There's really no way to give a set length of time that will work for all campaigns/keywords. Personally, I wait until I've had 200-300 clicks without a conversion before ruling out a particular keyword, especially on a new campaign. That might seem like a lot, given that 1 conversion out of 200-300 targeted clicks is probably not something that will work out financially, but it's not about being perfect from the start.
If you can get 1-2 conversions out of 200-300 clicks, it's a glimmer of hope. From there, you can adjust your landing page to see if you can increase that rate - do things like make the call to action more noticeable, ensure that the page layout makes sense, etc. Of course, if you're using the same landing page for other keywords and they all convert well, it's less likely that the landing page is the problem.
The other reason you might be experiencing a low conversion rate is that you're getting clicks from the wrong people. If you're using exact match, this isn't *too* likely, but it can happen. For instance, if you were bidding on the keyword "sail bags", your visitors might be looking for those bags that are made out of recycled sailcloth. They might also be looking for storage bags that hold sails for actual sailing purposes. If your keyword has potential for confusion like that, you need to try to eliminate confusion in the text of your ad. If that doesn't work, it may just be a dud.
If you're not getting a lot of volume on a keyword, don't kill it after some arbitrary amount of time just because it's not getting clicks. Eventually, almost everything will get clicks and they might just convert (and if not, get rid of them then). I would have lost thousands if I just killed things after some arbitrary amount of time because I hadn't yet seen a conversion.
Also - any Intro to Statistics book can help you out with more info on statistical significance (which is what you're asking when you said, "so as to know the results what your are getting are genuine and not coz of random change?"). 200-300 clicks is a good rough indicator, but if you want a better understanding of numbers in general, learning the basics of statistics never hurts. If you get into split testing and running regressions on different elements of your campaigns, that knowledge will come in very handy. You can probably pick up an older edition for $1-2+shipping on eBay/Amazon/Half.com.
