Say you have something like this:
glBindTexture(GL_TEXTURE_2D, my2dTex);
glBindTexture(GL_TEXTURE_1D, my1dTex);
glBegin...
What is the correct
The applied texture is the last specified with BindTexture routine.
From the specification:
The new texture object bound to target is, and remains a texture of the dimensionality and type specified by target until it is deleted. .... If the bind is successful no change is made to the state of the bound texture object, and any previous binding to target is broken.
Indeed in your example it will be applied the 1D texture, since it "overwrite" the state of the active texture unit.