In a two-dimensional frame or beam, a node represents a point where members or elements of the structure are connected. Each node has the potential to undergo linear displacement in different directions. The number of linear displacements a node can have depends on the type of support or constraint applied to the node.

Here are the possible linear displacements a node can have in a 2D frame/beam:

1. Translation in the X-direction:
A node can undergo linear displacement in the horizontal or X-direction. This displacement represents the node's movement along the X-axis.

2. Translation in the Y-direction:
A node can also undergo linear displacement in the vertical or Y-direction. This displacement represents the node's movement along the Y-axis.

3. Rotation about the Z-axis:
In addition to translations, a node can also undergo rotational displacement about the Z-axis. This rotation represents the node's movement around the Z-axis, perpendicular to the plane of the frame/beam.

Based on these possible displacements, we can categorize the nodes into different types of supports or constraints:

1. Pinned Support:
A pinned support allows a node to undergo both translations in the X and Y directions, as well as rotation about the Z-axis. Therefore, a node with a pinned support can have two linear displacements.

2. Roller Support:
A roller support allows a node to undergo translation in only one direction, either in the X or Y direction. It does not allow rotation about the Z-axis. Therefore, a node with a roller support can have one linear displacement.

3. Fixed Support:
A fixed support does not allow any linear displacement or rotation for a node. Therefore, a node with a fixed support has zero linear displacements.

Based on the above explanations, the correct answer to the question is option 'B' (2). A node in a 2D frame/beam can have two linear displacements, provided it is supported by a pinned support.