Sometimes obvious is not that obvious. And this why I had trouble. I simply did not look at the keyboard properly and was cussing Dell for not providing a dedicated key option for disabling the touchpad. It was the other day when I suddenly looked at one of the key which actually meant to disable the touchpad. Here is how it looks on my laptop keyboard:

Hope that it solves the problem for all the Dell variants like Dell Inspiron, Dell Vostro, Dell Studio etc. Enjoy