Sometimes there is gap up and gap down opening which happens in pre opening period, if someone want to buy or sell during this period in indexes, is it possible?

Not possible, no trading happens in pre open session.

Only the opening price calculation is done based on various orders placed by traders.

Cnce opening price is determined, the orders which are placed at the opening price only gets confirmed and remaining all orders are pushed to normal market which starts trading at 9:15 am.

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