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Solution


Q.

Let A = {1, 2, 3, ..., 10} and B={mn:m,n∈A, m<n and gcd(m,n)=1}.

Then n(B) is equal to :          [2025]
1 36  
2 31  
3 37  
4 29  

Ans.

(2)

We have, A = {1, 2, 3, ..., 10}

B={mn:m,n∈A, m<n and gcd(m,n)=1}

For  m = 1, n = 2, 3, ..., 10   ⇒ 9 cases

       m = 2, n = 3, 5, 7, 9      ⇒ 4 cases

       m = 3, n = 4, 5, 7, 8, 10 ⇒ 5 cases

       m = 4, n = 5, 7, 9         ⇒ 3 cases

       m = 5, n = 6, 7, 8, 9      ⇒ 4 cases

       m = 6, n = 7                  ⇒ 1 cases

       m = 7, n = 8, 9, 10       ⇒ 3 cases

       m = 8, n = 9                 ⇒ 1 cases

       m = 9, n = 10               ⇒ 1 cases

∴    n(B) = 31.