Check your manual Support for Alienware 15 R3 | Documentation | Dell US

See Crucial or Dell for replacement ram.

Direct link, guaranteed compatible.

https://www.crucial.com/compatible-upgrade-for/alienware/alienware-15-r3#memory

here is the main problem...

Alienware 15 R3 Setup and Specifications....says 2667 MHz is the max i can use 

but, 

Crucial website is saying 3200 MHz is the max i can use 

And not even clear about CAS latency . should i go for CL-15, CL-16, CL-17,CL-19,CL-22?

Hi @singhrahul117 welcome to this free user to user Alienware laptop discussion forum. This is not Dell Support. 

Dell do not update their documentation, unless many users complain on Dell webpage. Crucial Advisor tool database provides their test on more recent hardware upgrades. Have a free chat with Crucial Technical Support to get specific information about upgrading your system, with no obligation to purchase Crucial product. If you decide to purchase Crucial hardware and it does not fully perform, their warranty guarantee will replace and provide the best gaming hardware for your system, or full refund of money. 

Latency partially depends on RAM speed -- and though 3200 MHz may work, it's the CPU that controls the RAM speed, so don't expect it to run at 3200.  If your current RAM runs at 2400 or 2666, the replacement RAM will as well -- even if it is capable of 3200 MHz. 

Low-latency, high-performance RAM has a bad track record in Dell/Alienware systems, which do not have adjustable parameters for RAM.  You should carefully verify with wherever you want to buy the RAM, that what they sell is compatible with your system (and that they'll back that up with a no-charge return if the RAM does not work).

Its 2666Mhz or 2933Mhz XMP