JEE Main 12 Jan 2019 Evening Question 30
Question: 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 [JEE Main Online Paper Held On 12-Jan-2019 Evening]
Options:
A) $ 2^{18} $
B) $ 2^{12} $
C) $ 2^{15} $
D) $ 2^{10} $
Show Answer
Answer:
Correct Answer: C
Solution:
- Given, $ A={x\in Z:{2^{(x+2)(x^{2}-5x+6)}}=1} $
$ \therefore $ $ {2^{(x+2)(x^{2}-5x+6)}}=2^{0} $
$ \Rightarrow $ $ (x+2)(x^{2}-5x+6)=0 $
$ \Rightarrow $ $ (x+2)(x-2)(x-3)=0 $
$ \Rightarrow $ $ x=2,-2,3 $
$ \therefore $ $ A={-2,2,3} $
Also, $ B={x\in z:-3<2x-1<9} $ So, $ -3<2x-1<9\Rightarrow -2<2x<10 $
$ \Rightarrow $ $ -1<x<5 $
$ \therefore $ $ B={0,1,2,3,4} $
Thus, $ n(A\times B)=15 $
So, number of subsets of $ (A\times B) $ is $ 2^{15}. $
