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Normally IC Testers available are for digital ICs. To test 741 you can just do some basic gain tests if you have nice equipment. But best is to design some application and see if it works in that. The companies usually fully test all the EC specs before shipping the part.
an analog ic tester should suffice... otherwise to test it manually you need to check the cmrr and slew rate basically,and also the offset voltages and currents if you are particular. to check cmrr u may need separate circuits for common mode and difference mode signalling... to measure slew rate a high frequency square wave(1mhz) will suffice, u need to measure the tilt at the o/p.... but rather than going for these things an ic tester is simplest
I have never seen any analog IC tester, but I believe there is, and it must be hard to find and expensive.
Not all of the commercial semiconductor parts are tested at factories.
In my experience, I build a simple oscillator using the IC with the basic circuit in the datasheet or any book about opamp. The output via buffer drives the LED when I have no frequency meter, and the oscillator is calculated and built for the frequency of about 1Hz, with frequency meter, the oscillator can be built with high frequency.
Once the oscillator works, then the IC is good. I have never disappointed with this way of testing op amp.