The option you are searching at the BIOS level is called IGD Minimum memory. The motherboard DH77EB includes the video memory up to 256MB.
You need to access the Video options and you will find it as IGD Minimum Memory.
I searched my BIOS using the search tool and browsed through all the sub menus but could not find a setting named "IGD Minimum memory" but I found what I was looking for by switching my BIOS to classic mode. There was the exact option I was searching and it was named just like what I expected. It is called "IGD DVMT memory" under the configuration>video>IGD DVMT memory. Though the issue got solved for now as I changed the setting from "maximum DVMT" to "512 MB". But I wonder why it behaves strange when I put the setting as "Maximum DVMT" it shows only 64MB as dedicated minimum memory in the OS and when I change it to 512MB it shows 512MB dedicated memory. I found ASUS and others having an additional choice offering upto 1024MB to use as dedicated minimum memory. Why didn't intel use this ? Anyways the problem is solved for now. Thanks for the reply Kevin.