Of Sets - Question 16

N = 3
No. of subsets = 2N = 23 = 8

Test: Cartesian Product Of Sets - Question 17

If A, B and C are any three sets, then A × (B ∪ C) is equal to

Detailed Solution for Test: Cartesian Product Of Sets - Question 17

It is distributive law.

Test: Cartesian Product Of Sets - Question 18

If A = {1, 2, 4}, B = {2, 4, 5}, C = {2, 5}, then (A - C) × (B - C) is

Detailed Solution for Test: Cartesian Product Of Sets - Question 18

Correct option is D)

A={1,2,4}, B={2,4,5}, C={2,5}

A−C={1,4}

B−C={4}

(A−C)×(B−C)={1,4}×{4}

={1,4},{4,4}.

Test: Cartesian Product Of Sets - Question 19

Which of the following two sets are equal?

Detailed Solution for Test: Cartesian Product Of Sets - Question 19

To determine if two sets are equal, we need to check if they have exactly the same elements.

Let's analyze each option: a) A = {1, 2} and B = {1} - In this case, set A has two elements: 1 and 2, while set B has only one element: 1. Therefore, the two sets are not equal.

b) A = {1, 2} and B = {1, 2, 3} - Here, set A has two elements: 1 and 2, while set B has three elements: 1, 2, and 3. Thus, the two sets are not equal.

c) A = {1, 2, 3} and B = {2, 1, 3} - In this case, both sets have the same three elements: 1, 2, and 3. The order of the elements does not matter in set theory, so {1, 2, 3} and {2, 1, 3} represent the same set. Therefore, the two sets are equal.

d) A = {1, 2, 4} and B = {1, 2, 3} - In this case, set A has three elements: 1, 2, and 4, while set B has three elements: 1, 2, and 3.

Since the elements 4 and 3 are different, the two sets are not equal.

Test: Cartesian Product Of Sets - Question 20

If A = {1, 2, 3, 4}, B = {3, 4} and C = {2, 3} then n ((A ∩ B) x C)

Detailed Solution for Test: Cartesian Product Of Sets - Question 20

A = {1, 2, 3, 4}, B = {3, 4} and C = {2, 3}
(A ∩ B) = {3, 4} C = {2, 3}
(A ∩ B x C) = {3,4} x {2,3}
⇒ {(3,2) (3,3) (4,2) (4,3)}

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