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JEE Main 201912 JanuaryEvening Shift
Exam
JEE Main
Year
2019
Date
12 January
Shift
Evening Shift
Subject
Mathematics
Chapter
Sets and Relations

JEE Main 2019 · 12 January · Evening Shift · Mathematics · Sets and Relations

Let Z be the set of integers. If A = \ x ∈ Z: 2 ^ (x + 2)( x ^ 2 -...

Let ZZ be the set of integers. If A={x∈Z:2(x+2)(x2−5x+6)=1}A = \left\{x \in Z: {2}^{\left(x + 2\right)\left({x}^{2} - 5x + 6\right)} = 1\right\} and B=x∈Z:−3<2x−1<9B = { x \in Z: - 3 < 2x - 1 < 9 }, then the number of subsets of the set A×BA \times B, is :

Options

  1. A212{2}^{12}
  2. B210{2}^{10}
  3. C218{2}^{18}
  4. D215{2}^{15}

Correct answer

D. 215{2}^{15}

Step-by-step solution

Given 2(x+2)(x−2)(x−3)=1=20⇒x=−2,2,3{2}^{\left(x + 2\right)\left(x - 2\right)\left(x - 3\right)} = 1 = {2}^{0} ⇒ x = - 2, 2, 3.

∴n(A)=3∴ n\left(A\right) = 3

Again, −3<2x−1<9⇒−1<x<5- 3 < 2x - 1 < 9 ⇒ - 1 < x < 5

⇒x=0,1,2,3,4⇒ x = 0, 1, 2, 3, 4

∴n(B)=5∴ n\left(B\right) = 5

∴n(A×B)=3×5=15∴ n\left(A \times B\right) = 3 \times 5 = 15

∴∴Number of subset of A×B=215A \times B = {2}^{15}

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