Step 1: Understand the concept of different types of thermodynamic systems.
In thermodynamics, systems are classified based on their ability to exchange energy and matter with the surroundings. Additionally, systems can be classified based on phases present.
Step 2: Define a closed system.
A closed system can exchange only energy (like heat or work) with surroundings but not matter. Therefore, closed system corresponds to:
\[
(a) \rightarrow (v)
\]
Step 3: Define an open system.
An open system can exchange both energy and matter with surroundings. Hence:
\[
(b) \rightarrow (i)
\]
Step 4: Define an isolated system.
An isolated system cannot exchange either energy or matter with surroundings. Therefore:
\[
(c) \rightarrow (ii)
\]
Step 5: Define a homogeneous system.
A homogeneous system consists of only one phase and has uniform composition throughout. Thus:
\[
(d) \rightarrow (iii)
\]
Step 6: Define a heterogeneous system.
A heterogeneous system consists of two or more phases and has non-uniform composition. Hence:
\[
(e) \rightarrow (iv)
\]
Step 7: Combine all matches and select the correct option.
Putting all together:
\[
(a)-(v),\ (b)-(i),\ (c)-(ii),\ (d)-(iii),\ (e)-(iv)
\]
This corresponds to option \((4)\).