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NDA 2 2025 Maths, question 43

Topic: Algebra

Q43

Let A=A= {−3,−2,−1,0,1,2,3-3,-2,-1,0,1,2,3} and B=B= {0,1,4,90,1,4,9}. How many elements does the subset of A×BA\times B corresponding to the relation R=R= {(x,y):∣x∣<y(x,y):|x|<y} have, where x∈Ax\in A and y∈By\in B?

  1. (a) 99
  2. (b) 1212
  3. (c) 1515Correct answer
  4. (d) 1616

Solution.

Answer: (c) 1515

  1. Count allowed x for each y.
  2. For y=0 there are none; for y=1 only x=0 works; for y=4 and y=9 all seven x-values work.
  3. The total is 0+1+7+7=15.