High frequency transformer
You can test it at 50 Hz but the voltage you apply will have to be much lower than the voltage you can apply at 50 kHz. So, if at 50 kHz there is marginal core saturattion at (say) 10 volts p-p then at 50 Hz, you can use a voltage of 10 mVp-p.

If you put 20 Vp-p on it it would saturate too much and make the test results meaningless.

Other than that, Faraday's law of induction doesn't care about frequency when it comes to transformers, so it will work just fine. Don't even think about testing it at AC line voltage.


  My teacher said that I can test my transformer at 50hz, the output
  will be same because frequency has no effect on it.


Either your teacher is an idiot or you didn't listen correctly.