Final answer:
To buy 2,000 IBM shares at a maximum of $131 and have it filled immediately with the unfilled portion canceled, an Immediate or Cancel (IOC) order is appropriate.
Step-by-step explanation:
The type of order qualification you should enter when you wish to buy 2,000 shares of IBM at no more than $131 per share and want it filled right away, but are willing to accept fewer shares if necessary, is called an Immediate or Cancel (IOC) order. This order type allows you to buy as many shares as are available at your specified price or better, and the remainder of the order that cannot be filled immediately is canceled. It's a common type of order used in stock trading for investors who have a specific price in mind and are interested in immediate execution.