Class JEE Mathematics Sets, Relations, and Functions Q #1062
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4 Marks 2019 JEE Main 2019 (Online) 12th January Evening Slot MCQ SINGLE
Let $Z$ be the set of integers. If $A = {x \in Z : 2(x + 2) (x^2 - 5x + 6) = 1}$ and $B = {x \in Z : -3 < 2x - 1 < 9}$, then the number of subsets of the set $A \times B$, is
(A) $2^{12}$
(B) $2^{18}$
(C) $2^{10}$
(D) $2^{15}$
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Correct Answer: D
Explanation
Given $A = {x \in Z : 2(x+2)(x^2 - 5x + 6) = 1}$.
Since $2(x+2)(x^2 - 5x + 6) = 1$, we can rewrite it as $2(x+2)(x^2 - 5x + 6) = 2^0$.
This implies that $x = -2, 2, 3$, so $A = {-2, 2, 3}$.
Also, $B = {x \in Z : -3 < 2x - 1 < 9}$.
Adding 1 to all sides, we get $-2 < 2x < 10$.
Dividing by 2, we get $-1 < x < 5$.
Thus, $B = {0, 1, 2, 3, 4}$.
Now, $A \times B$ has $3 \times 5 = 15$ elements.
The number of subsets of $A \times B$ is $2^{15}$.

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