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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

If the difference between the number of subsets of two sets A and B...

If the difference between the number of subsets of two sets AA and BB is 120120, then n(A\timesB)isequalton \left(A \timesB\right) is equal to

Options

  1. A2121
  2. B2525
  3. C1818
  4. D2424

Correct answer

A. 2121

Step-by-step solution

Let,& n\left(A\right) = \alpha & n\left(B\right) = \beta
Given,~\left|{2}^{\alpha} - {2}^{\beta}\right| = 120 ⇒ \left(\alpha, \beta\right) ≡ \left(7,3\right), \left(3,7\right)<br/><br />∴ n ( A \times B ) = 7 \times 3 = 21
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