Yes, you can buy stock in NSE and sell the same in BSE or vice-versa but to that, the stock has to be in your Demat account since the delivery of a sell position goes to the exchange separately and the delivery of the buy position will be received from the exchange separately.

Example:

• Intraday scenario: If you have bought a stock today in NSE but intent to sell the same in BSE then you can’t sell since the stock does not exist in your Demat account. Stock are credited in your Demat Account only on T+2 day.
• Delivery scenario: If you have bought a share today in NSE and have held it until T+2 day that is when the stock gets credited in your Demat account then you can sell the same share in BSE on T+3 day.