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I am running into a consistent issue, my last two tubes replacement for the back tyre of my cycle got punctured same way at the neck of the tube. 
I am beginning to think if there is something fundamentally wrong. I biked for barely 25 min after installing brand new tube from sunlite and there was a puncture at tubes neck.
The dimensions were 26x1.5-1.75 of the tube, tyre is 26x2. Bicycle is a Schwinn Frontier. Please suggest me what should be my course of action here?
There is a mark in the middle of the valve stem as if something has pressed against it:
Given that it was a fresh new tube, it likely means that it had been installed with the valve protruding at a sharp angle from the rim hole. Externally, it will look like this:
This is bad because the air pressure creates additional uneven stress to the rubber around the valve. Which, in turn, may cause a blowout at the end of the metal tube of the valve, or even tear the whole piece apart.
At the installation time, while the air pressure is not too high (but not zero), pull the valve up with hand to ensure that it sits at an angle as straight as possible to the rim surface. If it is already stuck, deflate the tire again and repeat the attempt.
While you are dealing with the problem and have your rim exposed for inspection, check that the valve hole is smooth on its edges both inside and outside:
Any sharp burrs left in it will rub against the valve, which will also weaken it and will create a possibility for a blowout.
Check that the rim tape (tape or liner that sits in rim bed) is not loose or spinning. I had an identical issue where a brand new tube would be ruined after a 10 minute ride. The rim tape spins on braking and drags the tube with it effectively tearing the tube away from the valve.
If this the culprit, throw the current rim tape away, it can’t be fixed. Reline with something suitable. Gorilla tape is good but so is electrical tape if you lay down a few layers.
It appears to me that the valve is torn or cut. Check your rim for sharp edges at your valve hole. you could try to cover them with a tape. Make sure the valve sits straight when the tyre is pumped up. I suggest to insert the tyre slightly filled with air before pumping the tyre.
Also check the offending place o the rim for any other offending debris.
Normally we recommend to check the tyre thoroughly for sharp objects, but this hole appears to be at the rim side.
Are all of your inner tubes from the same batch, by the same manufacturer, manufactured at about the same time?
There has been occasionally failures of inner tube valve stems due to manufacturing defects.
It may be possible the defects are not a thing of the past but have returned again.
