I have actually given technical interviews for entry level engineers. Here is my list of questions:
1. Draw (on the chalkboard or whiteboard) an inverting amplifier using an op-amp.
1a. What is the gain?
1b. What is the input impedance?
1c. What is the output impedance?
1d. Why did you choose those values of input and feedback resistor?
1e. Discuss some of the limitations of this circuit (frequency response, gain limitations, gain stability (i.e. some op-amps are not stable at low gains), bias and offset currents and voltages, etc.
For more advanced engineers I would include more detailed aspects of the circuit.
One time some of us interviewers had a thing among ourselves to name as many 2nd and 3rd order error sources as we could, concerning op-amps. One guy came up with 22. The best I could do off the top-of-my head was 17 of them.
If you can name 15 2nd-order and 3rd-order error sources to an ideal op-amp and discuss how you could mitigate their effects, or why they wouldn't be a problem in certain circuits, you would impress the interviewer.
2. Draw a non-inverting amplifier using an op-amp.
2a, 2b, 2c, 2d, same as above.
Those are the basic 2 op-amp question groups. They may ask about active filters, but that is generally not for entry level engineers.
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