Let Z be the set of integers. If A=x∈Z : 2^(x+2x2-5x+6)=1 and B={x∈Z :- 3< 2x-1<9}, then the number of subsets of the set A×B, is :

Correct answer: (D) 2^15. Given 2^(x+2x-2x-3)=1=2^0⇒x=-2, 2, 3. ∴nA=3 Again, -3<2x-1<9⇒-1<x<5 ⇒x=0, 1, 2, 3, 4 ∴nB=5 ∴n A×B=3×5=15 ∴Number of subset of A×B=2^15

Q43 / 90 · JEE Main 2019 (12 Jan Shift 2) · Mathematics

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
$2^{12}$
B
$2^{10}$
C
$2^{18}$
Correct answer
D
$2^{15}$

Solution

Given $2^{(x + 2) (x - 2) (x - 3)} = 1 = 2^{0} \Rightarrow x = - 2, 2, 3$ .

$∴ n (A) = 3$

Again, $- 3 < 2 x - 1 < 9 \Rightarrow - 1 < x < 5$

$\Rightarrow x = 0, 1, 2, 3, 4$

$∴ n (B) = 5$

$∴ n (A \times B) = 3 \times 5 = 15$

$∴$ Number of subset of $A \times B = 2^{15}$

Hence, the correct answer is option: 'D'.

Relevant Questions

Let and . Then the number of elements, in the relation is _______.05 Apr, 2026 (E)Questions on number of relations and sets
Let . Let R be a relation on the set given by if and only if divides and . Then the number of elements in R is _______.02 Apr, 2026 (E)Questions on number of relations and sets
Let R be a relation defined on the set by . Then the number of elements in R is24 Jan, 2026 (M)Questions on number of relations and sets
The number of elements in the relation is22 Jan, 2026 (E)Questions on number of relations and sets
Let be the set of the first 11 natural numbers. Then the number of elements in and the product of all elements of is even is .22 Jan, 2026 (E)Questions on number of relations and sets
The number of relations, defined on the set , which are both reflexive and symmetric, is equal to:21 Jan, 2026 (M)Questions on number of relations and sets

Let Z be the set of integers. If A=x∈Z : 2x+2x2-5x+6=1 and B={x∈Z :- 3< 2x-1<9}, then the number of subsets of the set A×B, is :

Solution

Relevant Questions

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 :