Also how can verify the newly compiled qwt.so and qscintilla.so is taking QT symbols from my static library of QT libQtCore.a and libQtGui.a

I already told you in your previous thread not to do that! What you're attempting is to duplicate the symbols (i.e. putting QtCore both in qwt and scintilla) and then link both of those shared objects.

It's a mess! Symbols are getting hidden silently (or overwritten on Linux), globals are duplicated (or overwritten on Linux) and initialized in different binaries (without guarantee for order of initialization) ...
Even if you're able to make it work on Linux, which I really doubt, the moment you switch to Windows you're going to be neck deep in horse sh*t ...

1. Shared libraries QWt and Qscintilla an it should not depend on /include the code of QtCore and QtGui
2. Static libraries QWt and Qscintilla an it should not depend on /include the code of QtCore and QtGui

If i give

#QT -= gui core
#LIBS -= -lQtGui -lQtCore
option in qwtconfig.pri then my compliation for qwt fails

1)checkout code for qwt from my central repositry
2) It is for linux centos platform
3) set the qmake path where Qt Static libs have been built
for example
setenv PATH "path to qmake where where Qt Static libs have been built"
3) build the dynamic libraries

but in this case my tools crahes

One very basic question , If I have memory manger which is made as static library

1. libmymem.a
2. libgui.a application gui code is static library
3. we are using shared libraries of .so libQtgui.so , libQtCore.so , libqwt.so libscintilla.so

Is it not conceptually possible the the libgui.a can access the code from libmymem.a even if we use the shared libraries from of Qt libQtgui.so , libQtCore.so , libqwt.so libscintilla.so

-----------Also how can verify the newly compiled qwt.so and qscintilla.so is taking QT symbols from my static library of QT libQtCore.a and libQtGui.a

If you mean linking your application against static and dynamic dependencies, then yes you can.