Why does the air pressure inside a capped syringe increase if the volume decreases from 15cm3 to 10cm3 ???????

Answer 1

PV = nRT

You have decreased V, leaving everything the same, so the pressure has to go up.

From the point of view of kinetic theory, when you reduce the volume you have more molecules in each cm3, giving more collisions with the walls. Since the temperature is the same, the collisions are the same, but more of them means more pressure.