While extruding my whole mesh vertices doesn't remain connected creating a separate prt In vertex mode i am selecting whole object by pressing A ,and hitting E to extrude in y direction ...I want extrusion to remain connected at vertices but its not remaining connected here is the blend file?
As John wrote correctly, you have already done an extrusion and now you have doubled your vertices in place.
So what you can do is just box select your whole object (by this you just select the upper vertices), then press X -&gt; Vertices. Which deletes the upper vertices.
Then press A to select All and extrude as you want.