Cartesian Product of Sets

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JEE Main 2013

LEVELJEE Main

Let A and B two sets containing 2 elements and 4 elements respectively. The number of subsets of $A \times B$ having 3 or more elements is

JEE Main 2019 (12 January)

LEVELJEE Main

Let $Z$ be the set of integers. If $A = {x \in Z : 2^{(x + 2) (x^{2} - 5 x + 6)} = 1}$ and $B = {x \in Z : - 3 < 2 x - 1 < 9}$ , then the number of subsets of the set $A \times B$ , is :

(A)

2^{18}

(B)

2^{10}

(C)

2^{15}

(D)

2^{12}

JEE Main 2021 (27 Aug Shift 2)

LEVELJEE Main

Let $Z$ be the set of all integers, $A = {(x, y) \in Z \times Z : (x - 2)^{2} + y^{2} \leq 4}$ , $B = {(x, y) \in Z \times Z : x^{2} + y^{2} \leq 4}$ and $C = {(x, y) \in Z \times Z : (x - 2)^{2} + (y - 2)^{2} \leq 4}$ . If the total number of relation from $A \cap B$ to $A \cap C$ is $2^{p}$ , then the value of $p$ is :

JEE Main 2023 (08 Apr Shift 1)

LEVELJEE Main

Let the number of elements in sets $A$ and $B$ be five and two respectively. Then the number of subsets of $A \times B$ each having at least 3 and at most 6 elements is

JEE Main 2023 (10 Apr Shift 2)

LEVELJEE Main

Let $A = {2, 3, 4}$ and $B = {8, 9, 12}$ . Then the number of elements in the relation $R = {((a_{1}, b_{1}), (a_{2}, b_{2})) \in (A \times B, A \times B) : a_{1} divides b_{2} and a_{2} divides b_{1}}$ is

JEE Main 2023 (11 Apr Shift 2)

LEVELJEE Main

Let $A = {1, 3, 4, 6, 9}$ and $B = {2, 4, 5, 8, 10}$ . Let $R$ be a relation defined on $A \times B$ such that $R = {((a_{1}, b_{1}), (a_{2}, b_{2})) : a_{1} \leq b_{2} and b_{1} \leq a_{2}}$ . Then the number of elements in the set $R$ is

Comprehension Passage

Let

S = {1, 2, 3, 4, 5, 6}

and

X

be the set of all relations

R

from

S

S

that satisfy both the following properties: i.

R

has exactly 6 elements. ii. For each

(a, b) \in R

, we have

∣ a - b ∣ \geq 2

. Let

Y = {R \in X : The range of R has exactly one element}

and

Z = {R \in X : R is a function from S to S}

. Let

n (A)

denote the number of elements in a set

A

Question 1:

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let A and B two sets containing 2 elements and 4 elements respectively. The number of subsets of A×B having 3 or more elements is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let Z be the set of integers. If A={x∈Z:2(x+2)(x2−5x+6)=1} and B={x∈Z:−3<2x−1<9}, then the number of subsets of the set A×B, is :

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let the number of elements in sets A and B be five and two respectively. Then the number of subsets of A×B each having at least 3 and at most 6 elements is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let A={2,3,4} and B={8,9,12}. Then the number of elements in the relation R={((a1​,b1​),(a2​,b2​))∈(A×B,A×B):a1​ divides b2​ and a2​ divides b1​} is

Comprehension Passage

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If n(X)=mC6​, then the value of m is ________.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If the value of n(Y)+n(Z) is k2, then ∣k∣ is ________.

Which of the following options is the only INCORRECT combination ?

Let A and B two sets containing 2 elements and 4 elements respectively. The number of subsets of $A \times B$ having 3 or more elements is

Let $Z$ be the set of integers. If $A = {x \in Z : 2^{(x + 2) (x^{2} - 5 x + 6)} = 1}$ and $B = {x \in Z : - 3 < 2 x - 1 < 9}$ , then the number of subsets of the set $A \times B$ , is :

Let the number of elements in sets $A$ and $B$ be five and two respectively. Then the number of subsets of $A \times B$ each having at least 3 and at most 6 elements is

Let $A = {2, 3, 4}$ and $B = {8, 9, 12}$ . Then the number of elements in the relation $R = {((a_{1}, b_{1}), (a_{2}, b_{2})) \in (A \times B, A \times B) : a_{1} divides b_{2} and a_{2} divides b_{1}}$ is

If $n (X) =^{m} C_{6}$ , then the value of $m$ is ________.

If the value of $n (Y) + n (Z)$ is $k^{2}$ , then $∣ k ∣$ is ________.