I am intending to buy an Intel 915G Mother Board. I already have an old 512MB 266MHz DDR RAM and I have recently bought a new 512MB 400MHz DDR RAM. Can I install and use both the RAMs together in the Mother Board?

Most new motherboards use DDR2 RAM. If the 915G does, then you can't use the DDR RAM.

I am intending to buy an Intel 915G Mother Board. I already have an old 512MB 266MHz DDR RAM and I have recently bought a new 512MB 400MHz DDR RAM. Can I install and use both the RAMs together in the Mother Board?
I don't think the 915G supports 266 MHz DDR at all - Intel's site on the 915G Chipset indicates that it needs 333 or 400 MHz DDR.

Past that, IF it does, you're going to run at the slowest clock speed on the chips.

Finally, some motherboards get very sensitive to memory compatibility. For best results, I always try to get RAM sticks that are exactly the same - manufacturer, speed, and capacity- in the same memory bank (usually pairs).