In peroxides, the oxidation state of O is -1 and they give H2O2, with dilute acids, and have peroxide linkage.

In KO2,  +1 + (x× 2)=0.
       x = -1/2 (thus, it is a superoxide, not a peroxide.)
In BaO2,  +2 + (x ×2) = 0
x = -1
Thus, it is a peroxide. Only it gives H2O2 when reacts with dilute acids and has peroxide linkage as
Ba2+ [O - O]2- (peroxide linkage)
 InMnO2 andNO2, Mn and N exhibit variable oxidation states, thus, the oxidation state of O in these is - 2. Hence, these are not peroxides. Thus, it is clear, that among the given molecules only BaO2 is a peroxide.

Introduction:
In this response, we will discuss the compounds given and determine which one is a peroxide. Peroxides are compounds that contain an oxygen-oxygen single bond (O-O). They are characterized by the presence of the peroxide ion (O22-), which has an oxygen-oxygen single bond and a negative charge.

Explanation:
Let's analyze each of the compounds given and determine if they are peroxides:

1. KO2:
Potassium superoxide (KO2) is a compound that contains the peroxide ion (O22-). It is a peroxide due to the presence of the oxygen-oxygen single bond. Therefore, KO2 is a peroxide.

2. BaO2:
Barium peroxide (BaO2) is another compound that contains the peroxide ion (O22-). It is a peroxide due to the presence of the oxygen-oxygen single bond. Therefore, BaO2 is a peroxide.

3. MnO2:
Manganese dioxide (MnO2) is not a peroxide. It does not contain the peroxide ion or an oxygen-oxygen single bond. MnO2 is an oxide of manganese and does not exhibit peroxide properties.

4. NO2:
Nitrogen dioxide (NO2) is not a peroxide. It does not contain the peroxide ion or an oxygen-oxygen single bond. NO2 is a covalent compound composed of nitrogen and oxygen atoms.

Summary:
From the given compounds, both KO2 and BaO2 are peroxides as they contain the peroxide ion (O22-) and an oxygen-oxygen single bond. MnO2 and NO2 are not peroxides as they lack the peroxide ion and the oxygen-oxygen single bond. Therefore, the correct answer is either KO2 or BaO2, depending on the options provided.