The role of a PMO is : 1) Information provider. 2) Appointment & training of PM & Teams 3) Monitoring & Control of Projects. 4) Any one of them.

The Role of PMO is Monitoring and control of projects. Providing support to the project management team.

The first sekection is more closed to the role of the PMO 

because the second is the role of training departement in the big companies 

and the third is related to many sections and departements :

for Quality monitoring &controlling its the QA/QC departement

for Time & Cost its the Planning departement

I agree with the answer of Mohsin Agha that the role of PMO is monitoring and control of projects as the PMO is not a person but group of offices include for example and not limit to QC,Cost Controller,,planners..etc.

first pmo what is his resposibailetes and where they restrict.

In my opinion the correct answer is -4) Any one of them.

The reason is as follows :

 - As per PMBOK, a PMO can be effective if it takes up only one of the following roles and ensures that it specializes in the same.

 -  If a PMO takes up2 or more roles, it may fail to specialize and may eventually end up being ineffective.

 - For Projectized Organisations (running a large number of projects simultaneously) or Large Projects it is recommended to have3 or more PMOs, each assigned different roles. This will enable the Project Manager(s) to consult and seek the help & expertise of the concerned PMO as per their requirement.