Can I get 2560x1440 resolution on external monitor?

The problem is the cable you’re using to connect the monitor to the computer.

The easiest way to ensure that you have the full resolution is to use a standard mini-DisplayPort to DisplayPort cable and you should be able to use the full resolution without problems.

You can also use a mini-DisplayPort to DVI cable, but these are usually harder to come by in a standard home electronics store.

Last but not least, it might be possible to get the full resolution by using a better HDMI cable. You'll need one that supports HDMI 1.3 or 1.4 to support the 2560x1440 resolution.

Why did you not use a Mini DisplayPort to DVI adapter? For example, this item.

A mini-DisplayPort actually has the DVI signals. Only the jack is smaller. The converter does not need to convert the signals. There are just wires connected between the smaller mini-DisplayPort pins and the larger DVI jack pins.