Concept:
The correctness of the statements can be checked using molecular symmetry, boiling point trends, electrophilic substitution orientation and nucleophilic substitution reactivity.
Step 1: Analyze Statement-I.
Trans-but-2-ene is symmetrical.
The bond dipoles cancel each other.
\[\begin{aligned}
\mu = 0
\end{aligned}\]
Hence,
\[\begin{aligned}
\text{Statement-I is Correct}
\end{aligned}\]
Step 2: Analyze Statement-II.
Branching decreases boiling point.
\[
\begin{aligned}
\text{n-Butane} &:\quad \text{Higher boiling point} \\
\text{2-Methylpropane} &:\quad \text{Lower boiling point}
\end{aligned}
\]
Therefore,
\[\begin{aligned}
\text{Statement-II is Incorrect}
\end{aligned}\]
Step 3: Analyze Statement-III.
Chlorine is ortho-para directing.
However, due to steric effects, the para product predominates.
Major product:
\[\begin{aligned}
p\text{-chloroacetophenone}
\end{aligned}\]
Hence,
\[\begin{aligned}
\text{Statement-III is Incorrect}
\end{aligned}\]
Step 4: Analyze Statement-IV.
For \(S_N2\) reactions,
\[\begin{aligned}
RI \gt RBr \gt RCl \gt RF
\end{aligned}\]
because iodide is the best leaving group.
Therefore,
\[\begin{aligned}
\text{1-Iodobutane reacts faster than 1-chlorobutane}
\end{aligned}\]
Thus,
\[\begin{aligned}
\text{Statement-IV is Correct}
\end{aligned}\]
Step 5: Identify the correct set.
\[
\begin{aligned}
\text{Statement I} &:\quad \text{Correct} \\
\text{Statement II} &:\quad \text{Incorrect} \\
\text{Statement III} &:\quad \text{Incorrect} \\
\text{Statement IV} &:\quad \text{Correct}
\end{aligned}
\]
Therefore,
\[\begin{aligned}
\boxed{\text{I, IV}}
\end{aligned}\]
Hence, option \(\mathbf{(D)}\) is correct.