What is the minimum input current I for which the transistor will begin to turn on?
I dont understand why the answer is the same as the current through the 47k resistor (I = 1.489µA). Wouldnt the answer be different, since the current at the junction spilts? (some goes to the base and rest through the resistor?)
It is dependent on device. High beta devices will take less base current for given collector current. It also depends what temp the transistor is at as this effects Vbe. Different devices have different Vbe.
I assume the 47k is across the b-e based on your question. Sounds like someone is assuming the 47k dominates the current drawn and the Vbe for start of conduction would be same for different devices (which is not true).