Recall the trend in group 14 oxides

As we move down group 14, the metallic character of the elements increases: $\text{C} < \text{Si} < \text{Ge} < \text{Sn} < \text{Pb}$

Therefore, the nature of their oxides changes from acidic to amphoteric/basic down the group.

Classify the given oxides

• $\mathrm{CO}$: This is a neutral oxide.
• $\mathrm{SiO}_2$: This is an acidic oxide.
• $\mathrm{GeO}_2$: Generally behaves mainly as an acidic oxide at JEE level.
• $\mathrm{GeO}$: This is a lower oxide; not the standard amphoteric choice here.
• $\mathrm{SnO}_2$: Amphoteric oxide.
• $\mathrm{PbO}_2$: Amphoteric oxide.

Check each option

Option A: $\mathrm{SnO}_2, \mathrm{CO}$

• $\mathrm{SnO}_2$ is amphoteric, but $\mathrm{CO}$ is neutral.
• So, A is incorrect.

Option B: $\mathrm{SiO}_2, \mathrm{GeO}_2$

• $\mathrm{SiO}_2$ is acidic.
• Hence B is incorrect.

Option C: $\mathrm{SnO}_2, \mathrm{PbO}_2$

• Both are amphoteric.
• So, C is correct.

Option D: $\mathrm{GeO}, \mathrm{GeO}_2$

• These are not the standard amphoteric pair in this list for JEE classification.
• So, D is incorrect.

Final answer

The amphoteric oxides are: $\boxed{\mathrm{SnO}_2 \text{ and } \mathrm{PbO}_2}$

Hence, the correct option is: $\boxed{\text{C}}$