Hi,
I have just intalled Ubuntu in VirtualBox.
While I am configuring the display in System->Preferences->diaplay
only two modes are visible 640x480 and 800x600
I also tried xrandr to view what modes are supported
but it also shows only these two modes

I am using Dell Studio 1555 which is having max resolution
of 1920x1080.

How can I make my Ubuntu detect other resolutions ?

I think you need to add vbox guestadditions which will mount a vbox guest additions iso and you can install it in your vm.
I read somewhere that they're necessary to support higher resolutions but I'm not entirely sure about that.

If not this is some info on xrandr off the top of my head. If you're still having trouble I'll try to help out more later.
xrandr --auto
will try to guess and
xrandr -q
should show you the current supported modes
try googling "xrandr --newmode" and "xrandr --addmode" to see how to add new resolutions
and an asterisk* will show which mode is current.