Why does the rpm increases when the clutch is engaged?

When the clutch is engaged, it connects the engine to the transmission, allowing the engine's power to transfer to the wheels. This connection can cause the engine to work against a load, which can lead to an increase in RPM as the engine compensates for the resistance. Additionally, engaging the clutch usually involves applying throttle, which directly increases engine speed. Thus, the rise in RPM is a result of the engine's response to the load and throttle input.