Two-Body Friction question from JEE Main 2014 (9 Apr, Shift 1)

Answer: (c)

1. Standard method: the force on A that just makes it slip equals limiting friction, $\mu m_A g = 12$ N, so $\mu g = 3$ m/s$^2$.
2. When force is on B, A moves only through friction: $a_{max} = \mu g = 3$ m/s$^2$.
3. $F = (m_A + m_B)a_{max} = 9 \times 3$
4. $F = 27$ N, so the answer is (c).