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The co relation between index and heavy weight stocks in index is very strong(because its have max wattage in index)..When market up those heavy weight stock up and vice versa..So if fii buy index future and sell those stocks then market will stable..most of the time cash price is decided from future price..so if market is stable then those heavy wight stock price also stable.. It helps/give big players a exit rout without effecting market…
for more info please watch Nitin Sir’s Index Management videos
Hope this info can help you to understand the logic