Why does mi iPad return to the home screen when I am searching the net?

It sounds like Safari is crashing. Close Safari, clear Safari, close all apps and then reset the iPad.

Go to Settings>Safari>Clear History, Cookies and Data.

In order to close apps in iOS 5 or iOS 6, first tap the home button once. Then tap the home button twice and the recents tray will appear at the bottom of the screen. Tap and hold down on any app icon until it begins to wiggle. Tap the minus ➖ sign in the upper left corner of the app that you want to close. Tap the home button twice.

In order to close apps in iOS 7, you have to drag the app up from the multitasking display. Double tap the home button and you will see apps lined up going left to right across the screen. Swipe to get to the app that you want to close and then swipe "up" on the app preview thumbnail to close it.

Reset the iPad by holding down on the sleep and home buttons at the same time for about 10-15 seconds until the Apple Logo appears - ignore the red slider if it appears on the screen - let go of the buttons. Let the iPad start up.

So .... It happens with other browsers. Clear those as well. Did you try my suggestion? Explorer? On the iPad? I don't think so.