To select architecture principles, it is important to consider certain criteria to ensure that they promote the goals and objectives of the organization.

Option A: The principle is popular with IT management. This is not a key criteria for selecting architecture principles. Popularity does not necessarily equate to effectiveness or alignment with the organization's goals.

Option B: The principle promotes alignment of IT strategies with business strategies and visions. This is a key criteria for selecting architecture principles. Architecture principles should align with the business objectives and help achieve them.

Option C: The principle provides a high degree of control to IT management. This is not a key criteria for selecting architecture principles. Providing control to IT management does not necessarily ensure that the principles align with the goals of the organization.

Option D: The principle assures compliance by the business units. This is not a key criteria for selecting architecture principles. While compliance is important, it should not be the sole criteria for selecting architecture principles.

Option E: The principle assures uniform compliance to IT mandates. This is not a key criteria for selecting architecture principles. While compliance is important, the principles should also align with the business objectives.

Therefore, the correct answer is:

The Answer is: B