@Anonymous
Sorry, I misunderstood your question to be about aligning and then connecting the 2 lines to look like that in your posted image and it is still unclear to me exactly what you are asking. Some of the confusion may be related to Max terminology.
From your recent post you are saying that they are already aligned and it only took you 30 seconds. But in your original post you asked, "Is there a quick way to align them together and attach? Or do I have to painstakingly align them with the move tool every time" So, I am genuinely confused as to what is painstaking about a 30 second process?
Is there an option in 3ds max to connect a group of vertices from one object like for e.g the end of a pipe to another group of vertices on another pipe with a shortcut key?
In your new question, I am not sure what you mean by "connect" the group of vertices. I would interpret this to mean one of 2 possible Max terms, (1) Weld or ( 2) Bridge. And to do either, the vertices in question must be part of the same editable poly or editable mesh. So, you must first attach the objects using the edit poly rollout attach as I explained above. From there the workflow is slightly different for each case. For welding it is assumed that the pipe ends are already in position but the polygons at each pipe end must be deleted for the weld operation to work. Then you just select all of the vertices and weld with a low threshold value like 0.1 (obviously, you may need to tweak this depending on the dimensions of your mesh)
For bridging, the pipes can be any distance apart but the opposing faces still need to be lined up if you want a straight looking pipe. Then, it is easy to select the 2 opposing polygon pipe ends and click on "Bridge" in the Editable Poly Rollout.
Regarding a shortcut key, the above is a multi-step process (even if the steps are straightforward and simple) and no single shortcut exists since each step (align, attach, select and (possibly delete) specific subobjects, weld or bridge) requires user guidance.
So if I have again misunderstood your question, I apologize, but I do hope this helps.