A) \[{{2}^{18}}\]
B) \[{{2}^{12}}\]
C) \[{{2}^{15}}\]
D) \[{{2}^{10}}\]
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\[{{2}^{15}}.\]
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