Which Bluetooth mode rejects connection requests from any device nearby?

The mode that rejects connection requests from any device nearby is known as non-pairable mode. In this mode, a Bluetooth device will not accept any pairing requests, meaning it does not allow any other devices to connect to it. This is useful in scenarios where the user wants to maintain privacy and prevent unwanted connections, as the device remains hidden and does not engage in pairing protocols.

In contrast, discoverable mode allows other devices to see the device and send pairing requests, while pairable mode is explicitly designed for accepting connections under a controlled environment. Connectable mode, on the other hand, indicates the device's ability to accept connections but does not prevent or restrict connection requests as non-pairable mode does. Therefore, non-pairable mode is the correct answer for a scenario where no connection requests will be entertained.