How to determine peroxy oxygen?
I have become familiar with many peroxide like Na2O2, BaO2, etc. But not able to recognise between 1 and 2. Is there any way for this type of question to recognise peroxide oxygen? 


Yes. In the exam, if you do not know whether (1) or (2) contains peroxy, simply look at the charges of Chromium if all the oxygen is  in the -2 oxidation state.

For $\ce{CrO5}$, if all the oxygen have a charge of -2, then Cr would have to have a charge of +10, which is impossible, therefore you know that some of the oxygen must have a charge of -1(peroxy). On the other hand, for $\ce{Cr2O3}$, Cr has a charge of +3, which is possible (Cr(III) salts are plenty)