How will you know if the transistor is working or faulty?

Answer 1

Impossible to give a specific answer without more information. Is it a BJT or a FET?

Most general answer is you first have to understand the circuit using the transistor and what it's supposed to do. Then,

1. Check that the power supply voltages are correct.

2. Check that the DC biases are correct.

3. Check that the input signal is correct.

4. Check the output.

But you have to know in advance what to expect.

Answer 2

Sometimes this can be determined by measurement of the signals in the circuit containing the transistor.

Sometimes this requires special test equipment like transistor testers or transistor curve tracers, often this requires removal of the transistor from the circuit.

In one extremely difficult case I had to custom build an in-circuit curve tracer and perform a tedious good board/bad board comparison, walking through the circuit in the schematic looking at the same points in the circuit of both boards until what had originally looked like a tiny disturbance in the output circuits traced back to a shorted component way back in the input circuits (and in most cases that component was not even a transistor, but it destroyed thousands of dollars of transistors on each bad board before it was located and replaced).