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In this paper characterization of pseudo M-p-projective modules and quasi pseudo principally projective modules are given and discussed the various properties of it. It is proved that a pseudo M-pprojective module is Hopfian iff M/N is Hopfian, for each fully invariant small submodule N of M. It is also provided the sufficient condition for pseudo M-p-projective module to be discrete. Finally several equivalent conditions are given for a quasi pseudo principally projective module to have the finite exchange property.