<div class="new_service auto">
<label for="autoAppl">Список заявок</label>
<select id="autoAppl" class="form-control auto_applications">
<option class="auto" value="Y">Да</option>
<option class="auto" value="N" selected>Нет</option>
</select>
</div>
<div class="new_service applications" ng-show="">
<label for="listApplications">Список заявок</label>
<select id="listApplications" class="form-control list_applications">
<option class="application" value="{{app.id}}" ng-repeat="app in applications">{{app.name}}</option>
</select>
</div>
<select id="autoAppl" class="form-control auto_applications" ng-model="autoApplications">
<option class="auto" value="Y">Да</option>
<option class="auto" value="N" selected>Нет</option>
</select>
<div class="new_service applications" ng-show="autoApplications == 'Y'">
$scope.yesNoOptions = [
{value: 'Y', title: 'Да'},
{value: 'N', title: 'Нет'}
];
$scope.applications = [
{id: 1, title: 'Application title', ...},
...
];
<select id="autoAppl" class="form-control auto_applications" ng-model="autoApplication" ng-options="opt.value as opt.title for opt in yesNoOptions">
</select>
<div class="new_service applications" ng-show="autoApplication == 'Y'">
<label for="listApplications">Список заявок</label>
<select id="listApplications" class="form-control list_applications" ng-options="app.id as app.title for app in applications">
</select>
</div>