Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
KVPY2016MathematicsSets and Relations

Let A₁, A₂ , A_ m be non-empty subsets of 1,2,3, , 100 satisfying the following conditions: (1) the numbers | A ₁ |, | A ₂ |, , | A _ m | are distinct; (2) A ₁, ~A ₂, , A _ m are pairwise disjoint. (Here A denotes the number of elements in the set A .) Then the maximum possible value of m is

Options

  1. A13
  2. B14
  3. C15
  4. D16

Correct answer

A. 13

Step-by-step solution

The possibility is array l | A ₁ |=1 ; | A ₂ |=2 ; | A ₃ |=3 ; ., | A _ m |= m 1+2+3+ + m 100 Because all are disjoint m ( m +1) 2 100 m < 14 array 14^ th set will have the same size as that of one of the previous sets So, m =13

Practice Sets and Relations on Quantrex Academy →

More from Sets and Relations

Let A and B be two subsets of = 1, 2, 3, -------, 44, 45 such that A = x: x is divisible by 3 and 4 B = x: x is a perfect square number Then n(B - A) equals 2026Given the sets A = 1,2,3 ; B = 2,3,5 and C = 4,5,6 identify Which of the following statements is incorrect . 2026If A = x : x is the first three odd numbers B = 2x + 3 : 0 x true 2026The set expression A (B (A' B')) is equivalent to 2026Let C be the set of all the circles in a plane. If R = (C₁, C₂) C C C₁ and C₂ intersect , then which of the following statements is TRUE? 2026If A = a, b, c, d, e, f , then the number of subsets of A which contains at least 2 elements is 2026If A = 1, 2, 3, 4, , 10 , then the number of non-empty subsets of A containing only even number is 2026If n(A) = 2 and the number of relations from set A to set B is 1024 , then n(B) is 2026 Full Sets and Relations list All KVPY PYQs