IIT JEE Main Maths -Unit 1 -Sets - Exam Style Questions- New Syllabus

Ans. (1)

Sol. \( A = \{1, 2, \dots, 10\} \)

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

\( n(B) \)

\( n = 2 : \left\{ \frac{1}{2} \right\} \)

\( n = 3 : \left\{ \frac{1}{3}, \frac{2}{3} \right\} \)

\( n = 4 : \left\{ \frac{1}{4}, \frac{3}{4} \right\} \)

\( n = 5 : \left\{ \frac{1}{5}, \frac{2}{5}, \frac{3}{5}, \frac{4}{5} \right\} \)

\( n = 6 : \left\{ \frac{1}{6}, \frac{5}{6} \right\} \)

\( n = 7 : \left\{ \frac{1}{7}, \frac{2}{7}, \frac{3}{7}, \frac{4}{7}, \frac{5}{7}, \frac{6}{7} \right\} \)

\( n = 8 : \left\{ \frac{1}{8}, \frac{3}{8}, \frac{5}{8}, \frac{7}{8} \right\} \)

\( n = 9 : \left\{ \frac{1}{9}, \frac{2}{9}, \frac{4}{9}, \frac{5}{9}, \frac{7}{9}, \frac{8}{9} \right\} \)

\( n = 10 : \left\{ \frac{1}{10}, \frac{3}{10}, \frac{7}{10}, \frac{9}{10} \right\} \)

\( n(B) = 1 + 2 + 2 + 4 + 2 + 6 + 4 + 6 + 4 = 31 \)