Concept:
Many industrial processes use specific catalysts. Knowledge of important catalysts is frequently tested in coordination chemistry and industrial chemistry.
Step 1: Checking option (A).
\[
[RhCl(PPh_3)_3]
\]
is Wilkinson's catalyst.
It is used for hydrogenation of alkenes.
Hence this pair is correct.
Step 2: Checking option (B).
\[
TiCl_4 + Al(C_2H_5)_3
\]
forms Ziegler-Natta catalyst.
It is used for polymerisation of alkenes.
Hence this pair is correct.
Step 3: Checking option (C).
The Haber-Bosch process for ammonia manufacture uses finely divided iron catalyst with promoters such as
\[
K_2O,\quad Al_2O_3
\]
and not \(V_2O_3\).
Vanadium pentoxide
\[
V_2O_5
\]
is used in the Contact Process.
Therefore this pair is incorrect.
Step 4: Checking option (D).
Nickel is a common hydrogenation catalyst.
Example:
\[
\text{Vegetable oil}
\rightarrow
\text{Vanaspati ghee}
\]
Hence this pair is correct.
Therefore,
\[
\boxed{(C)}
\]
is the wrong pair.