How to list items as 1. i. ii., iii., 2. i., ii., ...?

Question

How to prepare a list of the items in the following manner:

1. i. Question

   ii. List item

   iii. Next item

2. i. New list

   ii. Next question

Below is the MWE of my attempt. The second item prints as '1. ii.' while I want the output to be simply `ii.' The margin for roman numerals should be aligned.

\documentclass[10pt]{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}

\usepackage{enumerate}
\usepackage[inline, shortlabels]{enumitem}

% 
\begin{document}

\begin{enumerate}[label=1.~\roman*.]
  \item Solve a given first order ordinary differential equation (ODE) like (a) Radioactive decay (b) Newton's law of cooling (c) Current in LR, RC circuit with DC source using Euler/RK 4 Order method.
  \item This item should print the output simply `ii.' instead of `1. ii.'
\end{enumerate}

\end{document}

Answer 1

This is the default behaviour if you don't add anything for the first level of enumeration. That is, the second level enumeration is set next to the first.

\documentclass{article}

\usepackage{enumitem}

\setlist[enumerate,1]{label=\arabic*.}
\setlist[enumerate,2]{label=\roman*.,align=left}

\begin{document}

\begin{enumerate}
  \item
  \begin{enumerate}
    \item Question
    \item List item
    \item Next item
  \end{enumerate}
  
  \item
  \begin{enumerate}
    \item New list
    \item Next question
  \end{enumerate}
\end{enumerate}

\end{document}

From here you can adjust the other elements (like spacing).