1. Concept used: Electron gain enthalpy trend

Electron gain enthalpy generally becomes less negative down a group, but in some cases the change is very small, so the values are nearly the same.

We check each pair:

2. Pair (A): Rb and Cs

Rb and Cs are alkali metals. Their electron gain enthalpies are both very small and negative, and for heavy alkali metals these values are nearly the same.

So, (A) is correct.

3. Pair (B): Na and K

For Na and K, the electron gain enthalpies are not identical and not usually considered nearly the same in standard periodic trend data. There is a noticeable difference between them.

So, (B) is incorrect.

4. Pair (C): Ar and Kr

Ar and Kr are noble gases. Their electron gain enthalpies are positive (since addition of electron is unfavorable), and these values are nearly the same / almost identical in the qualitative trend discussion.

So, (C) is correct.

5. Pair (D): I and At

I and At are halogens. Although electron gain enthalpy becomes less negative down the group, the values for I and At are not generally treated as identical/nearly same in the standard JEE trend comparison.

So, (D) is incorrect.

6. Select the correct option

Correct pairs are: $(A) \text{ and } (C)$

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

7. Comparison with stored answer

Stored correct answer = C

My derived answer = C

So, they agree.