JEE PYQ: Sets And Relations Question 16
Question 16 - 2019 (12 Jan Shift 1)
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:
(1) $2^{15}$
(2) $2^{18}$
(3) $2^{12}$
(4) $2^{10}$
Show Answer
Answer: (1)
Solution
Let $x \in A$, then
$2^{(x+2)(x^2 - 5x + 6)} = 1 \Rightarrow (x + 2)(x - 2)(x - 3) = 0$
$x = -2, 2, 3$
$A = {-2, 2, 3}$
Then, $n(A) = 3$
Let $x \in B$, then
$-3 < 2x - 1 < 9$
$-1 < x < 5$ and $x \in Z$
$\therefore B = {0, 1, 2, 3, 4}$
$n(B) = 5$
$n(A \times B) = 3 \times 5 = 15$
Hence, Number of subsets of $A \times B = 2^{15}$
BETA
