Step 1: Find oxidation state of nitrogen in \(N_2\).
In elemental form, oxidation state is always zero. Therefore,
\[
N_2 \rightarrow 0
\]
Thus,
\[
(i)\rightarrow (r)
\]
So, option (A) is incorrect.
Step 2: Find oxidation state of nitrogen in \(NO\).
Let oxidation state of nitrogen be \(x\). Oxygen has oxidation state \(-2\).
\[
x+(-2)=0
\]
\[
x=+2
\]
Hence,
\[
NO \rightarrow +2
\]
Thus,
\[
(ii)\rightarrow (s)
\]
So, option (B) is incorrect.
Step 3: Find oxidation state of nitrogen in \(N_2O\).
Let oxidation state of nitrogen be \(x\).
\[
2x+(-2)=0
\]
\[
2x=+2
\]
\[
x=+1
\]
Hence,
\[
N_2O \rightarrow +1
\]
Thus,
\[
(iii)\rightarrow (p)
\]
So, option (C) is incorrect.
Step 4: Find oxidation state of nitrogen in \(NO_2\).
Let oxidation state of nitrogen be \(x\).
\[
x+2(-2)=0
\]
\[
x-4=0
\]
\[
x=+4
\]
Hence,
\[
NO_2 \rightarrow +4
\]
Thus,
\[
(iv)\rightarrow (q)
\]
Step 5: Compare all matches.
The correct matching among the given options is only
\[
(iv)\rightarrow(q)
\]
Step 6: Verify the option carefully.
Option (D) correctly represents
\[
NO_2 \rightarrow +4
\]
Step 7: Final conclusion.
Therefore, the correct answer is option (D).
\[
\boxed{(iv)\rightarrow(q)}
\]