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

JEE Main · 2019 · 12 Jan 2019 · Shift 2 · Sets Relations and Functions

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 :

Answer: (A)

For

A

2^{(x + 2) (x^{2} - 5 x + 6)} = 1

needs

(x + 2) (x^{2} - 5 x + 6) = 0

, i.e.

(x + 2) (x - 2) (x - 3) = 0

, so

A = {- 2, 2, 3}

with three elements. For

B

- 3 < 2 x - 1 < 9

gives

- 1 < x < 5

, so the integers are

B = {0, 1, 2, 3, 4}

, five elements. Then

A \times B

has

3 \times 5 = 15

elements, and the number of its subsets is

2^{15}

JEE Main · 2019 · 12 Jan 2019 · Shift 2 · Single correct option