Hi,
Questions 1 and 2 are not so clear but I will try my best, assuming machine = PC.
1. in a organization 1000 systems are connected to multiple switches as well as routers, in out of 1000 systems one of the machines has down. so how we find out the route cause in which switch as well as router has down and how to troubleshoot
The user should report the problem first so you should to know what PC is, otherwise if the PC's mac address is still into the mac address table you could use show mac address-table | inc <mac address>, or find a PC down between a network built between 1000 networks devices you could first identify what network segment is using the PC and check the switches configured with the specific VLAN, and check logs, once identified the PC, you should check the physical layer first (cabling, power, hardware) , next troubleshoot the other layers.
2.in a organization wan network has implemented through the router as well as switches ok one of the machines has not connected wireless out of 1000, so how we find out the specific machine has down. and how to troubleshoot
Like the previous question, the user should report the problem so you could find the what device has problems, once it is identified you could verify physical layer (NIC o hardware) or drivers, then verify what credentials is using to connect to the WiFi, identify the logs on any closest access point, check the network association on the AP in order to verify if it is not in full capacity.
3. in one of the PC->connected to switch->connected router->internet ( Q: how the internet is coming to the pc and what is the process.
It looks like the network has a PAT configured on the router, basically the internal IP will be translated to a public IP, if you are using PAT, it will be works with ports, the PC will open a request using a random port, the PAT configured on the router will translate the internal IP to the public IP but it will also map the internal port and a random external port so the destination will know how to return the information to the source.
Hope it is useful
:-)
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