I was trying to list dropdown like widget, but luckily found the expansion panel list widget to get my desired UX to feel.
So, I am using ExpansionPanelList in my flutter app, but don't require the default elevation/border-shadow it comes with.
I have no idea how to remove it, so as to make it look part of the body rather than an elevated container.
Currently looking like this:

Following is my code:
class _PracticetestComp extends State<Practicetest> {
  var listofpracticetest;
  List<Item> _data = [
    Item(
      headerValue: 'Previous Question Papers',
      expandedValue: '',
    )
  ];
  @override
  Widget build(BuildContext context) {
    return Scaffold(
        backgroundColor: Color(0xffF8FDF7),
        appBar: AppBar(
          backgroundColor: Color(0xffF8FDF7), // status bar color
          brightness: Brightness.light,
          elevation: 0.0,
          leading: Container(
            margin: EdgeInsets.only(left: 17),
            child: RawMaterialButton(
              onPressed: () {
                Navigator.pushNamed(context, '/');
              },
              child: new Icon(
                Icons.keyboard_backspace,
                color: Colors.red[900],
                size: 25.0,
              ),
              shape: new CircleBorder(),
              elevation: 4.0,
              fillColor: Colors.white,
              padding: const EdgeInsets.all(5.0),
            ),
          ),
        ),
        body: Container(
          // height: 200,
          margin: EdgeInsets.only(top: 40),
          child: ListView(
            shrinkWrap: true,
            scrollDirection: Axis.vertical,
            children: [
              Column(
                crossAxisAlignment: CrossAxisAlignment.start,
                children: <Widget>[
                  Container(
                      margin: EdgeInsets.only(top: 30),
                      child: Theme(
                          data: Theme.of(context)
                              .copyWith(cardColor: Color(0xffF8FDF7)),
                          child: _buildPanelPreviousPapers()))
                ],
              )
            ],
          ),
        ));
  }
  Widget _buildPanelPreviousPapers() {
    return ExpansionPanelList(
      expansionCallback: (int index, bool isExpanded) {
        setState(() {
          _data[index].isExpanded = !isExpanded;
        });
      },
      children: _data.map<ExpansionPanel>((Item item) {
        return ExpansionPanel(
          headerBuilder: (BuildContext context, bool isExpanded) {
            return ListTile(
              title: Text(item.headerValue),
            );
          },
          body: Container(
            child: ListTile(
              leading: Text(
                'Alegbra',
                style:
                    TextStyle(color: Colors.black, fontWeight: FontWeight.w500),
              ),
              ),
            ),
          ),
          isExpanded: item.isExpanded,
        );
      }).toList(),
    );
  }
}
// stores ExpansionPanel state information
class Item {
  Item({
    this.expandedValue,
    this.headerValue,
    this.isExpanded = false,
  });
  String expandedValue;
  String headerValue;
  bool isExpanded;
}
wrap your entire expansion widget child inside Material widget and change the elevation based on expansion child is expanded or not with method
   Material(
        elevation: isSelected ? 4 : 0,
        child: ExpansionTile(
         onExpansionChanged:(value){
                            isSelected=value;
                            setState(){};
                                   },
         title: getExpantionTitle(context),
          children: getChildrentList(),
              ),
            ),
        ),
in case if you don't like divider in ExpansionTile tile do some thing like this
        final theme = Theme.of(context).copyWith(dividerColor: 
        Colors.transparent);
     //use as a child 
 child:Theme(data: theme, child: ExpansionTile(...));  
First, it isn't recommended to not use elevation for ExpansionPanelList according to Material design spec. 
However, if you really want to do that, there are 2 solutions for you, either you create your own custom ExpansionPanelList, or get ready to add couple of lines to the source file. I'm providing you the latter solution. 
Open expansion_panel.dart file, go to the build() method of _ExpansionPanelListState and make following changes
return MergeableMaterial(
  hasDividers: true,
  children: items,
  elevation: 0, // 1st add this line
);
Now open mergeable_material.dart file, navigate to _paintShadows method of _RenderMergeableMaterialListBody class and make following changes:
void _paintShadows(Canvas canvas, Rect rect) {
  // 2nd add this line
  if (boxShadows == null) return;
  for (final BoxShadow boxShadow in boxShadows) {
    final Paint paint = boxShadow.toPaint();
    canvas.drawRRect(kMaterialEdges[MaterialType.card].toRRect(rect), paint);
  }
}
Screenshot:

Just add this line:
ExpansionPanelList(
      elevation: 0, // this line
      expansionCallback: ...

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