JEE Main 2025 Jan 22 Shift 1, Mathematics Q17: Set

$ A=\{1,2,\ldots,10\} $

$ B=\left\{\dfrac{m}{n}:m,n\in A,\;m < n,\;gcd(m,n)=1\right\} $

$ n(B) $

$ n=2\qquad \left\{\dfrac{1}{2}\right\} $

$ n=3\qquad \left\{\dfrac{1}{3},\dfrac{2}{3}\right\} $

$ n=4\qquad \left\{\dfrac{1}{4},\dfrac{3}{4}\right\} $

$ n=5\qquad \left\{\dfrac{1}{5},\dfrac{2}{5},\dfrac{3}{5},\dfrac{4}{5}\right\} $

$ n=6\qquad \left\{\dfrac{1}{6},\dfrac{5}{6}\right\} $

$ n=7\qquad \left\{\dfrac{1}{7},\dfrac{2}{7},\dfrac{3}{7},\dfrac{4}{7},\dfrac{5}{7},\dfrac{6}{7}\right\} $

$ n=8\qquad \left\{\dfrac{1}{8},\dfrac{3}{8},\dfrac{5}{8},\dfrac{7}{8}\right\} $

$ n=9\qquad \left\{\dfrac{1}{9},\dfrac{2}{9},\dfrac{4}{9},\dfrac{5}{9},\dfrac{7}{9},\dfrac{8}{9}\right\} $

$ n=10\qquad \left\{\dfrac{1}{10},\dfrac{3}{10},\dfrac{7}{10},\dfrac{9}{10}\right\} $

$ n(B)=31 $