What is the correct behavior when both a 1D and a 2D texture are bound in OpenGL?

Say you have something like this:

glBindTexture(GL_TEXTURE_2D, my2dTex);
glBindTexture(GL_TEXTURE_1D, my1dTex);
glBegin...

What is the correct OpenGL behavior? To draw the 1d texture, the 2d or both? For each active texture are there actually multiple textures that can be bound to it at the same time (i.e. a 1d, 2d, 3d cube map, etc.)?