One way to populate your dropdown lists is by using ViewData. 
Let's assume that your calls to the API reside in a separate service. The API would need to return a List. In this example the List will be of a custom class: List<CustomClass>. Let's assume that your custom class contains a property Id, and a property Name. Your controller would look like:
public class HomeController : Controller
{
    private readonly IApiService _apiService;
    public HomeController(
        IApiService apiService)
    {
        _apiService = apiService;
    }
    public IActionResult Index()
    {
        // Get the data from the API into the ViewData
        // In this example, Id will be the Id of the dropdown option,
        // and the Name will be what's displayed to the user
        ViewData["DataFromArticle1"] = new SelectList(
                await _apiService.GetDataFromArticle1Async(), 
                "Id", "Name");
        ViewData["DataFromArticle2"] = new SelectList(
                await _apiService.GetDataFromArticle2Async(), 
                "Id", "Name");
        return View();
    }
}
Now, to populate the dropdowns in your View:
<select asp-items="ViewBag.DataFromArticle1"></select>
<select asp-items="ViewBag.DataFromArticle2"></select>
UPDATE
The following code will call your API endpoint by AJAX. We assume that you have created a WebApi, and that within your WebAPI you have an ArticleDataController with a method called GetDataFromArticle1.
Your view:
<select id="dataFromArticle1"></select>
Your JavaScript:
$(document).ready(function () {  
    $.ajax({  
        type: "GET",  
        url: "/api/ArticleData/GetDataFromArticle1",   
        success: function (data) {  
            var s = '<option value="-1">Please Select a Department</option>';  
            for (var i = 0; i < data.length; i++) {  
                s += '<option value="' + data[i].Id+ '">' + data[i].Name + '</option>';  
            }  
            $("#dataFromArticle1").html(s);  
        }  
    });  
});