Step 1: Plan an elimination route.
Instead of testing the four options one by one from the start, we first pick the pairs we are surest about. Each sure pair removes the options that disagree with it. We then confirm the survivor against the remaining pairs.
Step 2: Use pair A.
Tarh means the first design or composition of a painting. Hence A goes with IV. This removes options 1 and 4. Options still alive: option 2, option 3.
Step 3: Use pair B.
Rangamizi is the colouring stage, from rang (colour). Hence B goes with III. This removes option 3. Options still alive: option 2.
Step 4: Use pair C.
Chiharanama comes from chehra (face), so it is a portrait. Hence C goes with II. No option is removed by this pair because every option still agrees with it. Options still alive: option 2.
Step 5: Use pair D.
Nigaar Khana is the royal painting workshop. Hence D goes with I. No option is removed by this pair because every option still agrees with it. Options still alive: option 2.
Step 6: Why each rejected option fails.
Option 1 fails at A (it says I, but IV is the right partner), B (it says II, but III is the right partner), C (it says III, but II is the right partner), D (it says IV, but I is the right partner).
Option 3 fails at B (it says I, but III is the right partner), C (it says III, but II is the right partner), D (it says II, but I is the right partner).
Option 4 fails at A (it says III, but IV is the right partner), B (it says IV, but III is the right partner), C (it says I, but II is the right partner), D (it says II, but I is the right partner).
Step 7: Confirm the survivor.
Only option 2 is left. Reading it against all four verified pairs, A-IV, B-III, C-II, D-I, shows a complete match. The other options each break at least one verified pair, so none of them can be correct.
Final Answer:
The only option that survives every check is option 2.
\[ \boxed{2} \]