A) \[{{2}^{15}}\]
B) \[{{2}^{18}}\]
C) \[{{2}^{12}}\]
D) \[{{2}^{10}}\]
Correct Answer: A
Solution :
\[A=\left\{ x\in z:{{2}^{(x+2)({{x}^{2}}-5x+6)}}=1 \right\}\] |
\[{{2}^{(x+2)({{x}^{2}}-5x+6)}}={{2}^{0}}\] |
\[\Rightarrow \] \[x=-2,\,\,2,\,\,3\] |
\[A=\left\{ -2,\,\,2,\,\,3 \right\}\] |
\[B=\left\{ x\in z:-3<2x-1<9 \right\}\] |
\[B=\{0,1,2,3,4\}\] |
Hence, \[A\times B\]has 15 elements. |
So number of subsets of \[A\times B\] is \[{{2}^{15}}.\] |
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