Analyze Statement (I)

Statement (I): Oxygen being the first member of group 16 exhibits only $-2$ oxidation state.

This is incorrect.

Oxygen does not exhibit only $-2$ oxidation state. It shows other oxidation states as well:

• In peroxides, oxygen has oxidation state $-1$ (e.g. $H_2O_2$)
• In superoxides, oxygen has oxidation state $-\frac{1}{2}$ (e.g. $KO_2$)
• In compounds with fluorine, oxygen shows positive oxidation states:
  • In $OF_2$, oxygen is $+2$
  • In $O_2F_2$, oxygen is $+1$

Therefore, Statement (I) is false.

Analyze Statement (II)

Statement (II): Down group 16, stability of $+4$ oxidation state decreases and $+6$ oxidation state increases.

This is also incorrect.

In group 16, as we move down the group, the inert pair effect becomes more significant. Because of this:

• the lower oxidation state $+4$ becomes more stable
• the higher oxidation state $+6$ becomes less stable

For example:

• Sulfur commonly shows stable $+6$ state
• Tellurium and polonium show increasing stability of $+4$ relative to $+6$

Hence the statement given is the reverse of the correct trend.

Therefore, Statement (II) is false.

Choose the correct option

• Statement (I): Incorrect
• Statement (II): Incorrect

So, the correct option is:

$\boxed{\text{B}}$ : Both Statement I and Statement II are incorrect.

Comparison with stored correct answer

Stored correct answer = B

My derived answer = B

Hence, they agree.