select default option in dropdown dependent in ANGULAR.JS

One option is to use ng-change on the country input and assign the $scope.selectedState when that changes. I would also recommend adding a defaultStateId property to each country to make this more flexible.

So your country HTML would become:

<select id="country" ng-change="CountrySelected()" ng-model="selectedCountry" ng-options="country.id as country.name for country  in countries track by country.id">
    <option value="">Choose</option>
</select>

And your CountrySelected function would look something like this:

$scope.CountrySelected = function() {
    var countryId = $scope.selectedCountry;
    for (var i = 0; i < $scope.countries.length; ++i) {
        var country = $scope.countries[i];
        if (country.id === countryId) {
            $scope.selectedState = country.defaultStateId;
            break;
        }
    }
};

you just need to add an 'defaultIndex': 0 foreach father element, example here

var Aplic = angular.module("Aplic", []);

Aplic.controller('CountryCntrl', function($scope) {

$scope.countries = [{
    'id': '1',
    'name': "Colombia",
    'defaultIndex': 0,
    'states': [{
        'id': '12',
        'dep': "Manizales"
    }, {
        'id': '11',
        'dep': "Bogota"
    }]
}, {
    'id': '2',
    'name': "USA",
    'defaultIndex': 1,
    'states': [{
        'id': '3',
        'dep': "California"
    }, {
        'id': '15',
        'dep': "Chicago"
    }]
}];

$scope.selectedCountry = $scope.countries[0];

});

replace ng-model="selectedState"

with below code ng-model="(countries | filter:{'id':selectedCountry})[0].states[0]"

2 things you need to do:

1) add an ng-change to the selectedCountry dropdown that will set the selectedState model to the first state in your list

2) re-arrange the states in your json so that the default state is the first one.

Here is a working example

You could also extend it to add a default value to either the country list or a default boolean to the state object.