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sir,
1. can the sum of ARCH term (α ) and GARCH term (β ) for the GARCH (1,1) model be more than one ?
2. if yes, does it signify rise in volatility persistence level ?
please reply

That is the stability condition for garch process, which leads to explosive behavior when violated. There is a very nice TSDGP add-in which allows you to simulate ARIMA and/or GARCH processes. If you have an access to EViews 7.1, then you can try and see what actually happens in that case...