Most of the companies are listed on both exchanges, So which exchange to choose

Can i buy through one excahnge and sell through another one??

Use Only any one exchange always.

Better to be on NSE in my opinion.

There are companies which are listed on BSE as well as NSE and their shares are traded on these exchanges. That means you can buy shares (of these companies) on any of the two exchanges.  Once you buy the shares today, then those shares will be credited to your Demat account only after two days from the date of buying (as per T+2 model).

Additionally, most of the times we have seen that there is a difference of say 1, 3, 4  rupees in the prices on BSE and NSE.  This difference provides investors an arbitrage opportunity to make profits on their investment.  

Answer to your question is YES.  You can buy shares on one exchange and sell on the other only if you have shares in your Demat account.

For example, the stock XYZ is trading at 200 and 203 on BSE and NSE respectively.  Since the price on BSE is lower, one may buy shares on BSE.  These shares will get credited on his/her demat account on 29 June.  Now on 30 June, he can sell those shares either on BSE or NSE, wherever he is getting a good price.    

Exchange 27-Jun 28-Jun 29-Jun 30-Jun
BSE 200 203 211 219
NSE 203 205 214 221

However, for intraday, it is not possible because your position gets squared off on the same day.  So there is no question of "credit of shares" to your Demat Account.  Hence, whatever stocks you buy on any the exchanges, you have to squared it off on the same exchange.

Note:  The table has been used for the illustration purpose only.  Besides this, we may see innumerable scenarios.

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Choose the exchange where there is good volume / liquidity in ur stock. Also, the bid-ask spread should be less.

You buy the stock in that exchange where the quoted price is the smallest. You may also want to consider the volume in both the exchanges so that you get filled in on your order.

If There’s t+2 model in stock exchanges then how do we do intraday trading