Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
KCET2024MathematicsSets and Relations

Two finite sets have m and n elements respectively. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of m and n , respectively are

Options

  1. A7,6
  2. B5,1
  3. C6,3
  4. D8,7

Correct answer

C. 6,3

Step-by-step solution

Let set A have m elements and set B have n elements Now, 2^m-2^n=56 2^n (2^ m-n -1 )=8 7 2^n (2^ m-n -1 )=2^3 7 On comparing both sides, we get 2^n=2^3 or 2^ m-n -1=7 Now, n=3 ....(i) So, 2^ m-n -1=7 2^ m-n =8 m-n=3 ....(ii) From Eqs. (i) and (ii), we get m=6 and n=3

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 KCET PYQs