Step 1: What the question asks.
We must pick the items that truly belong to the basic structure of the Indian Constitution. The given list has five items, and we need the correct combination.
Step 2: What basic structure means.
The Supreme Court, in the famous Kesavananda Bharati case of $1973$, said some core features of the Constitution can never be removed, even by an amendment. These core features are called the basic structure.
Step 3: Check Fundamental Rights $(i)$.
Fundamental Rights are important, but courts have allowed limited changes to them. They are not counted as a separate fixed pillar of the basic structure in this list, so we leave $(i)$ aside here.
Step 4: Check Dual citizenship $(ii)$ and Supremacy of central cabinet $(v)$.
India follows single citizenship, not dual citizenship, so $(ii)$ is wrong. The cabinet is not supreme over the Constitution, so $(v)$ is also wrong. Both are removed.
Step 5: Check Federal system $(iii)$ and Secular character $(iv)$.
A federal set up, where power is shared between the Centre and the States, is a recognised part of the basic structure. Secular character, meaning the State treats all religions equally, is also a recognised part. So $(iii)$ and $(iv)$ both stay.
Step 6: Combine the correct items.
Only $(iii)$ and $(iv)$ survive every test. That matches the option giving just these two.
Step 7: Final choice.
The correct combination is $(iii), (iv)$.
\[ \boxed{(iii),\ (iv)} \]