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NDA 2 2025 Maths, question 42

Topic: Algebra

Q42

Set XX contains 3n3n elements and set YY contains 2n2n elements, and they have nn elements in common. How many elements does (X−Y)×(Y−X)(X-Y)\times (Y-X) have?

  1. (a) 5n25n^{2}
  2. (b) 4n24n^{2}
  3. (c) 3n23n^{2}
  4. (d) 2n22n^{2}Correct answer

Solution.

Answer: (d) 2n22n^{2}

  1. Remove the intersection from each set: |X−Y|=3n−n=2n and |Y−X|=2n−n=n.
  2. A Cartesian product has the product of the two cardinalities, hence 2n² elements.