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Can I do an arbitrage trade between the two exchanges?

This can be explained with an example: 

Assume Reliance stock is trading on NSE at 1000 and on BSE at 1004, you can do an arbitrage trade intraday, so you can buy on NSE at 1000 and short on BSE at 1004, when the price difference comes lower than 4 (1004-1000) sell on NSE and buy back the shares on BSE. When you cover, if the difference between NSE and BSE prices is lesser than 4 you make a profit, if not, losses. 

This is an arbitrage trade because it doesn’t matter to you if reliance goes up or down, all you are bothered is about the price difference between Reliance on NSE and BSE.

Currently, you can do an arbitrage trade only if you already have stocks in your DEMAT. So for example, if you held Reliance in your DEMAT, you could sell it at 1004 on BSE and immediately buy it on NSE for 1000, this way to reduce the cost of your holding. You will not be able to initiate a fresh intraday sell and buy on different exchanges.