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JEE Main202522 Jan 2025Morning ShiftMathematicsSets and RelationsActual

Let A= 1,2,3, , 10 and B= m n : m, n A, m n . and . gcd (m, n)=1 . Then n(B) is equal to :

Options

  1. A36
  2. B31
  3. C37
  4. D29

Correct answer

B. 31

Step-by-step solution

aligned & A = 1,2, , 10 & B m n = m , n A , m < n , gcd ( m , n )=1 & n ( B ) aligned n =2 1 2 n =3 1 3 , 2 3 array ll n =4 & 1 4 , 3 4 n =5 & 1 5 , 2 5 , 3 5 , 4 5 array array ll n =6 & 1 6 , 5 6 n =7 & 1 7 , 2 7 , 3 7 , 4 7 , 5 7 , 6 7 n =8 & 1 8 , 3 8 , 5 8 , 7 8 array array ll n =9 & 1 9 , 2 9 , 4 9 , 5 9 , 7 9 , 8 9 n =10 & 1 10 , 3 10 , 7 10 , 9 10 n ( B )=31 array

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