According to Timothy Shields's answer, it's hard to say that would be an invalid json if we have duplicated property keys. 
And when using ASP.NET Core 2.1, it won't throw at all. 
As of 12.0.1, the Newtonsoft.Json has a DuplicatePropertyNameHandling settings. It will throw if we set DuplicatePropertyNameHandling.Error and pass a duplicated property. So the easiest way I can come up is to create a custom model binder. We could deserialize the JSON and change the ModelState if it throws . 
Fristly, install the latest Newtonsoft.Json:
  <ItemGroup>
    <PackageReference Include="Newtonsoft.Json" Version="12.0.1" />
  </ItemGroup>
and then register a JsonLoadSettings option as a singleton service for later reuse :
services.AddSingleton<JsonLoadSettings>(sp =>{
    return new JsonLoadSettings { 
        DuplicatePropertyNameHandling =  DuplicatePropertyNameHandling.Error,
    };
});
Now we can create a custom model binder to deal with duplicated properties :
public class XJsonModelBinder: IModelBinder
{
    private JsonLoadSettings _loadSettings;
    public XJsonModelBinder(JsonLoadSettings loadSettings)
    {
        this._loadSettings = loadSettings;
    }
    public Task BindModelAsync(ModelBindingContext bindingContext)
    {
        if (bindingContext == null) { throw new ArgumentNullException(nameof(bindingContext)); }
        var modelName = bindingContext.BinderModelName?? "XJson";
        var modelType = bindingContext.ModelType;
        // create a JsonTextReader
        var req = bindingContext.HttpContext.Request;
        var raw= req.Body;
        if(raw == null){ 
            bindingContext.ModelState.AddModelError(modelName,"invalid request body stream");
            return Task.CompletedTask;
        }
        JsonTextReader reader = new JsonTextReader(new StreamReader(raw));
        // binding 
        try{
            var json= (JObject) JToken.Load(reader,this._loadSettings);
            var o  = json.ToObject(modelType);
            bindingContext.Result = ModelBindingResult.Success(o);
        }catch(Exception e){
            bindingContext.ModelState.AddModelError(modelName,e.ToString()); // you might want to custom the error info
            bindingContext.Result = ModelBindingResult.Failed();
        }
        return Task.CompletedTask;
    }
}
To enable read the Request.Body multiple times, we could also create a dummy Filter:
public class EnableRewindResourceFilterAttribute : Attribute, IResourceFilter
{
    public void OnResourceExecuting(ResourceExecutingContext context)
    {
        context.HttpContext.Request.EnableRewind();
    }
    public void OnResourceExecuted(ResourceExecutedContext context) { }
}
Lastly, decorate the action method with [ModelBinder(typeof(XJsonModelBinder))] and EnableRewindResourceFilter:
    [HttpPost]
    [EnableRewindResourceFilter]
    public JsonResult GetAnswer([ModelBinder(typeof(XJsonModelBinder))]SampleModel question)
    {               
        if(ModelState.IsValid){
            return Json(question.Answer);
        }
        else{
            // ... deal with invalid state
        }
    }
Demo :
