InvalidMonitorStateException

This exception is thrown when we call wait(), notify() or notifyAll() methods from any object when we are not having lock on that object.

This exception is a sub-class of RuntimeException. So we donot need to handle this.
Also this is the reason why the signatures of  wait(), notify() or notifyAll() do not have this exception declared .

Thread.run() and Thread.start()

Thread.start() essentially calls run() method only.
If we call Thread.run() directly, it will be executed in the same thread and a new thread would not be created.
So the purpose of multithreading is not fulfilled.