QJEEM19Ma626e: JEE Main 2019 Mathematics - Class 11 JEEM19Ma626e Solution: Let Z be the set of integers. If A = {x Z : 2 (x + 2) (x 2 5x + …

Question

Verified Solution • 2025–26 Session moderate

Let Z be the set of integers.
If A = {x

\in

Z : 2^{(x + 2) (x² $-$ 5x + 6)} = 1} and
B = {x

\in

Z :

-

3 < 2x

-

1 < 9},
then the number of subsets of the set A

\times

B, is

Accepted Answer

A ={x

\in

z : 2^{(x+2)(x² $-$ 5x + 6)} = 1}

2^{(x+2)(x² $-$ 5x + 6)} = 2⁰

\Rightarrow

x =

-

2, 2, 3

A = {

-

2, 2, 3}

B = {x

\varepsilon

Z :

-

< 2x

-

1 < 9}

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

A

\times

B has is 15 elements so number of subsets of A

\times

B is 2¹⁵.

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