To solve this problem, we need to determine the force exerted by block A on block B.$\\$Given:$\\$• Force $F = 10 \,$N applied to block A.$\\$• Mass of block A $m_A = 2 \,$kg.$\\$• Mass of block B $m_B = 3 \,$kg.$\\$Since the surface is frictionless, both blocks will accelerate together.$\\$First, calculate the total mass of the system:$\\ m_{total} = m_A + m_B = 2 + 3 = 5 \,$kg.$\\$Next, calculate the acceleration of the system using Newton's second law:$\\ F = m_{total} \cdot a \\ 10 = 5 \cdot a \\ a = \frac{10}{5} = 2 \,$m/s$^2 \\$Now, calculate the force exerted by block A on block B.$\\$This force is responsible for accelerating block B.$\\$Using Newton's second law for block B:$\\ F_{AB} = m_B \cdot a \\ F_{AB} = 3 \cdot 2 = 6 \,$N$\\$Therefore, the force exerted by block A on block B is $6 \,$N.$\\$This corresponds to Option 1.