JEE Mains · Maths · STD 11- 2. Relation and Function
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 \(2^{15}\)
- B \(2^{18}\)
- C \(2^{12}\)
- D \(2^{10}\)
Answer & Solution
Correct Answer
(A) \(2^{15}\)
Step-by-step Solution
Detailed explanation
\(A\, = \,\left\{ {x\, \in \,Z\,:\,{2^{(x\, + 2)({x^2} - 5x + 6)}}\, = \,1} \right\}\) \({2^{(x\, + 2)({x^2} - 5x + 6)}}\, = \,{2^0}\, \Rightarrow \,x\, = \, - \,2,2,3\) \(A\, = \,\{ - 2\,,\,2\,,3\} \) \(B\, = \,\{ x\, \in \,Z\,:\, - \,3\,\, < \,\,2x\, - \,1\, < \,9\} \)…
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