1. Redox reaction definition

A reaction is redox if there is a change in oxidation numbers, i.e. oxidation and reduction occur simultaneously.

2. Check each option

Option A: Reaction of $H_2SO_4$ with $NaOH$

This is a neutralization reaction: $H_2SO_4 + 2NaOH \rightarrow Na_2SO_4 + 2H_2O$

Oxidation numbers:

• In $H_2SO_4$, $H = +1$, $O = -2$, so $S = +6$
• In $Na_2SO_4$, $S = +6$
• $Na$ remains $+1$, $H$ remains $+1$, $O$ remains $-2$

No oxidation number changes occur.

So, A is not a redox reaction.

Option B: Formation of ozone from atmospheric oxygen in presence of sunlight

Overall: $3O_2 \rightarrow 2O_3$

Oxidation number of oxygen:

• In $O_2$, oxygen is $0$
• In $O_3$, oxygen is also $0$

No change in oxidation number occurs.

So, B is not a redox reaction.

Option C: Combination of dinitrogen with dioxygen at $2000\,K$

Reaction: $N_2 + O_2 \rightarrow 2NO$

Oxidation numbers:

• In $N_2$, $N = 0$
• In $O_2$, $O = 0$
• In $NO$, $O = -2$, so $N = +2$

Changes:

• Nitrogen: $0 \to +2$ → oxidation
• Oxygen: $0 \to -2$ → reduction

Both oxidation and reduction occur.

So, C is a redox reaction.

Option D: Reaction of $[Co(H_2O)_6]Cl_3$ with $AgNO_3$

This is essentially precipitation of chloride ions: $[Co(H_2O)_6]Cl_3 + 3AgNO_3 \rightarrow [Co(H_2O)_6](NO_3)_3 + 3AgCl \downarrow$

Cobalt remains in the same oxidation state:

• In $[Co(H_2O)_6]^{3+}$, since $H_2O$ is neutral, $Co = +3$
• In product complex also $Co = +3$
• $Ag$ remains $+1$, $Cl$ remains $-1$

No oxidation number changes occur.

So, D is not a redox reaction.

3. Final conclusion

Only option C involves change in oxidation numbers, so it is the redox reaction.

$\boxed{\text{C}}$

4. Comparison with stored correct answer

Stored correct answer = C

My derived answer = C

They agree.