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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 A and B be two sets. The set A has 2016 more subsets than B. If...

Let AA and BB be two sets. The set AA has 20162016 more subsets than B.B. If A∩BA \cap B has 33 members, then the number of members in A∪BA \cup B is

Options

  1. A1010
  2. B1111
  3. C1212
  4. D1313

Correct answer

D. 1313

Step-by-step solution

If Ahashasmmembersandmembers andBhashasnmembers,then<br/>members, then <br />{2}^{m} - {2}^{n} = 2016 = {2}^{5}. 63<br/><br />⇒ {2}^{n} \left({2}^{m - n} -1\right) =25(64−1)=25(26−1)<br/>{2}^{5} \left(64 - 1\right) = {2}^{5}\left({2}^{6} -1\right)<br />⇒ n = 5 and m - n = 6 ⇒ m = 11<br/>ThenumberofmembersinA∪B<br />The number of members in A \cup B
=11+5−3=13= 11 + 5 - 3 = 13
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