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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Sets and Relations

NTA Abhyas 2020 · Mathematics · Sets and Relations

Let Z be the set of integers, if A = \ x ∈ ℤ: |x - 3|(x^ 2 - 5x +...

Let ZZ be the set of integers, if A={x∈Z:∣x−3∣(x2−5x+6)=1}A = \left\{x \in \mathbb{Z}: \left|x - 3\right|\left(x^{2} - 5x + 6\right) = 1\right\} and B={x∈Z:10<3x+1<22}B = \left\{x \in \mathbb{Z}: 10 < 3x + 1 < 22\right\}, then the number of subsets of the set A×BA \times B is

Options

  1. A26{2}^{6}
  2. B28{2}^{8}
  3. C215{2}^{15}
  4. D29{2}^{9}

Correct answer

A. 26{2}^{6}

Step-by-step solution

For& AA,

~\left|x - 3\right| = 1 ⇒ x = 2,4 or<br/>~or<br />x^{2} - 5x + 6 = 0 ⇒ x = 2,3butbutx \ne 3<br/><br />∴ A = \left\{2,4\right\}

For~BB,

B={4,5,6}B = \left\{4 ,5 , 6\right\}
n(A×B)=6n\left(A \times B\right) = 6

∴∴~number of subsets =26= {2}^{6}

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