You don't need to close applications out of the multitasking tray unless they are currently being backgrounded and you no longer wish to keep them running. We've heard some folks say that you should close every application from the multitasking tray after you're done using it. That's simply not required.

Is it better to close apps or leave them open?

Wrong. In the last week or so, both Apple and Google have confirmed that closing your apps does absolutely nothing to improve your battery life. In fact, says Hiroshi Lockheimer, the VP of Engineering for Android, it might make things worse.

Is it good to clear recent apps?

Swiping away apps from recent tasks frequently is not a good practice, since it reduces the efficiency of process cache mechanism in Android, thus impact the performance of your device. Swiping away apps from recent tasks kills the process of those apps, thus prevent them from being cached in memory.