The primary purpose of a command object in ADO.NET is to execute SQL queries and stored procedures. It acts as a bridge between the application and the database, allowing for the execution of SQL commands and the retrieval of data.

A distributed transaction in ADO.NET involves multiple databases. It spans across multiple databases, allowing operations to be performed on different databases as part of a single transaction, ensuring data consistency across them.

The correct option for performing complex data transformations on a collection of customer records is Projection. Projection allows you to shape the data in the desired format by selecting specific fields or properties from the customer records, facilitating efficient data manipulation.

In ADO.NET, the methods Open() and Dispose() are used to respectively establish and release connections. The Open() method opens a connection to a data source, while the Dispose() method releases the resources used by the connection.

The correct option is Observer pattern. In this scenario, where real-time updates are needed in the UI, the Observer pattern would be suitable. The Observer pattern allows objects to subscribe to changes in other objects and receive notifications when those changes occur. This enables real-time updates in the UI whenever changes happen in the database, ensuring synchronization between the database and the UI. Two-way data binding allows updates from UI to data source and vice versa, but it might not provide real-time updates. One-way data binding only updates the UI from the data source, and Three-way data binding is not a standard concept in ADO.NET.

The correct option is "Add". When adding a new row to a DataTable in a dataset, the common method used is the Add method of the DataRow collection.

The SubmitChanges method in LINQ to SQL is used to commit changes made to objects in the DataContext to the associated database. This method ensures that changes are saved to the database.

In ADO.NET, you can execute a stored procedure using the ExecuteNonQuery method of the SqlCommand object. ExecuteNonQuery is typically used for executing commands that do not return any result set, such as INSERT, UPDATE, DELETE, or for executing stored procedures that do not return result sets.

The Sort property of a DataView is significant as it specifies the order in which the data rows are displayed. This property allows you to sort the DataView's rows based on the values of one or more columns, either in ascending or descending order, providing control over the presentation of data.

LINQ to Objects is specifically designed for querying in-memory data structures such as lists, arrays, and other collections. It allows developers to use LINQ query expressions to manipulate and retrieve data from these data structures efficiently.