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How can an activity with 'singleTask' launch mode be not root activity in a task?

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Activity Y has 'singleTask' launch mode but it is not root activity in the task, that is Activity X. How did it happen?
Upd.:
From the documentation:
"singleTask"
The system creates a new task and instantiates the activity at the root of the new task. However, if an instance of the activity already exists in a separate task, the system routes the intent to the existing instance through a call to its onNewIntent() method, rather than creating a new instance. Only one instance of the activity can exist at a time.
Note: Although the activity starts in a new task, the Back button still returns the user to the previous activity.

Single task only means that this activity can only be created once cf to this website: http://inthecheesefactory.com/blog/understand-android-activity-launchmode/en
It doesn't matter if the activity is root or not.
singleTask:
This mode is quite different from standard and singleTop. An Activity
with singleTask launchMode is allowed to have only one instance in the
system (a.k.a. Singleton). If there is an existed Activity instance in
the system, the whole Task hold the instance would be moved to top
while Intent would be delivered through onNewIntent() method.
Otherwise, new Activity would be created and placed in the proper
Task.

I think the answer is that this activity was launched with an intent with FLAG_ACTIVITY_SINGLE_TOP flag, because intents have higher priority than xml tags.

Is it possible to call one activity from two different activities in android

So, I have 2 activities, the first one(lets call this A) passes data to an activity with a list, lets call this B. B then uses the data from A and makes a list out of it.A service S is then called by B. The service then calls another activity lets say C, which in turn starts B. Should B still work with all the data?BTW all activities are ActionBarActivities.

In the general case, each time an activity in invoked using startActivity, a new instance is create.
This behavior can be modified by the use of the launchMode. singleTask will always be the same instance, but your activity must be at the root of the task
An existing activity can also be called back to the front of the stack using the flag FLAG_ACTIVITY_REORDER_TO_FRONT. It is unclear in the documentation how the new data is passed, or whether the previous data in the activity is kept.

Difference between singleTask and singleInstance

I did not find any thread on StackOverflow that answer my question. I have already seen this Android singletop singleinstance and singletask but that question is related to his project scenario.
What are the differences between singleTask and singleInstance?? I have read the docs but could not understand..
I have read this thread also Android singleTask or singleInstance launch mode? but I could not understand. Sorry

What is unclear from the docs ?
The "singleTask" and "singleInstance" modes also differ from each
other in only one respect: A "singleTask" activity allows other
activities to be part of its task. It's always at the root of its
task, but other activities (necessarily "standard" and "singleTop"
activities) can be launched into that task. A "singleInstance"
activity, on the other hand, permits no other activities to be part of
its task. It's the only activity in the task. If it starts another
activity, that activity is assigned to a different task — as if
FLAG_ACTIVITY_NEW_TASK was in the intent.

singleTask :- A new task will always be created and a new instance will be pushed to the task as the root. However, if any activity instance exists in any tasks, the system routes the intent to that activity instance through the onNewIntent() method call. In this mode, activity instances can be pushed to the same task. This mode is useful for activities that act as the entry points.
singleInstance:- Same as singleTask, except that the no activities instance can be pushed into the same task of the singleInstance’s. Accordingly, the activity with launch mode is always in a single activity instance task. This is a very specialized mode and should only be used in applications that are implemented entirely as one activity.

SingleInstance is just like a singleton and also its stack is like final class can't be extended.
Its always single in its stack.and always there.

Android default launchMode of LAUNCHER activity?

does the launchMode of the launcher activity in the manifest get ignored?
The android documentation says that the default launchMode is "standard" but this isn't logic for me if this would be applied to the main activity of an app because each time you start the app, another task would be created in the instance of the app.

Well, I delved into Android sources myself and found the following thing.
The launcher starts apps using the method startActivityAsUser in LauncherAppsService. The intent is constructed using these lines:
Intent launchIntent = new Intent(Intent.ACTION_MAIN);
launchIntent.addCategory(Intent.CATEGORY_LAUNCHER);
launchIntent.setComponent(component);
launchIntent.setSourceBounds(sourceBounds);
launchIntent.addFlags(Intent.FLAG_ACTIVITY_NEW_TASK);
According to Android documentation, the flag FLAG_ACTIVITY_NEW_TASK means:
When using this flag, if a task is already running for the activity you are now starting, then a new activity will not be started; instead, the current task will simply be brought to the front of the screen with the state it was last in.
This effectively and unconditionally overrides launchMode specified (or omitted to default behaviour) in the app, and ignores this attribute.
I think this demonstrates that the documentation is not clear (or complete) enough. Without such deep investigations of the core source codes everyone can get unexpected results now and then.

You are confusing two things. One is launchMode and the other is "what happens when the user selects an app icon from the HOME screen, or selects a task from the list of recent tasks". These are 2 completely different things.
launchMode
Each Activity has a specified launchMode (the default is "standard" or "multiple". This tells Android how to start this Activity, and there are many factors that can contribute to the "interpretation" of the launchMode. It depends on what other flags may have been specified in the Intent used. It depends on which task requested the launch of the Activity (or if the launch was requested from a non-activity context, like from a Service or BroadcastReceiver). It depends on whether or not an existing instance of the Activity is already active in the specified task, etc.
Behaviour on selecting an app icon from the HOME screen or list of installed applications
When the user selects an app icon, startActivity() is called with an Intent containing the following data:
ACTION=MAIN
CATEGORY=LAUNCHER
Component is set to the package name and the class name of the Activity that is defined in the manifest with ACTION=MAIN and CATEGORY=LAUNCHER
Flag FLAG_ACTIVITY_NEW_TASK and FLAG_ACTIVITY_RESET_TASK_IF_NEEDED are set.
Regardless of the launchMode definition of the Activity to be launched, calling startActivity() with an Intent like this causes the following behaviour:
If there is already an existing task whose task affinity matches the Activity being started (in simple terms, if the app is already running), Android will simply bring the existing task to the foreground. That's it. It doesn't create an instance of any Activity. It doesn't call onNewIntent() on any Activity. It does nothing other than bringing the existing task to the foreground. This is why, even if you specify launchMode="standard" for your launcher Activity, Android doesn't create a new instance every time you click on your app icon.
If there isn't already an existing task whose task affinity matches the Activity being started (in simple terms, if the app isn't already running), Android will create a new task and launch the Activity into that task. launchMode doesn't play a role here, since there is absolutely no difference between the launch modes when launching a single Activity into a new task. Android always creates a new task and always creates a new instance of the Activity as the root of that task.
This behaviour is also the same when the user selectsa task from the list of recent tasks. If the task is still running, Android just brings the task to the foreground, does not start any new Activity instances and does not call onNewIntent(). If the task is no longer running, Android creates a new task and launches the launcher Activity into that task. The only difference here is that the flag FLAG_ACTIVITY_LAUNCHED_FROM_HISTORY is also set in the Intent if the user selected a task from the list of recent tasks.
I hope this answers your question.
See this answer for a very detailed explanation of FLAG_ACTIVITY_RESET_TASK_IF_NEEDED and task reparenting in general.

Think of everything except the opening activity as an abstract implementation. Declaring an activity as
<intent-filter>
<action android:name="android.intent.action.MAIN" />
<category android:name="android.intent.category.LAUNCHER" />
</intent-filter>
Will cause it to open first. Subsequent activities are Overriden at the time an Intent is formed to navigate between activities. The overrides are represented as intent flags.
A list of intent extras:
http://developer.android.com/reference/android/content/Intent.html
With flags being commands you'd otherwise have written in the Manifest.

You are right.The default mode is "standard".
According to android documentation
*In standard mode ,Every time there's a new intent for a "standard" activity, a new instance of the class is created to respond to that intent. Each instance handles a single intent.
*.If the parent activity has launch mode standard (and the up intent does not contain FLAG_ACTIVITY_CLEAR_TOP), the current activity and its parent are both popped off the stack, and a new instance of the parent activity is created to receive the navigation intent.

The behavior of Activity set to standard mode is a new Activity will always be created to work separately with each Intent sent. Imagine, if there are 10 Intents sent to compose an email, there should be 10 Activities launch to serve each Intent separately. As a result, there could be an unlimited number of this kind of Activity launched in a device.
Behavior on Android pre-Lollipop
standard Activity would be created and placed on top of stack in the same task as one that sent an Intent.
For example, when we share an image from gallery to a standard Activity, It will be stacked in the same task as described although they are from the different application.
If we switch the application to the another one and then switch back to Gallery, we will still see that standard launchMode place on top of Gallery's task. As a result, if we need to do anything with Gallery, we have to finish our job in that additional Activity first.
Behavior on Android Lollipop
If the Activities are from the same application, it will work just like on pre-Lollipop, stacked on top of the task.
But in case that an Intent is sent from a different application. New task will be created and the newly created Activity will be placed as a root Activity like below.
Source from here

Android application's initial activity is not the launcher designated activity when re-entering the app with the back button

I ran into a similar issue with the recent list in that there seem to a handful of conditions where an app will be completely destroyed but some other process will launch the app cold from the last activity that was being used. Since my app has a state that is built up over several designated activities I need to prevent this (i.e. null refs from onCreate()).
Without checking for state is all my onCreate() functions is there a way to just prevent this?
Also, other than the launcher, recents, the back button from other apps - are there more conditions where another thing can launch my app if I have not giving manifest permission to launch it explicitly with an intent?
Thanks!

If I understand this correctly, you have initializations in activity B that rely on activity A having passed them in. If an intent launches activity B first, without it being active, or being launched by A first, your activity will crash.
Easiest solution I can come up with is make your activity A (I assume your main activity) the broadcast listener for all the intents you wish to handle, and based off the intent action, dispatch to the appropriate child activities (B, C, whatever). That way activity A does all your initialization, and you can still launch into the appropriate activity to handle the original intent you wanted to.
Alternatively. If you detect your children activities are in an invalid state, you could put initialization into a parent activity that all your activities extend from. That way you should be able to initialize properly if the activity is a fresh launch. I'm not really a fan of this, I prefer making sure my activities are dependency injected with appropriate data.