Hello Rashmi,
you can see in case of activity search, there is separate link for archive search as per Standard SAP. But, there is no link for business partner or product search. There is separate view in case of activity search as BT126S_APPT/ApptSQAC while there is no separate view in case of business partner search. so, you need to do something to filter archived account.
I want to know , how you want to achieve without adding any search criteria.
Thanks,
Amit