Let's think about what the SENSEX actually is before answering how often it gets calculated. The SENSEX is the main index of the Bombay Stock Exchange, built from 30 large and heavily traded companies, and it is meant to show investors how the overall market is moving at any given moment.
Stock prices on an exchange change continuously through the trading session, as buyers and sellers place orders every few seconds. For an index to be useful as a live gauge of the market, it has to keep pace with these constant price changes rather than update only occasionally.
If the SENSEX were only refreshed every half hour, every hour, or six times a day, it would show stale numbers for long stretches of the trading day, which would defeat its purpose as a live market indicator. That rules out those three fixed interval options.
In practice, the SENSEX value is recalculated continuously, using the free float market capitalisation method, every time the price of one of its component stocks changes. This is why it is described as being computed in real time.
So the correct answer is option 3, Real time, since the index is updated on a continuous, live basis during market hours.