Let Z be the set of integers. If A = \ x in Z:2^(x + 2)( x^2 - 5x + 6 ) = 1 \ and = \ x in Z : $- 3

(c) : Given, A = \ x in Z:2^(x + 2)( x^2 - 5x + 6 ) = 1 \ \ Therefore 2^(x + 2)( x^2 - 5x + 6 ) = 2^0 \ => (x + 2)( x^2 - 5x + 6 ) = 0 \ => (x + 2)(x - 2)(x - 3) = 0 => x = 2, - 2,3 \ Therefore A = \ - 2,2,3\ Also, $B = \ x in Z: - 3

Let Z be the set of integers. If A = { x in Z:2^{(x + ... | Relation (Mathematics)

JEE Mains (12$\ ^{th\ }$ Jan $2^{nd\ }$ Shift 2019) 12th January Shift 2

Mathematics

Let

Z

be the set of integers. If

A = \left\{ x \in Z:2^{(x + 2)\left( x^{2} - 5x + 6 \right)} = 1 \right\}

and

= \{ x \in Z

- 3 < 2x - 1 < 9\}

, then the . number of subsets of the set

A \times B

2^{18}

2^{12}

2^{15}

2^{10}

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Correct Answer:

Explanation

(c) : Given, $A = \left\{ x \in Z:2^{(x + 2)\left( x^{2} - 5x + 6 \right)} = 1 \right\}$ $\\ \therefore 2^{(x + 2)\left( x^{2} - 5x + 6 \right)} = 2^{0} \\ \Rightarrow (x + 2)\left( x^{2} - 5x + 6 \right) = 0 \\ \Rightarrow (x + 2)(x - 2)(x - 3) = 0 \Rightarrow x = 2, - 2,3 \\ \therefore A = \{ - 2,2,3\}\\$ 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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